LMFDB - Embedded newform 1175.2.a.h.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1175,2,Mod(1,1175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1175, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1175.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1175 = 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1175.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:	$9.38242223750$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 10x^{5} + 8x^{4} + 28x^{3} - 17x^{2} - 19x + 2 $ x^7 - x^6 - 10x^5 + 8x^4 + 28x^3 - 17x^2 - 19*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 235)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.0980806$ of defining polynomial
Character	$\chi$	$=$	1175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.0980806 q^{2} +3.03215 q^{3} -1.99038 q^{4} -0.297395 q^{6} -0.786854 q^{7} +0.391379 q^{8} +6.19391 q^{9} +O(q^{10})$	\(q-0.0980806 q^{2} +3.03215 q^{3} -1.99038 q^{4} -0.297395 q^{6} -0.786854 q^{7} +0.391379 q^{8} +6.19391 q^{9} +2.02793 q^{11} -6.03512 q^{12} -0.284798 q^{13} +0.0771751 q^{14} +3.94237 q^{16} -3.00421 q^{17} -0.607502 q^{18} +5.86539 q^{19} -2.38586 q^{21} -0.198901 q^{22} +5.11211 q^{23} +1.18672 q^{24} +0.0279331 q^{26} +9.68439 q^{27} +1.56614 q^{28} +3.80384 q^{29} -1.34961 q^{31} -1.16943 q^{32} +6.14899 q^{33} +0.294655 q^{34} -12.3282 q^{36} -5.63262 q^{37} -0.575281 q^{38} -0.863548 q^{39} +2.59479 q^{41} +0.234006 q^{42} +10.9411 q^{43} -4.03636 q^{44} -0.501398 q^{46} +1.00000 q^{47} +11.9539 q^{48} -6.38086 q^{49} -9.10921 q^{51} +0.566856 q^{52} -13.4823 q^{53} -0.949850 q^{54} -0.307958 q^{56} +17.7847 q^{57} -0.373083 q^{58} +14.5219 q^{59} +14.5192 q^{61} +0.132371 q^{62} -4.87370 q^{63} -7.77005 q^{64} -0.603096 q^{66} +3.02108 q^{67} +5.97952 q^{68} +15.5006 q^{69} +5.77685 q^{71} +2.42416 q^{72} -12.4386 q^{73} +0.552450 q^{74} -11.6744 q^{76} -1.59569 q^{77} +0.0846973 q^{78} -11.1604 q^{79} +10.7828 q^{81} -0.254498 q^{82} +0.810691 q^{83} +4.74876 q^{84} -1.07311 q^{86} +11.5338 q^{87} +0.793690 q^{88} -7.79832 q^{89} +0.224094 q^{91} -10.1750 q^{92} -4.09222 q^{93} -0.0980806 q^{94} -3.54587 q^{96} +12.1257 q^{97} +0.625838 q^{98} +12.5608 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} - q^{3} + 7 q^{4} + q^{6} + 3 q^{7} - 3 q^{8} + 10 q^{9}+O(q^{10}) $ 7 * q - q^2 - q^3 + 7 * q^4 + q^6 + 3 * q^7 - 3 * q^8 + 10 * q^9	$ 7 q - q^{2} - q^{3} + 7 q^{4} + q^{6} + 3 q^{7} - 3 q^{8} + 10 q^{9} + q^{11} + 4 q^{12} - 2 q^{13} + 10 q^{14} - q^{16} - 12 q^{17} + 17 q^{18} + 3 q^{19} + 7 q^{21} + 5 q^{22} - q^{23} + 8 q^{24} - 13 q^{26} - q^{27} + 27 q^{28} + 26 q^{29} - 5 q^{31} - 12 q^{32} + 15 q^{33} + 6 q^{34} - 34 q^{36} + 7 q^{38} + q^{39} + 12 q^{41} + 18 q^{42} + 33 q^{43} + 3 q^{44} - 36 q^{46} + 7 q^{47} + 25 q^{48} + 6 q^{49} - 14 q^{51} + 11 q^{52} - 4 q^{53} - 2 q^{54} - 27 q^{56} + 21 q^{57} + 38 q^{58} + 13 q^{59} + 20 q^{61} - 15 q^{62} + 10 q^{63} - 9 q^{64} - 41 q^{66} + 32 q^{67} - 15 q^{68} + 16 q^{69} + 11 q^{71} + 8 q^{72} + 8 q^{73} + 48 q^{74} + 11 q^{76} - 29 q^{77} + 17 q^{78} + 17 q^{79} + 15 q^{81} - 6 q^{82} - 19 q^{83} + 46 q^{84} - 30 q^{86} - 2 q^{87} - 7 q^{88} + 13 q^{89} - 11 q^{91} - 16 q^{92} + 29 q^{93} - q^{94} - 29 q^{96} + 12 q^{97} - 6 q^{98} - 32 q^{99}+O(q^{100}) $ 7 * q - q^2 - q^3 + 7 * q^4 + q^6 + 3 * q^7 - 3 * q^8 + 10 * q^9 + q^11 + 4 * q^12 - 2 * q^13 + 10 * q^14 - q^16 - 12 * q^17 + 17 * q^18 + 3 * q^19 + 7 * q^21 + 5 * q^22 - q^23 + 8 * q^24 - 13 * q^26 - q^27 + 27 * q^28 + 26 * q^29 - 5 * q^31 - 12 * q^32 + 15 * q^33 + 6 * q^34 - 34 * q^36 + 7 * q^38 + q^39 + 12 * q^41 + 18 * q^42 + 33 * q^43 + 3 * q^44 - 36 * q^46 + 7 * q^47 + 25 * q^48 + 6 * q^49 - 14 * q^51 + 11 * q^52 - 4 * q^53 - 2 * q^54 - 27 * q^56 + 21 * q^57 + 38 * q^58 + 13 * q^59 + 20 * q^61 - 15 * q^62 + 10 * q^63 - 9 * q^64 - 41 * q^66 + 32 * q^67 - 15 * q^68 + 16 * q^69 + 11 * q^71 + 8 * q^72 + 8 * q^73 + 48 * q^74 + 11 * q^76 - 29 * q^77 + 17 * q^78 + 17 * q^79 + 15 * q^81 - 6 * q^82 - 19 * q^83 + 46 * q^84 - 30 * q^86 - 2 * q^87 - 7 * q^88 + 13 * q^89 - 11 * q^91 - 16 * q^92 + 29 * q^93 - q^94 - 29 * q^96 + 12 * q^97 - 6 * q^98 - 32 * 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 $

$2$	−0.0980806	−0.0693534	−0.0346767	−	0.999399i	$-0.511040\pi$
$2$	−0.0980806	−0.0693534	−0.0346767	+	0.999399i	$0.511040\pi$
$3$	3.03215	1.75061	0.875305	−	0.483571i	$-0.160661\pi$
$3$	3.03215	1.75061	0.875305	+	0.483571i	$0.160661\pi$
$4$	−1.99038	−0.995190
$5$	0	0
$5$	0	0
$6$	−0.297395	−0.121411
$7$	−0.786854	−0.297403	−0.148701	−	0.988882i	$-0.547509\pi$
$7$	−0.786854	−0.297403	−0.148701	+	0.988882i	$0.547509\pi$
$8$	0.391379	0.138373
$9$	6.19391	2.06464
$10$	0	0
$11$	2.02793	0.611445	0.305722	−	0.952121i	$-0.401102\pi$
$11$	2.02793	0.611445	0.305722	+	0.952121i	$0.401102\pi$
$12$	−6.03512	−1.74219
$13$	−0.284798	−0.0789887	−0.0394944	−	0.999220i	$-0.512575\pi$
$13$	−0.284798	−0.0789887	−0.0394944	+	0.999220i	$0.512575\pi$
$14$	0.0771751	0.0206259
$15$	0	0
$16$	3.94237	0.985593
$17$	−3.00421	−0.728629	−0.364314	−	0.931276i	$-0.618697\pi$
$17$	−3.00421	−0.728629	−0.364314	+	0.931276i	$0.618697\pi$
$18$	−0.607502	−0.143190
$19$	5.86539	1.34561	0.672806	−	0.739819i	$-0.265089\pi$
$19$	5.86539	1.34561	0.672806	+	0.739819i	$0.265089\pi$
$20$	0	0
$21$	−2.38586	−0.520636
$22$	−0.198901	−0.0424058
$23$	5.11211	1.06595	0.532974	−	0.846132i	$-0.321074\pi$
$23$	5.11211	1.06595	0.532974	+	0.846132i	$0.321074\pi$
$24$	1.18672	0.242238
$25$	0	0
$26$	0.0279331	0.00547814
$27$	9.68439	1.86376
$28$	1.56614	0.295972
$29$	3.80384	0.706355	0.353178	−	0.935556i	$-0.385101\pi$
$29$	3.80384	0.706355	0.353178	+	0.935556i	$0.385101\pi$
$30$	0	0
$31$	−1.34961	−0.242398	−0.121199	−	0.992628i	$-0.538674\pi$
$31$	−1.34961	−0.242398	−0.121199	+	0.992628i	$0.538674\pi$
$32$	−1.16943	−0.206728
$33$	6.14899	1.07040
$34$	0.294655	0.0505329
$35$	0	0
$36$	−12.3282	−2.05470
$37$	−5.63262	−0.925997	−0.462998	−	0.886359i	$-0.653226\pi$
$37$	−5.63262	−0.925997	−0.462998	+	0.886359i	$0.653226\pi$
$38$	−0.575281	−0.0933229
$39$	−0.863548	−0.138278
$40$	0	0
$41$	2.59479	0.405238	0.202619	−	0.979258i	$-0.435055\pi$
$41$	2.59479	0.405238	0.202619	+	0.979258i	$0.435055\pi$
$42$	0.234006	0.0361079
$43$	10.9411	1.66851	0.834254	−	0.551380i	$-0.185899\pi$
$43$	10.9411	1.66851	0.834254	+	0.551380i	$0.185899\pi$
$44$	−4.03636	−0.608504
$45$	0	0
$46$	−0.501398	−0.0739271
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	11.9539	1.72539
$49$	−6.38086	−0.911552
$50$	0	0
$51$	−9.10921	−1.27554
$52$	0.566856	0.0786088
$53$	−13.4823	−1.85194	−0.925968	−	0.377603i	$-0.876748\pi$
$53$	−13.4823	−1.85194	−0.925968	+	0.377603i	$0.876748\pi$
$54$	−0.949850	−0.129258
$55$	0	0
$56$	−0.307958	−0.0411526
$57$	17.7847	2.35564
$58$	−0.373083	−0.0489882
$59$	14.5219	1.89059	0.945296	−	0.326214i	$-0.105773\pi$
$59$	14.5219	1.89059	0.945296	+	0.326214i	$0.105773\pi$
$60$	0	0
$61$	14.5192	1.85899	0.929495	−	0.368835i	$-0.120243\pi$
$61$	14.5192	1.85899	0.929495	+	0.368835i	$0.120243\pi$
$62$	0.132371	0.0168111
$63$	−4.87370	−0.614028
$64$	−7.77005	−0.971256
$65$	0	0
$66$	−0.603096	−0.0742360
$67$	3.02108	0.369084	0.184542	−	0.982825i	$-0.440920\pi$
$67$	3.02108	0.369084	0.184542	+	0.982825i	$0.440920\pi$
$68$	5.97952	0.725124
$69$	15.5006	1.86606
$70$	0	0
$71$	5.77685	0.685586	0.342793	−	0.939411i	$-0.388627\pi$
$71$	5.77685	0.685586	0.342793	+	0.939411i	$0.388627\pi$
$72$	2.42416	0.285690
$73$	−12.4386	−1.45582	−0.727912	−	0.685670i	$-0.759509\pi$
$73$	−12.4386	−1.45582	−0.727912	+	0.685670i	$0.759509\pi$
$74$	0.552450	0.0642211
$75$	0	0
$76$	−11.6744	−1.33914
$77$	−1.59569	−0.181845
$78$	0.0846973	0.00959008
$79$	−11.1604	−1.25564	−0.627819	−	0.778359i	$-0.716052\pi$
$79$	−11.1604	−1.25564	−0.627819	+	0.778359i	$0.716052\pi$
$80$	0	0
$81$	10.7828	1.19808
$82$	−0.254498	−0.0281046
$83$	0.810691	0.0889849	0.0444924	−	0.999010i	$-0.485833\pi$
$83$	0.810691	0.0889849	0.0444924	+	0.999010i	$0.485833\pi$
$84$	4.74876	0.518132
$85$	0	0
$86$	−1.07311	−0.115717
$87$	11.5338	1.23655
$88$	0.793690	0.0846076
$89$	−7.79832	−0.826620	−0.413310	−	0.910590i	$-0.635627\pi$
$89$	−7.79832	−0.826620	−0.413310	+	0.910590i	$0.635627\pi$
$90$	0	0
$91$	0.224094	0.0234915
$92$	−10.1750	−1.06082
$93$	−4.09222	−0.424344
$94$	−0.0980806	−0.0101162
$95$	0	0
$96$	−3.54587	−0.361899
$97$	12.1257	1.23117	0.615587	−	0.788069i	$-0.288919\pi$
$97$	12.1257	1.23117	0.615587	+	0.788069i	$0.288919\pi$
$98$	0.625838	0.0632192
$99$	12.5608	1.26241
$100$	0	0
$101$	−10.6242	−1.05714	−0.528572	−	0.848888i	$-0.677272\pi$
$101$	−10.6242	−1.05714	−0.528572	+	0.848888i	$0.677272\pi$
$102$	0.893436	0.0884634
$103$	−7.78223	−0.766806	−0.383403	−	0.923581i	$-0.625248\pi$
$103$	−7.78223	−0.766806	−0.383403	+	0.923581i	$0.625248\pi$
$104$	−0.111464	−0.0109299
$105$	0	0
$106$	1.32235	0.128438
$107$	−8.86603	−0.857112	−0.428556	−	0.903515i	$-0.640977\pi$
$107$	−8.86603	−0.857112	−0.428556	+	0.903515i	$0.640977\pi$
$108$	−19.2756	−1.85480
$109$	−11.8741	−1.13733	−0.568665	−	0.822569i	$-0.692540\pi$
$109$	−11.8741	−1.13733	−0.568665	+	0.822569i	$0.692540\pi$
$110$	0	0
$111$	−17.0789	−1.62106
$112$	−3.10207	−0.293118
$113$	7.79968	0.733732	0.366866	−	0.930274i	$-0.380431\pi$
$113$	7.79968	0.733732	0.366866	+	0.930274i	$0.380431\pi$
$114$	−1.74433	−0.163372
$115$	0	0
$116$	−7.57109	−0.702958
$117$	−1.76401	−0.163083
$118$	−1.42432	−0.131119
$119$	2.36388	0.216696
$120$	0	0
$121$	−6.88749	−0.626135
$122$	−1.42405	−0.128927
$123$	7.86778	0.709414
$124$	2.68624	0.241232
$125$	0	0
$126$	0.478015	0.0425850
$127$	−0.0399240	−0.00354268	−0.00177134	−	0.999998i	$-0.500564\pi$
$127$	−0.0399240	−0.00354268	−0.00177134	+	0.999998i	$0.500564\pi$
$128$	3.10095	0.274088
$129$	33.1751	2.92091
$130$	0	0
$131$	8.70370	0.760445	0.380223	−	0.924895i	$-0.375847\pi$
$131$	8.70370	0.760445	0.380223	+	0.924895i	$0.375847\pi$
$132$	−12.2388	−1.06525
$133$	−4.61520	−0.400189
$134$	−0.296309	−0.0255972
$135$	0	0
$136$	−1.17578	−0.100823
$137$	−17.1691	−1.46686	−0.733430	−	0.679765i	$-0.762082\pi$
$137$	−17.1691	−1.46686	−0.733430	+	0.679765i	$0.762082\pi$
$138$	−1.52031	−0.129418
$139$	−14.3566	−1.21771	−0.608855	−	0.793282i	$-0.708371\pi$
$139$	−14.3566	−1.21771	−0.608855	+	0.793282i	$0.708371\pi$
$140$	0	0
$141$	3.03215	0.255353
$142$	−0.566597	−0.0475478
$143$	−0.577551	−0.0482972
$144$	24.4187	2.03489
$145$	0	0
$146$	1.21998	0.100966
$147$	−19.3477	−1.59577
$148$	11.2111	0.921543
$149$	2.93508	0.240451	0.120226	−	0.992747i	$-0.461638\pi$
$149$	2.93508	0.240451	0.120226	+	0.992747i	$0.461638\pi$
$150$	0	0
$151$	−7.27656	−0.592158	−0.296079	−	0.955164i	$-0.595679\pi$
$151$	−7.27656	−0.592158	−0.296079	+	0.955164i	$0.595679\pi$
$152$	2.29559	0.186197
$153$	−18.6078	−1.50435
$154$	0.156506	0.0126116
$155$	0	0
$156$	1.71879	0.137613
$157$	21.3427	1.70333	0.851665	−	0.524086i	$-0.175593\pi$
$157$	21.3427	1.70333	0.851665	+	0.524086i	$0.175593\pi$
$158$	1.09461	0.0870828
$159$	−40.8803	−3.24202
$160$	0	0
$161$	−4.02248	−0.317016
$162$	−1.05758	−0.0830913
$163$	−1.31704	−0.103159	−0.0515794	−	0.998669i	$-0.516426\pi$
$163$	−1.31704	−0.103159	−0.0515794	+	0.998669i	$0.516426\pi$
$164$	−5.16462	−0.403289
$165$	0	0
$166$	−0.0795130	−0.00617140
$167$	−22.9528	−1.77614	−0.888071	−	0.459707i	$-0.847954\pi$
$167$	−22.9528	−1.77614	−0.888071	+	0.459707i	$0.847954\pi$
$168$	−0.933773	−0.0720422
$169$	−12.9189	−0.993761
$170$	0	0
$171$	36.3297	2.77820
$172$	−21.7770	−1.66048
$173$	−11.2581	−0.855936	−0.427968	−	0.903794i	$-0.640770\pi$
$173$	−11.2581	−0.855936	−0.427968	+	0.903794i	$0.640770\pi$
$174$	−1.13124	−0.0857592
$175$	0	0
$176$	7.99487	0.602636
$177$	44.0326	3.30969
$178$	0.764864	0.0573290
$179$	2.22648	0.166415	0.0832075	−	0.996532i	$-0.473484\pi$
$179$	2.22648	0.166415	0.0832075	+	0.996532i	$0.473484\pi$
$180$	0	0
$181$	5.90828	0.439159	0.219579	−	0.975595i	$-0.429532\pi$
$181$	5.90828	0.439159	0.219579	+	0.975595i	$0.429532\pi$
$182$	−0.0219793	−0.00162921
$183$	44.0242	3.25437
$184$	2.00077	0.147499
$185$	0	0
$186$	0.401368	0.0294297
$187$	−6.09234	−0.445516
$188$	−1.99038	−0.145163
$189$	−7.62020	−0.554288
$190$	0	0
$191$	−5.18744	−0.375350	−0.187675	−	0.982231i	$-0.560095\pi$
$191$	−5.18744	−0.375350	−0.187675	+	0.982231i	$0.560095\pi$
$192$	−23.5599	−1.70029
$193$	6.41183	0.461534	0.230767	−	0.973009i	$-0.425877\pi$
$193$	6.41183	0.461534	0.230767	+	0.973009i	$0.425877\pi$
$194$	−1.18929	−0.0853861
$195$	0	0
$196$	12.7003	0.907167
$197$	13.2201	0.941895	0.470948	−	0.882161i	$-0.343912\pi$
$197$	13.2201	0.941895	0.470948	+	0.882161i	$0.343912\pi$
$198$	−1.23197	−0.0875525
$199$	8.18903	0.580505	0.290252	−	0.956950i	$-0.406261\pi$
$199$	8.18903	0.580505	0.290252	+	0.956950i	$0.406261\pi$
$200$	0	0
$201$	9.16036	0.646122
$202$	1.04202	0.0733166
$203$	−2.99307	−0.210072
$204$	18.1308	1.26941
$205$	0	0
$206$	0.763285	0.0531806
$207$	31.6639	2.20079
$208$	−1.12278	−0.0778507
$209$	11.8946	0.822768
$210$	0	0
$211$	13.7119	0.943966	0.471983	−	0.881608i	$-0.343538\pi$
$211$	13.7119	0.943966	0.471983	+	0.881608i	$0.343538\pi$
$212$	26.8349	1.84303
$213$	17.5163	1.20019
$214$	0.869585	0.0594436
$215$	0	0
$216$	3.79026	0.257895
$217$	1.06195	0.0720898
$218$	1.16462	0.0788778
$219$	−37.7156	−2.54858
$220$	0	0
$221$	0.855593	0.0575534
$222$	1.67511	0.112426
$223$	−3.48569	−0.233419	−0.116710	−	0.993166i	$-0.537235\pi$
$223$	−3.48569	−0.233419	−0.116710	+	0.993166i	$0.537235\pi$
$224$	0.920169	0.0614814
$225$	0	0
$226$	−0.764997	−0.0508868
$227$	9.92227	0.658564	0.329282	−	0.944232i	$-0.393193\pi$
$227$	9.92227	0.658564	0.329282	+	0.944232i	$0.393193\pi$
$228$	−35.3983	−2.34431
$229$	−18.7609	−1.23975	−0.619877	−	0.784699i	$-0.712818\pi$
$229$	−18.7609	−1.23975	−0.619877	+	0.784699i	$0.712818\pi$
$230$	0	0
$231$	−4.83835	−0.318340
$232$	1.48874	0.0977407
$233$	24.9600	1.63518	0.817591	−	0.575800i	$-0.195309\pi$
$233$	24.9600	1.63518	0.817591	+	0.575800i	$0.195309\pi$
$234$	0.173015	0.0113104
$235$	0	0
$236$	−28.9041	−1.88150
$237$	−33.8398	−2.19813
$238$	−0.231850	−0.0150286
$239$	−13.5253	−0.874877	−0.437438	−	0.899248i	$-0.644114\pi$
$239$	−13.5253	−0.874877	−0.437438	+	0.899248i	$0.644114\pi$
$240$	0	0
$241$	−1.80479	−0.116257	−0.0581283	−	0.998309i	$-0.518513\pi$
$241$	−1.80479	−0.116257	−0.0581283	+	0.998309i	$0.518513\pi$
$242$	0.675529	0.0434246
$243$	3.64173	0.233617
$244$	−28.8987	−1.85005
$245$	0	0
$246$	−0.771676	−0.0492003
$247$	−1.67045	−0.106288
$248$	−0.528210	−0.0335414
$249$	2.45813	0.155778
$250$	0	0
$251$	5.86720	0.370335	0.185167	−	0.982707i	$-0.440717\pi$
$251$	5.86720	0.370335	0.185167	+	0.982707i	$0.440717\pi$
$252$	9.70051	0.611075
$253$	10.3670	0.651768
$254$	0.00391576	0.000245697 0
$255$	0	0
$256$	15.2360	0.952247
$257$	−20.0991	−1.25375	−0.626874	−	0.779121i	$-0.715666\pi$
$257$	−20.0991	−1.25375	−0.626874	+	0.779121i	$0.715666\pi$
$258$	−3.25383	−0.202575
$259$	4.43205	0.275394
$260$	0	0
$261$	23.5606	1.45837
$262$	−0.853663	−0.0527395
$263$	−2.71782	−0.167588	−0.0837940	−	0.996483i	$-0.526704\pi$
$263$	−2.71782	−0.167588	−0.0837940	+	0.996483i	$0.526704\pi$
$264$	2.40658	0.148115
$265$	0	0
$266$	0.452662	0.0277545
$267$	−23.6456	−1.44709
$268$	−6.01310	−0.367309
$269$	−6.05221	−0.369009	−0.184505	−	0.982832i	$-0.559068\pi$
$269$	−6.05221	−0.369009	−0.184505	+	0.982832i	$0.559068\pi$
$270$	0	0
$271$	25.9465	1.57614	0.788070	−	0.615585i	$-0.211080\pi$
$271$	25.9465	1.57614	0.788070	+	0.615585i	$0.211080\pi$
$272$	−11.8437	−0.718132
$273$	0.679486	0.0411244
$274$	1.68396	0.101732
$275$	0	0
$276$	−30.8522	−1.85708
$277$	−8.83062	−0.530581	−0.265290	−	0.964169i	$-0.585468\pi$
$277$	−8.83062	−0.530581	−0.265290	+	0.964169i	$0.585468\pi$
$278$	1.40810	0.0844523
$279$	−8.35938	−0.500463
$280$	0	0
$281$	−32.8385	−1.95898	−0.979491	−	0.201490i	$-0.935422\pi$
$281$	−32.8385	−1.95898	−0.979491	+	0.201490i	$0.935422\pi$
$282$	−0.297395	−0.0177096
$283$	3.68292	0.218927	0.109463	−	0.993991i	$-0.465087\pi$
$283$	3.68292	0.218927	0.109463	+	0.993991i	$0.465087\pi$
$284$	−11.4981	−0.682289
$285$	0	0
$286$	0.0566465	0.00334958
$287$	−2.04172	−0.120519
$288$	−7.24333	−0.426817
$289$	−7.97471	−0.469100
$290$	0	0
$291$	36.7667	2.15530
$292$	24.7575	1.44882
$293$	−23.7771	−1.38907	−0.694537	−	0.719457i	$-0.744391\pi$
$293$	−23.7771	−1.38907	−0.694537	+	0.719457i	$0.744391\pi$
$294$	1.89763	0.110672
$295$	0	0
$296$	−2.20449	−0.128133
$297$	19.6393	1.13959
$298$	−0.287875	−0.0166761
$299$	−1.45592	−0.0841978
$300$	0	0
$301$	−8.60908	−0.496219
$302$	0.713689	0.0410682
$303$	−32.2140	−1.85065
$304$	23.1236	1.32623
$305$	0	0
$306$	1.82506	0.104332
$307$	12.5221	0.714674	0.357337	−	0.933976i	$-0.383685\pi$
$307$	12.5221	0.714674	0.357337	+	0.933976i	$0.383685\pi$
$308$	3.17602	0.180971
$309$	−23.5969	−1.34238
$310$	0	0
$311$	−22.0198	−1.24863	−0.624313	−	0.781174i	$-0.714621\pi$
$311$	−22.0198	−1.24863	−0.624313	+	0.781174i	$0.714621\pi$
$312$	−0.337974	−0.0191340
$313$	−8.84409	−0.499897	−0.249949	−	0.968259i	$-0.580414\pi$
$313$	−8.84409	−0.499897	−0.249949	+	0.968259i	$0.580414\pi$
$314$	−2.09330	−0.118132
$315$	0	0
$316$	22.2133	1.24960
$317$	−12.9546	−0.727601	−0.363801	−	0.931477i	$-0.618521\pi$
$317$	−12.9546	−0.727601	−0.363801	+	0.931477i	$0.618521\pi$
$318$	4.00956	0.224845
$319$	7.71393	0.431897
$320$	0	0
$321$	−26.8831	−1.50047
$322$	0.394527	0.0219861
$323$	−17.6209	−0.980452
$324$	−21.4618	−1.19232
$325$	0	0
$326$	0.129176	0.00715442
$327$	−36.0040	−1.99102
$328$	1.01555	0.0560741
$329$	−0.786854	−0.0433807
$330$	0	0
$331$	18.1460	0.997393	0.498697	−	0.866777i	$-0.333812\pi$
$331$	18.1460	0.997393	0.498697	+	0.866777i	$0.333812\pi$
$332$	−1.61358	−0.0885568
$333$	−34.8879	−1.91185
$334$	2.25122	0.123181
$335$	0	0
$336$	−9.40593	−0.513136
$337$	14.8908	0.811154	0.405577	−	0.914061i	$-0.367071\pi$
$337$	14.8908	0.811154	0.405577	+	0.914061i	$0.367071\pi$
$338$	1.26709	0.0689207
$339$	23.6498	1.28448
$340$	0	0
$341$	−2.73693	−0.148213
$342$	−3.56324	−0.192678
$343$	10.5288	0.568501
$344$	4.28213	0.230877
$345$	0	0
$346$	1.10420	0.0593621
$347$	7.47712	0.401393	0.200696	−	0.979653i	$-0.435680\pi$
$347$	7.47712	0.401393	0.200696	+	0.979653i	$0.435680\pi$
$348$	−22.9566	−1.23060
$349$	30.1312	1.61289	0.806444	−	0.591310i	$-0.201389\pi$
$349$	30.1312	1.61289	0.806444	+	0.591310i	$0.201389\pi$
$350$	0	0
$351$	−2.75809	−0.147216
$352$	−2.37152	−0.126403
$353$	−10.6113	−0.564781	−0.282390	−	0.959300i	$-0.591127\pi$
$353$	−10.6113	−0.564781	−0.282390	+	0.959300i	$0.591127\pi$
$354$	−4.31874	−0.229538
$355$	0	0
$356$	15.5216	0.822644
$357$	7.16762	0.379350
$358$	−0.218375	−0.0115415
$359$	−11.9024	−0.628183	−0.314091	−	0.949393i	$-0.601700\pi$
$359$	−11.9024	−0.628183	−0.314091	+	0.949393i	$0.601700\pi$
$360$	0	0
$361$	15.4028	0.810674
$362$	−0.579487	−0.0304572
$363$	−20.8839	−1.09612
$364$	−0.446033	−0.0233785
$365$	0	0
$366$	−4.31792	−0.225701
$367$	−10.2653	−0.535847	−0.267923	−	0.963440i	$-0.586337\pi$
$367$	−10.2653	−0.535847	−0.267923	+	0.963440i	$0.586337\pi$
$368$	20.1538	1.05059
$369$	16.0719	0.836669
$370$	0	0
$371$	10.6086	0.550771
$372$	8.14508	0.422303
$373$	22.7454	1.17771	0.588855	−	0.808239i	$-0.299579\pi$
$373$	22.7454	1.17771	0.588855	+	0.808239i	$0.299579\pi$
$374$	0.597540	0.0308981
$375$	0	0
$376$	0.391379	0.0201838
$377$	−1.08333	−0.0557941
$378$	0.747393	0.0384418
$379$	30.1828	1.55039	0.775193	−	0.631724i	$-0.217652\pi$
$379$	30.1828	1.55039	0.775193	+	0.631724i	$0.217652\pi$
$380$	0	0
$381$	−0.121055	−0.00620185
$382$	0.508787	0.0260318
$383$	−11.3739	−0.581178	−0.290589	−	0.956848i	$-0.593851\pi$
$383$	−11.3739	−0.581178	−0.290589	+	0.956848i	$0.593851\pi$
$384$	9.40252	0.479820
$385$	0	0
$386$	−0.628876	−0.0320089
$387$	67.7684	3.44486
$388$	−24.1347	−1.22525
$389$	−32.3290	−1.63915	−0.819574	−	0.572974i	$-0.805790\pi$
$389$	−32.3290	−1.63915	−0.819574	+	0.572974i	$0.805790\pi$
$390$	0	0
$391$	−15.3579	−0.776680
$392$	−2.49733	−0.126134
$393$	26.3909	1.33124
$394$	−1.29664	−0.0653237
$395$	0	0
$396$	−25.0008	−1.25634
$397$	3.56833	0.179089	0.0895446	−	0.995983i	$-0.471459\pi$
$397$	3.56833	0.179089	0.0895446	+	0.995983i	$0.471459\pi$
$398$	−0.803185	−0.0402600
$399$	−13.9940	−0.700575
$400$	0	0
$401$	4.47529	0.223485	0.111743	−	0.993737i	$-0.464357\pi$
$401$	4.47529	0.223485	0.111743	+	0.993737i	$0.464357\pi$
$402$	−0.898453	−0.0448108
$403$	0.384367	0.0191467
$404$	21.1461	1.05206
$405$	0	0
$406$	0.293562	0.0145692
$407$	−11.4226	−0.566196
$408$	−3.56515	−0.176501
$409$	−20.4765	−1.01250	−0.506248	−	0.862388i	$-0.668968\pi$
$409$	−20.4765	−1.01250	−0.506248	+	0.862388i	$0.668968\pi$
$410$	0	0
$411$	−52.0594	−2.56790
$412$	15.4896	0.763118
$413$	−11.4266	−0.562267
$414$	−3.10561	−0.152633
$415$	0	0
$416$	0.333050	0.0163291
$417$	−43.5312	−2.13173
$418$	−1.16663	−0.0570618
$419$	−30.5073	−1.49038	−0.745191	−	0.666851i	$-0.767642\pi$
$419$	−30.5073	−1.49038	−0.745191	+	0.666851i	$0.767642\pi$
$420$	0	0
$421$	−20.8983	−1.01852	−0.509259	−	0.860613i	$-0.670081\pi$
$421$	−20.8983	−1.01852	−0.509259	+	0.860613i	$0.670081\pi$
$422$	−1.34487	−0.0654673
$423$	6.19391	0.301158
$424$	−5.27668	−0.256258
$425$	0	0
$426$	−1.71800	−0.0832376
$427$	−11.4245	−0.552869
$428$	17.6468	0.852989
$429$	−1.75122	−0.0845496
$430$	0	0
$431$	28.5149	1.37351	0.686757	−	0.726887i	$-0.259034\pi$
$431$	28.5149	1.37351	0.686757	+	0.726887i	$0.259034\pi$
$432$	38.1795	1.83691
$433$	−20.5473	−0.987439	−0.493719	−	0.869621i	$-0.664363\pi$
$433$	−20.5473	−0.987439	−0.493719	+	0.869621i	$0.664363\pi$
$434$	−0.104156	−0.00499967
$435$	0	0
$436$	23.6339	1.13186
$437$	29.9845	1.43435
$438$	3.69916	0.176753
$439$	−19.0193	−0.907743	−0.453872	−	0.891067i	$-0.649958\pi$
$439$	−19.0193	−0.907743	−0.453872	+	0.891067i	$0.649958\pi$
$440$	0	0
$441$	−39.5225	−1.88202
$442$	−0.0839171	−0.00399153
$443$	−27.9350	−1.32723	−0.663617	−	0.748072i	$-0.730980\pi$
$443$	−27.9350	−1.32723	−0.663617	+	0.748072i	$0.730980\pi$
$444$	33.9935	1.61326
$445$	0	0
$446$	0.341879	0.0161884
$447$	8.89960	0.420937
$448$	6.11389	0.288854
$449$	38.0726	1.79676	0.898378	−	0.439223i	$-0.144746\pi$
$449$	38.0726	1.79676	0.898378	+	0.439223i	$0.144746\pi$
$450$	0	0
$451$	5.26206	0.247781
$452$	−15.5243	−0.730203
$453$	−22.0636	−1.03664
$454$	−0.973182	−0.0456737
$455$	0	0
$456$	6.96056	0.325958
$457$	6.20936	0.290461	0.145231	−	0.989398i	$-0.453608\pi$
$457$	6.20936	0.290461	0.145231	+	0.989398i	$0.453608\pi$
$458$	1.84008	0.0859813
$459$	−29.0940	−1.35799
$460$	0	0
$461$	−7.78643	−0.362650	−0.181325	−	0.983423i	$-0.558039\pi$
$461$	−7.78643	−0.362650	−0.181325	+	0.983423i	$0.558039\pi$
$462$	0.474549	0.0220780
$463$	32.6222	1.51608	0.758040	−	0.652208i	$-0.226157\pi$
$463$	32.6222	1.51608	0.758040	+	0.652208i	$0.226157\pi$
$464$	14.9962	0.696179
$465$	0	0
$466$	−2.44809	−0.113405
$467$	3.05460	0.141350	0.0706751	−	0.997499i	$-0.477485\pi$
$467$	3.05460	0.141350	0.0706751	+	0.997499i	$0.477485\pi$
$468$	3.51105	0.162298
$469$	−2.37715	−0.109767
$470$	0	0
$471$	64.7141	2.98187
$472$	5.68357	0.261607
$473$	22.1879	1.02020
$474$	3.31903	0.152448
$475$	0	0
$476$	−4.70501	−0.215654
$477$	−83.5081	−3.82357
$478$	1.32657	0.0606757
$479$	16.6175	0.759275	0.379637	−	0.925135i	$-0.376049\pi$
$479$	16.6175	0.759275	0.379637	+	0.925135i	$0.376049\pi$
$480$	0	0
$481$	1.60416	0.0731433
$482$	0.177015	0.00806279
$483$	−12.1967	−0.554971
$484$	13.7087	0.623124
$485$	0	0
$486$	−0.357183	−0.0162021
$487$	−23.0542	−1.04468	−0.522342	−	0.852736i	$-0.674941\pi$
$487$	−23.0542	−1.04468	−0.522342	+	0.852736i	$0.674941\pi$
$488$	5.68250	0.257235
$489$	−3.99347	−0.180591
$490$	0	0
$491$	−33.6974	−1.52074	−0.760370	−	0.649490i	$-0.774982\pi$
$491$	−33.6974	−1.52074	−0.760370	+	0.649490i	$0.774982\pi$
$492$	−15.6599	−0.706001
$493$	−11.4275	−0.514671
$494$	0.163839	0.00737145
$495$	0	0
$496$	−5.32068	−0.238906
$497$	−4.54554	−0.203895
$498$	−0.241095	−0.0108037
$499$	9.90582	0.443445	0.221723	−	0.975110i	$-0.428832\pi$
$499$	9.90582	0.443445	0.221723	+	0.975110i	$0.428832\pi$
$500$	0	0
$501$	−69.5962	−3.10933
$502$	−0.575459	−0.0256840
$503$	28.6035	1.27537	0.637683	−	0.770299i	$-0.279893\pi$
$503$	28.6035	1.27537	0.637683	+	0.770299i	$0.279893\pi$
$504$	−1.90746	−0.0849651
$505$	0	0
$506$	−1.01680	−0.0452024
$507$	−39.1720	−1.73969
$508$	0.0794639	0.00352564
$509$	40.6924	1.80366	0.901828	−	0.432094i	$-0.142225\pi$
$509$	40.6924	1.80366	0.901828	+	0.432094i	$0.142225\pi$
$510$	0	0
$511$	9.78734	0.432966
$512$	−7.69624	−0.340129
$513$	56.8027	2.50790
$514$	1.97133	0.0869517
$515$	0	0
$516$	−66.0311	−2.90686
$517$	2.02793	0.0891884
$518$	−0.434698	−0.0190995
$519$	−34.1361	−1.49841
$520$	0	0
$521$	−40.2341	−1.76269	−0.881343	−	0.472476i	$-0.843360\pi$
$521$	−40.2341	−1.76269	−0.881343	+	0.472476i	$0.843360\pi$
$522$	−2.31084	−0.101143
$523$	38.0417	1.66345	0.831723	−	0.555190i	$-0.187355\pi$
$523$	38.0417	1.66345	0.831723	+	0.555190i	$0.187355\pi$
$524$	−17.3237	−0.756788
$525$	0	0
$526$	0.266565	0.0116228
$527$	4.05453	0.176618
$528$	24.2416	1.05498
$529$	3.13363	0.136245
$530$	0	0
$531$	89.9474	3.90338
$532$	9.18601	0.398264
$533$	−0.738990	−0.0320092
$534$	2.31918	0.100361
$535$	0	0
$536$	1.18239	0.0510713
$537$	6.75102	0.291328
$538$	0.593604	0.0255921
$539$	−12.9400	−0.557364
$540$	0	0
$541$	20.1597	0.866734	0.433367	−	0.901218i	$-0.357325\pi$
$541$	20.1597	0.866734	0.433367	+	0.901218i	$0.357325\pi$
$542$	−2.54485	−0.109311
$543$	17.9148	0.768796
$544$	3.51321	0.150628
$545$	0	0
$546$	−0.0666444	−0.00285212
$547$	29.0063	1.24022	0.620110	−	0.784515i	$-0.287088\pi$
$547$	29.0063	1.24022	0.620110	+	0.784515i	$0.287088\pi$
$548$	34.1731	1.45980
$549$	89.9304	3.83814
$550$	0	0
$551$	22.3110	0.950481
$552$	6.06662	0.258213
$553$	8.78157	0.373430
$554$	0.866112	0.0367976
$555$	0	0
$556$	28.5751	1.21185
$557$	0.765733	0.0324452	0.0162226	−	0.999868i	$-0.494836\pi$
$557$	0.765733	0.0324452	0.0162226	+	0.999868i	$0.494836\pi$
$558$	0.819893	0.0347088
$559$	−3.11601	−0.131793
$560$	0	0
$561$	−18.4729	−0.779925
$562$	3.22082	0.135862
$563$	23.3802	0.985357	0.492679	−	0.870211i	$-0.336018\pi$
$563$	23.3802	0.985357	0.492679	+	0.870211i	$0.336018\pi$
$564$	−6.03512	−0.254124
$565$	0	0
$566$	−0.361223	−0.0151833
$567$	−8.48446	−0.356314
$568$	2.26094	0.0948668
$569$	−6.28317	−0.263404	−0.131702	−	0.991289i	$-0.542044\pi$
$569$	−6.28317	−0.263404	−0.131702	+	0.991289i	$0.542044\pi$
$570$	0	0
$571$	−5.17476	−0.216557	−0.108279	−	0.994121i	$-0.534534\pi$
$571$	−5.17476	−0.216557	−0.108279	+	0.994121i	$0.534534\pi$
$572$	1.14955	0.0480649
$573$	−15.7291	−0.657092
$574$	0.200253	0.00835840
$575$	0	0
$576$	−48.1270	−2.00529
$577$	25.6174	1.06647	0.533233	−	0.845969i	$-0.320977\pi$
$577$	25.6174	1.06647	0.533233	+	0.845969i	$0.320977\pi$
$578$	0.782164	0.0325337
$579$	19.4416	0.807965
$580$	0	0
$581$	−0.637895	−0.0264643
$582$	−3.60610	−0.149478
$583$	−27.3412	−1.13236
$584$	−4.86819	−0.201447
$585$	0	0
$586$	2.33207	0.0963370
$587$	20.0265	0.826580	0.413290	−	0.910599i	$-0.364380\pi$
$587$	20.0265	0.826580	0.413290	+	0.910599i	$0.364380\pi$
$588$	38.5093	1.58810
$589$	−7.91601	−0.326173
$590$	0	0
$591$	40.0854	1.64889
$592$	−22.2059	−0.912657
$593$	−30.5266	−1.25358	−0.626789	−	0.779189i	$-0.715631\pi$
$593$	−30.5266	−1.25358	−0.626789	+	0.779189i	$0.715631\pi$
$594$	−1.92623	−0.0790343
$595$	0	0
$596$	−5.84193	−0.239295
$597$	24.8303	1.01624
$598$	0.142797	0.00583941
$599$	−28.3375	−1.15784	−0.578919	−	0.815385i	$-0.696525\pi$
$599$	−28.3375	−1.15784	−0.578919	+	0.815385i	$0.696525\pi$
$600$	0	0
$601$	10.8841	0.443970	0.221985	−	0.975050i	$-0.428746\pi$
$601$	10.8841	0.443970	0.221985	+	0.975050i	$0.428746\pi$
$602$	0.844383	0.0344145
$603$	18.7123	0.762024
$604$	14.4831	0.589309
$605$	0	0
$606$	3.15957	0.128349
$607$	22.6230	0.918241	0.459121	−	0.888374i	$-0.348165\pi$
$607$	22.6230	0.918241	0.459121	+	0.888374i	$0.348165\pi$
$608$	−6.85915	−0.278175
$609$	−9.07541	−0.367754
$610$	0	0
$611$	−0.284798	−0.0115217
$612$	37.0366	1.49712
$613$	26.6935	1.07814	0.539069	−	0.842261i	$-0.318776\pi$
$613$	26.6935	1.07814	0.539069	+	0.842261i	$0.318776\pi$
$614$	−1.22817	−0.0495651
$615$	0	0
$616$	−0.624518	−0.0251625
$617$	32.4671	1.30707	0.653537	−	0.756894i	$-0.273284\pi$
$617$	32.4671	1.30707	0.653537	+	0.756894i	$0.273284\pi$
$618$	2.31439	0.0930985
$619$	11.0222	0.443019	0.221509	−	0.975158i	$-0.428902\pi$
$619$	11.0222	0.443019	0.221509	+	0.975158i	$0.428902\pi$
$620$	0	0
$621$	49.5076	1.98667
$622$	2.15971	0.0865966
$623$	6.13614	0.245839
$624$	−3.40443	−0.136286
$625$	0	0
$626$	0.867433	0.0346696
$627$	36.0662	1.44035
$628$	−42.4800	−1.69514
$629$	16.9216	0.674708
$630$	0	0
$631$	−29.3212	−1.16726	−0.583630	−	0.812020i	$-0.698368\pi$
$631$	−29.3212	−1.16726	−0.583630	+	0.812020i	$0.698368\pi$
$632$	−4.36793	−0.173747
$633$	41.5765	1.65252
$634$	1.27059	0.0504616
$635$	0	0
$636$	81.3673	3.22642
$637$	1.81726	0.0720023
$638$	−0.756587	−0.0299536
$639$	35.7813	1.41549
$640$	0	0
$641$	28.5133	1.12621	0.563104	−	0.826386i	$-0.309607\pi$
$641$	28.5133	1.12621	0.563104	+	0.826386i	$0.309607\pi$
$642$	2.63671	0.104063
$643$	−2.08556	−0.0822466	−0.0411233	−	0.999154i	$-0.513094\pi$
$643$	−2.08556	−0.0822466	−0.0411233	+	0.999154i	$0.513094\pi$
$644$	8.00626	0.315491
$645$	0	0
$646$	1.72827	0.0679977
$647$	23.9037	0.939750	0.469875	−	0.882733i	$-0.344299\pi$
$647$	23.9037	0.939750	0.469875	+	0.882733i	$0.344299\pi$
$648$	4.22014	0.165783
$649$	29.4495	1.15599
$650$	0	0
$651$	3.21998	0.126201
$652$	2.62142	0.102663
$653$	−6.93579	−0.271419	−0.135709	−	0.990749i	$-0.543331\pi$
$653$	−6.93579	−0.271419	−0.135709	+	0.990749i	$0.543331\pi$
$654$	3.53129	0.138084
$655$	0	0
$656$	10.2296	0.399400
$657$	−77.0434	−3.00575
$658$	0.0771751	0.00300860
$659$	1.31205	0.0511103	0.0255551	−	0.999673i	$-0.491865\pi$
$659$	1.31205	0.0511103	0.0255551	+	0.999673i	$0.491865\pi$
$660$	0	0
$661$	−24.3125	−0.945648	−0.472824	−	0.881157i	$-0.656765\pi$
$661$	−24.3125	−0.945648	−0.472824	+	0.881157i	$0.656765\pi$
$662$	−1.77977	−0.0691726
$663$	2.59428	0.100754
$664$	0.317287	0.0123131
$665$	0	0
$666$	3.42183	0.132593
$667$	19.4456	0.752938
$668$	45.6848	1.76760
$669$	−10.5691	−0.408626
$670$	0	0
$671$	29.4439	1.13667
$672$	2.79009	0.107630
$673$	8.52948	0.328787	0.164394	−	0.986395i	$-0.447433\pi$
$673$	8.52948	0.328787	0.164394	+	0.986395i	$0.447433\pi$
$674$	−1.46050	−0.0562563
$675$	0	0
$676$	25.7135	0.988981
$677$	−9.98631	−0.383805	−0.191902	−	0.981414i	$-0.561466\pi$
$677$	−9.98631	−0.383805	−0.191902	+	0.981414i	$0.561466\pi$
$678$	−2.31958	−0.0890830
$679$	−9.54112	−0.366154
$680$	0	0
$681$	30.0858	1.15289
$682$	0.268439	0.0102791
$683$	−22.7350	−0.869932	−0.434966	−	0.900447i	$-0.643240\pi$
$683$	−22.7350	−0.869932	−0.434966	+	0.900447i	$0.643240\pi$
$684$	−72.3099	−2.76484
$685$	0	0
$686$	−1.03267	−0.0394275
$687$	−56.8858	−2.17033
$688$	43.1341	1.64447
$689$	3.83973	0.146282
$690$	0	0
$691$	15.8090	0.601404	0.300702	−	0.953718i	$-0.402779\pi$
$691$	15.8090	0.601404	0.300702	+	0.953718i	$0.402779\pi$
$692$	22.4079	0.851819
$693$	−9.88354	−0.375444
$694$	−0.733360	−0.0278380
$695$	0	0
$696$	4.51408	0.171106
$697$	−7.79530	−0.295268
$698$	−2.95529	−0.111859
$699$	75.6822	2.86256
$700$	0	0
$701$	15.2568	0.576240	0.288120	−	0.957594i	$-0.406970\pi$
$701$	15.2568	0.576240	0.288120	+	0.957594i	$0.406970\pi$
$702$	0.270515	0.0102099
$703$	−33.0375	−1.24603
$704$	−15.7571	−0.593870
$705$	0	0
$706$	1.04076	0.0391695
$707$	8.35967	0.314398
$708$	−87.6415	−3.29377
$709$	38.6425	1.45125	0.725625	−	0.688091i	$-0.241551\pi$
$709$	38.6425	1.45125	0.725625	+	0.688091i	$0.241551\pi$
$710$	0	0
$711$	−69.1262	−2.59243
$712$	−3.05210	−0.114382
$713$	−6.89937	−0.258383
$714$	−0.703004	−0.0263093
$715$	0	0
$716$	−4.43155	−0.165615
$717$	−41.0106	−1.53157
$718$	1.16739	0.0435666
$719$	−8.25769	−0.307960	−0.153980	−	0.988074i	$-0.549209\pi$
$719$	−8.25769	−0.307960	−0.153980	+	0.988074i	$0.549209\pi$
$720$	0	0
$721$	6.12348	0.228050
$722$	−1.51072	−0.0562230
$723$	−5.47238	−0.203520
$724$	−11.7597	−0.437046
$725$	0	0
$726$	2.04830	0.0760196
$727$	−36.4929	−1.35345	−0.676723	−	0.736238i	$-0.736600\pi$
$727$	−36.4929	−1.35345	−0.676723	+	0.736238i	$0.736600\pi$
$728$	0.0877057	0.00325059
$729$	−21.3060	−0.789112
$730$	0	0
$731$	−32.8695	−1.21572
$732$	−87.6250	−3.23871
$733$	0.351077	0.0129673	0.00648366	−	0.999979i	$-0.497936\pi$
$733$	0.351077	0.0129673	0.00648366	+	0.999979i	$0.497936\pi$
$734$	1.00683	0.0371628
$735$	0	0
$736$	−5.97824	−0.220361
$737$	6.12655	0.225674
$738$	−1.57634	−0.0580258
$739$	−6.71349	−0.246960	−0.123480	−	0.992347i	$-0.539405\pi$
$739$	−6.71349	−0.246960	−0.123480	+	0.992347i	$0.539405\pi$
$740$	0	0
$741$	−5.06505	−0.186069
$742$	−1.04050	−0.0381978
$743$	5.97874	0.219339	0.109669	−	0.993968i	$-0.465021\pi$
$743$	5.97874	0.219339	0.109669	+	0.993968i	$0.465021\pi$
$744$	−1.60161	−0.0587179
$745$	0	0
$746$	−2.23088	−0.0816782
$747$	5.02134	0.183721
$748$	12.1261	0.443373
$749$	6.97627	0.254907
$750$	0	0
$751$	−19.9757	−0.728924	−0.364462	−	0.931218i	$-0.618747\pi$
$751$	−19.9757	−0.728924	−0.364462	+	0.931218i	$0.618747\pi$
$752$	3.94237	0.143764
$753$	17.7902	0.648311
$754$	0.106253	0.00386951
$755$	0	0
$756$	15.1671	0.551622
$757$	46.2702	1.68172	0.840859	−	0.541254i	$-0.182050\pi$
$757$	46.2702	1.68172	0.840859	+	0.541254i	$0.182050\pi$
$758$	−2.96035	−0.107525
$759$	31.4343	1.14099
$760$	0	0
$761$	−12.7227	−0.461197	−0.230598	−	0.973049i	$-0.574068\pi$
$761$	−12.7227	−0.461197	−0.230598	+	0.973049i	$0.574068\pi$
$762$	0.0118732	0.000430120 0
$763$	9.34317	0.338245
$764$	10.3250	0.373545
$765$	0	0
$766$	1.11556	0.0403067
$767$	−4.13581	−0.149335
$768$	46.1976	1.66701
$769$	54.3996	1.96170	0.980851	−	0.194762i	$-0.0623935\pi$
$769$	54.3996	1.96170	0.980851	+	0.194762i	$0.0623935\pi$
$770$	0	0
$771$	−60.9434	−2.19482
$772$	−12.7620	−0.459314
$773$	−35.0461	−1.26052	−0.630261	−	0.776383i	$-0.717052\pi$
$773$	−35.0461	−1.26052	−0.630261	+	0.776383i	$0.717052\pi$
$774$	−6.64676	−0.238913
$775$	0	0
$776$	4.74572	0.170362
$777$	13.4386	0.482108
$778$	3.17085	0.113681
$779$	15.2195	0.545293
$780$	0	0
$781$	11.7151	0.419198
$782$	1.50631	0.0538654
$783$	36.8379	1.31648
$784$	−25.1557	−0.898419
$785$	0	0
$786$	−2.58843	−0.0923263
$787$	34.1749	1.21820	0.609102	−	0.793092i	$-0.291530\pi$
$787$	34.1749	1.21820	0.609102	+	0.793092i	$0.291530\pi$
$788$	−26.3131	−0.937365
$789$	−8.24083	−0.293381
$790$	0	0
$791$	−6.13721	−0.218214
$792$	4.91604	0.174684
$793$	−4.13503	−0.146839
$794$	−0.349984	−0.0124205
$795$	0	0
$796$	−16.2993	−0.577713
$797$	2.34868	0.0831945	0.0415972	−	0.999134i	$-0.486755\pi$
$797$	2.34868	0.0831945	0.0415972	+	0.999134i	$0.486755\pi$
$798$	1.37254	0.0485873
$799$	−3.00421	−0.106281
$800$	0	0
$801$	−48.3021	−1.70667
$802$	−0.438939	−0.0154995
$803$	−25.2246	−0.890157
$804$	−18.2326	−0.643014
$805$	0	0
$806$	−0.0376989	−0.00132789
$807$	−18.3512	−0.645992
$808$	−4.15807	−0.146281
$809$	13.2246	0.464950	0.232475	−	0.972602i	$-0.425318\pi$
$809$	13.2246	0.464950	0.232475	+	0.972602i	$0.425318\pi$
$810$	0	0
$811$	−44.8476	−1.57481	−0.787406	−	0.616435i	$-0.788576\pi$
$811$	−44.8476	−1.57481	−0.787406	+	0.616435i	$0.788576\pi$
$812$	5.95734	0.209062
$813$	78.6737	2.75921
$814$	1.12033	0.0392676
$815$	0	0
$816$	−35.9119	−1.25717
$817$	64.1740	2.24517
$818$	2.00834	0.0702201
$819$	1.38802	0.0485013
$820$	0	0
$821$	−25.6718	−0.895952	−0.447976	−	0.894045i	$-0.647855\pi$
$821$	−25.6718	−0.895952	−0.447976	+	0.894045i	$0.647855\pi$
$822$	5.10601	0.178093
$823$	−22.5549	−0.786213	−0.393107	−	0.919493i	$-0.628600\pi$
$823$	−22.5549	−0.786213	−0.393107	+	0.919493i	$0.628600\pi$
$824$	−3.04580	−0.106105
$825$	0	0
$826$	1.12073	0.0389952
$827$	−3.36308	−0.116946	−0.0584728	−	0.998289i	$-0.518623\pi$
$827$	−3.36308	−0.116946	−0.0584728	+	0.998289i	$0.518623\pi$
$828$	−63.0232	−2.19021
$829$	−17.3515	−0.602641	−0.301321	−	0.953523i	$-0.597427\pi$
$829$	−17.3515	−0.602641	−0.301321	+	0.953523i	$0.597427\pi$
$830$	0	0
$831$	−26.7757	−0.928840
$832$	2.21289	0.0767183
$833$	19.1695	0.664182
$834$	4.26957	0.147843
$835$	0	0
$836$	−23.6748	−0.818811
$837$	−13.0702	−0.451772
$838$	2.99218	0.103363
$839$	14.0207	0.484048	0.242024	−	0.970270i	$-0.422189\pi$
$839$	14.0207	0.484048	0.242024	+	0.970270i	$0.422189\pi$
$840$	0	0
$841$	−14.5308	−0.501062
$842$	2.04971	0.0706378
$843$	−99.5711	−3.42941
$844$	−27.2919	−0.939425
$845$	0	0
$846$	−0.607502	−0.0208863
$847$	5.41945	0.186214
$848$	−53.1522	−1.82526
$849$	11.1671	0.383255
$850$	0	0
$851$	−28.7945	−0.987064
$852$	−34.8640	−1.19442
$853$	22.3546	0.765406	0.382703	−	0.923871i	$-0.374993\pi$
$853$	22.3546	0.765406	0.382703	+	0.923871i	$0.374993\pi$
$854$	1.12052	0.0383433
$855$	0	0
$856$	−3.46998	−0.118601
$857$	33.7764	1.15378	0.576889	−	0.816822i	$-0.304266\pi$
$857$	33.7764	1.15378	0.576889	+	0.816822i	$0.304266\pi$
$858$	0.171760	0.00586381
$859$	32.2743	1.10118	0.550592	−	0.834774i	$-0.314402\pi$
$859$	32.2743	1.10118	0.550592	+	0.834774i	$0.314402\pi$
$860$	0	0
$861$	−6.19079	−0.210982
$862$	−2.79676	−0.0952579
$863$	−18.6945	−0.636368	−0.318184	−	0.948029i	$-0.603073\pi$
$863$	−18.6945	−0.636368	−0.318184	+	0.948029i	$0.603073\pi$
$864$	−11.3252	−0.385291
$865$	0	0
$866$	2.01529	0.0684823
$867$	−24.1805	−0.821212
$868$	−2.11368	−0.0717430
$869$	−22.6325	−0.767753
$870$	0	0
$871$	−0.860397	−0.0291535
$872$	−4.64726	−0.157376
$873$	75.1052	2.54192
$874$	−2.94090	−0.0994773
$875$	0	0
$876$	75.0683	2.53632
$877$	8.87518	0.299694	0.149847	−	0.988709i	$-0.452122\pi$
$877$	8.87518	0.299694	0.149847	+	0.988709i	$0.452122\pi$
$878$	1.86543	0.0629551
$879$	−72.0956	−2.43173
$880$	0	0
$881$	−38.5427	−1.29854	−0.649268	−	0.760560i	$-0.724924\pi$
$881$	−38.5427	−1.29854	−0.649268	+	0.760560i	$0.724924\pi$
$882$	3.87638	0.130525
$883$	−57.1719	−1.92399	−0.961994	−	0.273071i	$-0.911960\pi$
$883$	−57.1719	−1.92399	−0.961994	+	0.273071i	$0.911960\pi$
$884$	−1.70296	−0.0572766
$885$	0	0
$886$	2.73988	0.0920482
$887$	−21.2329	−0.712933	−0.356466	−	0.934308i	$-0.616019\pi$
$887$	−21.2329	−0.712933	−0.356466	+	0.934308i	$0.616019\pi$
$888$	−6.68433	−0.224311
$889$	0.0314143	0.00105360
$890$	0	0
$891$	21.8667	0.732562
$892$	6.93785	0.232296
$893$	5.86539	0.196278
$894$	−0.872878	−0.0291934
$895$	0	0
$896$	−2.43999	−0.0815144
$897$	−4.41455	−0.147398
$898$	−3.73418	−0.124611
$899$	−5.13371	−0.171219
$900$	0	0
$901$	40.5037	1.34937
$902$	−0.516106	−0.0171844
$903$	−26.1040	−0.868686
$904$	3.05263	0.101529
$905$	0	0
$906$	2.16401	0.0718943
$907$	37.3480	1.24012	0.620060	−	0.784554i	$-0.287108\pi$
$907$	37.3480	1.24012	0.620060	+	0.784554i	$0.287108\pi$
$908$	−19.7491	−0.655397
$909$	−65.8051	−2.18262
$910$	0	0
$911$	−4.00318	−0.132631	−0.0663156	−	0.997799i	$-0.521124\pi$
$911$	−4.00318	−0.132631	−0.0663156	+	0.997799i	$0.521124\pi$
$912$	70.1140	2.32171
$913$	1.64403	0.0544093
$914$	−0.609017	−0.0201445
$915$	0	0
$916$	37.3413	1.23379
$917$	−6.84854	−0.226159
$918$	2.85355	0.0941813
$919$	10.2974	0.339679	0.169839	−	0.985472i	$-0.445675\pi$
$919$	10.2974	0.339679	0.169839	+	0.985472i	$0.445675\pi$
$920$	0	0
$921$	37.9688	1.25112
$922$	0.763697	0.0251510
$923$	−1.64524	−0.0541536
$924$	9.63017	0.316809
$925$	0	0
$926$	−3.19960	−0.105145
$927$	−48.2024	−1.58317
$928$	−4.44831	−0.146023
$929$	−20.1164	−0.659998	−0.329999	−	0.943981i	$-0.607048\pi$
$929$	−20.1164	−0.659998	−0.329999	+	0.943981i	$0.607048\pi$
$930$	0	0
$931$	−37.4262	−1.22660
$932$	−49.6798	−1.62732
$933$	−66.7672	−2.18586
$934$	−0.299597	−0.00980312
$935$	0	0
$936$	−0.690396	−0.0225663
$937$	55.8929	1.82594	0.912970	−	0.408027i	$-0.133783\pi$
$937$	55.8929	1.82594	0.912970	+	0.408027i	$0.133783\pi$
$938$	0.233152	0.00761269
$939$	−26.8166	−0.875125
$940$	0	0
$941$	36.2007	1.18011	0.590054	−	0.807364i	$-0.299107\pi$
$941$	36.2007	1.18011	0.590054	+	0.807364i	$0.299107\pi$
$942$	−6.34719	−0.206803
$943$	13.2648	0.431963
$944$	57.2508	1.86336
$945$	0	0
$946$	−2.17620	−0.0707544
$947$	9.28232	0.301635	0.150817	−	0.988562i	$-0.451809\pi$
$947$	9.28232	0.301635	0.150817	+	0.988562i	$0.451809\pi$
$948$	67.3541	2.18756
$949$	3.54248	0.114994
$950$	0	0
$951$	−39.2802	−1.27375
$952$	0.925171	0.0299850
$953$	22.9732	0.744174	0.372087	−	0.928198i	$-0.378642\pi$
$953$	22.9732	0.744174	0.372087	+	0.928198i	$0.378642\pi$
$954$	8.19052	0.265178
$955$	0	0
$956$	26.9204	0.870669
$957$	23.3898	0.756084
$958$	−1.62986	−0.0526583
$959$	13.5096	0.436248
$960$	0	0
$961$	−29.1785	−0.941243
$962$	−0.157337	−0.00507274
$963$	−54.9154	−1.76962
$964$	3.59221	0.115697
$965$	0	0
$966$	1.19626	0.0384892
$967$	−28.2285	−0.907769	−0.453884	−	0.891061i	$-0.649962\pi$
$967$	−28.2285	−0.907769	−0.453884	+	0.891061i	$0.649962\pi$
$968$	−2.69562	−0.0866404
$969$	−53.4291	−1.71639
$970$	0	0
$971$	−9.10293	−0.292127	−0.146063	−	0.989275i	$-0.546660\pi$
$971$	−9.10293	−0.292127	−0.146063	+	0.989275i	$0.546660\pi$
$972$	−7.24842	−0.232493
$973$	11.2965	0.362150
$974$	2.26116	0.0724524
$975$	0	0
$976$	57.2400	1.83221
$977$	19.0197	0.608493	0.304247	−	0.952593i	$-0.401595\pi$
$977$	19.0197	0.608493	0.304247	+	0.952593i	$0.401595\pi$
$978$	0.391682	0.0125246
$979$	−15.8145	−0.505433
$980$	0	0
$981$	−73.5470	−2.34817
$982$	3.30505	0.105469
$983$	−16.9312	−0.540021	−0.270011	−	0.962857i	$-0.587027\pi$
$983$	−16.9312	−0.540021	−0.270011	+	0.962857i	$0.587027\pi$
$984$	3.07928	0.0981639
$985$	0	0
$986$	1.12082	0.0356942
$987$	−2.38586	−0.0759426
$988$	3.32483	0.105777
$989$	55.9323	1.77854
$990$	0	0
$991$	−21.0761	−0.669504	−0.334752	−	0.942306i	$-0.608653\pi$
$991$	−21.0761	−0.669504	−0.334752	+	0.942306i	$0.608653\pi$
$992$	1.57828	0.0501103
$993$	55.0212	1.74605
$994$	0.445829	0.0141408
$995$	0	0
$996$	−4.89262	−0.155028
$997$	−39.0731	−1.23746	−0.618729	−	0.785604i	$-0.712352\pi$
$997$	−39.0731	−1.23746	−0.618729	+	0.785604i	$0.712352\pi$
$998$	−0.971568	−0.0307545
$999$	−54.5485	−1.72584

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1175.2.a.h.1.4		7
5.2	odd	4		1175.2.c.g.424.7		14
5.3	odd	4		1175.2.c.g.424.8		14
5.4	even	2		235.2.a.e.1.4	✓	7
15.14	odd	2		2115.2.a.v.1.4		7
20.19	odd	2		3760.2.a.bi.1.7		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
235.2.a.e.1.4	✓	7	5.4	even	2
1175.2.a.h.1.4		7	1.1	even	1	trivial
1175.2.c.g.424.7		14	5.2	odd	4
1175.2.c.g.424.8		14	5.3	odd	4
2115.2.a.v.1.4		7	15.14	odd	2
3760.2.a.bi.1.7		7	20.19	odd	2

Overview	Random
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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:	\( N \)	\(=\)	\( 1175 = 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1175.a (trivial)

\(f(q)\)	\(=\)	\(q-0.0980806 q^{2} +3.03215 q^{3} -1.99038 q^{4} -0.297395 q^{6} -0.786854 q^{7} +0.391379 q^{8} +6.19391 q^{9} +O(q^{10})\)	\(q-0.0980806 q^{2} +3.03215 q^{3} -1.99038 q^{4} -0.297395 q^{6} -0.786854 q^{7} +0.391379 q^{8} +6.19391 q^{9} +2.02793 q^{11} -6.03512 q^{12} -0.284798 q^{13} +0.0771751 q^{14} +3.94237 q^{16} -3.00421 q^{17} -0.607502 q^{18} +5.86539 q^{19} -2.38586 q^{21} -0.198901 q^{22} +5.11211 q^{23} +1.18672 q^{24} +0.0279331 q^{26} +9.68439 q^{27} +1.56614 q^{28} +3.80384 q^{29} -1.34961 q^{31} -1.16943 q^{32} +6.14899 q^{33} +0.294655 q^{34} -12.3282 q^{36} -5.63262 q^{37} -0.575281 q^{38} -0.863548 q^{39} +2.59479 q^{41} +0.234006 q^{42} +10.9411 q^{43} -4.03636 q^{44} -0.501398 q^{46} +1.00000 q^{47} +11.9539 q^{48} -6.38086 q^{49} -9.10921 q^{51} +0.566856 q^{52} -13.4823 q^{53} -0.949850 q^{54} -0.307958 q^{56} +17.7847 q^{57} -0.373083 q^{58} +14.5219 q^{59} +14.5192 q^{61} +0.132371 q^{62} -4.87370 q^{63} -7.77005 q^{64} -0.603096 q^{66} +3.02108 q^{67} +5.97952 q^{68} +15.5006 q^{69} +5.77685 q^{71} +2.42416 q^{72} -12.4386 q^{73} +0.552450 q^{74} -11.6744 q^{76} -1.59569 q^{77} +0.0846973 q^{78} -11.1604 q^{79} +10.7828 q^{81} -0.254498 q^{82} +0.810691 q^{83} +4.74876 q^{84} -1.07311 q^{86} +11.5338 q^{87} +0.793690 q^{88} -7.79832 q^{89} +0.224094 q^{91} -10.1750 q^{92} -4.09222 q^{93} -0.0980806 q^{94} -3.54587 q^{96} +12.1257 q^{97} +0.625838 q^{98} +12.5608 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} - q^{3} + 7 q^{4} + q^{6} + 3 q^{7} - 3 q^{8} + 10 q^{9}+O(q^{10}) \) 7 * q - q^2 - q^3 + 7 * q^4 + q^6 + 3 * q^7 - 3 * q^8 + 10 * q^9	\( 7 q - q^{2} - q^{3} + 7 q^{4} + q^{6} + 3 q^{7} - 3 q^{8} + 10 q^{9} + q^{11} + 4 q^{12} - 2 q^{13} + 10 q^{14} - q^{16} - 12 q^{17} + 17 q^{18} + 3 q^{19} + 7 q^{21} + 5 q^{22} - q^{23} + 8 q^{24} - 13 q^{26} - q^{27} + 27 q^{28} + 26 q^{29} - 5 q^{31} - 12 q^{32} + 15 q^{33} + 6 q^{34} - 34 q^{36} + 7 q^{38} + q^{39} + 12 q^{41} + 18 q^{42} + 33 q^{43} + 3 q^{44} - 36 q^{46} + 7 q^{47} + 25 q^{48} + 6 q^{49} - 14 q^{51} + 11 q^{52} - 4 q^{53} - 2 q^{54} - 27 q^{56} + 21 q^{57} + 38 q^{58} + 13 q^{59} + 20 q^{61} - 15 q^{62} + 10 q^{63} - 9 q^{64} - 41 q^{66} + 32 q^{67} - 15 q^{68} + 16 q^{69} + 11 q^{71} + 8 q^{72} + 8 q^{73} + 48 q^{74} + 11 q^{76} - 29 q^{77} + 17 q^{78} + 17 q^{79} + 15 q^{81} - 6 q^{82} - 19 q^{83} + 46 q^{84} - 30 q^{86} - 2 q^{87} - 7 q^{88} + 13 q^{89} - 11 q^{91} - 16 q^{92} + 29 q^{93} - q^{94} - 29 q^{96} + 12 q^{97} - 6 q^{98} - 32 q^{99}+O(q^{100}) \) 7 * q - q^2 - q^3 + 7 * q^4 + q^6 + 3 * q^7 - 3 * q^8 + 10 * q^9 + q^11 + 4 * q^12 - 2 * q^13 + 10 * q^14 - q^16 - 12 * q^17 + 17 * q^18 + 3 * q^19 + 7 * q^21 + 5 * q^22 - q^23 + 8 * q^24 - 13 * q^26 - q^27 + 27 * q^28 + 26 * q^29 - 5 * q^31 - 12 * q^32 + 15 * q^33 + 6 * q^34 - 34 * q^36 + 7 * q^38 + q^39 + 12 * q^41 + 18 * q^42 + 33 * q^43 + 3 * q^44 - 36 * q^46 + 7 * q^47 + 25 * q^48 + 6 * q^49 - 14 * q^51 + 11 * q^52 - 4 * q^53 - 2 * q^54 - 27 * q^56 + 21 * q^57 + 38 * q^58 + 13 * q^59 + 20 * q^61 - 15 * q^62 + 10 * q^63 - 9 * q^64 - 41 * q^66 + 32 * q^67 - 15 * q^68 + 16 * q^69 + 11 * q^71 + 8 * q^72 + 8 * q^73 + 48 * q^74 + 11 * q^76 - 29 * q^77 + 17 * q^78 + 17 * q^79 + 15 * q^81 - 6 * q^82 - 19 * q^83 + 46 * q^84 - 30 * q^86 - 2 * q^87 - 7 * q^88 + 13 * q^89 - 11 * q^91 - 16 * q^92 + 29 * q^93 - q^94 - 29 * q^96 + 12 * q^97 - 6 * q^98 - 32 * q^99

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