LMFDB - Embedded newform 2175.2.a.w.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2175,2,Mod(1,2175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2175, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2175.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2175 = 3 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2175.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:	$17.3674624396$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.246832.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 5x^{3} + 6x^{2} + 7x - 2 $ x^5 - 2x^4 - 5x^3 + 6x^2 + 7x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 435)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.245526$ of defining polynomial
Character	$\chi$	$=$	2175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.754474 q^{2} -1.00000 q^{3} -1.43077 q^{4} +0.754474 q^{6} -4.18524 q^{7} +2.58843 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.754474 q^{2} -1.00000 q^{3} -1.43077 q^{4} +0.754474 q^{6} -4.18524 q^{7} +2.58843 q^{8} +1.00000 q^{9} +0.596817 q^{11} +1.43077 q^{12} +2.18524 q^{13} +3.15766 q^{14} +0.908639 q^{16} -2.81314 q^{17} -0.754474 q^{18} +0.528904 q^{19} +4.18524 q^{21} -0.450283 q^{22} -0.590044 q^{23} -2.58843 q^{24} -1.64871 q^{26} -1.00000 q^{27} +5.98812 q^{28} +1.00000 q^{29} +8.02005 q^{31} -5.86240 q^{32} -0.596817 q^{33} +2.12244 q^{34} -1.43077 q^{36} +2.52465 q^{37} -0.399044 q^{38} -2.18524 q^{39} +1.57110 q^{41} -3.15766 q^{42} +6.98484 q^{43} -0.853908 q^{44} +0.445173 q^{46} +2.57524 q^{47} -0.908639 q^{48} +10.5163 q^{49} +2.81314 q^{51} -3.12658 q^{52} -10.3878 q^{53} +0.754474 q^{54} -10.8332 q^{56} -0.528904 q^{57} -0.754474 q^{58} +13.9168 q^{59} -11.1942 q^{61} -6.05092 q^{62} -4.18524 q^{63} +2.60575 q^{64} +0.450283 q^{66} -0.614139 q^{67} +4.02495 q^{68} +0.590044 q^{69} +9.28010 q^{71} +2.58843 q^{72} -9.59116 q^{73} -1.90478 q^{74} -0.756739 q^{76} -2.49783 q^{77} +1.64871 q^{78} -10.3396 q^{79} +1.00000 q^{81} -1.18536 q^{82} -3.92531 q^{83} -5.98812 q^{84} -5.26988 q^{86} -1.00000 q^{87} +1.54482 q^{88} -12.3352 q^{89} -9.14577 q^{91} +0.844217 q^{92} -8.02005 q^{93} -1.94295 q^{94} +5.86240 q^{96} -3.21794 q^{97} -7.93424 q^{98} +0.596817 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 3 q^{2} - 5 q^{3} + 5 q^{4} + 3 q^{6} - 8 q^{7} - 9 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q - 3 * q^2 - 5 * q^3 + 5 * q^4 + 3 * q^6 - 8 * q^7 - 9 * q^8 + 5 * q^9	$ 5 q - 3 q^{2} - 5 q^{3} + 5 q^{4} + 3 q^{6} - 8 q^{7} - 9 q^{8} + 5 q^{9} + 12 q^{11} - 5 q^{12} - 2 q^{13} + 6 q^{14} + q^{16} - 3 q^{18} - 2 q^{19} + 8 q^{21} - 14 q^{22} - 8 q^{23} + 9 q^{24} - 5 q^{27} + 6 q^{28} + 5 q^{29} + 2 q^{31} - q^{32} - 12 q^{33} + 4 q^{34} + 5 q^{36} - 16 q^{37} + 14 q^{38} + 2 q^{39} - 14 q^{41} - 6 q^{42} + 20 q^{44} - 6 q^{46} - 2 q^{47} - q^{48} - 7 q^{49} - 16 q^{52} - 26 q^{53} + 3 q^{54} - 2 q^{56} + 2 q^{57} - 3 q^{58} + 4 q^{59} - 12 q^{61} - 8 q^{63} - 9 q^{64} + 14 q^{66} - 12 q^{67} + 20 q^{68} + 8 q^{69} + 30 q^{71} - 9 q^{72} + 12 q^{73} + 2 q^{74} - 44 q^{76} - 18 q^{77} - 18 q^{79} + 5 q^{81} - 10 q^{82} - 2 q^{83} - 6 q^{84} + 30 q^{86} - 5 q^{87} - 42 q^{88} - 22 q^{89} - 12 q^{91} - 20 q^{92} - 2 q^{93} - 50 q^{94} + q^{96} - 20 q^{97} + 9 q^{98} + 12 q^{99}+O(q^{100}) $ 5 * q - 3 * q^2 - 5 * q^3 + 5 * q^4 + 3 * q^6 - 8 * q^7 - 9 * q^8 + 5 * q^9 + 12 * q^11 - 5 * q^12 - 2 * q^13 + 6 * q^14 + q^16 - 3 * q^18 - 2 * q^19 + 8 * q^21 - 14 * q^22 - 8 * q^23 + 9 * q^24 - 5 * q^27 + 6 * q^28 + 5 * q^29 + 2 * q^31 - q^32 - 12 * q^33 + 4 * q^34 + 5 * q^36 - 16 * q^37 + 14 * q^38 + 2 * q^39 - 14 * q^41 - 6 * q^42 + 20 * q^44 - 6 * q^46 - 2 * q^47 - q^48 - 7 * q^49 - 16 * q^52 - 26 * q^53 + 3 * q^54 - 2 * q^56 + 2 * q^57 - 3 * q^58 + 4 * q^59 - 12 * q^61 - 8 * q^63 - 9 * q^64 + 14 * q^66 - 12 * q^67 + 20 * q^68 + 8 * q^69 + 30 * q^71 - 9 * q^72 + 12 * q^73 + 2 * q^74 - 44 * q^76 - 18 * q^77 - 18 * q^79 + 5 * q^81 - 10 * q^82 - 2 * q^83 - 6 * q^84 + 30 * q^86 - 5 * q^87 - 42 * q^88 - 22 * q^89 - 12 * q^91 - 20 * q^92 - 2 * q^93 - 50 * q^94 + q^96 - 20 * q^97 + 9 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.754474	−0.533494	−0.266747	−	0.963767i	$-0.585949\pi$
$2$	−0.754474	−0.533494	−0.266747	+	0.963767i	$0.585949\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.43077	−0.715385
$5$	0	0
$5$	0	0
$6$	0.754474	0.308013
$7$	−4.18524	−1.58187	−0.790937	−	0.611898i	$-0.790406\pi$
$7$	−4.18524	−1.58187	−0.790937	+	0.611898i	$0.790406\pi$
$8$	2.58843	0.915147
$9$	1.00000	0.333333
$10$	0	0
$11$	0.596817	0.179947	0.0899736	−	0.995944i	$-0.471322\pi$
$11$	0.596817	0.179947	0.0899736	+	0.995944i	$0.471322\pi$
$12$	1.43077	0.413027
$13$	2.18524	0.606077	0.303039	−	0.952978i	$-0.401999\pi$
$13$	2.18524	0.606077	0.303039	+	0.952978i	$0.401999\pi$
$14$	3.15766	0.843919
$15$	0	0
$16$	0.908639	0.227160
$17$	−2.81314	−0.682286	−0.341143	−	0.940011i	$-0.610814\pi$
$17$	−2.81314	−0.682286	−0.341143	+	0.940011i	$0.610814\pi$
$18$	−0.754474	−0.177831
$19$	0.528904	0.121339	0.0606694	−	0.998158i	$-0.480676\pi$
$19$	0.528904	0.121339	0.0606694	+	0.998158i	$0.480676\pi$
$20$	0	0
$21$	4.18524	0.913295
$22$	−0.450283	−0.0960007
$23$	−0.590044	−0.123033	−0.0615163	−	0.998106i	$-0.519594\pi$
$23$	−0.590044	−0.123033	−0.0615163	+	0.998106i	$0.519594\pi$
$24$	−2.58843	−0.528360
$25$	0	0
$26$	−1.64871	−0.323338
$27$	−1.00000	−0.192450
$28$	5.98812	1.13165
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0	0
$31$	8.02005	1.44044	0.720222	−	0.693744i	$-0.244040\pi$
$31$	8.02005	1.44044	0.720222	+	0.693744i	$0.244040\pi$
$32$	−5.86240	−1.03633
$33$	−0.596817	−0.103893
$34$	2.12244	0.363995
$35$	0	0
$36$	−1.43077	−0.238462
$37$	2.52465	0.415050	0.207525	−	0.978230i	$-0.433459\pi$
$37$	2.52465	0.415050	0.207525	+	0.978230i	$0.433459\pi$
$38$	−0.399044	−0.0647335
$39$	−2.18524	−0.349919
$40$	0	0
$41$	1.57110	0.245365	0.122683	−	0.992446i	$-0.460850\pi$
$41$	1.57110	0.245365	0.122683	+	0.992446i	$0.460850\pi$
$42$	−3.15766	−0.487237
$43$	6.98484	1.06518	0.532589	−	0.846374i	$-0.321219\pi$
$43$	6.98484	1.06518	0.532589	+	0.846374i	$0.321219\pi$
$44$	−0.853908	−0.128731
$45$	0	0
$46$	0.445173	0.0656372
$47$	2.57524	0.375638	0.187819	−	0.982204i	$-0.439858\pi$
$47$	2.57524	0.375638	0.187819	+	0.982204i	$0.439858\pi$
$48$	−0.908639	−0.131151
$49$	10.5163	1.50232
$50$	0	0
$51$	2.81314	0.393918
$52$	−3.12658	−0.433578
$53$	−10.3878	−1.42688	−0.713438	−	0.700719i	$-0.752863\pi$
$53$	−10.3878	−1.42688	−0.713438	+	0.700719i	$0.752863\pi$
$54$	0.754474	0.102671
$55$	0	0
$56$	−10.8332	−1.44765
$57$	−0.528904	−0.0700550
$58$	−0.754474	−0.0990673
$59$	13.9168	1.81181	0.905907	−	0.423477i	$-0.139190\pi$
$59$	13.9168	1.81181	0.905907	+	0.423477i	$0.139190\pi$
$60$	0	0
$61$	−11.1942	−1.43327	−0.716633	−	0.697450i	$-0.754318\pi$
$61$	−11.1942	−1.43327	−0.716633	+	0.697450i	$0.754318\pi$
$62$	−6.05092	−0.768468
$63$	−4.18524	−0.527291
$64$	2.60575	0.325718
$65$	0	0
$66$	0.450283	0.0554260
$67$	−0.614139	−0.0750290	−0.0375145	−	0.999296i	$-0.511944\pi$
$67$	−0.614139	−0.0750290	−0.0375145	+	0.999296i	$0.511944\pi$
$68$	4.02495	0.488097
$69$	0.590044	0.0710330
$70$	0	0
$71$	9.28010	1.10134	0.550672	−	0.834721i	$-0.314371\pi$
$71$	9.28010	1.10134	0.550672	+	0.834721i	$0.314371\pi$
$72$	2.58843	0.305049
$73$	−9.59116	−1.12256	−0.561280	−	0.827626i	$-0.689691\pi$
$73$	−9.59116	−1.12256	−0.561280	+	0.827626i	$0.689691\pi$
$74$	−1.90478	−0.221427
$75$	0	0
$76$	−0.756739	−0.0868039
$77$	−2.49783	−0.284654
$78$	1.64871	0.186680
$79$	−10.3396	−1.16330	−0.581649	−	0.813440i	$-0.697592\pi$
$79$	−10.3396	−1.16330	−0.581649	+	0.813440i	$0.697592\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−1.18536	−0.130901
$83$	−3.92531	−0.430859	−0.215430	−	0.976519i	$-0.569115\pi$
$83$	−3.92531	−0.430859	−0.215430	+	0.976519i	$0.569115\pi$
$84$	−5.98812	−0.653357
$85$	0	0
$86$	−5.26988	−0.568265
$87$	−1.00000	−0.107211
$88$	1.54482	0.164678
$89$	−12.3352	−1.30752	−0.653762	−	0.756700i	$-0.726810\pi$
$89$	−12.3352	−1.30752	−0.653762	+	0.756700i	$0.726810\pi$
$90$	0	0
$91$	−9.14577	−0.958738
$92$	0.844217	0.0880157
$93$	−8.02005	−0.831641
$94$	−1.94295	−0.200400
$95$	0	0
$96$	5.86240	0.598328
$97$	−3.21794	−0.326732	−0.163366	−	0.986566i	$-0.552235\pi$
$97$	−3.21794	−0.326732	−0.163366	+	0.986566i	$0.552235\pi$
$98$	−7.93424	−0.801480
$99$	0.596817	0.0599824
$100$	0	0
$101$	9.31726	0.927102	0.463551	−	0.886070i	$-0.346575\pi$
$101$	9.31726	0.927102	0.463551	+	0.886070i	$0.346575\pi$
$102$	−2.12244	−0.210153
$103$	−20.1574	−1.98617	−0.993085	−	0.117393i	$-0.962546\pi$
$103$	−20.1574	−1.98617	−0.993085	+	0.117393i	$0.962546\pi$
$104$	5.65634	0.554650
$105$	0	0
$106$	7.83733	0.761229
$107$	−1.58569	−0.153295	−0.0766475	−	0.997058i	$-0.524422\pi$
$107$	−1.58569	−0.153295	−0.0766475	+	0.997058i	$0.524422\pi$
$108$	1.43077	0.137676
$109$	−7.91051	−0.757690	−0.378845	−	0.925460i	$-0.623679\pi$
$109$	−7.91051	−0.757690	−0.378845	+	0.925460i	$0.623679\pi$
$110$	0	0
$111$	−2.52465	−0.239629
$112$	−3.80287	−0.359338
$113$	3.07328	0.289110	0.144555	−	0.989497i	$-0.453825\pi$
$113$	3.07328	0.289110	0.144555	+	0.989497i	$0.453825\pi$
$114$	0.399044	0.0373739
$115$	0	0
$116$	−1.43077	−0.132844
$117$	2.18524	0.202026
$118$	−10.4999	−0.966591
$119$	11.7737	1.07929
$120$	0	0
$121$	−10.6438	−0.967619
$122$	8.44571	0.764639
$123$	−1.57110	−0.141662
$124$	−11.4748	−1.03047
$125$	0	0
$126$	3.15766	0.281306
$127$	12.9254	1.14694	0.573472	−	0.819225i	$-0.305596\pi$
$127$	12.9254	1.14694	0.573472	+	0.819225i	$0.305596\pi$
$128$	9.75882	0.862566
$129$	−6.98484	−0.614980
$130$	0	0
$131$	−5.69473	−0.497551	−0.248775	−	0.968561i	$-0.580028\pi$
$131$	−5.69473	−0.497551	−0.248775	+	0.968561i	$0.580028\pi$
$132$	0.853908	0.0743231
$133$	−2.21359	−0.191943
$134$	0.463352	0.0400275
$135$	0	0
$136$	−7.28160	−0.624392
$137$	−18.7274	−1.59999	−0.799996	−	0.600005i	$-0.795165\pi$
$137$	−18.7274	−1.59999	−0.799996	+	0.600005i	$0.795165\pi$
$138$	−0.445173	−0.0378956
$139$	1.34376	0.113976	0.0569880	−	0.998375i	$-0.481850\pi$
$139$	1.34376	0.113976	0.0569880	+	0.998375i	$0.481850\pi$
$140$	0	0
$141$	−2.57524	−0.216875
$142$	−7.00159	−0.587560
$143$	1.30419	0.109062
$144$	0.908639	0.0757199
$145$	0	0
$146$	7.23628	0.598879
$147$	−10.5163	−0.867366
$148$	−3.61219	−0.296920
$149$	−15.9925	−1.31016	−0.655079	−	0.755561i	$-0.727365\pi$
$149$	−15.9925	−1.31016	−0.655079	+	0.755561i	$0.727365\pi$
$150$	0	0
$151$	17.9595	1.46152	0.730760	−	0.682635i	$-0.239166\pi$
$151$	17.9595	1.46152	0.730760	+	0.682635i	$0.239166\pi$
$152$	1.36903	0.111043
$153$	−2.81314	−0.227429
$154$	1.88454	0.151861
$155$	0	0
$156$	3.12658	0.250327
$157$	−6.78158	−0.541229	−0.270615	−	0.962688i	$-0.587227\pi$
$157$	−6.78158	−0.541229	−0.270615	+	0.962688i	$0.587227\pi$
$158$	7.80097	0.620612
$159$	10.3878	0.823807
$160$	0	0
$161$	2.46948	0.194622
$162$	−0.754474	−0.0592771
$163$	−20.9951	−1.64447	−0.822233	−	0.569151i	$-0.807272\pi$
$163$	−20.9951	−1.64447	−0.822233	+	0.569151i	$0.807272\pi$
$164$	−2.24789	−0.175531
$165$	0	0
$166$	2.96155	0.229861
$167$	14.9135	1.15404	0.577020	−	0.816730i	$-0.304216\pi$
$167$	14.9135	1.15404	0.577020	+	0.816730i	$0.304216\pi$
$168$	10.8332	0.835799
$169$	−8.22471	−0.632670
$170$	0	0
$171$	0.528904	0.0404463
$172$	−9.99369	−0.762011
$173$	10.8685	0.826318	0.413159	−	0.910659i	$-0.364425\pi$
$173$	10.8685	0.826318	0.413159	+	0.910659i	$0.364425\pi$
$174$	0.754474	0.0571965
$175$	0	0
$176$	0.542291	0.0408767
$177$	−13.9168	−1.04605
$178$	9.30655	0.697556
$179$	1.26613	0.0946349	0.0473175	−	0.998880i	$-0.484933\pi$
$179$	1.26613	0.0946349	0.0473175	+	0.998880i	$0.484933\pi$
$180$	0	0
$181$	−5.80673	−0.431611	−0.215805	−	0.976436i	$-0.569238\pi$
$181$	−5.80673	−0.431611	−0.215805	+	0.976436i	$0.569238\pi$
$182$	6.90025	0.511480
$183$	11.1942	0.827497
$184$	−1.52729	−0.112593
$185$	0	0
$186$	6.05092	0.443675
$187$	−1.67893	−0.122776
$188$	−3.68458	−0.268725
$189$	4.18524	0.304432
$190$	0	0
$191$	15.3358	1.10966	0.554830	−	0.831964i	$-0.312783\pi$
$191$	15.3358	1.10966	0.554830	+	0.831964i	$0.312783\pi$
$192$	−2.60575	−0.188054
$193$	16.4946	1.18731	0.593653	−	0.804721i	$-0.297685\pi$
$193$	16.4946	1.18731	0.593653	+	0.804721i	$0.297685\pi$
$194$	2.42785	0.174310
$195$	0	0
$196$	−15.0463	−1.07474
$197$	−24.2353	−1.72670	−0.863348	−	0.504609i	$-0.831637\pi$
$197$	−24.2353	−1.72670	−0.863348	+	0.504609i	$0.831637\pi$
$198$	−0.450283	−0.0320002
$199$	17.4875	1.23965	0.619826	−	0.784739i	$-0.287203\pi$
$199$	17.4875	1.23965	0.619826	+	0.784739i	$0.287203\pi$
$200$	0	0
$201$	0.614139	0.0433180
$202$	−7.02963	−0.494603
$203$	−4.18524	−0.293746
$204$	−4.02495	−0.281803
$205$	0	0
$206$	15.2083	1.05961
$207$	−0.590044	−0.0410109
$208$	1.98560	0.137676
$209$	0.315659	0.0218346
$210$	0	0
$211$	−26.0504	−1.79338	−0.896692	−	0.442655i	$-0.854037\pi$
$211$	−26.0504	−1.79338	−0.896692	+	0.442655i	$0.854037\pi$
$212$	14.8626	1.02076
$213$	−9.28010	−0.635862
$214$	1.19637	0.0817819
$215$	0	0
$216$	−2.58843	−0.176120
$217$	−33.5659	−2.27860
$218$	5.96827	0.404223
$219$	9.59116	0.648110
$220$	0	0
$221$	−6.14739	−0.413518
$222$	1.90478	0.127841
$223$	−10.7895	−0.722519	−0.361259	−	0.932465i	$-0.617653\pi$
$223$	−10.7895	−0.722519	−0.361259	+	0.932465i	$0.617653\pi$
$224$	24.5356	1.63935
$225$	0	0
$226$	−2.31871	−0.154238
$227$	6.99182	0.464063	0.232032	−	0.972708i	$-0.425463\pi$
$227$	6.99182	0.464063	0.232032	+	0.972708i	$0.425463\pi$
$228$	0.756739	0.0501163
$229$	−20.9503	−1.38444	−0.692218	−	0.721689i	$-0.743366\pi$
$229$	−20.9503	−1.38444	−0.692218	+	0.721689i	$0.743366\pi$
$230$	0	0
$231$	2.49783	0.164345
$232$	2.58843	0.169938
$233$	3.85567	0.252593	0.126297	−	0.991993i	$-0.459691\pi$
$233$	3.85567	0.252593	0.126297	+	0.991993i	$0.459691\pi$
$234$	−1.64871	−0.107779
$235$	0	0
$236$	−19.9117	−1.29614
$237$	10.3396	0.671630
$238$	−8.88293	−0.575795
$239$	−25.3084	−1.63706	−0.818532	−	0.574461i	$-0.805212\pi$
$239$	−25.3084	−1.63706	−0.818532	+	0.574461i	$0.805212\pi$
$240$	0	0
$241$	−22.8510	−1.47196	−0.735981	−	0.677002i	$-0.763279\pi$
$241$	−22.8510	−1.47196	−0.735981	+	0.677002i	$0.763279\pi$
$242$	8.03048	0.516219
$243$	−1.00000	−0.0641500
$244$	16.0163	1.02534
$245$	0	0
$246$	1.18536	0.0755756
$247$	1.15578	0.0735407
$248$	20.7593	1.31822
$249$	3.92531	0.248757
$250$	0	0
$251$	−7.37025	−0.465206	−0.232603	−	0.972572i	$-0.574724\pi$
$251$	−7.37025	−0.465206	−0.232603	+	0.972572i	$0.574724\pi$
$252$	5.98812	0.377216
$253$	−0.352149	−0.0221394
$254$	−9.75188	−0.611888
$255$	0	0
$256$	−12.5743	−0.785892
$257$	3.21575	0.200593	0.100296	−	0.994958i	$-0.468021\pi$
$257$	3.21575	0.200593	0.100296	+	0.994958i	$0.468021\pi$
$258$	5.26988	0.328088
$259$	−10.5663	−0.656557
$260$	0	0
$261$	1.00000	0.0618984
$262$	4.29652	0.265440
$263$	16.0190	0.987774	0.493887	−	0.869526i	$-0.335576\pi$
$263$	16.0190	0.987774	0.493887	+	0.869526i	$0.335576\pi$
$264$	−1.54482	−0.0950769
$265$	0	0
$266$	1.67010	0.102400
$267$	12.3352	0.754899
$268$	0.878691	0.0536746
$269$	−19.9820	−1.21832	−0.609161	−	0.793047i	$-0.708494\pi$
$269$	−19.9820	−1.21832	−0.609161	+	0.793047i	$0.708494\pi$
$270$	0	0
$271$	−8.72743	−0.530153	−0.265077	−	0.964227i	$-0.585397\pi$
$271$	−8.72743	−0.530153	−0.265077	+	0.964227i	$0.585397\pi$
$272$	−2.55613	−0.154988
$273$	9.14577	0.553527
$274$	14.1294	0.853585
$275$	0	0
$276$	−0.844217	−0.0508159
$277$	30.5856	1.83771	0.918856	−	0.394594i	$-0.129115\pi$
$277$	30.5856	1.83771	0.918856	+	0.394594i	$0.129115\pi$
$278$	−1.01383	−0.0608055
$279$	8.02005	0.480148
$280$	0	0
$281$	30.2570	1.80498	0.902490	−	0.430712i	$-0.141737\pi$
$281$	30.2570	1.80498	0.902490	+	0.430712i	$0.141737\pi$
$282$	1.94295	0.115701
$283$	9.35107	0.555863	0.277932	−	0.960601i	$-0.410351\pi$
$283$	9.35107	0.555863	0.277932	+	0.960601i	$0.410351\pi$
$284$	−13.2777	−0.787885
$285$	0	0
$286$	−0.983978	−0.0581838
$287$	−6.57545	−0.388137
$288$	−5.86240	−0.345445
$289$	−9.08625	−0.534485
$290$	0	0
$291$	3.21794	0.188639
$292$	13.7227	0.803062
$293$	8.47749	0.495260	0.247630	−	0.968855i	$-0.420348\pi$
$293$	8.47749	0.495260	0.247630	+	0.968855i	$0.420348\pi$
$294$	7.93424	0.462734
$295$	0	0
$296$	6.53487	0.379832
$297$	−0.596817	−0.0346309
$298$	12.0659	0.698961
$299$	−1.28939	−0.0745673
$300$	0	0
$301$	−29.2332	−1.68498
$302$	−13.5499	−0.779711
$303$	−9.31726	−0.535263
$304$	0.480582	0.0275633
$305$	0	0
$306$	2.12244	0.121332
$307$	−19.8740	−1.13427	−0.567135	−	0.823625i	$-0.691948\pi$
$307$	−19.8740	−1.13427	−0.567135	+	0.823625i	$0.691948\pi$
$308$	3.57381	0.203637
$309$	20.1574	1.14672
$310$	0	0
$311$	−12.5476	−0.711507	−0.355754	−	0.934580i	$-0.615776\pi$
$311$	−12.5476	−0.711507	−0.355754	+	0.934580i	$0.615776\pi$
$312$	−5.65634	−0.320227
$313$	2.82942	0.159928	0.0799640	−	0.996798i	$-0.474519\pi$
$313$	2.82942	0.159928	0.0799640	+	0.996798i	$0.474519\pi$
$314$	5.11653	0.288742
$315$	0	0
$316$	14.7936	0.832205
$317$	−6.27390	−0.352377	−0.176189	−	0.984356i	$-0.556377\pi$
$317$	−6.27390	−0.352377	−0.176189	+	0.984356i	$0.556377\pi$
$318$	−7.83733	−0.439496
$319$	0.596817	0.0334154
$320$	0	0
$321$	1.58569	0.0885049
$322$	−1.86316	−0.103830
$323$	−1.48788	−0.0827878
$324$	−1.43077	−0.0794872
$325$	0	0
$326$	15.8403	0.877312
$327$	7.91051	0.437452
$328$	4.06669	0.224545
$329$	−10.7780	−0.594211
$330$	0	0
$331$	−4.47271	−0.245843	−0.122921	−	0.992416i	$-0.539226\pi$
$331$	−4.47271	−0.245843	−0.122921	+	0.992416i	$0.539226\pi$
$332$	5.61622	0.308230
$333$	2.52465	0.138350
$334$	−11.2518	−0.615673
$335$	0	0
$336$	3.80287	0.207464
$337$	3.62191	0.197298	0.0986489	−	0.995122i	$-0.468548\pi$
$337$	3.62191	0.197298	0.0986489	+	0.995122i	$0.468548\pi$
$338$	6.20533	0.337526
$339$	−3.07328	−0.166918
$340$	0	0
$341$	4.78651	0.259204
$342$	−0.399044	−0.0215778
$343$	−14.7164	−0.794611
$344$	18.0797	0.974794
$345$	0	0
$346$	−8.20002	−0.440836
$347$	34.4636	1.85010	0.925051	−	0.379844i	$-0.124022\pi$
$347$	34.4636	1.85010	0.925051	+	0.379844i	$0.124022\pi$
$348$	1.43077	0.0766973
$349$	−18.0401	−0.965665	−0.482832	−	0.875713i	$-0.660392\pi$
$349$	−18.0401	−0.965665	−0.482832	+	0.875713i	$0.660392\pi$
$350$	0	0
$351$	−2.18524	−0.116640
$352$	−3.49878	−0.186486
$353$	−7.60470	−0.404757	−0.202379	−	0.979307i	$-0.564867\pi$
$353$	−7.60470	−0.404757	−0.202379	+	0.979307i	$0.564867\pi$
$354$	10.4999	0.558062
$355$	0	0
$356$	17.6488	0.935382
$357$	−11.7737	−0.623129
$358$	−0.955261	−0.0504871
$359$	−2.32286	−0.122596	−0.0612980	−	0.998120i	$-0.519524\pi$
$359$	−2.32286	−0.122596	−0.0612980	+	0.998120i	$0.519524\pi$
$360$	0	0
$361$	−18.7203	−0.985277
$362$	4.38103	0.230262
$363$	10.6438	0.558655
$364$	13.0855	0.685866
$365$	0	0
$366$	−8.44571	−0.441464
$367$	6.38930	0.333519	0.166759	−	0.985998i	$-0.446670\pi$
$367$	6.38930	0.333519	0.166759	+	0.985998i	$0.446670\pi$
$368$	−0.536137	−0.0279481
$369$	1.57110	0.0817884
$370$	0	0
$371$	43.4755	2.25714
$372$	11.4748	0.594943
$373$	24.1627	1.25110	0.625549	−	0.780185i	$-0.284875\pi$
$373$	24.1627	1.25110	0.625549	+	0.780185i	$0.284875\pi$
$374$	1.26671	0.0654999
$375$	0	0
$376$	6.66583	0.343764
$377$	2.18524	0.112546
$378$	−3.15766	−0.162412
$379$	−29.2093	−1.50038	−0.750191	−	0.661222i	$-0.770038\pi$
$379$	−29.2093	−1.50038	−0.750191	+	0.661222i	$0.770038\pi$
$380$	0	0
$381$	−12.9254	−0.662189
$382$	−11.5705	−0.591997
$383$	−31.7731	−1.62353	−0.811766	−	0.583983i	$-0.801493\pi$
$383$	−31.7731	−1.62353	−0.811766	+	0.583983i	$0.801493\pi$
$384$	−9.75882	−0.498003
$385$	0	0
$386$	−12.4447	−0.633420
$387$	6.98484	0.355059
$388$	4.60413	0.233739
$389$	23.7158	1.20244	0.601220	−	0.799084i	$-0.294682\pi$
$389$	23.7158	1.20244	0.601220	+	0.799084i	$0.294682\pi$
$390$	0	0
$391$	1.65988	0.0839435
$392$	27.2206	1.37485
$393$	5.69473	0.287261
$394$	18.2849	0.921181
$395$	0	0
$396$	−0.853908	−0.0429105
$397$	32.8280	1.64759	0.823794	−	0.566889i	$-0.191853\pi$
$397$	32.8280	1.64759	0.823794	+	0.566889i	$0.191853\pi$
$398$	−13.1938	−0.661347
$399$	2.21359	0.110818
$400$	0	0
$401$	−8.21905	−0.410440	−0.205220	−	0.978716i	$-0.565791\pi$
$401$	−8.21905	−0.410440	−0.205220	+	0.978716i	$0.565791\pi$
$402$	−0.463352	−0.0231099
$403$	17.5258	0.873020
$404$	−13.3308	−0.663234
$405$	0	0
$406$	3.15766	0.156712
$407$	1.50676	0.0746871
$408$	7.28160	0.360493
$409$	27.9114	1.38013	0.690065	−	0.723748i	$-0.257582\pi$
$409$	27.9114	1.38013	0.690065	+	0.723748i	$0.257582\pi$
$410$	0	0
$411$	18.7274	0.923756
$412$	28.8406	1.42088
$413$	−58.2452	−2.86606
$414$	0.445173	0.0218791
$415$	0	0
$416$	−12.8108	−0.628099
$417$	−1.34376	−0.0658041
$418$	−0.238156	−0.0116486
$419$	27.0379	1.32089	0.660445	−	0.750874i	$-0.270368\pi$
$419$	27.0379	1.32089	0.660445	+	0.750874i	$0.270368\pi$
$420$	0	0
$421$	3.79559	0.184986	0.0924928	−	0.995713i	$-0.470516\pi$
$421$	3.79559	0.184986	0.0924928	+	0.995713i	$0.470516\pi$
$422$	19.6544	0.956759
$423$	2.57524	0.125213
$424$	−26.8881	−1.30580
$425$	0	0
$426$	7.00159	0.339228
$427$	46.8503	2.26725
$428$	2.26876	0.109665
$429$	−1.30419	−0.0629669
$430$	0	0
$431$	−0.405550	−0.0195347	−0.00976733	−	0.999952i	$-0.503109\pi$
$431$	−0.405550	−0.0195347	−0.00976733	+	0.999952i	$0.503109\pi$
$432$	−0.908639	−0.0437169
$433$	25.5978	1.23015	0.615075	−	0.788468i	$-0.289126\pi$
$433$	25.5978	1.23015	0.615075	+	0.788468i	$0.289126\pi$
$434$	25.3246	1.21562
$435$	0	0
$436$	11.3181	0.542039
$437$	−0.312077	−0.0149286
$438$	−7.23628	−0.345763
$439$	−26.2378	−1.25226	−0.626132	−	0.779717i	$-0.715363\pi$
$439$	−26.2378	−1.25226	−0.626132	+	0.779717i	$0.715363\pi$
$440$	0	0
$441$	10.5163	0.500774
$442$	4.63805	0.220609
$443$	−26.5050	−1.25929	−0.629645	−	0.776883i	$-0.716800\pi$
$443$	−26.5050	−1.25929	−0.629645	+	0.776883i	$0.716800\pi$
$444$	3.61219	0.171427
$445$	0	0
$446$	8.14040	0.385459
$447$	15.9925	0.756420
$448$	−10.9057	−0.515245
$449$	5.57064	0.262895	0.131447	−	0.991323i	$-0.458038\pi$
$449$	5.57064	0.262895	0.131447	+	0.991323i	$0.458038\pi$
$450$	0	0
$451$	0.937662	0.0441528
$452$	−4.39715	−0.206825
$453$	−17.9595	−0.843809
$454$	−5.27514	−0.247575
$455$	0	0
$456$	−1.36903	−0.0641106
$457$	−25.3774	−1.18710	−0.593551	−	0.804796i	$-0.702275\pi$
$457$	−25.3774	−1.18710	−0.593551	+	0.804796i	$0.702275\pi$
$458$	15.8065	0.738587
$459$	2.81314	0.131306
$460$	0	0
$461$	2.20886	0.102877	0.0514384	−	0.998676i	$-0.483619\pi$
$461$	2.20886	0.102877	0.0514384	+	0.998676i	$0.483619\pi$
$462$	−1.88454	−0.0876769
$463$	−7.56591	−0.351618	−0.175809	−	0.984424i	$-0.556254\pi$
$463$	−7.56591	−0.351618	−0.175809	+	0.984424i	$0.556254\pi$
$464$	0.908639	0.0421825
$465$	0	0
$466$	−2.90900	−0.134757
$467$	−19.9056	−0.921120	−0.460560	−	0.887629i	$-0.652351\pi$
$467$	−19.9056	−0.921120	−0.460560	+	0.887629i	$0.652351\pi$
$468$	−3.12658	−0.144526
$469$	2.57032	0.118686
$470$	0	0
$471$	6.78158	0.312479
$472$	36.0226	1.65808
$473$	4.16867	0.191676
$474$	−7.80097	−0.358311
$475$	0	0
$476$	−16.8454	−0.772108
$477$	−10.3878	−0.475625
$478$	19.0945	0.873363
$479$	10.3910	0.474778	0.237389	−	0.971415i	$-0.423708\pi$
$479$	10.3910	0.474778	0.237389	+	0.971415i	$0.423708\pi$
$480$	0	0
$481$	5.51698	0.251552
$482$	17.2405	0.785282
$483$	−2.46948	−0.112365
$484$	15.2288	0.692220
$485$	0	0
$486$	0.754474	0.0342236
$487$	−10.0574	−0.455744	−0.227872	−	0.973691i	$-0.573177\pi$
$487$	−10.0574	−0.455744	−0.227872	+	0.973691i	$0.573177\pi$
$488$	−28.9753	−1.31165
$489$	20.9951	0.949433
$490$	0	0
$491$	−0.193599	−0.00873699	−0.00436849	−	0.999990i	$-0.501391\pi$
$491$	−0.193599	−0.00873699	−0.00436849	+	0.999990i	$0.501391\pi$
$492$	2.24789	0.101343
$493$	−2.81314	−0.126697
$494$	−0.872008	−0.0392335
$495$	0	0
$496$	7.28733	0.327211
$497$	−38.8395	−1.74219
$498$	−2.96155	−0.132710
$499$	13.6181	0.609630	0.304815	−	0.952412i	$-0.401405\pi$
$499$	13.6181	0.609630	0.304815	+	0.952412i	$0.401405\pi$
$500$	0	0
$501$	−14.9135	−0.666285
$502$	5.56066	0.248185
$503$	30.7553	1.37131	0.685655	−	0.727926i	$-0.259516\pi$
$503$	30.7553	1.37131	0.685655	+	0.727926i	$0.259516\pi$
$504$	−10.8332	−0.482549
$505$	0	0
$506$	0.265687	0.0118112
$507$	8.22471	0.365272
$508$	−18.4933	−0.820506
$509$	−1.01272	−0.0448881	−0.0224441	−	0.999748i	$-0.507145\pi$
$509$	−1.01272	−0.0448881	−0.0224441	+	0.999748i	$0.507145\pi$
$510$	0	0
$511$	40.1413	1.77575
$512$	−10.0307	−0.443298
$513$	−0.528904	−0.0233517
$514$	−2.42620	−0.107015
$515$	0	0
$516$	9.99369	0.439948
$517$	1.53695	0.0675950
$518$	7.97198	0.350269
$519$	−10.8685	−0.477075
$520$	0	0
$521$	6.02284	0.263865	0.131933	−	0.991259i	$-0.457882\pi$
$521$	6.02284	0.263865	0.131933	+	0.991259i	$0.457882\pi$
$522$	−0.754474	−0.0330224
$523$	−20.3870	−0.891460	−0.445730	−	0.895167i	$-0.647056\pi$
$523$	−20.3870	−0.891460	−0.445730	+	0.895167i	$0.647056\pi$
$524$	8.14784	0.355940
$525$	0	0
$526$	−12.0859	−0.526971
$527$	−22.5615	−0.982795
$528$	−0.542291	−0.0236002
$529$	−22.6518	−0.984863
$530$	0	0
$531$	13.9168	0.603938
$532$	3.16714	0.137313
$533$	3.43324	0.148710
$534$	−9.30655	−0.402734
$535$	0	0
$536$	−1.58965	−0.0686625
$537$	−1.26613	−0.0546375
$538$	15.0759	0.649967
$539$	6.27629	0.270339
$540$	0	0
$541$	−16.4420	−0.706895	−0.353448	−	0.935454i	$-0.614991\pi$
$541$	−16.4420	−0.706895	−0.353448	+	0.935454i	$0.614991\pi$
$542$	6.58461	0.282833
$543$	5.80673	0.249191
$544$	16.4917	0.707077
$545$	0	0
$546$	−6.90025	−0.295303
$547$	28.2531	1.20802	0.604008	−	0.796979i	$-0.293570\pi$
$547$	28.2531	1.20802	0.604008	+	0.796979i	$0.293570\pi$
$548$	26.7946	1.14461
$549$	−11.1942	−0.477756
$550$	0	0
$551$	0.528904	0.0225321
$552$	1.52729	0.0650056
$553$	43.2738	1.84019
$554$	−23.0760	−0.980407
$555$	0	0
$556$	−1.92261	−0.0815367
$557$	−36.3662	−1.54089	−0.770443	−	0.637508i	$-0.779965\pi$
$557$	−36.3662	−1.54089	−0.770443	+	0.637508i	$0.779965\pi$
$558$	−6.05092	−0.256156
$559$	15.2636	0.645580
$560$	0	0
$561$	1.67893	0.0708845
$562$	−22.8281	−0.962945
$563$	5.24750	0.221156	0.110578	−	0.993867i	$-0.464730\pi$
$563$	5.24750	0.221156	0.110578	+	0.993867i	$0.464730\pi$
$564$	3.68458	0.155149
$565$	0	0
$566$	−7.05514	−0.296550
$567$	−4.18524	−0.175764
$568$	24.0208	1.00789
$569$	17.3773	0.728495	0.364248	−	0.931302i	$-0.381326\pi$
$569$	17.3773	0.728495	0.364248	+	0.931302i	$0.381326\pi$
$570$	0	0
$571$	−22.2889	−0.932760	−0.466380	−	0.884584i	$-0.654442\pi$
$571$	−22.2889	−0.932760	−0.466380	+	0.884584i	$0.654442\pi$
$572$	−1.86600	−0.0780212
$573$	−15.3358	−0.640663
$574$	4.96101	0.207068
$575$	0	0
$576$	2.60575	0.108573
$577$	−26.1738	−1.08963	−0.544816	−	0.838556i	$-0.683400\pi$
$577$	−26.1738	−1.08963	−0.544816	+	0.838556i	$0.683400\pi$
$578$	6.85534	0.285145
$579$	−16.4946	−0.685491
$580$	0	0
$581$	16.4284	0.681564
$582$	−2.42785	−0.100638
$583$	−6.19962	−0.256762
$584$	−24.8260	−1.02731
$585$	0	0
$586$	−6.39604	−0.264218
$587$	26.4002	1.08965	0.544827	−	0.838549i	$-0.316595\pi$
$587$	26.4002	1.08965	0.544827	+	0.838549i	$0.316595\pi$
$588$	15.0463	0.620501
$589$	4.24184	0.174782
$590$	0	0
$591$	24.2353	0.996908
$592$	2.29400	0.0942826
$593$	−19.4942	−0.800532	−0.400266	−	0.916399i	$-0.631082\pi$
$593$	−19.4942	−0.800532	−0.400266	+	0.916399i	$0.631082\pi$
$594$	0.450283	0.0184753
$595$	0	0
$596$	22.8816	0.937266
$597$	−17.4875	−0.715714
$598$	0.972811	0.0397812
$599$	20.9453	0.855800	0.427900	−	0.903826i	$-0.359254\pi$
$599$	20.9453	0.855800	0.427900	+	0.903826i	$0.359254\pi$
$600$	0	0
$601$	14.3956	0.587208	0.293604	−	0.955927i	$-0.405145\pi$
$601$	14.3956	0.587208	0.293604	+	0.955927i	$0.405145\pi$
$602$	22.0557	0.898924
$603$	−0.614139	−0.0250097
$604$	−25.6958	−1.04555
$605$	0	0
$606$	7.02963	0.285559
$607$	8.53979	0.346620	0.173310	−	0.984867i	$-0.444554\pi$
$607$	8.53979	0.346620	0.173310	+	0.984867i	$0.444554\pi$
$608$	−3.10064	−0.125748
$609$	4.18524	0.169595
$610$	0	0
$611$	5.62753	0.227666
$612$	4.02495	0.162699
$613$	−36.7173	−1.48300	−0.741499	−	0.670954i	$-0.765885\pi$
$613$	−36.7173	−1.48300	−0.741499	+	0.670954i	$0.765885\pi$
$614$	14.9944	0.605125
$615$	0	0
$616$	−6.46544	−0.260500
$617$	45.1304	1.81688	0.908441	−	0.418014i	$-0.137274\pi$
$617$	45.1304	1.81688	0.908441	+	0.418014i	$0.137274\pi$
$618$	−15.2083	−0.611766
$619$	−18.9737	−0.762618	−0.381309	−	0.924448i	$-0.624527\pi$
$619$	−18.9737	−0.762618	−0.381309	+	0.924448i	$0.624527\pi$
$620$	0	0
$621$	0.590044	0.0236777
$622$	9.46681	0.379585
$623$	51.6256	2.06834
$624$	−1.98560	−0.0794875
$625$	0	0
$626$	−2.13472	−0.0853206
$627$	−0.315659	−0.0126062
$628$	9.70288	0.387187
$629$	−7.10219	−0.283183
$630$	0	0
$631$	−18.5514	−0.738518	−0.369259	−	0.929327i	$-0.620388\pi$
$631$	−18.5514	−0.738518	−0.369259	+	0.929327i	$0.620388\pi$
$632$	−26.7633	−1.06459
$633$	26.0504	1.03541
$634$	4.73349	0.187991
$635$	0	0
$636$	−14.8626	−0.589339
$637$	22.9806	0.910524
$638$	−0.450283	−0.0178269
$639$	9.28010	0.367115
$640$	0	0
$641$	−34.5735	−1.36557	−0.682785	−	0.730619i	$-0.739231\pi$
$641$	−34.5735	−1.36557	−0.682785	+	0.730619i	$0.739231\pi$
$642$	−1.19637	−0.0472168
$643$	−6.58510	−0.259691	−0.129846	−	0.991534i	$-0.541448\pi$
$643$	−6.58510	−0.259691	−0.129846	+	0.991534i	$0.541448\pi$
$644$	−3.53325	−0.139230
$645$	0	0
$646$	1.12257	0.0441668
$647$	−10.0375	−0.394614	−0.197307	−	0.980342i	$-0.563220\pi$
$647$	−10.0375	−0.394614	−0.197307	+	0.980342i	$0.563220\pi$
$648$	2.58843	0.101683
$649$	8.30579	0.326031
$650$	0	0
$651$	33.5659	1.31555
$652$	30.0392	1.17643
$653$	−3.25188	−0.127256	−0.0636280	−	0.997974i	$-0.520267\pi$
$653$	−3.25188	−0.127256	−0.0636280	+	0.997974i	$0.520267\pi$
$654$	−5.96827	−0.233378
$655$	0	0
$656$	1.42757	0.0557371
$657$	−9.59116	−0.374187
$658$	8.13173	0.317008
$659$	−9.93148	−0.386875	−0.193438	−	0.981113i	$-0.561964\pi$
$659$	−9.93148	−0.386875	−0.193438	+	0.981113i	$0.561964\pi$
$660$	0	0
$661$	−9.44925	−0.367533	−0.183767	−	0.982970i	$-0.558829\pi$
$661$	−9.44925	−0.367533	−0.183767	+	0.982970i	$0.558829\pi$
$662$	3.37455	0.131155
$663$	6.14739	0.238745
$664$	−10.1604	−0.394299
$665$	0	0
$666$	−1.90478	−0.0738088
$667$	−0.590044	−0.0228466
$668$	−21.3377	−0.825582
$669$	10.7895	0.417146
$670$	0	0
$671$	−6.68088	−0.257912
$672$	−24.5356	−0.946479
$673$	−11.1154	−0.428468	−0.214234	−	0.976782i	$-0.568725\pi$
$673$	−11.1154	−0.428468	−0.214234	+	0.976782i	$0.568725\pi$
$674$	−2.73263	−0.105257
$675$	0	0
$676$	11.7677	0.452603
$677$	44.6045	1.71429	0.857145	−	0.515075i	$-0.172236\pi$
$677$	44.6045	1.71429	0.857145	+	0.515075i	$0.172236\pi$
$678$	2.31871	0.0890495
$679$	13.4679	0.516849
$680$	0	0
$681$	−6.99182	−0.267927
$682$	−3.61129	−0.138284
$683$	−0.490486	−0.0187679	−0.00938396	−	0.999956i	$-0.502987\pi$
$683$	−0.490486	−0.0187679	−0.00938396	+	0.999956i	$0.502987\pi$
$684$	−0.756739	−0.0289346
$685$	0	0
$686$	11.1031	0.423920
$687$	20.9503	0.799304
$688$	6.34669	0.241965
$689$	−22.6999	−0.864797
$690$	0	0
$691$	−6.72252	−0.255737	−0.127868	−	0.991791i	$-0.540814\pi$
$691$	−6.72252	−0.255737	−0.127868	+	0.991791i	$0.540814\pi$
$692$	−15.5503	−0.591135
$693$	−2.49783	−0.0948845
$694$	−26.0019	−0.987017
$695$	0	0
$696$	−2.58843	−0.0981140
$697$	−4.41973	−0.167409
$698$	13.6108	0.515176
$699$	−3.85567	−0.145835
$700$	0	0
$701$	−32.2913	−1.21963	−0.609813	−	0.792546i	$-0.708755\pi$
$701$	−32.2913	−1.21963	−0.609813	+	0.792546i	$0.708755\pi$
$702$	1.64871	0.0622265
$703$	1.33530	0.0503617
$704$	1.55515	0.0586121
$705$	0	0
$706$	5.73755	0.215936
$707$	−38.9950	−1.46656
$708$	19.9117	0.748329
$709$	9.75887	0.366502	0.183251	−	0.983066i	$-0.441338\pi$
$709$	9.75887	0.366502	0.183251	+	0.983066i	$0.441338\pi$
$710$	0	0
$711$	−10.3396	−0.387766
$712$	−31.9286	−1.19658
$713$	−4.73218	−0.177222
$714$	8.88293	0.332435
$715$	0	0
$716$	−1.81154	−0.0677004
$717$	25.3084	0.945159
$718$	1.75254	0.0654042
$719$	44.2063	1.64862	0.824308	−	0.566142i	$-0.191565\pi$
$719$	44.2063	1.64862	0.824308	+	0.566142i	$0.191565\pi$
$720$	0	0
$721$	84.3638	3.14187
$722$	14.1239	0.525639
$723$	22.8510	0.849837
$724$	8.30809	0.308768
$725$	0	0
$726$	−8.03048	−0.298039
$727$	−44.9849	−1.66840	−0.834199	−	0.551463i	$-0.814070\pi$
$727$	−44.9849	−1.66840	−0.834199	+	0.551463i	$0.814070\pi$
$728$	−23.6732	−0.877385
$729$	1.00000	0.0370370
$730$	0	0
$731$	−19.6493	−0.726756
$732$	−16.0163	−0.591979
$733$	−1.59233	−0.0588142	−0.0294071	−	0.999568i	$-0.509362\pi$
$733$	−1.59233	−0.0588142	−0.0294071	+	0.999568i	$0.509362\pi$
$734$	−4.82056	−0.177930
$735$	0	0
$736$	3.45907	0.127503
$737$	−0.366529	−0.0135013
$738$	−1.18536	−0.0436336
$739$	−37.2457	−1.37011	−0.685053	−	0.728493i	$-0.740221\pi$
$739$	−37.2457	−1.37011	−0.685053	+	0.728493i	$0.740221\pi$
$740$	0	0
$741$	−1.15578	−0.0424588
$742$	−32.8011	−1.20417
$743$	−41.1086	−1.50813	−0.754065	−	0.656800i	$-0.771909\pi$
$743$	−41.1086	−1.50813	−0.754065	+	0.656800i	$0.771909\pi$
$744$	−20.7593	−0.761073
$745$	0	0
$746$	−18.2301	−0.667452
$747$	−3.92531	−0.143620
$748$	2.40216	0.0878317
$749$	6.63652	0.242493
$750$	0	0
$751$	−44.6707	−1.63006	−0.815029	−	0.579420i	$-0.803279\pi$
$751$	−44.6707	−1.63006	−0.815029	+	0.579420i	$0.803279\pi$
$752$	2.33997	0.0853298
$753$	7.37025	0.268587
$754$	−1.64871	−0.0600424
$755$	0	0
$756$	−5.98812	−0.217786
$757$	−13.8828	−0.504577	−0.252289	−	0.967652i	$-0.581183\pi$
$757$	−13.8828	−0.504577	−0.252289	+	0.967652i	$0.581183\pi$
$758$	22.0377	0.800444
$759$	0.352149	0.0127822
$760$	0	0
$761$	−30.9137	−1.12062	−0.560310	−	0.828283i	$-0.689318\pi$
$761$	−30.9137	−1.12062	−0.560310	+	0.828283i	$0.689318\pi$
$762$	9.75188	0.353273
$763$	33.1074	1.19857
$764$	−21.9420	−0.793834
$765$	0	0
$766$	23.9720	0.866144
$767$	30.4116	1.09810
$768$	12.5743	0.453735
$769$	31.1489	1.12326	0.561630	−	0.827389i	$-0.310175\pi$
$769$	31.1489	1.12326	0.561630	+	0.827389i	$0.310175\pi$
$770$	0	0
$771$	−3.21575	−0.115812
$772$	−23.5999	−0.849380
$773$	25.7705	0.926902	0.463451	−	0.886123i	$-0.346611\pi$
$773$	25.7705	0.926902	0.463451	+	0.886123i	$0.346611\pi$
$774$	−5.26988	−0.189422
$775$	0	0
$776$	−8.32940	−0.299008
$777$	10.5663	0.379063
$778$	−17.8930	−0.641494
$779$	0.830963	0.0297723
$780$	0	0
$781$	5.53852	0.198184
$782$	−1.25233	−0.0447833
$783$	−1.00000	−0.0357371
$784$	9.55548	0.341267
$785$	0	0
$786$	−4.29652	−0.153252
$787$	−26.2806	−0.936802	−0.468401	−	0.883516i	$-0.655170\pi$
$787$	−26.2806	−0.936802	−0.468401	+	0.883516i	$0.655170\pi$
$788$	34.6752	1.23525
$789$	−16.0190	−0.570292
$790$	0	0
$791$	−12.8624	−0.457335
$792$	1.54482	0.0548927
$793$	−24.4620	−0.868671
$794$	−24.7678	−0.878978
$795$	0	0
$796$	−25.0205	−0.886828
$797$	−53.7239	−1.90300	−0.951500	−	0.307650i	$-0.900457\pi$
$797$	−53.7239	−1.90300	−0.951500	+	0.307650i	$0.900457\pi$
$798$	−1.67010	−0.0591208
$799$	−7.24452	−0.256293
$800$	0	0
$801$	−12.3352	−0.435841
$802$	6.20106	0.218967
$803$	−5.72417	−0.202002
$804$	−0.878691	−0.0309890
$805$	0	0
$806$	−13.2227	−0.465751
$807$	19.9820	0.703398
$808$	24.1170	0.848434
$809$	−6.02488	−0.211824	−0.105912	−	0.994376i	$-0.533776\pi$
$809$	−6.02488	−0.211824	−0.105912	+	0.994376i	$0.533776\pi$
$810$	0	0
$811$	−7.70554	−0.270578	−0.135289	−	0.990806i	$-0.543196\pi$
$811$	−7.70554	−0.270578	−0.135289	+	0.990806i	$0.543196\pi$
$812$	5.98812	0.210142
$813$	8.72743	0.306084
$814$	−1.13681	−0.0398451
$815$	0	0
$816$	2.55613	0.0894823
$817$	3.69431	0.129247
$818$	−21.0584	−0.736290
$819$	−9.14577	−0.319579
$820$	0	0
$821$	16.4338	0.573543	0.286772	−	0.957999i	$-0.407418\pi$
$821$	16.4338	0.573543	0.286772	+	0.957999i	$0.407418\pi$
$822$	−14.1294	−0.492818
$823$	−45.4920	−1.58575	−0.792876	−	0.609383i	$-0.791417\pi$
$823$	−45.4920	−1.58575	−0.792876	+	0.609383i	$0.791417\pi$
$824$	−52.1760	−1.81764
$825$	0	0
$826$	43.9445	1.52902
$827$	33.1498	1.15273	0.576367	−	0.817191i	$-0.304470\pi$
$827$	33.1498	1.15273	0.576367	+	0.817191i	$0.304470\pi$
$828$	0.844217	0.0293386
$829$	27.9403	0.970407	0.485203	−	0.874401i	$-0.338746\pi$
$829$	27.9403	0.970407	0.485203	+	0.874401i	$0.338746\pi$
$830$	0	0
$831$	−30.5856	−1.06100
$832$	5.69419	0.197411
$833$	−29.5837	−1.02501
$834$	1.01383	0.0351060
$835$	0	0
$836$	−0.451635	−0.0156201
$837$	−8.02005	−0.277214
$838$	−20.3994	−0.704686
$839$	27.5639	0.951610	0.475805	−	0.879551i	$-0.342157\pi$
$839$	27.5639	0.951610	0.475805	+	0.879551i	$0.342157\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	−2.86367	−0.0986886
$843$	−30.2570	−1.04211
$844$	37.2721	1.28296
$845$	0	0
$846$	−1.94295	−0.0668001
$847$	44.5469	1.53065
$848$	−9.43876	−0.324128
$849$	−9.35107	−0.320928
$850$	0	0
$851$	−1.48966	−0.0510647
$852$	13.2777	0.454886
$853$	14.4467	0.494645	0.247323	−	0.968933i	$-0.420449\pi$
$853$	14.4467	0.494645	0.247323	+	0.968933i	$0.420449\pi$
$854$	−35.3474	−1.20956
$855$	0	0
$856$	−4.10445	−0.140287
$857$	20.6065	0.703904	0.351952	−	0.936018i	$-0.385518\pi$
$857$	20.6065	0.703904	0.351952	+	0.936018i	$0.385518\pi$
$858$	0.983978	0.0335925
$859$	−22.6473	−0.772717	−0.386358	−	0.922349i	$-0.626267\pi$
$859$	−22.6473	−0.772717	−0.386358	+	0.922349i	$0.626267\pi$
$860$	0	0
$861$	6.57545	0.224091
$862$	0.305977	0.0104216
$863$	18.3880	0.625935	0.312967	−	0.949764i	$-0.398677\pi$
$863$	18.3880	0.625935	0.312967	+	0.949764i	$0.398677\pi$
$864$	5.86240	0.199443
$865$	0	0
$866$	−19.3129	−0.656278
$867$	9.08625	0.308585
$868$	48.0250	1.63007
$869$	−6.17086	−0.209332
$870$	0	0
$871$	−1.34204	−0.0454734
$872$	−20.4758	−0.693397
$873$	−3.21794	−0.108911
$874$	0.235454	0.00796434
$875$	0	0
$876$	−13.7227	−0.463648
$877$	20.7681	0.701289	0.350645	−	0.936509i	$-0.385962\pi$
$877$	20.7681	0.701289	0.350645	+	0.936509i	$0.385962\pi$
$878$	19.7958	0.668075
$879$	−8.47749	−0.285939
$880$	0	0
$881$	25.7085	0.866140	0.433070	−	0.901360i	$-0.357430\pi$
$881$	25.7085	0.866140	0.433070	+	0.901360i	$0.357430\pi$
$882$	−7.93424	−0.267160
$883$	−48.3574	−1.62736	−0.813679	−	0.581315i	$-0.802539\pi$
$883$	−48.3574	−1.62736	−0.813679	+	0.581315i	$0.802539\pi$
$884$	8.79550	0.295825
$885$	0	0
$886$	19.9973	0.671824
$887$	48.7809	1.63790	0.818951	−	0.573864i	$-0.194556\pi$
$887$	48.7809	1.63790	0.818951	+	0.573864i	$0.194556\pi$
$888$	−6.53487	−0.219296
$889$	−54.0960	−1.81432
$890$	0	0
$891$	0.596817	0.0199941
$892$	15.4373	0.516879
$893$	1.36206	0.0455795
$894$	−12.0659	−0.403545
$895$	0	0
$896$	−40.8430	−1.36447
$897$	1.28939	0.0430515
$898$	−4.20291	−0.140253
$899$	8.02005	0.267484
$900$	0	0
$901$	29.2223	0.973537
$902$	−0.707442	−0.0235552
$903$	29.2332	0.972821
$904$	7.95495	0.264578
$905$	0	0
$906$	13.5499	0.450166
$907$	−10.8048	−0.358767	−0.179383	−	0.983779i	$-0.557410\pi$
$907$	−10.8048	−0.358767	−0.179383	+	0.983779i	$0.557410\pi$
$908$	−10.0037	−0.331984
$909$	9.31726	0.309034
$910$	0	0
$911$	22.2530	0.737274	0.368637	−	0.929573i	$-0.379825\pi$
$911$	22.2530	0.737274	0.368637	+	0.929573i	$0.379825\pi$
$912$	−0.480582	−0.0159137
$913$	−2.34269	−0.0775319
$914$	19.1466	0.633312
$915$	0	0
$916$	29.9751	0.990404
$917$	23.8338	0.787062
$918$	−2.12244	−0.0700509
$919$	47.1476	1.55526	0.777628	−	0.628724i	$-0.216423\pi$
$919$	47.1476	1.55526	0.777628	+	0.628724i	$0.216423\pi$
$920$	0	0
$921$	19.8740	0.654871
$922$	−1.66653	−0.0548841
$923$	20.2793	0.667500
$924$	−3.57381	−0.117570
$925$	0	0
$926$	5.70828	0.187586
$927$	−20.1574	−0.662057
$928$	−5.86240	−0.192443
$929$	13.0115	0.426893	0.213446	−	0.976955i	$-0.431531\pi$
$929$	13.0115	0.426893	0.213446	+	0.976955i	$0.431531\pi$
$930$	0	0
$931$	5.56209	0.182290
$932$	−5.51657	−0.180701
$933$	12.5476	0.410789
$934$	15.0182	0.491412
$935$	0	0
$936$	5.65634	0.184883
$937$	−19.4077	−0.634021	−0.317011	−	0.948422i	$-0.602679\pi$
$937$	−19.4077	−0.634021	−0.317011	+	0.948422i	$0.602679\pi$
$938$	−1.93924	−0.0633184
$939$	−2.82942	−0.0923345
$940$	0	0
$941$	16.3192	0.531990	0.265995	−	0.963974i	$-0.414299\pi$
$941$	16.3192	0.531990	0.265995	+	0.963974i	$0.414299\pi$
$942$	−5.11653	−0.166705
$943$	−0.927021	−0.0301880
$944$	12.6453	0.411571
$945$	0	0
$946$	−3.14515	−0.102258
$947$	−20.0894	−0.652819	−0.326409	−	0.945229i	$-0.605839\pi$
$947$	−20.0894	−0.652819	−0.326409	+	0.945229i	$0.605839\pi$
$948$	−14.7936	−0.480474
$949$	−20.9590	−0.680358
$950$	0	0
$951$	6.27390	0.203445
$952$	30.4753	0.987709
$953$	−23.6518	−0.766158	−0.383079	−	0.923716i	$-0.625136\pi$
$953$	−23.6518	−0.766158	−0.383079	+	0.923716i	$0.625136\pi$
$954$	7.83733	0.253743
$955$	0	0
$956$	36.2105	1.17113
$957$	−0.596817	−0.0192924
$958$	−7.83975	−0.253291
$959$	78.3788	2.53098
$960$	0	0
$961$	33.3212	1.07488
$962$	−4.16241	−0.134202
$963$	−1.58569	−0.0510983
$964$	32.6945	1.05302
$965$	0	0
$966$	1.86316	0.0599461
$967$	5.19177	0.166956	0.0834780	−	0.996510i	$-0.473397\pi$
$967$	5.19177	0.166956	0.0834780	+	0.996510i	$0.473397\pi$
$968$	−27.5507	−0.885513
$969$	1.48788	0.0477976
$970$	0	0
$971$	−31.0165	−0.995366	−0.497683	−	0.867359i	$-0.665816\pi$
$971$	−31.0165	−0.995366	−0.497683	+	0.867359i	$0.665816\pi$
$972$	1.43077	0.0458919
$973$	−5.62395	−0.180296
$974$	7.58804	0.243137
$975$	0	0
$976$	−10.1715	−0.325580
$977$	−35.0578	−1.12160	−0.560798	−	0.827952i	$-0.689506\pi$
$977$	−35.0578	−1.12160	−0.560798	+	0.827952i	$0.689506\pi$
$978$	−15.8403	−0.506517
$979$	−7.36183	−0.235285
$980$	0	0
$981$	−7.91051	−0.252563
$982$	0.146065	0.00466113
$983$	11.3717	0.362702	0.181351	−	0.983418i	$-0.441953\pi$
$983$	11.3717	0.362702	0.181351	+	0.983418i	$0.441953\pi$
$984$	−4.06669	−0.129641
$985$	0	0
$986$	2.12244	0.0675922
$987$	10.7780	0.343068
$988$	−1.65366	−0.0526099
$989$	−4.12136	−0.131052
$990$	0	0
$991$	−20.5008	−0.651230	−0.325615	−	0.945503i	$-0.605571\pi$
$991$	−20.5008	−0.651230	−0.325615	+	0.945503i	$0.605571\pi$
$992$	−47.0167	−1.49278
$993$	4.47271	0.141937
$994$	29.3034	0.929446
$995$	0	0
$996$	−5.61622	−0.177957
$997$	−8.50559	−0.269375	−0.134687	−	0.990888i	$-0.543003\pi$
$997$	−8.50559	−0.269375	−0.134687	+	0.990888i	$0.543003\pi$
$998$	−10.2745	−0.325234
$999$	−2.52465	−0.0798764

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2175.2.a.w.1.3		5
3.2	odd	2		6525.2.a.bs.1.3		5
5.2	odd	4		435.2.c.e.349.4	✓	10
5.3	odd	4		435.2.c.e.349.7	yes	10
5.4	even	2		2175.2.a.z.1.3		5
15.2	even	4		1305.2.c.j.784.7		10
15.8	even	4		1305.2.c.j.784.4		10
15.14	odd	2		6525.2.a.bl.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.2.c.e.349.4	✓	10	5.2	odd	4
435.2.c.e.349.7	yes	10	5.3	odd	4
1305.2.c.j.784.4		10	15.8	even	4
1305.2.c.j.784.7		10	15.2	even	4
2175.2.a.w.1.3		5	1.1	even	1	trivial
2175.2.a.z.1.3		5	5.4	even	2
6525.2.a.bl.1.3		5	15.14	odd	2
6525.2.a.bs.1.3		5	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2175 = 3 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2175.a (trivial)

\(f(q)\)	\(=\)	\(q-0.754474 q^{2} -1.00000 q^{3} -1.43077 q^{4} +0.754474 q^{6} -4.18524 q^{7} +2.58843 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.754474 q^{2} -1.00000 q^{3} -1.43077 q^{4} +0.754474 q^{6} -4.18524 q^{7} +2.58843 q^{8} +1.00000 q^{9} +0.596817 q^{11} +1.43077 q^{12} +2.18524 q^{13} +3.15766 q^{14} +0.908639 q^{16} -2.81314 q^{17} -0.754474 q^{18} +0.528904 q^{19} +4.18524 q^{21} -0.450283 q^{22} -0.590044 q^{23} -2.58843 q^{24} -1.64871 q^{26} -1.00000 q^{27} +5.98812 q^{28} +1.00000 q^{29} +8.02005 q^{31} -5.86240 q^{32} -0.596817 q^{33} +2.12244 q^{34} -1.43077 q^{36} +2.52465 q^{37} -0.399044 q^{38} -2.18524 q^{39} +1.57110 q^{41} -3.15766 q^{42} +6.98484 q^{43} -0.853908 q^{44} +0.445173 q^{46} +2.57524 q^{47} -0.908639 q^{48} +10.5163 q^{49} +2.81314 q^{51} -3.12658 q^{52} -10.3878 q^{53} +0.754474 q^{54} -10.8332 q^{56} -0.528904 q^{57} -0.754474 q^{58} +13.9168 q^{59} -11.1942 q^{61} -6.05092 q^{62} -4.18524 q^{63} +2.60575 q^{64} +0.450283 q^{66} -0.614139 q^{67} +4.02495 q^{68} +0.590044 q^{69} +9.28010 q^{71} +2.58843 q^{72} -9.59116 q^{73} -1.90478 q^{74} -0.756739 q^{76} -2.49783 q^{77} +1.64871 q^{78} -10.3396 q^{79} +1.00000 q^{81} -1.18536 q^{82} -3.92531 q^{83} -5.98812 q^{84} -5.26988 q^{86} -1.00000 q^{87} +1.54482 q^{88} -12.3352 q^{89} -9.14577 q^{91} +0.844217 q^{92} -8.02005 q^{93} -1.94295 q^{94} +5.86240 q^{96} -3.21794 q^{97} -7.93424 q^{98} +0.596817 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 3 q^{2} - 5 q^{3} + 5 q^{4} + 3 q^{6} - 8 q^{7} - 9 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q - 3 * q^2 - 5 * q^3 + 5 * q^4 + 3 * q^6 - 8 * q^7 - 9 * q^8 + 5 * q^9	\( 5 q - 3 q^{2} - 5 q^{3} + 5 q^{4} + 3 q^{6} - 8 q^{7} - 9 q^{8} + 5 q^{9} + 12 q^{11} - 5 q^{12} - 2 q^{13} + 6 q^{14} + q^{16} - 3 q^{18} - 2 q^{19} + 8 q^{21} - 14 q^{22} - 8 q^{23} + 9 q^{24} - 5 q^{27} + 6 q^{28} + 5 q^{29} + 2 q^{31} - q^{32} - 12 q^{33} + 4 q^{34} + 5 q^{36} - 16 q^{37} + 14 q^{38} + 2 q^{39} - 14 q^{41} - 6 q^{42} + 20 q^{44} - 6 q^{46} - 2 q^{47} - q^{48} - 7 q^{49} - 16 q^{52} - 26 q^{53} + 3 q^{54} - 2 q^{56} + 2 q^{57} - 3 q^{58} + 4 q^{59} - 12 q^{61} - 8 q^{63} - 9 q^{64} + 14 q^{66} - 12 q^{67} + 20 q^{68} + 8 q^{69} + 30 q^{71} - 9 q^{72} + 12 q^{73} + 2 q^{74} - 44 q^{76} - 18 q^{77} - 18 q^{79} + 5 q^{81} - 10 q^{82} - 2 q^{83} - 6 q^{84} + 30 q^{86} - 5 q^{87} - 42 q^{88} - 22 q^{89} - 12 q^{91} - 20 q^{92} - 2 q^{93} - 50 q^{94} + q^{96} - 20 q^{97} + 9 q^{98} + 12 q^{99}+O(q^{100}) \) 5 * q - 3 * q^2 - 5 * q^3 + 5 * q^4 + 3 * q^6 - 8 * q^7 - 9 * q^8 + 5 * q^9 + 12 * q^11 - 5 * q^12 - 2 * q^13 + 6 * q^14 + q^16 - 3 * q^18 - 2 * q^19 + 8 * q^21 - 14 * q^22 - 8 * q^23 + 9 * q^24 - 5 * q^27 + 6 * q^28 + 5 * q^29 + 2 * q^31 - q^32 - 12 * q^33 + 4 * q^34 + 5 * q^36 - 16 * q^37 + 14 * q^38 + 2 * q^39 - 14 * q^41 - 6 * q^42 + 20 * q^44 - 6 * q^46 - 2 * q^47 - q^48 - 7 * q^49 - 16 * q^52 - 26 * q^53 + 3 * q^54 - 2 * q^56 + 2 * q^57 - 3 * q^58 + 4 * q^59 - 12 * q^61 - 8 * q^63 - 9 * q^64 + 14 * q^66 - 12 * q^67 + 20 * q^68 + 8 * q^69 + 30 * q^71 - 9 * q^72 + 12 * q^73 + 2 * q^74 - 44 * q^76 - 18 * q^77 - 18 * q^79 + 5 * q^81 - 10 * q^82 - 2 * q^83 - 6 * q^84 + 30 * q^86 - 5 * q^87 - 42 * q^88 - 22 * q^89 - 12 * q^91 - 20 * q^92 - 2 * q^93 - 50 * q^94 + q^96 - 20 * q^97 + 9 * q^98 + 12 * q^99

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