LMFDB - Embedded newform 2671.2.a.a.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2671,2,Mod(1,2671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2671, 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("2671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2671.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:	$21.3280423799$
Analytic rank:	$1$
Dimension:	$100$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	2671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.48716 q^{2} +0.674976 q^{3} +4.18594 q^{4} -1.47569 q^{5} -1.67877 q^{6} +0.0650875 q^{7} -5.43678 q^{8} -2.54441 q^{9} +O(q^{10})$	\(q-2.48716 q^{2} +0.674976 q^{3} +4.18594 q^{4} -1.47569 q^{5} -1.67877 q^{6} +0.0650875 q^{7} -5.43678 q^{8} -2.54441 q^{9} +3.67028 q^{10} +3.92132 q^{11} +2.82541 q^{12} +5.49172 q^{13} -0.161883 q^{14} -0.996058 q^{15} +5.15022 q^{16} -3.93851 q^{17} +6.32833 q^{18} +4.25660 q^{19} -6.17716 q^{20} +0.0439325 q^{21} -9.75293 q^{22} -9.41230 q^{23} -3.66970 q^{24} -2.82233 q^{25} -13.6588 q^{26} -3.74234 q^{27} +0.272452 q^{28} -1.89116 q^{29} +2.47735 q^{30} -3.01200 q^{31} -1.93585 q^{32} +2.64680 q^{33} +9.79570 q^{34} -0.0960491 q^{35} -10.6507 q^{36} +0.553801 q^{37} -10.5868 q^{38} +3.70678 q^{39} +8.02301 q^{40} +0.496516 q^{41} -0.109267 q^{42} +10.6085 q^{43} +16.4144 q^{44} +3.75476 q^{45} +23.4098 q^{46} +2.40538 q^{47} +3.47628 q^{48} -6.99576 q^{49} +7.01957 q^{50} -2.65840 q^{51} +22.9880 q^{52} +11.3442 q^{53} +9.30779 q^{54} -5.78666 q^{55} -0.353866 q^{56} +2.87310 q^{57} +4.70360 q^{58} -11.5619 q^{59} -4.16944 q^{60} -11.9612 q^{61} +7.49132 q^{62} -0.165609 q^{63} -5.48568 q^{64} -8.10409 q^{65} -6.58300 q^{66} -12.1179 q^{67} -16.4864 q^{68} -6.35308 q^{69} +0.238889 q^{70} +3.89106 q^{71} +13.8334 q^{72} +9.38779 q^{73} -1.37739 q^{74} -1.90501 q^{75} +17.8179 q^{76} +0.255229 q^{77} -9.21934 q^{78} +12.5233 q^{79} -7.60015 q^{80} +5.10723 q^{81} -1.23491 q^{82} +5.42106 q^{83} +0.183899 q^{84} +5.81204 q^{85} -26.3850 q^{86} -1.27649 q^{87} -21.3193 q^{88} -12.4174 q^{89} -9.33868 q^{90} +0.357442 q^{91} -39.3993 q^{92} -2.03303 q^{93} -5.98255 q^{94} -6.28143 q^{95} -1.30666 q^{96} +7.15420 q^{97} +17.3996 q^{98} -9.97743 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9}+O(q^{10}) $ 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9	\( 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9} - 18 q^{10} - 47 q^{11} - 27 q^{12} - 29 q^{13} - 51 q^{14} - 36 q^{15} + 71 q^{16} - 99 q^{17} - 27 q^{18} - 45 q^{19} - 75 q^{20} - 79 q^{21} - 2 q^{22} - 25 q^{23} - 66 q^{24} + 67 q^{25} - 73 q^{26} - 42 q^{27} - 31 q^{28} - 78 q^{29} - 29 q^{30} - 41 q^{31} - 95 q^{32} - 83 q^{33} - 44 q^{34} - 45 q^{35} + 23 q^{36} - 16 q^{37} - 29 q^{38} - 42 q^{39} - 37 q^{40} - 235 q^{41} + 16 q^{42} - 6 q^{43} - 122 q^{44} - 79 q^{45} - 17 q^{46} - 67 q^{47} - 25 q^{48} + 30 q^{49} - 68 q^{50} - 18 q^{51} - 41 q^{52} - 69 q^{53} - 63 q^{54} - 32 q^{55} - 120 q^{56} - 63 q^{57} - 7 q^{58} - 118 q^{59} - 49 q^{60} - 60 q^{61} - 23 q^{62} - 43 q^{63} + 43 q^{64} - 181 q^{65} - 4 q^{66} - 18 q^{67} - 130 q^{68} - 80 q^{69} + 12 q^{70} - 77 q^{71} - 40 q^{72} - 64 q^{73} - 48 q^{74} - 18 q^{75} - 134 q^{76} - 87 q^{77} + 65 q^{78} - 48 q^{79} - 95 q^{80} - 20 q^{81} + 45 q^{82} - 108 q^{83} - 97 q^{84} - 21 q^{85} - 73 q^{86} - 3 q^{87} + 23 q^{88} - 325 q^{89} + 6 q^{90} - 17 q^{91} - 19 q^{92} + 2 q^{93} - 5 q^{94} - 54 q^{95} - 105 q^{96} - 81 q^{97} - 61 q^{98} - 76 q^{99}+O(q^{100}) \) 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9 - 18 * q^10 - 47 * q^11 - 27 * q^12 - 29 * q^13 - 51 * q^14 - 36 * q^15 + 71 * q^16 - 99 * q^17 - 27 * q^18 - 45 * q^19 - 75 * q^20 - 79 * q^21 - 2 * q^22 - 25 * q^23 - 66 * q^24 + 67 * q^25 - 73 * q^26 - 42 * q^27 - 31 * q^28 - 78 * q^29 - 29 * q^30 - 41 * q^31 - 95 * q^32 - 83 * q^33 - 44 * q^34 - 45 * q^35 + 23 * q^36 - 16 * q^37 - 29 * q^38 - 42 * q^39 - 37 * q^40 - 235 * q^41 + 16 * q^42 - 6 * q^43 - 122 * q^44 - 79 * q^45 - 17 * q^46 - 67 * q^47 - 25 * q^48 + 30 * q^49 - 68 * q^50 - 18 * q^51 - 41 * q^52 - 69 * q^53 - 63 * q^54 - 32 * q^55 - 120 * q^56 - 63 * q^57 - 7 * q^58 - 118 * q^59 - 49 * q^60 - 60 * q^61 - 23 * q^62 - 43 * q^63 + 43 * q^64 - 181 * q^65 - 4 * q^66 - 18 * q^67 - 130 * q^68 - 80 * q^69 + 12 * q^70 - 77 * q^71 - 40 * q^72 - 64 * q^73 - 48 * q^74 - 18 * q^75 - 134 * q^76 - 87 * q^77 + 65 * q^78 - 48 * q^79 - 95 * q^80 - 20 * q^81 + 45 * q^82 - 108 * q^83 - 97 * q^84 - 21 * q^85 - 73 * q^86 - 3 * q^87 + 23 * q^88 - 325 * q^89 + 6 * q^90 - 17 * q^91 - 19 * q^92 + 2 * q^93 - 5 * q^94 - 54 * q^95 - 105 * q^96 - 81 * q^97 - 61 * q^98 - 76 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.48716	−1.75868	−0.879342	−	0.476190i	$-0.842017\pi$
$2$	−2.48716	−1.75868	−0.879342	+	0.476190i	$0.842017\pi$
$3$	0.674976	0.389698	0.194849	−	0.980833i	$-0.437578\pi$
$3$	0.674976	0.389698	0.194849	+	0.980833i	$0.437578\pi$
$4$	4.18594	2.09297
$5$	−1.47569	−0.659950	−0.329975	−	0.943990i	$-0.607040\pi$
$5$	−1.47569	−0.659950	−0.329975	+	0.943990i	$0.607040\pi$
$6$	−1.67877	−0.685355
$7$	0.0650875	0.0246008	0.0123004	−	0.999924i	$-0.496085\pi$
$7$	0.0650875	0.0246008	0.0123004	+	0.999924i	$0.496085\pi$
$8$	−5.43678	−1.92219
$9$	−2.54441	−0.848136
$10$	3.67028	1.16064
$11$	3.92132	1.18232	0.591161	−	0.806554i	$-0.298670\pi$
$11$	3.92132	1.18232	0.591161	+	0.806554i	$0.298670\pi$
$12$	2.82541	0.815626
$13$	5.49172	1.52313	0.761565	−	0.648089i	$-0.224432\pi$
$13$	5.49172	1.52313	0.761565	+	0.648089i	$0.224432\pi$
$14$	−0.161883	−0.0432650
$15$	−0.996058	−0.257181
$16$	5.15022	1.28756
$17$	−3.93851	−0.955230	−0.477615	−	0.878569i	$-0.658499\pi$
$17$	−3.93851	−0.955230	−0.477615	+	0.878569i	$0.658499\pi$
$18$	6.32833	1.49160
$19$	4.25660	0.976531	0.488265	−	0.872695i	$-0.337630\pi$
$19$	4.25660	0.976531	0.488265	+	0.872695i	$0.337630\pi$
$20$	−6.17716	−1.38126
$21$	0.0439325	0.00958686
$22$	−9.75293	−2.07933
$23$	−9.41230	−1.96260	−0.981300	−	0.192486i	$-0.938345\pi$
$23$	−9.41230	−1.96260	−0.981300	+	0.192486i	$0.938345\pi$
$24$	−3.66970	−0.749074
$25$	−2.82233	−0.564466
$26$	−13.6588	−2.67870
$27$	−3.74234	−0.720214
$28$	0.272452	0.0514887
$29$	−1.89116	−0.351179	−0.175589	−	0.984464i	$-0.556183\pi$
$29$	−1.89116	−0.351179	−0.175589	+	0.984464i	$0.556183\pi$
$30$	2.47735	0.452300
$31$	−3.01200	−0.540972	−0.270486	−	0.962724i	$-0.587184\pi$
$31$	−3.01200	−0.540972	−0.270486	+	0.962724i	$0.587184\pi$
$32$	−1.93585	−0.342214
$33$	2.64680	0.460748
$34$	9.79570	1.67995
$35$	−0.0960491	−0.0162353
$36$	−10.6507	−1.77512
$37$	0.553801	0.0910443	0.0455221	−	0.998963i	$-0.485505\pi$
$37$	0.553801	0.0910443	0.0455221	+	0.998963i	$0.485505\pi$
$38$	−10.5868	−1.71741
$39$	3.70678	0.593560
$40$	8.02301	1.26855
$41$	0.496516	0.0775428	0.0387714	−	0.999248i	$-0.487656\pi$
$41$	0.496516	0.0775428	0.0387714	+	0.999248i	$0.487656\pi$
$42$	−0.109267	−0.0168603
$43$	10.6085	1.61778	0.808889	−	0.587961i	$-0.200069\pi$
$43$	10.6085	1.61778	0.808889	+	0.587961i	$0.200069\pi$
$44$	16.4144	2.47457
$45$	3.75476	0.559727
$46$	23.4098	3.45159
$47$	2.40538	0.350861	0.175430	−	0.984492i	$-0.443868\pi$
$47$	2.40538	0.350861	0.175430	+	0.984492i	$0.443868\pi$
$48$	3.47628	0.501758
$49$	−6.99576	−0.999395
$50$	7.01957	0.992718
$51$	−2.65840	−0.372251
$52$	22.9880	3.18786
$53$	11.3442	1.55825	0.779123	−	0.626871i	$-0.215665\pi$
$53$	11.3442	1.55825	0.779123	+	0.626871i	$0.215665\pi$
$54$	9.30779	1.26663
$55$	−5.78666	−0.780273
$56$	−0.353866	−0.0472874
$57$	2.87310	0.380552
$58$	4.70360	0.617612
$59$	−11.5619	−1.50523	−0.752615	−	0.658461i	$-0.771208\pi$
$59$	−11.5619	−1.50523	−0.752615	+	0.658461i	$0.771208\pi$
$60$	−4.16944	−0.538272
$61$	−11.9612	−1.53148	−0.765738	−	0.643153i	$-0.777626\pi$
$61$	−11.9612	−1.53148	−0.765738	+	0.643153i	$0.777626\pi$
$62$	7.49132	0.951399
$63$	−0.165609	−0.0208648
$64$	−5.48568	−0.685710
$65$	−8.10409	−1.00519
$66$	−6.58300	−0.810311
$67$	−12.1179	−1.48043	−0.740216	−	0.672369i	$-0.765277\pi$
$67$	−12.1179	−1.48043	−0.740216	+	0.672369i	$0.765277\pi$
$68$	−16.4864	−1.99927
$69$	−6.35308	−0.764821
$70$	0.238889	0.0285527
$71$	3.89106	0.461783	0.230892	−	0.972979i	$-0.425836\pi$
$71$	3.89106	0.461783	0.230892	+	0.972979i	$0.425836\pi$
$72$	13.8334	1.63028
$73$	9.38779	1.09876	0.549379	−	0.835573i	$-0.314864\pi$
$73$	9.38779	1.09876	0.549379	+	0.835573i	$0.314864\pi$
$74$	−1.37739	−0.160118
$75$	−1.90501	−0.219971
$76$	17.8179	2.04385
$77$	0.255229	0.0290860
$78$	−9.21934	−1.04388
$79$	12.5233	1.40899	0.704493	−	0.709711i	$-0.251175\pi$
$79$	12.5233	1.40899	0.704493	+	0.709711i	$0.251175\pi$
$80$	−7.60015	−0.849722
$81$	5.10723	0.567470
$82$	−1.23491	−0.136373
$83$	5.42106	0.595038	0.297519	−	0.954716i	$-0.403841\pi$
$83$	5.42106	0.595038	0.297519	+	0.954716i	$0.403841\pi$
$84$	0.183899	0.0200650
$85$	5.81204	0.630404
$86$	−26.3850	−2.84516
$87$	−1.27649	−0.136854
$88$	−21.3193	−2.27265
$89$	−12.4174	−1.31625	−0.658123	−	0.752910i	$-0.728649\pi$
$89$	−12.4174	−1.31625	−0.658123	+	0.752910i	$0.728649\pi$
$90$	−9.33868	−0.984383
$91$	0.357442	0.0374701
$92$	−39.3993	−4.10766
$93$	−2.03303	−0.210816
$94$	−5.98255	−0.617053
$95$	−6.28143	−0.644461
$96$	−1.30666	−0.133360
$97$	7.15420	0.726399	0.363199	−	0.931711i	$-0.381684\pi$
$97$	7.15420	0.726399	0.363199	+	0.931711i	$0.381684\pi$
$98$	17.3996	1.75762
$99$	−9.97743	−1.00277
$100$	−11.8141	−1.18141
$101$	−17.5620	−1.74748	−0.873740	−	0.486393i	$-0.838312\pi$
$101$	−17.5620	−1.74748	−0.873740	+	0.486393i	$0.838312\pi$
$102$	6.61187	0.654672
$103$	−7.31695	−0.720961	−0.360480	−	0.932767i	$-0.617387\pi$
$103$	−7.31695	−0.720961	−0.360480	+	0.932767i	$0.617387\pi$
$104$	−29.8573	−2.92774
$105$	−0.0648309	−0.00632685
$106$	−28.2148	−2.74046
$107$	−5.03362	−0.486618	−0.243309	−	0.969949i	$-0.578233\pi$
$107$	−5.03362	−0.486618	−0.243309	+	0.969949i	$0.578233\pi$
$108$	−15.6652	−1.50739
$109$	15.7535	1.50892	0.754458	−	0.656348i	$-0.227900\pi$
$109$	15.7535	1.50892	0.754458	+	0.656348i	$0.227900\pi$
$110$	14.3923	1.37225
$111$	0.373802	0.0354798
$112$	0.335215	0.0316749
$113$	−0.800210	−0.0752775	−0.0376387	−	0.999291i	$-0.511984\pi$
$113$	−0.800210	−0.0752775	−0.0376387	+	0.999291i	$0.511984\pi$
$114$	−7.14585	−0.669271
$115$	13.8897	1.29522
$116$	−7.91626	−0.735007
$117$	−13.9732	−1.29182
$118$	28.7562	2.64722
$119$	−0.256348	−0.0234994
$120$	5.41534	0.494351
$121$	4.37674	0.397886
$122$	29.7494	2.69338
$123$	0.335137	0.0302182
$124$	−12.6081	−1.13224
$125$	11.5434	1.03247
$126$	0.411895	0.0366946
$127$	−8.07270	−0.716336	−0.358168	−	0.933657i	$-0.616599\pi$
$127$	−8.07270	−0.716336	−0.358168	+	0.933657i	$0.616599\pi$
$128$	17.5154	1.54816
$129$	7.16048	0.630445
$130$	20.1561	1.76781
$131$	−1.07337	−0.0937803	−0.0468902	−	0.998900i	$-0.514931\pi$
$131$	−1.07337	−0.0937803	−0.0468902	+	0.998900i	$0.514931\pi$
$132$	11.0793	0.964333
$133$	0.277051	0.0240234
$134$	30.1390	2.60361
$135$	5.52255	0.475305
$136$	21.4128	1.83613
$137$	3.32429	0.284013	0.142006	−	0.989866i	$-0.454645\pi$
$137$	3.32429	0.284013	0.142006	+	0.989866i	$0.454645\pi$
$138$	15.8011	1.34508
$139$	2.23279	0.189383	0.0946915	−	0.995507i	$-0.469814\pi$
$139$	2.23279	0.189383	0.0946915	+	0.995507i	$0.469814\pi$
$140$	−0.402056	−0.0339799
$141$	1.62357	0.136730
$142$	−9.67766	−0.812131
$143$	21.5348	1.80083
$144$	−13.1043	−1.09202
$145$	2.79076	0.231760
$146$	−23.3489	−1.93237
$147$	−4.72198	−0.389462
$148$	2.31818	0.190553
$149$	−11.2513	−0.921739	−0.460870	−	0.887468i	$-0.652462\pi$
$149$	−11.2513	−0.921739	−0.460870	+	0.887468i	$0.652462\pi$
$150$	4.73805	0.386860
$151$	3.23999	0.263667	0.131834	−	0.991272i	$-0.457914\pi$
$151$	3.23999	0.263667	0.131834	+	0.991272i	$0.457914\pi$
$152$	−23.1422	−1.87708
$153$	10.0212	0.810165
$154$	−0.634794	−0.0511531
$155$	4.44479	0.357014
$156$	15.5164	1.24230
$157$	−19.6806	−1.57068	−0.785341	−	0.619063i	$-0.787512\pi$
$157$	−19.6806	−1.57068	−0.785341	+	0.619063i	$0.787512\pi$
$158$	−31.1475	−2.47796
$159$	7.65707	0.607245
$160$	2.85673	0.225844
$161$	−0.612623	−0.0482814
$162$	−12.7025	−0.998000
$163$	−13.4555	−1.05391	−0.526957	−	0.849892i	$-0.676667\pi$
$163$	−13.4555	−1.05391	−0.526957	+	0.849892i	$0.676667\pi$
$164$	2.07839	0.162295
$165$	−3.90586	−0.304071
$166$	−13.4830	−1.04648
$167$	3.43313	0.265663	0.132832	−	0.991139i	$-0.457593\pi$
$167$	3.43313	0.265663	0.132832	+	0.991139i	$0.457593\pi$
$168$	−0.238851	−0.0184278
$169$	17.1590	1.31992
$170$	−14.4554	−1.10868
$171$	−10.8305	−0.828230
$172$	44.4065	3.38596
$173$	−4.25813	−0.323740	−0.161870	−	0.986812i	$-0.551752\pi$
$173$	−4.25813	−0.323740	−0.161870	+	0.986812i	$0.551752\pi$
$174$	3.17482	0.240682
$175$	−0.183698	−0.0138863
$176$	20.1957	1.52231
$177$	−7.80400	−0.586585
$178$	30.8841	2.31486
$179$	−16.2124	−1.21177	−0.605885	−	0.795553i	$-0.707181\pi$
$179$	−16.2124	−1.21177	−0.605885	+	0.795553i	$0.707181\pi$
$180$	15.7172	1.17149
$181$	7.97305	0.592632	0.296316	−	0.955090i	$-0.404242\pi$
$181$	7.97305	0.592632	0.296316	+	0.955090i	$0.404242\pi$
$182$	−0.889014	−0.0658981
$183$	−8.07353	−0.596813
$184$	51.1726	3.77249
$185$	−0.817240	−0.0600847
$186$	5.05647	0.370758
$187$	−15.4442	−1.12939
$188$	10.0688	0.734341
$189$	−0.243580	−0.0177178
$190$	15.6229	1.13340
$191$	−8.68431	−0.628375	−0.314187	−	0.949361i	$-0.601732\pi$
$191$	−8.68431	−0.628375	−0.314187	+	0.949361i	$0.601732\pi$
$192$	−3.70270	−0.267220
$193$	−6.03109	−0.434128	−0.217064	−	0.976157i	$-0.569648\pi$
$193$	−6.03109	−0.434128	−0.217064	+	0.976157i	$0.569648\pi$
$194$	−17.7936	−1.27751
$195$	−5.47007	−0.391720
$196$	−29.2839	−2.09170
$197$	3.16779	0.225695	0.112848	−	0.993612i	$-0.464003\pi$
$197$	3.16779	0.225695	0.112848	+	0.993612i	$0.464003\pi$
$198$	24.8154	1.76356
$199$	−28.0511	−1.98849	−0.994246	−	0.107117i	$-0.965838\pi$
$199$	−28.0511	−1.98849	−0.994246	+	0.107117i	$0.965838\pi$
$200$	15.3444	1.08501
$201$	−8.17927	−0.576921
$202$	43.6793	3.07327
$203$	−0.123091	−0.00863926
$204$	−11.1279	−0.779111
$205$	−0.732705	−0.0511743
$206$	18.1984	1.26794
$207$	23.9487	1.66455
$208$	28.2836	1.96111
$209$	16.6915	1.15457
$210$	0.161245	0.0111269
$211$	−2.99366	−0.206092	−0.103046	−	0.994677i	$-0.532859\pi$
$211$	−2.99366	−0.206092	−0.103046	+	0.994677i	$0.532859\pi$
$212$	47.4862	3.26136
$213$	2.62637	0.179956
$214$	12.5194	0.855807
$215$	−15.6549	−1.06765
$216$	20.3463	1.38439
$217$	−0.196044	−0.0133083
$218$	−39.1815	−2.65371
$219$	6.33654	0.428184
$220$	−24.2226	−1.63309
$221$	−21.6292	−1.45494
$222$	−0.929705	−0.0623977
$223$	−21.3374	−1.42886	−0.714428	−	0.699709i	$-0.753313\pi$
$223$	−21.3374	−1.42886	−0.714428	+	0.699709i	$0.753313\pi$
$224$	−0.126000	−0.00841872
$225$	7.18116	0.478744
$226$	1.99025	0.132389
$227$	−11.6207	−0.771293	−0.385647	−	0.922647i	$-0.626022\pi$
$227$	−11.6207	−0.771293	−0.385647	+	0.922647i	$0.626022\pi$
$228$	12.0266	0.796484
$229$	−1.29656	−0.0856790	−0.0428395	−	0.999082i	$-0.513640\pi$
$229$	−1.29656	−0.0856790	−0.0428395	+	0.999082i	$0.513640\pi$
$230$	−34.5457	−2.27788
$231$	0.172273	0.0113348
$232$	10.2818	0.675032
$233$	−5.88748	−0.385702	−0.192851	−	0.981228i	$-0.561773\pi$
$233$	−5.88748	−0.385702	−0.192851	+	0.981228i	$0.561773\pi$
$234$	34.7534	2.27190
$235$	−3.54960	−0.231550
$236$	−48.3974	−3.15040
$237$	8.45296	0.549079
$238$	0.637577	0.0413280
$239$	1.07890	0.0697881	0.0348940	−	0.999391i	$-0.488891\pi$
$239$	1.07890	0.0697881	0.0348940	+	0.999391i	$0.488891\pi$
$240$	−5.12992	−0.331135
$241$	10.1450	0.653498	0.326749	−	0.945111i	$-0.394047\pi$
$241$	10.1450	0.653498	0.326749	+	0.945111i	$0.394047\pi$
$242$	−10.8856	−0.699755
$243$	14.6743	0.941356
$244$	−50.0689	−3.20533
$245$	10.3236	0.659550
$246$	−0.833537	−0.0531444
$247$	23.3760	1.48738
$248$	16.3756	1.03985
$249$	3.65908	0.231885
$250$	−28.7101	−1.81579
$251$	−11.2447	−0.709760	−0.354880	−	0.934912i	$-0.615478\pi$
$251$	−11.2447	−0.709760	−0.354880	+	0.934912i	$0.615478\pi$
$252$	−0.693230	−0.0436694
$253$	−36.9086	−2.32042
$254$	20.0781	1.25981
$255$	3.92299	0.245667
$256$	−32.5923	−2.03702
$257$	6.28932	0.392317	0.196158	−	0.980572i	$-0.437153\pi$
$257$	6.28932	0.392317	0.196158	+	0.980572i	$0.437153\pi$
$258$	−17.8092	−1.10875
$259$	0.0360455	0.00223976
$260$	−33.9233	−2.10383
$261$	4.81187	0.297847
$262$	2.66963	0.164930
$263$	22.4666	1.38535	0.692675	−	0.721250i	$-0.256432\pi$
$263$	22.4666	1.38535	0.692675	+	0.721250i	$0.256432\pi$
$264$	−14.3900	−0.885646
$265$	−16.7406	−1.02836
$266$	−0.689070	−0.0422496
$267$	−8.38148	−0.512939
$268$	−50.7246	−3.09850
$269$	−27.0637	−1.65010	−0.825050	−	0.565059i	$-0.808853\pi$
$269$	−27.0637	−1.65010	−0.825050	+	0.565059i	$0.808853\pi$
$270$	−13.7354	−0.835912
$271$	−28.9224	−1.75691	−0.878455	−	0.477825i	$-0.841425\pi$
$271$	−28.9224	−1.75691	−0.878455	+	0.477825i	$0.841425\pi$
$272$	−20.2842	−1.22991
$273$	0.241265	0.0146020
$274$	−8.26801	−0.499489
$275$	−11.0673	−0.667381
$276$	−26.5936	−1.60075
$277$	5.00438	0.300684	0.150342	−	0.988634i	$-0.451962\pi$
$277$	5.00438	0.300684	0.150342	+	0.988634i	$0.451962\pi$
$278$	−5.55330	−0.333065
$279$	7.66376	0.458818
$280$	0.522198	0.0312073
$281$	15.0074	0.895266	0.447633	−	0.894217i	$-0.352267\pi$
$281$	15.0074	0.895266	0.447633	+	0.894217i	$0.352267\pi$
$282$	−4.03808	−0.240464
$283$	6.01902	0.357794	0.178897	−	0.983868i	$-0.442747\pi$
$283$	6.01902	0.357794	0.178897	+	0.983868i	$0.442747\pi$
$284$	16.2877	0.966499
$285$	−4.23982	−0.251145
$286$	−53.5604	−3.16709
$287$	0.0323170	0.00190761
$288$	4.92560	0.290244
$289$	−1.48810	−0.0875354
$290$	−6.94106	−0.407593
$291$	4.82892	0.283076
$292$	39.2968	2.29967
$293$	20.9192	1.22211	0.611056	−	0.791588i	$-0.290745\pi$
$293$	20.9192	1.22211	0.611056	+	0.791588i	$0.290745\pi$
$294$	11.7443	0.684941
$295$	17.0618	0.993376
$296$	−3.01089	−0.175004
$297$	−14.6749	−0.851525
$298$	27.9836	1.62105
$299$	−51.6897	−2.98929
$300$	−7.97425	−0.460393
$301$	0.690480	0.0397986
$302$	−8.05837	−0.463707
$303$	−11.8539	−0.680989
$304$	21.9224	1.25734
$305$	17.6511	1.01070
$306$	−24.9242	−1.42482
$307$	14.0452	0.801604	0.400802	−	0.916165i	$-0.368732\pi$
$307$	14.0452	0.801604	0.400802	+	0.916165i	$0.368732\pi$
$308$	1.06837	0.0608762
$309$	−4.93877	−0.280957
$310$	−11.0549	−0.627876
$311$	13.5635	0.769115	0.384557	−	0.923101i	$-0.374354\pi$
$311$	13.5635	0.769115	0.384557	+	0.923101i	$0.374354\pi$
$312$	−20.1529	−1.14094
$313$	0.282075	0.0159438	0.00797192	−	0.999968i	$-0.497462\pi$
$313$	0.282075	0.0159438	0.00797192	+	0.999968i	$0.497462\pi$
$314$	48.9487	2.76233
$315$	0.244388	0.0137697
$316$	52.4220	2.94897
$317$	−9.40805	−0.528409	−0.264204	−	0.964467i	$-0.585109\pi$
$317$	−9.40805	−0.528409	−0.264204	+	0.964467i	$0.585109\pi$
$318$	−19.0443	−1.06795
$319$	−7.41582	−0.415206
$320$	8.09518	0.452534
$321$	−3.39757	−0.189634
$322$	1.52369	0.0849118
$323$	−16.7647	−0.932811
$324$	21.3786	1.18770
$325$	−15.4994	−0.859755
$326$	33.4659	1.85350
$327$	10.6333	0.588021
$328$	−2.69945	−0.149052
$329$	0.156560	0.00863144
$330$	9.71448	0.534765
$331$	−2.15756	−0.118590	−0.0592951	−	0.998240i	$-0.518885\pi$
$331$	−2.15756	−0.118590	−0.0592951	+	0.998240i	$0.518885\pi$
$332$	22.6922	1.24540
$333$	−1.40909	−0.0772179
$334$	−8.53872	−0.467218
$335$	17.8822	0.977011
$336$	0.226262	0.0123436
$337$	−3.45055	−0.187963	−0.0939816	−	0.995574i	$-0.529959\pi$
$337$	−3.45055	−0.187963	−0.0939816	+	0.995574i	$0.529959\pi$
$338$	−42.6771	−2.32133
$339$	−0.540123	−0.0293355
$340$	24.3289	1.31942
$341$	−11.8110	−0.639603
$342$	26.9372	1.45660
$343$	−0.910949	−0.0491866
$344$	−57.6760	−3.10968
$345$	9.37519	0.504743
$346$	10.5906	0.569356
$347$	−35.7665	−1.92005	−0.960024	−	0.279919i	$-0.909692\pi$
$347$	−35.7665	−1.92005	−0.960024	+	0.279919i	$0.909692\pi$
$348$	−5.34329	−0.286431
$349$	−15.3134	−0.819709	−0.409855	−	0.912151i	$-0.634421\pi$
$349$	−15.3134	−0.819709	−0.409855	+	0.912151i	$0.634421\pi$
$350$	0.456887	0.0244216
$351$	−20.5519	−1.09698
$352$	−7.59110	−0.404607
$353$	−25.2342	−1.34308	−0.671541	−	0.740967i	$-0.734367\pi$
$353$	−25.2342	−1.34308	−0.671541	+	0.740967i	$0.734367\pi$
$354$	19.4098	1.03162
$355$	−5.74200	−0.304754
$356$	−51.9787	−2.75487
$357$	−0.173029	−0.00915766
$358$	40.3227	2.13112
$359$	−36.5134	−1.92710	−0.963551	−	0.267525i	$-0.913794\pi$
$359$	−36.5134	−1.92710	−0.963551	+	0.267525i	$0.913794\pi$
$360$	−20.4138	−1.07590
$361$	−0.881370	−0.0463879
$362$	−19.8302	−1.04225
$363$	2.95420	0.155055
$364$	1.49623	0.0784239
$365$	−13.8535	−0.725125
$366$	20.0801	1.04960
$367$	−22.6005	−1.17974	−0.589869	−	0.807499i	$-0.700821\pi$
$367$	−22.6005	−1.17974	−0.589869	+	0.807499i	$0.700821\pi$
$368$	−48.4754	−2.52696
$369$	−1.26334	−0.0657668
$370$	2.03260	0.105670
$371$	0.738366	0.0383341
$372$	−8.51015	−0.441231
$373$	11.1458	0.577106	0.288553	−	0.957464i	$-0.406826\pi$
$373$	11.1458	0.577106	0.288553	+	0.957464i	$0.406826\pi$
$374$	38.4121	1.98624
$375$	7.79149	0.402351
$376$	−13.0775	−0.674421
$377$	−10.3857	−0.534890
$378$	0.605821	0.0311601
$379$	17.4381	0.895733	0.447866	−	0.894101i	$-0.352184\pi$
$379$	17.4381	0.895733	0.447866	+	0.894101i	$0.352184\pi$
$380$	−26.2937	−1.34884
$381$	−5.44888	−0.279155
$382$	21.5992	1.10511
$383$	11.1980	0.572189	0.286095	−	0.958201i	$-0.407643\pi$
$383$	11.1980	0.572189	0.286095	+	0.958201i	$0.407643\pi$
$384$	11.8225	0.603315
$385$	−0.376639	−0.0191953
$386$	15.0003	0.763493
$387$	−26.9923	−1.37210
$388$	29.9471	1.52033
$389$	0.987130	0.0500495	0.0250247	−	0.999687i	$-0.492034\pi$
$389$	0.987130	0.0500495	0.0250247	+	0.999687i	$0.492034\pi$
$390$	13.6049	0.688912
$391$	37.0705	1.87473
$392$	38.0344	1.92103
$393$	−0.724496	−0.0365460
$394$	−7.87878	−0.396927
$395$	−18.4806	−0.929860
$396$	−41.7649	−2.09877
$397$	−19.4717	−0.977258	−0.488629	−	0.872492i	$-0.662503\pi$
$397$	−19.4717	−0.977258	−0.488629	+	0.872492i	$0.662503\pi$
$398$	69.7675	3.49713
$399$	0.187003	0.00936187
$400$	−14.5356	−0.726782
$401$	−34.0842	−1.70208	−0.851042	−	0.525098i	$-0.824029\pi$
$401$	−34.0842	−1.70208	−0.851042	+	0.525098i	$0.824029\pi$
$402$	20.3431	1.01462
$403$	−16.5411	−0.823970
$404$	−73.5133	−3.65742
$405$	−7.53670	−0.374501
$406$	0.306145	0.0151937
$407$	2.17163	0.107644
$408$	14.4532	0.715538
$409$	33.4859	1.65577	0.827887	−	0.560895i	$-0.189543\pi$
$409$	33.4859	1.65577	0.827887	+	0.560895i	$0.189543\pi$
$410$	1.82235	0.0899995
$411$	2.24381	0.110679
$412$	−30.6283	−1.50895
$413$	−0.752534	−0.0370298
$414$	−59.5642	−2.92742
$415$	−7.99981	−0.392695
$416$	−10.6312	−0.521236
$417$	1.50708	0.0738022
$418$	−41.5143	−2.03053
$419$	−4.67769	−0.228520	−0.114260	−	0.993451i	$-0.536450\pi$
$419$	−4.67769	−0.228520	−0.114260	+	0.993451i	$0.536450\pi$
$420$	−0.271378	−0.0132419
$421$	32.0871	1.56383	0.781916	−	0.623384i	$-0.214243\pi$
$421$	32.0871	1.56383	0.781916	+	0.623384i	$0.214243\pi$
$422$	7.44570	0.362451
$423$	−6.12026	−0.297577
$424$	−61.6759	−2.99525
$425$	11.1158	0.539195
$426$	−6.53219	−0.316486
$427$	−0.778525	−0.0376755
$428$	−21.0704	−1.01848
$429$	14.5355	0.701779
$430$	38.9361	1.87766
$431$	3.66935	0.176746	0.0883731	−	0.996087i	$-0.471833\pi$
$431$	3.66935	0.176746	0.0883731	+	0.996087i	$0.471833\pi$
$432$	−19.2739	−0.927316
$433$	−17.3887	−0.835646	−0.417823	−	0.908528i	$-0.637207\pi$
$433$	−17.3887	−0.835646	−0.417823	+	0.908528i	$0.637207\pi$
$434$	0.487591	0.0234051
$435$	1.88370	0.0903165
$436$	65.9434	3.15812
$437$	−40.0644	−1.91654
$438$	−15.7600	−0.753040
$439$	9.06118	0.432467	0.216233	−	0.976342i	$-0.430623\pi$
$439$	9.06118	0.432467	0.216233	+	0.976342i	$0.430623\pi$
$440$	31.4608	1.49983
$441$	17.8001	0.847622
$442$	53.7952	2.55878
$443$	16.2197	0.770621	0.385311	−	0.922787i	$-0.374094\pi$
$443$	16.2197	0.770621	0.385311	+	0.922787i	$0.374094\pi$
$444$	1.56472	0.0742581
$445$	18.3243	0.868657
$446$	53.0694	2.51291
$447$	−7.59434	−0.359200
$448$	−0.357049	−0.0168690
$449$	−38.7949	−1.83084	−0.915421	−	0.402497i	$-0.868142\pi$
$449$	−38.7949	−1.83084	−0.915421	+	0.402497i	$0.868142\pi$
$450$	−17.8607	−0.841959
$451$	1.94700	0.0916805
$452$	−3.34963	−0.157554
$453$	2.18692	0.102750
$454$	28.9025	1.35646
$455$	−0.527475	−0.0247284
$456$	−15.6204	−0.731493
$457$	0.00162168	7.58588e−5 0	3.79294e−5	−	1.00000i	$-0.499988\pi$
$457$	0.00162168	7.58588e−5 0	3.79294e−5		1.00000i	$0.499988\pi$
$458$	3.22474	0.150682
$459$	14.7393	0.687971
$460$	58.1413	2.71085
$461$	−9.85826	−0.459145	−0.229572	−	0.973292i	$-0.573733\pi$
$461$	−9.85826	−0.459145	−0.229572	+	0.973292i	$0.573733\pi$
$462$	−0.428471	−0.0199343
$463$	−31.0873	−1.44475	−0.722375	−	0.691501i	$-0.756950\pi$
$463$	−31.0873	−1.44475	−0.722375	+	0.691501i	$0.756950\pi$
$464$	−9.73987	−0.452162
$465$	3.00013	0.139128
$466$	14.6431	0.678328
$467$	−27.1179	−1.25487	−0.627434	−	0.778670i	$-0.715895\pi$
$467$	−27.1179	−1.25487	−0.627434	+	0.778670i	$0.715895\pi$
$468$	−58.4909	−2.70374
$469$	−0.788721	−0.0364197
$470$	8.82841	0.407224
$471$	−13.2839	−0.612091
$472$	62.8594	2.89334
$473$	41.5993	1.91274
$474$	−21.0238	−0.965656
$475$	−12.0135	−0.551218
$476$	−1.07306	−0.0491835
$477$	−28.8643	−1.32160
$478$	−2.68338	−0.122735
$479$	19.3630	0.884719	0.442359	−	0.896838i	$-0.354142\pi$
$479$	19.3630	0.884719	0.442359	+	0.896838i	$0.354142\pi$
$480$	1.92822	0.0880109
$481$	3.04132	0.138672
$482$	−25.2322	−1.14930
$483$	−0.413506	−0.0188152
$484$	18.3208	0.832763
$485$	−10.5574	−0.479387
$486$	−36.4972	−1.65555
$487$	9.41468	0.426620	0.213310	−	0.976985i	$-0.431576\pi$
$487$	9.41468	0.426620	0.213310	+	0.976985i	$0.431576\pi$
$488$	65.0304	2.94379
$489$	−9.08213	−0.410708
$490$	−25.6764	−1.15994
$491$	−23.1272	−1.04372	−0.521858	−	0.853032i	$-0.674761\pi$
$491$	−23.1272	−1.04372	−0.521858	+	0.853032i	$0.674761\pi$
$492$	1.40286	0.0632459
$493$	7.44834	0.335456
$494$	−58.1399	−2.61584
$495$	14.7236	0.661778
$496$	−15.5125	−0.696532
$497$	0.253259	0.0113602
$498$	−9.10071	−0.407813
$499$	−33.2534	−1.48863	−0.744314	−	0.667830i	$-0.767223\pi$
$499$	−33.2534	−1.48863	−0.744314	+	0.667830i	$0.767223\pi$
$500$	48.3198	2.16093
$501$	2.31728	0.103528
$502$	27.9674	1.24824
$503$	−7.28392	−0.324774	−0.162387	−	0.986727i	$-0.551919\pi$
$503$	−7.28392	−0.324774	−0.162387	+	0.986727i	$0.551919\pi$
$504$	0.900379	0.0401061
$505$	25.9161	1.15325
$506$	91.7975	4.08090
$507$	11.5819	0.514371
$508$	−33.7918	−1.49927
$509$	30.1057	1.33441	0.667207	−	0.744873i	$-0.267490\pi$
$509$	30.1057	1.33441	0.667207	+	0.744873i	$0.267490\pi$
$510$	−9.75708	−0.432051
$511$	0.611028	0.0270303
$512$	46.0311	2.03431
$513$	−15.9297	−0.703311
$514$	−15.6425	−0.689961
$515$	10.7976	0.475798
$516$	29.9733	1.31950
$517$	9.43226	0.414830
$518$	−0.0896508	−0.00393903
$519$	−2.87414	−0.126161
$520$	44.0601	1.93216
$521$	−12.8277	−0.561991	−0.280996	−	0.959709i	$-0.590665\pi$
$521$	−12.8277	−0.561991	−0.280996	+	0.959709i	$0.590665\pi$
$522$	−11.9679	−0.523819
$523$	18.5309	0.810301	0.405150	−	0.914250i	$-0.367219\pi$
$523$	18.5309	0.810301	0.405150	+	0.914250i	$0.367219\pi$
$524$	−4.49304	−0.196280
$525$	−0.123992	−0.00541146
$526$	−55.8780	−2.43639
$527$	11.8628	0.516753
$528$	13.6316	0.593239
$529$	65.5913	2.85180
$530$	41.6364	1.80857
$531$	29.4181	1.27664
$532$	1.15972	0.0502803
$533$	2.72673	0.118108
$534$	20.8461	0.902097
$535$	7.42807	0.321143
$536$	65.8821	2.84567
$537$	−10.9430	−0.472224
$538$	67.3115	2.90201
$539$	−27.4326	−1.18161
$540$	23.1171	0.994800
$541$	38.2940	1.64639	0.823195	−	0.567759i	$-0.192190\pi$
$541$	38.2940	1.64639	0.823195	+	0.567759i	$0.192190\pi$
$542$	71.9345	3.08985
$543$	5.38162	0.230947
$544$	7.62439	0.326893
$545$	−23.2474	−0.995809
$546$	−0.600064	−0.0256804
$547$	−9.85485	−0.421363	−0.210682	−	0.977555i	$-0.567568\pi$
$547$	−9.85485	−0.421363	−0.210682	+	0.977555i	$0.567568\pi$
$548$	13.9153	0.594431
$549$	30.4342	1.29890
$550$	27.5260	1.17371
$551$	−8.04989	−0.342937
$552$	34.5403	1.47013
$553$	0.815113	0.0346621
$554$	−12.4467	−0.528809
$555$	−0.551618	−0.0234149
$556$	9.34634	0.396373
$557$	−7.05639	−0.298989	−0.149494	−	0.988763i	$-0.547765\pi$
$557$	−7.05639	−0.298989	−0.149494	+	0.988763i	$0.547765\pi$
$558$	−19.0610	−0.806915
$559$	58.2588	2.46409
$560$	−0.494675	−0.0209038
$561$	−10.4245	−0.440121
$562$	−37.3257	−1.57449
$563$	19.2150	0.809815	0.404907	−	0.914358i	$-0.367304\pi$
$563$	19.2150	0.809815	0.404907	+	0.914358i	$0.367304\pi$
$564$	6.79619	0.286171
$565$	1.18086	0.0496794
$566$	−14.9702	−0.629246
$567$	0.332417	0.0139602
$568$	−21.1548	−0.887636
$569$	3.57253	0.149768	0.0748842	−	0.997192i	$-0.476141\pi$
$569$	3.57253	0.149768	0.0748842	+	0.997192i	$0.476141\pi$
$570$	10.5451	0.441685
$571$	−25.4771	−1.06618	−0.533092	−	0.846057i	$-0.678970\pi$
$571$	−25.4771	−1.06618	−0.533092	+	0.846057i	$0.678970\pi$
$572$	90.1434	3.76908
$573$	−5.86170	−0.244876
$574$	−0.0803773	−0.00335489
$575$	26.5646	1.10782
$576$	13.9578	0.581575
$577$	34.0671	1.41823	0.709115	−	0.705093i	$-0.249095\pi$
$577$	34.0671	1.41823	0.709115	+	0.705093i	$0.249095\pi$
$578$	3.70114	0.153947
$579$	−4.07085	−0.169179
$580$	11.6820	0.485068
$581$	0.352843	0.0146384
$582$	−12.0103	−0.497841
$583$	44.4843	1.84235
$584$	−51.0393	−2.11202
$585$	20.6201	0.852536
$586$	−52.0292	−2.14931
$587$	−24.3204	−1.00381	−0.501906	−	0.864922i	$-0.667368\pi$
$587$	−24.3204	−1.00381	−0.501906	+	0.864922i	$0.667368\pi$
$588$	−19.7659	−0.815133
$589$	−12.8209	−0.528276
$590$	−42.4353	−1.74703
$591$	2.13818	0.0879530
$592$	2.85220	0.117225
$593$	10.9723	0.450577	0.225288	−	0.974292i	$-0.427668\pi$
$593$	10.9723	0.450577	0.225288	+	0.974292i	$0.427668\pi$
$594$	36.4988	1.49756
$595$	0.378291	0.0155084
$596$	−47.0971	−1.92917
$597$	−18.9339	−0.774911
$598$	128.560	5.25722
$599$	20.4044	0.833702	0.416851	−	0.908975i	$-0.363134\pi$
$599$	20.4044	0.833702	0.416851	+	0.908975i	$0.363134\pi$
$600$	10.3571	0.422827
$601$	−41.6699	−1.69975	−0.849875	−	0.526985i	$-0.823323\pi$
$601$	−41.6699	−1.69975	−0.849875	+	0.526985i	$0.823323\pi$
$602$	−1.71733	−0.0699932
$603$	30.8328	1.25561
$604$	13.5624	0.551847
$605$	−6.45873	−0.262585
$606$	29.4825	1.19764
$607$	22.6078	0.917624	0.458812	−	0.888533i	$-0.348275\pi$
$607$	22.6078	0.917624	0.458812	+	0.888533i	$0.348275\pi$
$608$	−8.24015	−0.334182
$609$	−0.0830832	−0.00336670
$610$	−43.9009	−1.77750
$611$	13.2097	0.534406
$612$	41.9481	1.69565
$613$	−43.6483	−1.76294	−0.881470	−	0.472241i	$-0.843445\pi$
$613$	−43.6483	−1.76294	−0.881470	+	0.472241i	$0.843445\pi$
$614$	−34.9327	−1.40977
$615$	−0.494559	−0.0199425
$616$	−1.38762	−0.0559089
$617$	31.6100	1.27257	0.636285	−	0.771454i	$-0.280470\pi$
$617$	31.6100	1.27257	0.636285	+	0.771454i	$0.280470\pi$
$618$	12.2835	0.494114
$619$	−41.1637	−1.65451	−0.827254	−	0.561828i	$-0.810098\pi$
$619$	−41.1637	−1.65451	−0.827254	+	0.561828i	$0.810098\pi$
$620$	18.6056	0.747221
$621$	35.2241	1.41349
$622$	−33.7345	−1.35263
$623$	−0.808221	−0.0323807
$624$	19.0908	0.764242
$625$	−2.92280	−0.116912
$626$	−0.701565	−0.0280402
$627$	11.2664	0.449935
$628$	−82.3818	−3.28739
$629$	−2.18115	−0.0869683
$630$	−0.607831	−0.0242166
$631$	−25.4104	−1.01157	−0.505785	−	0.862659i	$-0.668797\pi$
$631$	−25.4104	−1.01157	−0.505785	+	0.862659i	$0.668797\pi$
$632$	−68.0866	−2.70834
$633$	−2.02065	−0.0803137
$634$	23.3993	0.929304
$635$	11.9128	0.472746
$636$	32.0521	1.27095
$637$	−38.4188	−1.52221
$638$	18.4443	0.730217
$639$	−9.90043	−0.391655
$640$	−25.8474	−1.02171
$641$	−15.1779	−0.599490	−0.299745	−	0.954019i	$-0.596902\pi$
$641$	−15.1779	−0.599490	−0.299745	+	0.954019i	$0.596902\pi$
$642$	8.45029	0.333506
$643$	47.2650	1.86395	0.931974	−	0.362525i	$-0.118085\pi$
$643$	47.2650	1.86395	0.931974	+	0.362525i	$0.118085\pi$
$644$	−2.56440	−0.101052
$645$	−10.5667	−0.416062
$646$	41.6964	1.64052
$647$	41.5440	1.63326	0.816632	−	0.577159i	$-0.195839\pi$
$647$	41.5440	1.63326	0.816632	+	0.577159i	$0.195839\pi$
$648$	−27.7668	−1.09078
$649$	−45.3378	−1.77967
$650$	38.5495	1.51204
$651$	−0.132325	−0.00518622
$652$	−56.3239	−2.20581
$653$	37.5206	1.46829	0.734146	−	0.678991i	$-0.237583\pi$
$653$	37.5206	1.46829	0.734146	+	0.678991i	$0.237583\pi$
$654$	−26.4466	−1.03414
$655$	1.58396	0.0618903
$656$	2.55717	0.0998406
$657$	−23.8864	−0.931896
$658$	−0.389389	−0.0151800
$659$	12.7680	0.497371	0.248686	−	0.968584i	$-0.420001\pi$
$659$	12.7680	0.497371	0.248686	+	0.968584i	$0.420001\pi$
$660$	−16.3497	−0.636411
$661$	6.88304	0.267719	0.133860	−	0.991000i	$-0.457263\pi$
$661$	6.88304	0.267719	0.133860	+	0.991000i	$0.457263\pi$
$662$	5.36618	0.208563
$663$	−14.5992	−0.566986
$664$	−29.4731	−1.14378
$665$	−0.408843	−0.0158542
$666$	3.50464	0.135802
$667$	17.8001	0.689223
$668$	14.3709	0.556026
$669$	−14.4022	−0.556822
$670$	−44.4759	−1.71825
$671$	−46.9037	−1.81070
$672$	−0.0850469	−0.00328076
$673$	−27.9866	−1.07881	−0.539403	−	0.842048i	$-0.681350\pi$
$673$	−27.9866	−1.07881	−0.539403	+	0.842048i	$0.681350\pi$
$674$	8.58205	0.330568
$675$	10.5621	0.406537
$676$	71.8265	2.76256
$677$	34.5963	1.32964	0.664821	−	0.747003i	$-0.268508\pi$
$677$	34.5963	1.32964	0.664821	+	0.747003i	$0.268508\pi$
$678$	1.34337	0.0515918
$679$	0.465649	0.0178700
$680$	−31.5987	−1.21176
$681$	−7.84370	−0.300571
$682$	29.3759	1.12486
$683$	−22.3511	−0.855239	−0.427620	−	0.903959i	$-0.640648\pi$
$683$	−22.3511	−0.855239	−0.427620	+	0.903959i	$0.640648\pi$
$684$	−45.3359	−1.73346
$685$	−4.90562	−0.187434
$686$	2.26567	0.0865038
$687$	−0.875147	−0.0333889
$688$	54.6361	2.08298
$689$	62.2992	2.37341
$690$	−23.3176	−0.887684
$691$	−9.51758	−0.362066	−0.181033	−	0.983477i	$-0.557944\pi$
$691$	−9.51758	−0.362066	−0.181033	+	0.983477i	$0.557944\pi$
$692$	−17.8243	−0.677577
$693$	−0.649406	−0.0246689
$694$	88.9569	3.37676
$695$	−3.29492	−0.124983
$696$	6.93996	0.263059
$697$	−1.95554	−0.0740712
$698$	38.0869	1.44161
$699$	−3.97391	−0.150307
$700$	−0.768951	−0.0290636
$701$	−15.2164	−0.574714	−0.287357	−	0.957824i	$-0.592777\pi$
$701$	−15.2164	−0.574714	−0.287357	+	0.957824i	$0.592777\pi$
$702$	51.1158	1.92924
$703$	2.35731	0.0889075
$704$	−21.5111	−0.810730
$705$	−2.39590	−0.0902347
$706$	62.7614	2.36206
$707$	−1.14306	−0.0429893
$708$	−32.6671	−1.22770
$709$	−43.7069	−1.64145	−0.820724	−	0.571325i	$-0.806430\pi$
$709$	−43.7069	−1.64145	−0.820724	+	0.571325i	$0.806430\pi$
$710$	14.2813	0.535966
$711$	−31.8645	−1.19501
$712$	67.5109	2.53008
$713$	28.3499	1.06171
$714$	0.430350	0.0161054
$715$	−31.7787	−1.18846
$716$	−67.8640	−2.53620
$717$	0.728230	0.0271963
$718$	90.8144	3.38916
$719$	5.55979	0.207345	0.103673	−	0.994611i	$-0.466941\pi$
$719$	5.55979	0.207345	0.103673	+	0.994611i	$0.466941\pi$
$720$	19.3379	0.720680
$721$	−0.476242	−0.0177362
$722$	2.19211	0.0815817
$723$	6.84765	0.254667
$724$	33.3747	1.24036
$725$	5.33746	0.198228
$726$	−7.34755	−0.272693
$727$	45.7070	1.69518	0.847590	−	0.530651i	$-0.178053\pi$
$727$	45.7070	1.69518	0.847590	+	0.530651i	$0.178053\pi$
$728$	−1.94333	−0.0720247
$729$	−5.41688	−0.200625
$730$	34.4558	1.27527
$731$	−41.7817	−1.54535
$732$	−33.7953	−1.24911
$733$	−41.5538	−1.53483	−0.767413	−	0.641153i	$-0.778456\pi$
$733$	−41.5538	−1.53483	−0.767413	+	0.641153i	$0.778456\pi$
$734$	56.2110	2.07479
$735$	6.96819	0.257025
$736$	18.2208	0.671629
$737$	−47.5180	−1.75035
$738$	3.14212	0.115663
$739$	35.3061	1.29876	0.649378	−	0.760466i	$-0.275029\pi$
$739$	35.3061	1.29876	0.649378	+	0.760466i	$0.275029\pi$
$740$	−3.42092	−0.125755
$741$	15.7783	0.579630
$742$	−1.83643	−0.0674175
$743$	43.9733	1.61322	0.806612	−	0.591081i	$-0.201299\pi$
$743$	43.9733	1.61322	0.806612	+	0.591081i	$0.201299\pi$
$744$	11.0531	0.405228
$745$	16.6034	0.608302
$746$	−27.7213	−1.01495
$747$	−13.7934	−0.504673
$748$	−64.6484	−2.36378
$749$	−0.327625	−0.0119712
$750$	−19.3787	−0.707608
$751$	46.1541	1.68419	0.842093	−	0.539333i	$-0.181323\pi$
$751$	46.1541	1.68419	0.842093	+	0.539333i	$0.181323\pi$
$752$	12.3882	0.451753
$753$	−7.58992	−0.276592
$754$	25.8308	0.940703
$755$	−4.78124	−0.174007
$756$	−1.01961	−0.0370829
$757$	32.0340	1.16430	0.582148	−	0.813083i	$-0.302212\pi$
$757$	32.0340	1.16430	0.582148	+	0.813083i	$0.302212\pi$
$758$	−43.3711	−1.57531
$759$	−24.9124	−0.904265
$760$	34.1507	1.23878
$761$	0.443825	0.0160886	0.00804432	−	0.999968i	$-0.497439\pi$
$761$	0.443825	0.0160886	0.00804432	+	0.999968i	$0.497439\pi$
$762$	13.5522	0.490945
$763$	1.02536	0.0371205
$764$	−36.3520	−1.31517
$765$	−14.7882	−0.534668
$766$	−27.8511	−1.00630
$767$	−63.4946	−2.29266
$768$	−21.9990	−0.793821
$769$	−29.3958	−1.06004	−0.530020	−	0.847985i	$-0.677816\pi$
$769$	−29.3958	−1.06004	−0.530020	+	0.847985i	$0.677816\pi$
$770$	0.936761	0.0337585
$771$	4.24514	0.152885
$772$	−25.2458	−0.908616
$773$	13.0597	0.469724	0.234862	−	0.972029i	$-0.424536\pi$
$773$	13.0597	0.469724	0.234862	+	0.972029i	$0.424536\pi$
$774$	67.1341	2.41308
$775$	8.50087	0.305360
$776$	−38.8958	−1.39628
$777$	0.0243299	0.000872829 0
$778$	−2.45515	−0.0880212
$779$	2.11347	0.0757229
$780$	−22.8974	−0.819858
$781$	15.2581	0.545977
$782$	−92.2000	−3.29707
$783$	7.07735	0.252924
$784$	−36.0297	−1.28678
$785$	29.0425	1.03657
$786$	1.80193	0.0642729
$787$	−16.3834	−0.584005	−0.292003	−	0.956418i	$-0.594322\pi$
$787$	−16.3834	−0.584005	−0.292003	+	0.956418i	$0.594322\pi$
$788$	13.2602	0.472374
$789$	15.1644	0.539868
$790$	45.9641	1.63533
$791$	−0.0520837	−0.00185188
$792$	54.2451	1.92751
$793$	−65.6876	−2.33263
$794$	48.4292	1.71869
$795$	−11.2995	−0.400751
$796$	−117.420	−4.16186
$797$	51.4875	1.82378	0.911891	−	0.410434i	$-0.134623\pi$
$797$	51.4875	1.82378	0.911891	+	0.410434i	$0.134623\pi$
$798$	−0.465106	−0.0164646
$799$	−9.47362	−0.335153
$800$	5.46362	0.193168
$801$	31.5950	1.11636
$802$	84.7727	2.99343
$803$	36.8125	1.29909
$804$	−34.2379	−1.20748
$805$	0.904043	0.0318633
$806$	41.1402	1.44910
$807$	−18.2673	−0.643041
$808$	95.4804	3.35899
$809$	11.6637	0.410073	0.205037	−	0.978754i	$-0.434269\pi$
$809$	11.6637	0.410073	0.205037	+	0.978754i	$0.434269\pi$
$810$	18.7449	0.658630
$811$	1.58533	0.0556684	0.0278342	−	0.999613i	$-0.491139\pi$
$811$	1.58533	0.0556684	0.0278342	+	0.999613i	$0.491139\pi$
$812$	−0.515250	−0.0180817
$813$	−19.5219	−0.684664
$814$	−5.40118	−0.189311
$815$	19.8562	0.695531
$816$	−13.6914	−0.479294
$817$	45.1561	1.57981
$818$	−83.2847	−2.91198
$819$	−0.909479	−0.0317798
$820$	−3.06706	−0.107106
$821$	−0.721121	−0.0251673	−0.0125836	−	0.999921i	$-0.504006\pi$
$821$	−0.721121	−0.0251673	−0.0125836	+	0.999921i	$0.504006\pi$
$822$	−5.58071	−0.194650
$823$	41.6371	1.45138	0.725688	−	0.688024i	$-0.241521\pi$
$823$	41.6371	1.45138	0.725688	+	0.688024i	$0.241521\pi$
$824$	39.7806	1.38582
$825$	−7.47014	−0.260077
$826$	1.87167	0.0651237
$827$	11.4693	0.398827	0.199413	−	0.979915i	$-0.436096\pi$
$827$	11.4693	0.398827	0.199413	+	0.979915i	$0.436096\pi$
$828$	100.248	3.48386
$829$	−14.3906	−0.499805	−0.249903	−	0.968271i	$-0.580399\pi$
$829$	−14.3906	−0.499805	−0.249903	+	0.968271i	$0.580399\pi$
$830$	19.8968	0.690627
$831$	3.37784	0.117176
$832$	−30.1258	−1.04442
$833$	27.5529	0.954652
$834$	−3.74835	−0.129795
$835$	−5.06624	−0.175325
$836$	69.8696	2.41649
$837$	11.2720	0.389616
$838$	11.6341	0.401895
$839$	18.2829	0.631196	0.315598	−	0.948893i	$-0.397795\pi$
$839$	18.2829	0.631196	0.315598	+	0.948893i	$0.397795\pi$
$840$	0.352471	0.0121614
$841$	−25.4235	−0.876674
$842$	−79.8057	−2.75029
$843$	10.1296	0.348883
$844$	−12.5313	−0.431345
$845$	−25.3214	−0.871082
$846$	15.2220	0.523345
$847$	0.284871	0.00978829
$848$	58.4252	2.00633
$849$	4.06270	0.139431
$850$	−27.6467	−0.948274
$851$	−5.21254	−0.178683
$852$	10.9938	0.376643
$853$	−24.1638	−0.827352	−0.413676	−	0.910424i	$-0.635755\pi$
$853$	−24.1638	−0.827352	−0.413676	+	0.910424i	$0.635755\pi$
$854$	1.93631	0.0662592
$855$	15.9825	0.546591
$856$	27.3666	0.935372
$857$	7.86046	0.268508	0.134254	−	0.990947i	$-0.457136\pi$
$857$	7.86046	0.268508	0.134254	+	0.990947i	$0.457136\pi$
$858$	−36.1520	−1.23421
$859$	−29.9226	−1.02095	−0.510473	−	0.859894i	$-0.670530\pi$
$859$	−29.9226	−1.02095	−0.510473	+	0.859894i	$0.670530\pi$
$860$	−65.5304	−2.23457
$861$	0.0218132	0.000743392 0
$862$	−9.12623	−0.310841
$863$	−7.16710	−0.243971	−0.121985	−	0.992532i	$-0.538926\pi$
$863$	−7.16710	−0.243971	−0.121985	+	0.992532i	$0.538926\pi$
$864$	7.24463	0.246467
$865$	6.28369	0.213652
$866$	43.2483	1.46964
$867$	−1.00443	−0.0341124
$868$	−0.820628	−0.0278539
$869$	49.1080	1.66587
$870$	−4.68505	−0.158838
$871$	−66.5479	−2.25489
$872$	−85.6485	−2.90043
$873$	−18.2032	−0.616085
$874$	99.6463	3.37059
$875$	0.751328	0.0253995
$876$	26.5244	0.896176
$877$	−24.3252	−0.821403	−0.410701	−	0.911770i	$-0.634716\pi$
$877$	−24.3252	−0.821403	−0.410701	+	0.911770i	$0.634716\pi$
$878$	−22.5366	−0.760572
$879$	14.1200	0.476254
$880$	−29.8026	−1.00465
$881$	11.0474	0.372197	0.186098	−	0.982531i	$-0.440416\pi$
$881$	11.0474	0.372197	0.186098	+	0.982531i	$0.440416\pi$
$882$	−44.2715	−1.49070
$883$	−13.5601	−0.456335	−0.228167	−	0.973622i	$-0.573273\pi$
$883$	−13.5601	−0.456335	−0.228167	+	0.973622i	$0.573273\pi$
$884$	−90.5386	−3.04514
$885$	11.5163	0.387116
$886$	−40.3409	−1.35528
$887$	8.66745	0.291025	0.145512	−	0.989356i	$-0.453517\pi$
$887$	8.66745	0.291025	0.145512	+	0.989356i	$0.453517\pi$
$888$	−2.03228	−0.0681989
$889$	−0.525432	−0.0176224
$890$	−45.5755	−1.52769
$891$	20.0271	0.670932
$892$	−89.3170	−2.99055
$893$	10.2387	0.342626
$894$	18.8883	0.631719
$895$	23.9245	0.799707
$896$	1.14004	0.0380859
$897$	−34.8893	−1.16492
$898$	96.4888	3.21987
$899$	5.69617	0.189978
$900$	30.0599	1.00200
$901$	−44.6793	−1.48848
$902$	−4.84249	−0.161237
$903$	0.466058	0.0155094
$904$	4.35056	0.144698
$905$	−11.7658	−0.391107
$906$	−5.43921	−0.180706
$907$	49.6737	1.64939	0.824694	−	0.565579i	$-0.191347\pi$
$907$	49.6737	1.64939	0.824694	+	0.565579i	$0.191347\pi$
$908$	−48.6436	−1.61429
$909$	44.6848	1.48210
$910$	1.31191	0.0434895
$911$	−0.377283	−0.0124999	−0.00624997	−	0.999980i	$-0.501989\pi$
$911$	−0.377283	−0.0124999	−0.00624997	+	0.999980i	$0.501989\pi$
$912$	14.7971	0.489982
$913$	21.2577	0.703527
$914$	−0.00403336	−0.000133412 0
$915$	11.9141	0.393866
$916$	−5.42732	−0.179324
$917$	−0.0698626	−0.00230707
$918$	−36.6589	−1.20992
$919$	12.4176	0.409619	0.204809	−	0.978802i	$-0.434343\pi$
$919$	12.4176	0.409619	0.204809	+	0.978802i	$0.434343\pi$
$920$	−75.5150	−2.48965
$921$	9.48020	0.312383
$922$	24.5190	0.807491
$923$	21.3686	0.703356
$924$	0.721127	0.0237233
$925$	−1.56301	−0.0513914
$926$	77.3190	2.54086
$927$	18.6173	0.611473
$928$	3.66100	0.120178
$929$	−13.0936	−0.429587	−0.214793	−	0.976659i	$-0.568908\pi$
$929$	−13.0936	−0.429587	−0.214793	+	0.976659i	$0.568908\pi$
$930$	−7.46179	−0.244682
$931$	−29.7782	−0.975940
$932$	−24.6447	−0.807263
$933$	9.15504	0.299722
$934$	67.4465	2.20692
$935$	22.7909	0.745341
$936$	75.9690	2.48312
$937$	27.1237	0.886092	0.443046	−	0.896499i	$-0.353898\pi$
$937$	27.1237	0.886092	0.443046	+	0.896499i	$0.353898\pi$
$938$	1.96167	0.0640508
$939$	0.190394	0.00621328
$940$	−14.8584	−0.484628
$941$	−26.0559	−0.849397	−0.424699	−	0.905335i	$-0.639620\pi$
$941$	−26.0559	−0.849397	−0.424699	+	0.905335i	$0.639620\pi$
$942$	33.0392	1.07648
$943$	−4.67336	−0.152185
$944$	−59.5463	−1.93807
$945$	0.359449	0.0116929
$946$	−103.464	−3.36390
$947$	−20.1689	−0.655402	−0.327701	−	0.944781i	$-0.606274\pi$
$947$	−20.1689	−0.655402	−0.327701	+	0.944781i	$0.606274\pi$
$948$	35.3836	1.14921
$949$	51.5551	1.67355
$950$	29.8795	0.969419
$951$	−6.35021	−0.205920
$952$	1.39371	0.0451703
$953$	25.4475	0.824326	0.412163	−	0.911110i	$-0.364773\pi$
$953$	25.4475	0.824326	0.412163	+	0.911110i	$0.364773\pi$
$954$	71.7899	2.32429
$955$	12.8154	0.414696
$956$	4.51620	0.146064
$957$	−5.00551	−0.161805
$958$	−48.1588	−1.55594
$959$	0.216369	0.00698693
$960$	5.46405	0.176352
$961$	−21.9278	−0.707349
$962$	−7.56423	−0.243881
$963$	12.8076	0.412718
$964$	42.4665	1.36775
$965$	8.90004	0.286502
$966$	1.02845	0.0330900
$967$	−26.5411	−0.853505	−0.426752	−	0.904368i	$-0.640342\pi$
$967$	−26.5411	−0.853505	−0.426752	+	0.904368i	$0.640342\pi$
$968$	−23.7954	−0.764812
$969$	−11.3158	−0.363515
$970$	26.2579	0.843090
$971$	41.7031	1.33832	0.669158	−	0.743120i	$-0.266655\pi$
$971$	41.7031	1.33832	0.669158	+	0.743120i	$0.266655\pi$
$972$	61.4257	1.97023
$973$	0.145327	0.00465897
$974$	−23.4158	−0.750290
$975$	−10.4618	−0.335045
$976$	−61.6029	−1.97186
$977$	−48.1170	−1.53940	−0.769699	−	0.638407i	$-0.779594\pi$
$977$	−48.1170	−1.53940	−0.769699	+	0.638407i	$0.779594\pi$
$978$	22.5887	0.722306
$979$	−48.6928	−1.55623
$980$	43.2140	1.38042
$981$	−40.0834	−1.27977
$982$	57.5209	1.83557
$983$	26.8409	0.856092	0.428046	−	0.903757i	$-0.359202\pi$
$983$	26.8409	0.856092	0.428046	+	0.903757i	$0.359202\pi$
$984$	−1.82206	−0.0580852
$985$	−4.67468	−0.148948
$986$	−18.5252	−0.589962
$987$	0.105674	0.00336365
$988$	97.8508	3.11305
$989$	−99.8502	−3.17505
$990$	−36.6199	−1.16386
$991$	−28.1953	−0.895654	−0.447827	−	0.894120i	$-0.647802\pi$
$991$	−28.1953	−0.895654	−0.447827	+	0.894120i	$0.647802\pi$
$992$	5.83080	0.185128
$993$	−1.45630	−0.0462143
$994$	−0.629895	−0.0199790
$995$	41.3949	1.31231
$996$	15.3167	0.485329
$997$	−14.9289	−0.472804	−0.236402	−	0.971655i	$-0.575968\pi$
$997$	−14.9289	−0.472804	−0.236402	+	0.971655i	$0.575968\pi$
$998$	82.7064	2.61803
$999$	−2.07251	−0.0655714

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2671.2.a.a.1.9	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2671.2.a.a.1.9	✓	100	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2671.a (trivial)

\(f(q)\)	\(=\)	\(q-2.48716 q^{2} +0.674976 q^{3} +4.18594 q^{4} -1.47569 q^{5} -1.67877 q^{6} +0.0650875 q^{7} -5.43678 q^{8} -2.54441 q^{9} +O(q^{10})\)	\(q-2.48716 q^{2} +0.674976 q^{3} +4.18594 q^{4} -1.47569 q^{5} -1.67877 q^{6} +0.0650875 q^{7} -5.43678 q^{8} -2.54441 q^{9} +3.67028 q^{10} +3.92132 q^{11} +2.82541 q^{12} +5.49172 q^{13} -0.161883 q^{14} -0.996058 q^{15} +5.15022 q^{16} -3.93851 q^{17} +6.32833 q^{18} +4.25660 q^{19} -6.17716 q^{20} +0.0439325 q^{21} -9.75293 q^{22} -9.41230 q^{23} -3.66970 q^{24} -2.82233 q^{25} -13.6588 q^{26} -3.74234 q^{27} +0.272452 q^{28} -1.89116 q^{29} +2.47735 q^{30} -3.01200 q^{31} -1.93585 q^{32} +2.64680 q^{33} +9.79570 q^{34} -0.0960491 q^{35} -10.6507 q^{36} +0.553801 q^{37} -10.5868 q^{38} +3.70678 q^{39} +8.02301 q^{40} +0.496516 q^{41} -0.109267 q^{42} +10.6085 q^{43} +16.4144 q^{44} +3.75476 q^{45} +23.4098 q^{46} +2.40538 q^{47} +3.47628 q^{48} -6.99576 q^{49} +7.01957 q^{50} -2.65840 q^{51} +22.9880 q^{52} +11.3442 q^{53} +9.30779 q^{54} -5.78666 q^{55} -0.353866 q^{56} +2.87310 q^{57} +4.70360 q^{58} -11.5619 q^{59} -4.16944 q^{60} -11.9612 q^{61} +7.49132 q^{62} -0.165609 q^{63} -5.48568 q^{64} -8.10409 q^{65} -6.58300 q^{66} -12.1179 q^{67} -16.4864 q^{68} -6.35308 q^{69} +0.238889 q^{70} +3.89106 q^{71} +13.8334 q^{72} +9.38779 q^{73} -1.37739 q^{74} -1.90501 q^{75} +17.8179 q^{76} +0.255229 q^{77} -9.21934 q^{78} +12.5233 q^{79} -7.60015 q^{80} +5.10723 q^{81} -1.23491 q^{82} +5.42106 q^{83} +0.183899 q^{84} +5.81204 q^{85} -26.3850 q^{86} -1.27649 q^{87} -21.3193 q^{88} -12.4174 q^{89} -9.33868 q^{90} +0.357442 q^{91} -39.3993 q^{92} -2.03303 q^{93} -5.98255 q^{94} -6.28143 q^{95} -1.30666 q^{96} +7.15420 q^{97} +17.3996 q^{98} -9.97743 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9}+O(q^{10}) \) 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9	\( 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9} - 18 q^{10} - 47 q^{11} - 27 q^{12} - 29 q^{13} - 51 q^{14} - 36 q^{15} + 71 q^{16} - 99 q^{17} - 27 q^{18} - 45 q^{19} - 75 q^{20} - 79 q^{21} - 2 q^{22} - 25 q^{23} - 66 q^{24} + 67 q^{25} - 73 q^{26} - 42 q^{27} - 31 q^{28} - 78 q^{29} - 29 q^{30} - 41 q^{31} - 95 q^{32} - 83 q^{33} - 44 q^{34} - 45 q^{35} + 23 q^{36} - 16 q^{37} - 29 q^{38} - 42 q^{39} - 37 q^{40} - 235 q^{41} + 16 q^{42} - 6 q^{43} - 122 q^{44} - 79 q^{45} - 17 q^{46} - 67 q^{47} - 25 q^{48} + 30 q^{49} - 68 q^{50} - 18 q^{51} - 41 q^{52} - 69 q^{53} - 63 q^{54} - 32 q^{55} - 120 q^{56} - 63 q^{57} - 7 q^{58} - 118 q^{59} - 49 q^{60} - 60 q^{61} - 23 q^{62} - 43 q^{63} + 43 q^{64} - 181 q^{65} - 4 q^{66} - 18 q^{67} - 130 q^{68} - 80 q^{69} + 12 q^{70} - 77 q^{71} - 40 q^{72} - 64 q^{73} - 48 q^{74} - 18 q^{75} - 134 q^{76} - 87 q^{77} + 65 q^{78} - 48 q^{79} - 95 q^{80} - 20 q^{81} + 45 q^{82} - 108 q^{83} - 97 q^{84} - 21 q^{85} - 73 q^{86} - 3 q^{87} + 23 q^{88} - 325 q^{89} + 6 q^{90} - 17 q^{91} - 19 q^{92} + 2 q^{93} - 5 q^{94} - 54 q^{95} - 105 q^{96} - 81 q^{97} - 61 q^{98} - 76 q^{99}+O(q^{100}) \) 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9 - 18 * q^10 - 47 * q^11 - 27 * q^12 - 29 * q^13 - 51 * q^14 - 36 * q^15 + 71 * q^16 - 99 * q^17 - 27 * q^18 - 45 * q^19 - 75 * q^20 - 79 * q^21 - 2 * q^22 - 25 * q^23 - 66 * q^24 + 67 * q^25 - 73 * q^26 - 42 * q^27 - 31 * q^28 - 78 * q^29 - 29 * q^30 - 41 * q^31 - 95 * q^32 - 83 * q^33 - 44 * q^34 - 45 * q^35 + 23 * q^36 - 16 * q^37 - 29 * q^38 - 42 * q^39 - 37 * q^40 - 235 * q^41 + 16 * q^42 - 6 * q^43 - 122 * q^44 - 79 * q^45 - 17 * q^46 - 67 * q^47 - 25 * q^48 + 30 * q^49 - 68 * q^50 - 18 * q^51 - 41 * q^52 - 69 * q^53 - 63 * q^54 - 32 * q^55 - 120 * q^56 - 63 * q^57 - 7 * q^58 - 118 * q^59 - 49 * q^60 - 60 * q^61 - 23 * q^62 - 43 * q^63 + 43 * q^64 - 181 * q^65 - 4 * q^66 - 18 * q^67 - 130 * q^68 - 80 * q^69 + 12 * q^70 - 77 * q^71 - 40 * q^72 - 64 * q^73 - 48 * q^74 - 18 * q^75 - 134 * q^76 - 87 * q^77 + 65 * q^78 - 48 * q^79 - 95 * q^80 - 20 * q^81 + 45 * q^82 - 108 * q^83 - 97 * q^84 - 21 * q^85 - 73 * q^86 - 3 * q^87 + 23 * q^88 - 325 * q^89 + 6 * q^90 - 17 * q^91 - 19 * q^92 + 2 * q^93 - 5 * q^94 - 54 * q^95 - 105 * q^96 - 81 * q^97 - 61 * q^98 - 76 * q^99

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