LMFDB - Embedded newform 1075.2.a.p.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1075,2,Mod(1,1075)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1075, 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("1075.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1075 = 5^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1075.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:	$8.58391821729$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.32503921.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 5x^{4} + 13x^{3} + 9x^{2} - 11x - 7 $ x^6 - 3x^5 - 5x^4 + 13x^3 + 9x^2 - 11*x - 7
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 215)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.72658$ of defining polynomial
Character	$\chi$	$=$	1075.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.72658 q^{2} +0.195967 q^{3} +5.43426 q^{4} -0.534322 q^{6} +2.90692 q^{7} -9.36379 q^{8} -2.96160 q^{9} +O(q^{10})$	\(q-2.72658 q^{2} +0.195967 q^{3} +5.43426 q^{4} -0.534322 q^{6} +2.90692 q^{7} -9.36379 q^{8} -2.96160 q^{9} +0.418923 q^{11} +1.06494 q^{12} +3.45317 q^{13} -7.92596 q^{14} +14.6626 q^{16} -5.68396 q^{17} +8.07504 q^{18} -4.52181 q^{19} +0.569662 q^{21} -1.14223 q^{22} -5.80728 q^{23} -1.83500 q^{24} -9.41535 q^{26} -1.16828 q^{27} +15.7970 q^{28} -3.10646 q^{29} -2.95215 q^{31} -21.2514 q^{32} +0.0820953 q^{33} +15.4978 q^{34} -16.0941 q^{36} -11.2093 q^{37} +12.3291 q^{38} +0.676708 q^{39} +0.464582 q^{41} -1.55323 q^{42} -1.00000 q^{43} +2.27654 q^{44} +15.8340 q^{46} +6.75261 q^{47} +2.87340 q^{48} +1.45018 q^{49} -1.11387 q^{51} +18.7654 q^{52} +13.2292 q^{53} +3.18541 q^{54} -27.2198 q^{56} -0.886128 q^{57} +8.47003 q^{58} -4.42676 q^{59} +11.6664 q^{61} +8.04928 q^{62} -8.60913 q^{63} +28.6183 q^{64} -0.223840 q^{66} -6.40590 q^{67} -30.8881 q^{68} -1.13804 q^{69} +0.0452288 q^{71} +27.7318 q^{72} -15.0645 q^{73} +30.5632 q^{74} -24.5727 q^{76} +1.21778 q^{77} -1.84510 q^{78} -11.2496 q^{79} +8.65585 q^{81} -1.26672 q^{82} +10.2370 q^{83} +3.09569 q^{84} +2.72658 q^{86} -0.608765 q^{87} -3.92271 q^{88} +4.96944 q^{89} +10.0381 q^{91} -31.5583 q^{92} -0.578525 q^{93} -18.4116 q^{94} -4.16457 q^{96} -2.50160 q^{97} -3.95405 q^{98} -1.24068 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 4 q^{3} + 7 q^{4} - 8 q^{7} - 9 q^{8} + 8 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - 4 * q^3 + 7 * q^4 - 8 * q^7 - 9 * q^8 + 8 * q^9	$ 6 q - 3 q^{2} - 4 q^{3} + 7 q^{4} - 8 q^{7} - 9 q^{8} + 8 q^{9} - 5 q^{12} - 6 q^{13} - 4 q^{14} + 5 q^{16} - 6 q^{17} + 11 q^{18} + 6 q^{19} - 12 q^{21} + q^{22} - 32 q^{26} - 10 q^{27} + 10 q^{28} - 10 q^{29} - 11 q^{32} - 6 q^{33} + 14 q^{34} - 41 q^{36} - 28 q^{37} + 6 q^{38} + 8 q^{39} - 6 q^{41} - 5 q^{42} - 6 q^{43} + 4 q^{44} - 8 q^{46} + 6 q^{47} + 32 q^{48} + 20 q^{49} - 8 q^{51} + 16 q^{52} + 4 q^{53} - 5 q^{54} - 35 q^{56} - 4 q^{57} + 26 q^{58} - 20 q^{59} - 8 q^{61} - 2 q^{62} + 2 q^{63} + 17 q^{64} - 35 q^{66} - 22 q^{67} - 22 q^{68} - 42 q^{69} + 8 q^{71} + 2 q^{72} - 34 q^{73} + 45 q^{74} - 16 q^{76} - 8 q^{77} + 26 q^{78} - 16 q^{79} + 46 q^{81} - 22 q^{82} + 14 q^{83} + 37 q^{84} + 3 q^{86} + 2 q^{87} - 20 q^{88} + 24 q^{91} - 46 q^{92} - 30 q^{93} + 12 q^{94} - 23 q^{96} - 34 q^{97} - 32 q^{98} - 16 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 4 * q^3 + 7 * q^4 - 8 * q^7 - 9 * q^8 + 8 * q^9 - 5 * q^12 - 6 * q^13 - 4 * q^14 + 5 * q^16 - 6 * q^17 + 11 * q^18 + 6 * q^19 - 12 * q^21 + q^22 - 32 * q^26 - 10 * q^27 + 10 * q^28 - 10 * q^29 - 11 * q^32 - 6 * q^33 + 14 * q^34 - 41 * q^36 - 28 * q^37 + 6 * q^38 + 8 * q^39 - 6 * q^41 - 5 * q^42 - 6 * q^43 + 4 * q^44 - 8 * q^46 + 6 * q^47 + 32 * q^48 + 20 * q^49 - 8 * q^51 + 16 * q^52 + 4 * q^53 - 5 * q^54 - 35 * q^56 - 4 * q^57 + 26 * q^58 - 20 * q^59 - 8 * q^61 - 2 * q^62 + 2 * q^63 + 17 * q^64 - 35 * q^66 - 22 * q^67 - 22 * q^68 - 42 * q^69 + 8 * q^71 + 2 * q^72 - 34 * q^73 + 45 * q^74 - 16 * q^76 - 8 * q^77 + 26 * q^78 - 16 * q^79 + 46 * q^81 - 22 * q^82 + 14 * q^83 + 37 * q^84 + 3 * q^86 + 2 * q^87 - 20 * q^88 + 24 * q^91 - 46 * q^92 - 30 * q^93 + 12 * q^94 - 23 * q^96 - 34 * q^97 - 32 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.72658	−1.92799	−0.963993	−	0.265928i	$-0.914322\pi$
$2$	−2.72658	−1.92799	−0.963993	+	0.265928i	$0.914322\pi$
$3$	0.195967	0.113142	0.0565709	−	0.998399i	$-0.481983\pi$
$3$	0.195967	0.113142	0.0565709	+	0.998399i	$0.481983\pi$
$4$	5.43426	2.71713
$5$	0	0
$5$	0	0
$6$	−0.534322	−0.218136
$7$	2.90692	1.09871	0.549356	−	0.835588i	$-0.314873\pi$
$7$	2.90692	1.09871	0.549356	+	0.835588i	$0.314873\pi$
$8$	−9.36379	−3.31060
$9$	−2.96160	−0.987199
$10$	0	0
$11$	0.418923	0.126310	0.0631550	−	0.998004i	$-0.479884\pi$
$11$	0.418923	0.126310	0.0631550	+	0.998004i	$0.479884\pi$
$12$	1.06494	0.307421
$13$	3.45317	0.957736	0.478868	−	0.877887i	$-0.341047\pi$
$13$	3.45317	0.957736	0.478868	+	0.877887i	$0.341047\pi$
$14$	−7.92596	−2.11830
$15$	0	0
$16$	14.6626	3.66566
$17$	−5.68396	−1.37856	−0.689282	−	0.724493i	$-0.742074\pi$
$17$	−5.68396	−1.37856	−0.689282	+	0.724493i	$0.742074\pi$
$18$	8.07504	1.90331
$19$	−4.52181	−1.03737	−0.518687	−	0.854964i	$-0.673579\pi$
$19$	−4.52181	−1.03737	−0.518687	+	0.854964i	$0.673579\pi$
$20$	0	0
$21$	0.569662	0.124310
$22$	−1.14223	−0.243524
$23$	−5.80728	−1.21090	−0.605451	−	0.795882i	$-0.707007\pi$
$23$	−5.80728	−1.21090	−0.605451	+	0.795882i	$0.707007\pi$
$24$	−1.83500	−0.374568
$25$	0	0
$26$	−9.41535	−1.84650
$27$	−1.16828	−0.224835
$28$	15.7970	2.98534
$29$	−3.10646	−0.576855	−0.288428	−	0.957502i	$-0.593132\pi$
$29$	−3.10646	−0.576855	−0.288428	+	0.957502i	$0.593132\pi$
$30$	0	0
$31$	−2.95215	−0.530222	−0.265111	−	0.964218i	$-0.585409\pi$
$31$	−2.95215	−0.530222	−0.265111	+	0.964218i	$0.585409\pi$
$32$	−21.2514	−3.75674
$33$	0.0820953	0.0142910
$34$	15.4978	2.65785
$35$	0	0
$36$	−16.0941	−2.68235
$37$	−11.2093	−1.84281	−0.921403	−	0.388609i	$-0.872956\pi$
$37$	−11.2093	−1.84281	−0.921403	+	0.388609i	$0.872956\pi$
$38$	12.3291	2.00004
$39$	0.676708	0.108360
$40$	0	0
$41$	0.464582	0.0725556	0.0362778	−	0.999342i	$-0.488450\pi$
$41$	0.464582	0.0725556	0.0362778	+	0.999342i	$0.488450\pi$
$42$	−1.55323	−0.239669
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	2.27654	0.343201
$45$	0	0
$46$	15.8340	2.33460
$47$	6.75261	0.984969	0.492485	−	0.870321i	$-0.336089\pi$
$47$	6.75261	0.984969	0.492485	+	0.870321i	$0.336089\pi$
$48$	2.87340	0.414740
$49$	1.45018	0.207169
$50$	0	0
$51$	−1.11387	−0.155973
$52$	18.7654	2.60229
$53$	13.2292	1.81717	0.908584	−	0.417701i	$-0.137164\pi$
$53$	13.2292	1.81717	0.908584	+	0.417701i	$0.137164\pi$
$54$	3.18541	0.433479
$55$	0	0
$56$	−27.2198	−3.63740
$57$	−0.886128	−0.117370
$58$	8.47003	1.11217
$59$	−4.42676	−0.576316	−0.288158	−	0.957583i	$-0.593043\pi$
$59$	−4.42676	−0.576316	−0.288158	+	0.957583i	$0.593043\pi$
$60$	0	0
$61$	11.6664	1.49372	0.746862	−	0.664979i	$-0.231560\pi$
$61$	11.6664	1.49372	0.746862	+	0.664979i	$0.231560\pi$
$62$	8.04928	1.02226
$63$	−8.60913	−1.08465
$64$	28.6183	3.57729
$65$	0	0
$66$	−0.223840	−0.0275528
$67$	−6.40590	−0.782605	−0.391303	−	0.920262i	$-0.627975\pi$
$67$	−6.40590	−0.782605	−0.391303	+	0.920262i	$0.627975\pi$
$68$	−30.8881	−3.74574
$69$	−1.13804	−0.137004
$70$	0	0
$71$	0.0452288	0.00536767	0.00268383	−	0.999996i	$-0.499146\pi$
$71$	0.0452288	0.00536767	0.00268383	+	0.999996i	$0.499146\pi$
$72$	27.7318	3.26822
$73$	−15.0645	−1.76316	−0.881582	−	0.472030i	$-0.843521\pi$
$73$	−15.0645	−1.76316	−0.881582	+	0.472030i	$0.843521\pi$
$74$	30.5632	3.55290
$75$	0	0
$76$	−24.5727	−2.81868
$77$	1.21778	0.138778
$78$	−1.84510	−0.208917
$79$	−11.2496	−1.26568	−0.632841	−	0.774282i	$-0.718111\pi$
$79$	−11.2496	−1.26568	−0.632841	+	0.774282i	$0.718111\pi$
$80$	0	0
$81$	8.65585	0.961761
$82$	−1.26672	−0.139886
$83$	10.2370	1.12366	0.561830	−	0.827252i	$-0.310097\pi$
$83$	10.2370	1.12366	0.561830	+	0.827252i	$0.310097\pi$
$84$	3.09569	0.337767
$85$	0	0
$86$	2.72658	0.294015
$87$	−0.608765	−0.0652665
$88$	−3.92271	−0.418162
$89$	4.96944	0.526759	0.263380	−	0.964692i	$-0.415163\pi$
$89$	4.96944	0.526759	0.263380	+	0.964692i	$0.415163\pi$
$90$	0	0
$91$	10.0381	1.05228
$92$	−31.5583	−3.29018
$93$	−0.578525	−0.0599903
$94$	−18.4116	−1.89901
$95$	0	0
$96$	−4.16457	−0.425045
$97$	−2.50160	−0.253999	−0.127000	−	0.991903i	$-0.540535\pi$
$97$	−2.50160	−0.253999	−0.127000	+	0.991903i	$0.540535\pi$
$98$	−3.95405	−0.399419
$99$	−1.24068	−0.124693
$100$	0	0
$101$	−3.13090	−0.311536	−0.155768	−	0.987794i	$-0.549785\pi$
$101$	−3.13090	−0.311536	−0.155768	+	0.987794i	$0.549785\pi$
$102$	3.03707	0.300714
$103$	2.11489	0.208386	0.104193	−	0.994557i	$-0.466774\pi$
$103$	2.11489	0.208386	0.104193	+	0.994557i	$0.466774\pi$
$104$	−32.3347	−3.17068
$105$	0	0
$106$	−36.0705	−3.50348
$107$	−13.7749	−1.33167	−0.665833	−	0.746101i	$-0.731924\pi$
$107$	−13.7749	−1.33167	−0.665833	+	0.746101i	$0.731924\pi$
$108$	−6.34873	−0.610907
$109$	−1.96160	−0.187887	−0.0939434	−	0.995578i	$-0.529947\pi$
$109$	−1.96160	−0.187887	−0.0939434	+	0.995578i	$0.529947\pi$
$110$	0	0
$111$	−2.19667	−0.208498
$112$	42.6231	4.02751
$113$	−5.22296	−0.491334	−0.245667	−	0.969354i	$-0.579007\pi$
$113$	−5.22296	−0.491334	−0.245667	+	0.969354i	$0.579007\pi$
$114$	2.41610	0.226289
$115$	0	0
$116$	−16.8813	−1.56739
$117$	−10.2269	−0.945476
$118$	12.0699	1.11113
$119$	−16.5228	−1.51465
$120$	0	0
$121$	−10.8245	−0.984046
$122$	−31.8093	−2.87988
$123$	0.0910430	0.00820908
$124$	−16.0427	−1.44068
$125$	0	0
$126$	23.4735	2.09119
$127$	11.7308	1.04094	0.520470	−	0.853880i	$-0.325757\pi$
$127$	11.7308	1.04094	0.520470	+	0.853880i	$0.325757\pi$
$128$	−35.5275	−3.14021
$129$	−0.195967	−0.0172540
$130$	0	0
$131$	−21.7888	−1.90370	−0.951849	−	0.306567i	$-0.900820\pi$
$131$	−21.7888	−1.90370	−0.951849	+	0.306567i	$0.900820\pi$
$132$	0.446127	0.0388304
$133$	−13.1445	−1.13978
$134$	17.4662	1.50885
$135$	0	0
$136$	53.2235	4.56387
$137$	−14.2806	−1.22008	−0.610038	−	0.792372i	$-0.708846\pi$
$137$	−14.2806	−1.22008	−0.610038	+	0.792372i	$0.708846\pi$
$138$	3.10296	0.264141
$139$	2.47957	0.210314	0.105157	−	0.994456i	$-0.466465\pi$
$139$	2.47957	0.210314	0.105157	+	0.994456i	$0.466465\pi$
$140$	0	0
$141$	1.32329	0.111441
$142$	−0.123320	−0.0103488
$143$	1.44661	0.120972
$144$	−43.4249	−3.61874
$145$	0	0
$146$	41.0746	3.39936
$147$	0.284189	0.0234395
$148$	−60.9145	−5.00714
$149$	0.521811	0.0427484	0.0213742	−	0.999772i	$-0.493196\pi$
$149$	0.521811	0.0427484	0.0213742	+	0.999772i	$0.493196\pi$
$150$	0	0
$151$	14.2510	1.15973	0.579865	−	0.814712i	$-0.303105\pi$
$151$	14.2510	1.15973	0.579865	+	0.814712i	$0.303105\pi$
$152$	42.3413	3.43433
$153$	16.8336	1.36092
$154$	−3.32037	−0.267563
$155$	0	0
$156$	3.67741	0.294428
$157$	6.99482	0.558248	0.279124	−	0.960255i	$-0.409956\pi$
$157$	6.99482	0.558248	0.279124	+	0.960255i	$0.409956\pi$
$158$	30.6730	2.44022
$159$	2.59249	0.205598
$160$	0	0
$161$	−16.8813	−1.33043
$162$	−23.6009	−1.85426
$163$	−14.5252	−1.13770	−0.568852	−	0.822440i	$-0.692612\pi$
$163$	−14.5252	−1.13770	−0.568852	+	0.822440i	$0.692612\pi$
$164$	2.52466	0.197143
$165$	0	0
$166$	−27.9121	−2.16640
$167$	4.05178	0.313537	0.156768	−	0.987635i	$-0.449892\pi$
$167$	4.05178	0.313537	0.156768	+	0.987635i	$0.449892\pi$
$168$	−5.33420	−0.411542
$169$	−1.07564	−0.0827412
$170$	0	0
$171$	13.3918	1.02410
$172$	−5.43426	−0.414358
$173$	1.56908	0.119295	0.0596473	−	0.998220i	$-0.481002\pi$
$173$	1.56908	0.119295	0.0596473	+	0.998220i	$0.481002\pi$
$174$	1.65985	0.125833
$175$	0	0
$176$	6.14252	0.463010
$177$	−0.867502	−0.0652054
$178$	−13.5496	−1.01558
$179$	−9.31588	−0.696302	−0.348151	−	0.937439i	$-0.613190\pi$
$179$	−9.31588	−0.696302	−0.348151	+	0.937439i	$0.613190\pi$
$180$	0	0
$181$	6.19511	0.460479	0.230240	−	0.973134i	$-0.426049\pi$
$181$	6.19511	0.460479	0.230240	+	0.973134i	$0.426049\pi$
$182$	−27.3697	−2.02877
$183$	2.28623	0.169003
$184$	54.3782	4.00881
$185$	0	0
$186$	1.57740	0.115660
$187$	−2.38114	−0.174126
$188$	36.6954	2.67629
$189$	−3.39609	−0.247029
$190$	0	0
$191$	−12.3133	−0.890956	−0.445478	−	0.895293i	$-0.646966\pi$
$191$	−12.3133	−0.890956	−0.445478	+	0.895293i	$0.646966\pi$
$192$	5.60825	0.404741
$193$	1.14454	0.0823860	0.0411930	−	0.999151i	$-0.486884\pi$
$193$	1.14454	0.0823860	0.0411930	+	0.999151i	$0.486884\pi$
$194$	6.82083	0.489707
$195$	0	0
$196$	7.88068	0.562906
$197$	15.1595	1.08007	0.540036	−	0.841642i	$-0.318411\pi$
$197$	15.1595	1.08007	0.540036	+	0.841642i	$0.318411\pi$
$198$	3.38282	0.240407
$199$	−18.2194	−1.29154	−0.645770	−	0.763532i	$-0.723464\pi$
$199$	−18.2194	−1.29154	−0.645770	+	0.763532i	$0.723464\pi$
$200$	0	0
$201$	−1.25535	−0.0885454
$202$	8.53665	0.600637
$203$	−9.03023	−0.633798
$204$	−6.05307	−0.423800
$205$	0	0
$206$	−5.76642	−0.401766
$207$	17.1988	1.19540
$208$	50.6326	3.51074
$209$	−1.89429	−0.131031
$210$	0	0
$211$	−16.0974	−1.10819	−0.554097	−	0.832452i	$-0.686936\pi$
$211$	−16.0974	−1.10819	−0.554097	+	0.832452i	$0.686936\pi$
$212$	71.8908	4.93748
$213$	0.00886336	0.000607308 0
$214$	37.5583	2.56743
$215$	0	0
$216$	10.9395	0.744340
$217$	−8.58166	−0.582561
$218$	5.34846	0.362243
$219$	−2.95215	−0.199488
$220$	0	0
$221$	−19.6277	−1.32030
$222$	5.98940	0.401982
$223$	−6.39704	−0.428377	−0.214189	−	0.976792i	$-0.568711\pi$
$223$	−6.39704	−0.428377	−0.214189	+	0.976792i	$0.568711\pi$
$224$	−61.7760	−4.12758
$225$	0	0
$226$	14.2408	0.947286
$227$	12.1556	0.806795	0.403398	−	0.915025i	$-0.367829\pi$
$227$	12.1556	0.806795	0.403398	+	0.915025i	$0.367829\pi$
$228$	−4.81545	−0.318911
$229$	15.9685	1.05523	0.527615	−	0.849484i	$-0.323087\pi$
$229$	15.9685	1.05523	0.527615	+	0.849484i	$0.323087\pi$
$230$	0	0
$231$	0.238644	0.0157017
$232$	29.0883	1.90974
$233$	−0.653654	−0.0428223	−0.0214111	−	0.999771i	$-0.506816\pi$
$233$	−0.653654	−0.0428223	−0.0214111	+	0.999771i	$0.506816\pi$
$234$	27.8845	1.82286
$235$	0	0
$236$	−24.0562	−1.56592
$237$	−2.20456	−0.143202
$238$	45.0509	2.92021
$239$	0.662420	0.0428484	0.0214242	−	0.999770i	$-0.493180\pi$
$239$	0.662420	0.0428484	0.0214242	+	0.999770i	$0.493180\pi$
$240$	0	0
$241$	10.5533	0.679800	0.339900	−	0.940462i	$-0.389607\pi$
$241$	10.5533	0.679800	0.339900	+	0.940462i	$0.389607\pi$
$242$	29.5139	1.89723
$243$	5.20110	0.333651
$244$	63.3980	4.05864
$245$	0	0
$246$	−0.248236	−0.0158270
$247$	−15.6146	−0.993531
$248$	27.6433	1.75535
$249$	2.00613	0.127133
$250$	0	0
$251$	8.35021	0.527061	0.263530	−	0.964651i	$-0.415113\pi$
$251$	8.35021	0.527061	0.263530	+	0.964651i	$0.415113\pi$
$252$	−46.7842	−2.94713
$253$	−2.43281	−0.152949
$254$	−31.9850	−2.00692
$255$	0	0
$256$	39.6320	2.47700
$257$	−23.3872	−1.45885	−0.729426	−	0.684059i	$-0.760213\pi$
$257$	−23.3872	−1.45885	−0.729426	+	0.684059i	$0.760213\pi$
$258$	0.534322	0.0332654
$259$	−32.5847	−2.02471
$260$	0	0
$261$	9.20009	0.569471
$262$	59.4090	3.67030
$263$	23.5063	1.44946	0.724731	−	0.689032i	$-0.241964\pi$
$263$	23.5063	1.44946	0.724731	+	0.689032i	$0.241964\pi$
$264$	−0.768723	−0.0473117
$265$	0	0
$266$	35.8397	2.19747
$267$	0.973848	0.0595985
$268$	−34.8113	−2.12644
$269$	−16.4430	−1.00255	−0.501275	−	0.865288i	$-0.667135\pi$
$269$	−16.4430	−1.00255	−0.501275	+	0.865288i	$0.667135\pi$
$270$	0	0
$271$	−1.46388	−0.0889245	−0.0444623	−	0.999011i	$-0.514157\pi$
$271$	−1.46388	−0.0889245	−0.0444623	+	0.999011i	$0.514157\pi$
$272$	−83.3420	−5.05335
$273$	1.96714	0.119057
$274$	38.9373	2.35229
$275$	0	0
$276$	−6.18440	−0.372257
$277$	20.2543	1.21696	0.608482	−	0.793567i	$-0.291779\pi$
$277$	20.2543	1.21696	0.608482	+	0.793567i	$0.291779\pi$
$278$	−6.76075	−0.405483
$279$	8.74307	0.523434
$280$	0	0
$281$	8.22433	0.490623	0.245311	−	0.969444i	$-0.421110\pi$
$281$	8.22433	0.490623	0.245311	+	0.969444i	$0.421110\pi$
$282$	−3.60807	−0.214857
$283$	26.2663	1.56137	0.780683	−	0.624927i	$-0.214871\pi$
$283$	26.2663	1.56137	0.780683	+	0.624927i	$0.214871\pi$
$284$	0.245785	0.0145846
$285$	0	0
$286$	−3.94431	−0.233232
$287$	1.35050	0.0797177
$288$	62.9379	3.70865
$289$	15.3075	0.900438
$290$	0	0
$291$	−0.490233	−0.0287380
$292$	−81.8643	−4.79075
$293$	−27.1338	−1.58517	−0.792585	−	0.609761i	$-0.791265\pi$
$293$	−27.1338	−1.58517	−0.792585	+	0.609761i	$0.791265\pi$
$294$	−0.774865	−0.0451911
$295$	0	0
$296$	104.962	6.10079
$297$	−0.489419	−0.0283990
$298$	−1.42276	−0.0824183
$299$	−20.0535	−1.15973
$300$	0	0
$301$	−2.90692	−0.167552
$302$	−38.8566	−2.23594
$303$	−0.613554	−0.0352478
$304$	−66.3017	−3.80266
$305$	0	0
$306$	−45.8982	−2.62383
$307$	−10.7440	−0.613194	−0.306597	−	0.951839i	$-0.599190\pi$
$307$	−10.7440	−0.613194	−0.306597	+	0.951839i	$0.599190\pi$
$308$	6.61771	0.377079
$309$	0.414449	0.0235772
$310$	0	0
$311$	29.2154	1.65665	0.828327	−	0.560244i	$-0.189293\pi$
$311$	29.2154	1.65665	0.828327	+	0.560244i	$0.189293\pi$
$312$	−6.33656	−0.358737
$313$	−20.5141	−1.15952	−0.579762	−	0.814786i	$-0.696855\pi$
$313$	−20.5141	−1.15952	−0.579762	+	0.814786i	$0.696855\pi$
$314$	−19.0720	−1.07629
$315$	0	0
$316$	−61.1334	−3.43902
$317$	10.6736	0.599490	0.299745	−	0.954019i	$-0.403098\pi$
$317$	10.6736	0.599490	0.299745	+	0.954019i	$0.403098\pi$
$318$	−7.06864	−0.396390
$319$	−1.30137	−0.0728626
$320$	0	0
$321$	−2.69942	−0.150667
$322$	46.0283	2.56506
$323$	25.7018	1.43009
$324$	47.0381	2.61323
$325$	0	0
$326$	39.6043	2.19348
$327$	−0.384409	−0.0212579
$328$	−4.35025	−0.240203
$329$	19.6293	1.08220
$330$	0	0
$331$	0.671489	0.0369084	0.0184542	−	0.999830i	$-0.494126\pi$
$331$	0.671489	0.0369084	0.0184542	+	0.999830i	$0.494126\pi$
$332$	55.6307	3.05313
$333$	33.1976	1.81922
$334$	−11.0475	−0.604494
$335$	0	0
$336$	8.35275	0.455680
$337$	−8.47222	−0.461511	−0.230756	−	0.973012i	$-0.574120\pi$
$337$	−8.47222	−0.461511	−0.230756	+	0.973012i	$0.574120\pi$
$338$	2.93281	0.159524
$339$	−1.02353	−0.0555905
$340$	0	0
$341$	−1.23672	−0.0669723
$342$	−36.5138	−1.97444
$343$	−16.1329	−0.871093
$344$	9.36379	0.504862
$345$	0	0
$346$	−4.27822	−0.229998
$347$	10.3740	0.556903	0.278452	−	0.960450i	$-0.410179\pi$
$347$	10.3740	0.556903	0.278452	+	0.960450i	$0.410179\pi$
$348$	−3.30819	−0.177338
$349$	1.05468	0.0564555	0.0282278	−	0.999602i	$-0.491014\pi$
$349$	1.05468	0.0564555	0.0282278	+	0.999602i	$0.491014\pi$
$350$	0	0
$351$	−4.03426	−0.215333
$352$	−8.90268	−0.474515
$353$	−6.74739	−0.359127	−0.179564	−	0.983746i	$-0.557469\pi$
$353$	−6.74739	−0.359127	−0.179564	+	0.983746i	$0.557469\pi$
$354$	2.36532	0.125715
$355$	0	0
$356$	27.0052	1.43127
$357$	−3.23794	−0.171370
$358$	25.4005	1.34246
$359$	30.6245	1.61630	0.808149	−	0.588978i	$-0.200470\pi$
$359$	30.6245	1.61630	0.808149	+	0.588978i	$0.200470\pi$
$360$	0	0
$361$	1.44677	0.0761459
$362$	−16.8915	−0.887797
$363$	−2.12125	−0.111337
$364$	54.5495	2.85917
$365$	0	0
$366$	−6.23359	−0.325835
$367$	16.4843	0.860472	0.430236	−	0.902716i	$-0.358430\pi$
$367$	16.4843	0.860472	0.430236	+	0.902716i	$0.358430\pi$
$368$	−85.1502	−4.43876
$369$	−1.37591	−0.0716268
$370$	0	0
$371$	38.4562	1.99655
$372$	−3.14386	−0.163001
$373$	−28.5277	−1.47711	−0.738555	−	0.674193i	$-0.764491\pi$
$373$	−28.5277	−1.47711	−0.738555	+	0.674193i	$0.764491\pi$
$374$	6.49239	0.335713
$375$	0	0
$376$	−63.2300	−3.26084
$377$	−10.7271	−0.552475
$378$	9.25973	0.476269
$379$	23.7237	1.21860	0.609302	−	0.792938i	$-0.291450\pi$
$379$	23.7237	1.21860	0.609302	+	0.792938i	$0.291450\pi$
$380$	0	0
$381$	2.29885	0.117774
$382$	33.5731	1.71775
$383$	−15.4734	−0.790656	−0.395328	−	0.918540i	$-0.629369\pi$
$383$	−15.4734	−0.790656	−0.395328	+	0.918540i	$0.629369\pi$
$384$	−6.96223	−0.355290
$385$	0	0
$386$	−3.12069	−0.158839
$387$	2.96160	0.150546
$388$	−13.5944	−0.690149
$389$	−24.5757	−1.24604	−0.623020	−	0.782206i	$-0.714094\pi$
$389$	−24.5757	−1.24604	−0.623020	+	0.782206i	$0.714094\pi$
$390$	0	0
$391$	33.0084	1.66931
$392$	−13.5792	−0.685855
$393$	−4.26990	−0.215388
$394$	−41.3337	−2.08236
$395$	0	0
$396$	−6.74218	−0.338807
$397$	16.4718	0.826694	0.413347	−	0.910574i	$-0.364360\pi$
$397$	16.4718	0.826694	0.413347	+	0.910574i	$0.364360\pi$
$398$	49.6768	2.49007
$399$	−2.57590	−0.128956
$400$	0	0
$401$	−26.9520	−1.34592	−0.672958	−	0.739680i	$-0.734977\pi$
$401$	−26.9520	−1.34592	−0.672958	+	0.739680i	$0.734977\pi$
$402$	3.42281	0.170714
$403$	−10.1943	−0.507812
$404$	−17.0141	−0.846483
$405$	0	0
$406$	24.6217	1.22195
$407$	−4.69585	−0.232765
$408$	10.4301	0.516365
$409$	19.9119	0.984579	0.492289	−	0.870432i	$-0.336160\pi$
$409$	19.9119	0.984579	0.492289	+	0.870432i	$0.336160\pi$
$410$	0	0
$411$	−2.79854	−0.138042
$412$	11.4928	0.566212
$413$	−12.8683	−0.633205
$414$	−46.8941	−2.30472
$415$	0	0
$416$	−73.3845	−3.59797
$417$	0.485915	0.0237954
$418$	5.16494	0.252626
$419$	20.0092	0.977511	0.488756	−	0.872421i	$-0.337451\pi$
$419$	20.0092	0.977511	0.488756	+	0.872421i	$0.337451\pi$
$420$	0	0
$421$	−2.08433	−0.101584	−0.0507920	−	0.998709i	$-0.516175\pi$
$421$	−2.08433	−0.101584	−0.0507920	+	0.998709i	$0.516175\pi$
$422$	43.8910	2.13658
$423$	−19.9985	−0.972360
$424$	−123.875	−6.01592
$425$	0	0
$426$	−0.0241667	−0.00117088
$427$	33.9132	1.64117
$428$	−74.8561	−3.61831
$429$	0.283489	0.0136870
$430$	0	0
$431$	17.2895	0.832805	0.416402	−	0.909180i	$-0.363291\pi$
$431$	17.2895	0.832805	0.416402	+	0.909180i	$0.363291\pi$
$432$	−17.1301	−0.824171
$433$	−38.0117	−1.82672	−0.913362	−	0.407148i	$-0.866523\pi$
$433$	−38.0117	−1.82672	−0.913362	+	0.407148i	$0.866523\pi$
$434$	23.3986	1.12317
$435$	0	0
$436$	−10.6598	−0.510513
$437$	26.2594	1.25616
$438$	8.04928	0.384610
$439$	21.7588	1.03849	0.519245	−	0.854625i	$-0.326213\pi$
$439$	21.7588	1.03849	0.519245	+	0.854625i	$0.326213\pi$
$440$	0	0
$441$	−4.29486	−0.204517
$442$	53.5165	2.54552
$443$	9.42755	0.447917	0.223958	−	0.974599i	$-0.428102\pi$
$443$	9.42755	0.447917	0.223958	+	0.974599i	$0.428102\pi$
$444$	−11.9373	−0.566517
$445$	0	0
$446$	17.4421	0.825906
$447$	0.102258	0.00483663
$448$	83.1911	3.93041
$449$	0.391654	0.0184833	0.00924164	−	0.999957i	$-0.497058\pi$
$449$	0.391654	0.0184833	0.00924164	+	0.999957i	$0.497058\pi$
$450$	0	0
$451$	0.194624	0.00916450
$452$	−28.3829	−1.33502
$453$	2.79273	0.131214
$454$	−33.1433	−1.55549
$455$	0	0
$456$	8.29752	0.388567
$457$	−34.6017	−1.61860	−0.809300	−	0.587396i	$-0.800153\pi$
$457$	−34.6017	−1.61860	−0.809300	+	0.587396i	$0.800153\pi$
$458$	−43.5395	−2.03447
$459$	6.64046	0.309950
$460$	0	0
$461$	−25.3702	−1.18161	−0.590803	−	0.806816i	$-0.701189\pi$
$461$	−25.3702	−1.18161	−0.590803	+	0.806816i	$0.701189\pi$
$462$	−0.650684	−0.0302726
$463$	7.39899	0.343860	0.171930	−	0.985109i	$-0.445000\pi$
$463$	7.39899	0.343860	0.171930	+	0.985109i	$0.445000\pi$
$464$	−45.5489	−2.11456
$465$	0	0
$466$	1.78224	0.0825608
$467$	−21.3868	−0.989664	−0.494832	−	0.868989i	$-0.664770\pi$
$467$	−21.3868	−0.989664	−0.494832	+	0.868989i	$0.664770\pi$
$468$	−55.5756	−2.56898
$469$	−18.6214	−0.859858
$470$	0	0
$471$	1.37076	0.0631612
$472$	41.4513	1.90795
$473$	−0.418923	−0.0192621
$474$	6.01092	0.276091
$475$	0	0
$476$	−89.7893	−4.11549
$477$	−39.1795	−1.79391
$478$	−1.80614	−0.0826111
$479$	34.0234	1.55457	0.777284	−	0.629150i	$-0.216597\pi$
$479$	34.0234	1.55457	0.777284	+	0.629150i	$0.216597\pi$
$480$	0	0
$481$	−38.7078	−1.76492
$482$	−28.7746	−1.31065
$483$	−3.30819	−0.150528
$484$	−58.8231	−2.67378
$485$	0	0
$486$	−14.1812	−0.643274
$487$	−13.1300	−0.594976	−0.297488	−	0.954725i	$-0.596149\pi$
$487$	−13.1300	−0.594976	−0.297488	+	0.954725i	$0.596149\pi$
$488$	−109.241	−4.94512
$489$	−2.84647	−0.128722
$490$	0	0
$491$	−3.37758	−0.152428	−0.0762141	−	0.997091i	$-0.524283\pi$
$491$	−3.37758	−0.152428	−0.0762141	+	0.997091i	$0.524283\pi$
$492$	0.494751	0.0223051
$493$	17.6570	0.795232
$494$	42.5744	1.91551
$495$	0	0
$496$	−43.2863	−1.94361
$497$	0.131476	0.00589752
$498$	−5.46987	−0.245111
$499$	20.5550	0.920168	0.460084	−	0.887875i	$-0.347819\pi$
$499$	20.5550	0.920168	0.460084	+	0.887875i	$0.347819\pi$
$500$	0	0
$501$	0.794018	0.0354741
$502$	−22.7675	−1.01617
$503$	−11.7944	−0.525884	−0.262942	−	0.964812i	$-0.584693\pi$
$503$	−11.7944	−0.525884	−0.262942	+	0.964812i	$0.584693\pi$
$504$	80.6141	3.59084
$505$	0	0
$506$	6.63325	0.294884
$507$	−0.210790	−0.00936149
$508$	63.7482	2.82837
$509$	−0.239385	−0.0106106	−0.00530528	−	0.999986i	$-0.501689\pi$
$509$	−0.239385	−0.0106106	−0.00530528	+	0.999986i	$0.501689\pi$
$510$	0	0
$511$	−43.7913	−1.93721
$512$	−37.0051	−1.63541
$513$	5.28274	0.233239
$514$	63.7671	2.81265
$515$	0	0
$516$	−1.06494	−0.0468813
$517$	2.82882	0.124412
$518$	88.8449	3.90362
$519$	0.307488	0.0134972
$520$	0	0
$521$	0.960627	0.0420858	0.0210429	−	0.999779i	$-0.493301\pi$
$521$	0.960627	0.0420858	0.0210429	+	0.999779i	$0.493301\pi$
$522$	−25.0848	−1.09793
$523$	−33.4712	−1.46360	−0.731798	−	0.681522i	$-0.761318\pi$
$523$	−33.4712	−1.46360	−0.731798	+	0.681522i	$0.761318\pi$
$524$	−118.406	−5.17259
$525$	0	0
$526$	−64.0920	−2.79454
$527$	16.7799	0.730944
$528$	1.20373	0.0523858
$529$	10.7246	0.466285
$530$	0	0
$531$	13.1103	0.568938
$532$	−71.4308	−3.09692
$533$	1.60428	0.0694891
$534$	−2.65528	−0.114905
$535$	0	0
$536$	59.9835	2.59089
$537$	−1.82561	−0.0787809
$538$	44.8333	1.93290
$539$	0.607516	0.0261676
$540$	0	0
$541$	21.4521	0.922297	0.461148	−	0.887323i	$-0.347438\pi$
$541$	21.4521	0.922297	0.461148	+	0.887323i	$0.347438\pi$
$542$	3.99140	0.171445
$543$	1.21404	0.0520995
$544$	120.792	5.17891
$545$	0	0
$546$	−5.36357	−0.229539
$547$	23.0304	0.984709	0.492354	−	0.870395i	$-0.336136\pi$
$547$	23.0304	0.984709	0.492354	+	0.870395i	$0.336136\pi$
$548$	−77.6046	−3.31510
$549$	−34.5510	−1.47460
$550$	0	0
$551$	14.0468	0.598415
$552$	10.6564	0.453565
$553$	−32.7018	−1.39062
$554$	−55.2251	−2.34629
$555$	0	0
$556$	13.4746	0.571451
$557$	32.4240	1.37385	0.686925	−	0.726728i	$-0.258960\pi$
$557$	32.4240	1.37385	0.686925	+	0.726728i	$0.258960\pi$
$558$	−23.8387	−1.00917
$559$	−3.45317	−0.146053
$560$	0	0
$561$	−0.466627	−0.0197010
$562$	−22.4243	−0.945913
$563$	23.9281	1.00845	0.504225	−	0.863572i	$-0.331778\pi$
$563$	23.9281	1.00845	0.504225	+	0.863572i	$0.331778\pi$
$564$	7.19111	0.302800
$565$	0	0
$566$	−71.6171	−3.01029
$567$	25.1619	1.05670
$568$	−0.423513	−0.0177702
$569$	−1.37175	−0.0575069	−0.0287534	−	0.999587i	$-0.509154\pi$
$569$	−1.37175	−0.0575069	−0.0287534	+	0.999587i	$0.509154\pi$
$570$	0	0
$571$	−12.2987	−0.514684	−0.257342	−	0.966320i	$-0.582847\pi$
$571$	−12.2987	−0.514684	−0.257342	+	0.966320i	$0.582847\pi$
$572$	7.86126	0.328696
$573$	−2.41300	−0.100804
$574$	−3.68226	−0.153695
$575$	0	0
$576$	−84.7558	−3.53149
$577$	14.1518	0.589147	0.294574	−	0.955629i	$-0.404822\pi$
$577$	14.1518	0.589147	0.294574	+	0.955629i	$0.404822\pi$
$578$	−41.7371	−1.73603
$579$	0.224293	0.00932131
$580$	0	0
$581$	29.7583	1.23458
$582$	1.33666	0.0554064
$583$	5.54201	0.229527
$584$	141.061	5.83713
$585$	0	0
$586$	73.9824	3.05619
$587$	−2.52267	−0.104122	−0.0520609	−	0.998644i	$-0.516579\pi$
$587$	−2.52267	−0.104122	−0.0520609	+	0.998644i	$0.516579\pi$
$588$	1.54436	0.0636882
$589$	13.3491	0.550038
$590$	0	0
$591$	2.97077	0.122201
$592$	−164.359	−6.75510
$593$	33.1453	1.36112	0.680558	−	0.732695i	$-0.261738\pi$
$593$	33.1453	1.36112	0.680558	+	0.732695i	$0.261738\pi$
$594$	1.33444	0.0547528
$595$	0	0
$596$	2.83565	0.116153
$597$	−3.57041	−0.146127
$598$	54.6776	2.23593
$599$	−1.38441	−0.0565654	−0.0282827	−	0.999600i	$-0.509004\pi$
$599$	−1.38441	−0.0565654	−0.0282827	+	0.999600i	$0.509004\pi$
$600$	0	0
$601$	9.79740	0.399644	0.199822	−	0.979832i	$-0.435964\pi$
$601$	9.79740	0.399644	0.199822	+	0.979832i	$0.435964\pi$
$602$	7.92596	0.323038
$603$	18.9717	0.772587
$604$	77.4436	3.15114
$605$	0	0
$606$	1.67291	0.0679572
$607$	45.3962	1.84257	0.921287	−	0.388883i	$-0.127139\pi$
$607$	45.3962	1.84257	0.921287	+	0.388883i	$0.127139\pi$
$608$	96.0946	3.89715
$609$	−1.76963	−0.0717091
$610$	0	0
$611$	23.3179	0.943341
$612$	91.4782	3.69779
$613$	23.5063	0.949410	0.474705	−	0.880145i	$-0.342555\pi$
$613$	23.5063	0.949410	0.474705	+	0.880145i	$0.342555\pi$
$614$	29.2945	1.18223
$615$	0	0
$616$	−11.4030	−0.459440
$617$	14.1230	0.568570	0.284285	−	0.958740i	$-0.408244\pi$
$617$	14.1230	0.568570	0.284285	+	0.958740i	$0.408244\pi$
$618$	−1.13003	−0.0454565
$619$	1.73398	0.0696944	0.0348472	−	0.999393i	$-0.488906\pi$
$619$	1.73398	0.0696944	0.0348472	+	0.999393i	$0.488906\pi$
$620$	0	0
$621$	6.78453	0.272254
$622$	−79.6583	−3.19401
$623$	14.4458	0.578757
$624$	9.92234	0.397211
$625$	0	0
$626$	55.9334	2.23555
$627$	−0.371219	−0.0148251
$628$	38.0117	1.51683
$629$	63.7135	2.54043
$630$	0	0
$631$	−6.33491	−0.252189	−0.126094	−	0.992018i	$-0.540244\pi$
$631$	−6.33491	−0.252189	−0.126094	+	0.992018i	$0.540244\pi$
$632$	105.339	4.19017
$633$	−3.15458	−0.125383
$634$	−29.1025	−1.15581
$635$	0	0
$636$	14.0883	0.558636
$637$	5.00773	0.198414
$638$	3.54829	0.140478
$639$	−0.133949	−0.00529895
$640$	0	0
$641$	−16.7226	−0.660504	−0.330252	−	0.943893i	$-0.607134\pi$
$641$	−16.7226	−0.660504	−0.330252	+	0.943893i	$0.607134\pi$
$642$	7.36020	0.290484
$643$	−1.00945	−0.0398087	−0.0199044	−	0.999802i	$-0.506336\pi$
$643$	−1.00945	−0.0398087	−0.0199044	+	0.999802i	$0.506336\pi$
$644$	−91.7374	−3.61496
$645$	0	0
$646$	−70.0781	−2.75719
$647$	−0.462180	−0.0181702	−0.00908509	−	0.999959i	$-0.502892\pi$
$647$	−0.462180	−0.0181702	−0.00908509	+	0.999959i	$0.502892\pi$
$648$	−81.0515	−3.18401
$649$	−1.85447	−0.0727945
$650$	0	0
$651$	−1.68173	−0.0659121
$652$	−78.9339	−3.09129
$653$	21.8663	0.855695	0.427848	−	0.903851i	$-0.359272\pi$
$653$	21.8663	0.855695	0.427848	+	0.903851i	$0.359272\pi$
$654$	1.04812	0.0409849
$655$	0	0
$656$	6.81201	0.265964
$657$	44.6149	1.74059
$658$	−53.5209	−2.08646
$659$	−40.1885	−1.56552	−0.782761	−	0.622322i	$-0.786189\pi$
$659$	−40.1885	−1.56552	−0.782761	+	0.622322i	$0.786189\pi$
$660$	0	0
$661$	−45.6907	−1.77716	−0.888582	−	0.458719i	$-0.848309\pi$
$661$	−45.6907	−1.77716	−0.888582	+	0.458719i	$0.848309\pi$
$662$	−1.83087	−0.0711588
$663$	−3.84639	−0.149381
$664$	−95.8575	−3.71999
$665$	0	0
$666$	−90.5160	−3.50742
$667$	18.0401	0.698516
$668$	22.0184	0.851919
$669$	−1.25361	−0.0484674
$670$	0	0
$671$	4.88730	0.188672
$672$	−12.1061	−0.467002
$673$	2.93134	0.112995	0.0564975	−	0.998403i	$-0.482007\pi$
$673$	2.93134	0.112995	0.0564975	+	0.998403i	$0.482007\pi$
$674$	23.1002	0.889787
$675$	0	0
$676$	−5.84528	−0.224818
$677$	7.27240	0.279501	0.139751	−	0.990187i	$-0.455370\pi$
$677$	7.27240	0.279501	0.139751	+	0.990187i	$0.455370\pi$
$678$	2.79074	0.107178
$679$	−7.27196	−0.279072
$680$	0	0
$681$	2.38210	0.0912823
$682$	3.37203	0.129122
$683$	−31.9236	−1.22152	−0.610761	−	0.791815i	$-0.709136\pi$
$683$	−31.9236	−1.22152	−0.610761	+	0.791815i	$0.709136\pi$
$684$	72.7744	2.78260
$685$	0	0
$686$	43.9876	1.67946
$687$	3.12931	0.119391
$688$	−14.6626	−0.559008
$689$	45.6826	1.74037
$690$	0	0
$691$	5.11083	0.194425	0.0972125	−	0.995264i	$-0.469007\pi$
$691$	5.11083	0.194425	0.0972125	+	0.995264i	$0.469007\pi$
$692$	8.52677	0.324139
$693$	−3.60656	−0.137002
$694$	−28.2855	−1.07370
$695$	0	0
$696$	5.70035	0.216071
$697$	−2.64067	−0.100023
$698$	−2.87566	−0.108845
$699$	−0.128095	−0.00484499
$700$	0	0
$701$	−20.9307	−0.790541	−0.395270	−	0.918565i	$-0.629349\pi$
$701$	−20.9307	−0.790541	−0.395270	+	0.918565i	$0.629349\pi$
$702$	10.9998	0.415159
$703$	50.6866	1.91168
$704$	11.9889	0.451847
$705$	0	0
$706$	18.3973	0.692392
$707$	−9.10127	−0.342288
$708$	−4.71423	−0.177172
$709$	−18.2147	−0.684068	−0.342034	−	0.939687i	$-0.611116\pi$
$709$	−18.2147	−0.684068	−0.342034	+	0.939687i	$0.611116\pi$
$710$	0	0
$711$	33.3168	1.24948
$712$	−46.5328	−1.74389
$713$	17.1440	0.642047
$714$	8.82851	0.330399
$715$	0	0
$716$	−50.6249	−1.89194
$717$	0.129813	0.00484795
$718$	−83.5002	−3.11620
$719$	38.6692	1.44212	0.721059	−	0.692874i	$-0.243656\pi$
$719$	38.6692	1.44212	0.721059	+	0.692874i	$0.243656\pi$
$720$	0	0
$721$	6.14781	0.228956
$722$	−3.94475	−0.146808
$723$	2.06811	0.0769139
$724$	33.6658	1.25118
$725$	0	0
$726$	5.78377	0.214656
$727$	18.6658	0.692276	0.346138	−	0.938184i	$-0.387493\pi$
$727$	18.6658	0.692276	0.346138	+	0.938184i	$0.387493\pi$
$728$	−93.9945	−3.48367
$729$	−24.9483	−0.924011
$730$	0	0
$731$	5.68396	0.210229
$732$	12.4239	0.459202
$733$	11.8900	0.439168	0.219584	−	0.975594i	$-0.429530\pi$
$733$	11.8900	0.439168	0.219584	+	0.975594i	$0.429530\pi$
$734$	−44.9458	−1.65898
$735$	0	0
$736$	123.413	4.54905
$737$	−2.68358	−0.0988509
$738$	3.75152	0.138095
$739$	−14.1661	−0.521107	−0.260554	−	0.965459i	$-0.583905\pi$
$739$	−14.1661	−0.521107	−0.260554	+	0.965459i	$0.583905\pi$
$740$	0	0
$741$	−3.05995	−0.112410
$742$	−104.854	−3.84931
$743$	22.2684	0.816948	0.408474	−	0.912770i	$-0.366061\pi$
$743$	22.2684	0.816948	0.408474	+	0.912770i	$0.366061\pi$
$744$	5.41719	0.198604
$745$	0	0
$746$	77.7832	2.84785
$747$	−30.3180	−1.10928
$748$	−12.9398	−0.473124
$749$	−40.0424	−1.46312
$750$	0	0
$751$	36.2377	1.32233	0.661167	−	0.750239i	$-0.270062\pi$
$751$	36.2377	1.32233	0.661167	+	0.750239i	$0.270062\pi$
$752$	99.0111	3.61056
$753$	1.63637	0.0596326
$754$	29.2484	1.06516
$755$	0	0
$756$	−18.4553	−0.671211
$757$	−11.3722	−0.413329	−0.206665	−	0.978412i	$-0.566261\pi$
$757$	−11.3722	−0.413329	−0.206665	+	0.978412i	$0.566261\pi$
$758$	−64.6846	−2.34945
$759$	−0.476751	−0.0173050
$760$	0	0
$761$	4.08698	0.148153	0.0740764	−	0.997253i	$-0.476399\pi$
$761$	4.08698	0.148153	0.0740764	+	0.997253i	$0.476399\pi$
$762$	−6.26802	−0.227066
$763$	−5.70221	−0.206434
$764$	−66.9134	−2.42084
$765$	0	0
$766$	42.1896	1.52437
$767$	−15.2864	−0.551958
$768$	7.76659	0.280253
$769$	50.0025	1.80314	0.901569	−	0.432636i	$-0.142416\pi$
$769$	50.0025	1.80314	0.901569	+	0.432636i	$0.142416\pi$
$770$	0	0
$771$	−4.58313	−0.165057
$772$	6.21974	0.223853
$773$	−17.5918	−0.632731	−0.316366	−	0.948637i	$-0.602463\pi$
$773$	−17.5918	−0.632731	−0.316366	+	0.948637i	$0.602463\pi$
$774$	−8.07504	−0.290251
$775$	0	0
$776$	23.4245	0.840891
$777$	−6.38554	−0.229080
$778$	67.0078	2.40235
$779$	−2.10075	−0.0752673
$780$	0	0
$781$	0.0189474	0.000677990 0
$782$	−90.0002	−3.21840
$783$	3.62921	0.129698
$784$	21.2636	0.759413
$785$	0	0
$786$	11.6422	0.415265
$787$	14.1271	0.503576	0.251788	−	0.967782i	$-0.418981\pi$
$787$	14.1271	0.503576	0.251788	+	0.967782i	$0.418981\pi$
$788$	82.3808	2.93469
$789$	4.60648	0.163995
$790$	0	0
$791$	−15.1827	−0.539835
$792$	11.6175	0.412809
$793$	40.2859	1.43059
$794$	−44.9117	−1.59385
$795$	0	0
$796$	−99.0091	−3.50928
$797$	−9.27254	−0.328450	−0.164225	−	0.986423i	$-0.552512\pi$
$797$	−9.27254	−0.328450	−0.164225	+	0.986423i	$0.552512\pi$
$798$	7.02341	0.248626
$799$	−38.3816	−1.35784
$800$	0	0
$801$	−14.7175	−0.520016
$802$	73.4868	2.59491
$803$	−6.31086	−0.222705
$804$	−6.82189	−0.240589
$805$	0	0
$806$	27.7955	0.979055
$807$	−3.22230	−0.113430
$808$	29.3171	1.03137
$809$	−2.60785	−0.0916870	−0.0458435	−	0.998949i	$-0.514598\pi$
$809$	−2.60785	−0.0916870	−0.0458435	+	0.998949i	$0.514598\pi$
$810$	0	0
$811$	7.59133	0.266568	0.133284	−	0.991078i	$-0.457448\pi$
$811$	7.59133	0.266568	0.133284	+	0.991078i	$0.457448\pi$
$812$	−49.0726	−1.72211
$813$	−0.286873	−0.0100611
$814$	12.8036	0.448767
$815$	0	0
$816$	−16.3323	−0.571745
$817$	4.52181	0.158198
$818$	−54.2914	−1.89825
$819$	−29.7288	−1.03881
$820$	0	0
$821$	−17.3629	−0.605970	−0.302985	−	0.952995i	$-0.597983\pi$
$821$	−17.3629	−0.605970	−0.302985	+	0.952995i	$0.597983\pi$
$822$	7.63044	0.266142
$823$	−15.8168	−0.551337	−0.275669	−	0.961253i	$-0.588899\pi$
$823$	−15.8168	−0.551337	−0.275669	+	0.961253i	$0.588899\pi$
$824$	−19.8034	−0.689883
$825$	0	0
$826$	35.0864	1.22081
$827$	−5.01450	−0.174371	−0.0871856	−	0.996192i	$-0.527787\pi$
$827$	−5.01450	−0.174371	−0.0871856	+	0.996192i	$0.527787\pi$
$828$	93.4629	3.24806
$829$	−28.2113	−0.979819	−0.489910	−	0.871773i	$-0.662970\pi$
$829$	−28.2113	−0.979819	−0.489910	+	0.871773i	$0.662970\pi$
$830$	0	0
$831$	3.96919	0.137690
$832$	98.8237	3.42610
$833$	−8.24280	−0.285596
$834$	−1.32489	−0.0458771
$835$	0	0
$836$	−10.2941	−0.356028
$837$	3.44893	0.119213
$838$	−54.5566	−1.88463
$839$	18.6120	0.642556	0.321278	−	0.946985i	$-0.395888\pi$
$839$	18.6120	0.642556	0.321278	+	0.946985i	$0.395888\pi$
$840$	0	0
$841$	−19.3499	−0.667238
$842$	5.68310	0.195853
$843$	1.61170	0.0555099
$844$	−87.4777	−3.01111
$845$	0	0
$846$	54.5276	1.87470
$847$	−31.4660	−1.08118
$848$	193.975	6.66113
$849$	5.14733	0.176656
$850$	0	0
$851$	65.0959	2.23146
$852$	0.0481658	0.00165013
$853$	16.8504	0.576946	0.288473	−	0.957488i	$-0.406853\pi$
$853$	16.8504	0.576946	0.288473	+	0.957488i	$0.406853\pi$
$854$	−92.4671	−3.16416
$855$	0	0
$856$	128.985	4.40861
$857$	−37.9323	−1.29574	−0.647871	−	0.761750i	$-0.724341\pi$
$857$	−37.9323	−1.29574	−0.647871	+	0.761750i	$0.724341\pi$
$858$	−0.772956	−0.0263883
$859$	8.36453	0.285394	0.142697	−	0.989766i	$-0.454423\pi$
$859$	8.36453	0.285394	0.142697	+	0.989766i	$0.454423\pi$
$860$	0	0
$861$	0.264655	0.00901941
$862$	−47.1412	−1.60564
$863$	−8.21929	−0.279788	−0.139894	−	0.990166i	$-0.544676\pi$
$863$	−8.21929	−0.279788	−0.139894	+	0.990166i	$0.544676\pi$
$864$	24.8275	0.844649
$865$	0	0
$866$	103.642	3.52190
$867$	2.99976	0.101877
$868$	−46.6350	−1.58289
$869$	−4.71273	−0.159868
$870$	0	0
$871$	−22.1207	−0.749530
$872$	18.3680	0.622018
$873$	7.40874	0.250748
$874$	−71.5986	−2.42186
$875$	0	0
$876$	−16.0427	−0.542034
$877$	−49.0024	−1.65469	−0.827347	−	0.561691i	$-0.810151\pi$
$877$	−49.0024	−1.65469	−0.827347	+	0.561691i	$0.810151\pi$
$878$	−59.3271	−2.00219
$879$	−5.31733	−0.179349
$880$	0	0
$881$	−30.7711	−1.03670	−0.518352	−	0.855168i	$-0.673454\pi$
$881$	−30.7711	−1.03670	−0.518352	+	0.855168i	$0.673454\pi$
$882$	11.7103	0.394306
$883$	−40.3398	−1.35754	−0.678771	−	0.734350i	$-0.737487\pi$
$883$	−40.3398	−1.35754	−0.678771	+	0.734350i	$0.737487\pi$
$884$	−106.662	−3.58743
$885$	0	0
$886$	−25.7050	−0.863577
$887$	3.27480	0.109957	0.0549785	−	0.998488i	$-0.482491\pi$
$887$	3.27480	0.109957	0.0549785	+	0.998488i	$0.482491\pi$
$888$	20.5691	0.690255
$889$	34.1005	1.14369
$890$	0	0
$891$	3.62613	0.121480
$892$	−34.7632	−1.16396
$893$	−30.5340	−1.02178
$894$	−0.278815	−0.00932496
$895$	0	0
$896$	−103.275	−3.45019
$897$	−3.92984	−0.131213
$898$	−1.06788	−0.0356355
$899$	9.17074	0.305861
$900$	0	0
$901$	−75.1942	−2.50508
$902$	−0.530659	−0.0176690
$903$	−0.569662	−0.0189572
$904$	48.9067	1.62661
$905$	0	0
$906$	−7.61462	−0.252979
$907$	−25.7005	−0.853372	−0.426686	−	0.904400i	$-0.640319\pi$
$907$	−25.7005	−0.853372	−0.426686	+	0.904400i	$0.640319\pi$
$908$	66.0567	2.19217
$909$	9.27246	0.307548
$910$	0	0
$911$	13.6546	0.452396	0.226198	−	0.974081i	$-0.427370\pi$
$911$	13.6546	0.452396	0.226198	+	0.974081i	$0.427370\pi$
$912$	−12.9930	−0.430241
$913$	4.28853	0.141930
$914$	94.3445	3.12064
$915$	0	0
$916$	86.7770	2.86719
$917$	−63.3384	−2.09162
$918$	−18.1058	−0.597579
$919$	25.9446	0.855832	0.427916	−	0.903818i	$-0.359248\pi$
$919$	25.9446	0.855832	0.427916	+	0.903818i	$0.359248\pi$
$920$	0	0
$921$	−2.10548	−0.0693779
$922$	69.1739	2.27812
$923$	0.156182	0.00514081
$924$	1.29686	0.0426634
$925$	0	0
$926$	−20.1740	−0.662957
$927$	−6.26345	−0.205719
$928$	66.0165	2.16710
$929$	20.4971	0.672487	0.336244	−	0.941775i	$-0.390843\pi$
$929$	20.4971	0.672487	0.336244	+	0.941775i	$0.390843\pi$
$930$	0	0
$931$	−6.55746	−0.214912
$932$	−3.55212	−0.116354
$933$	5.72527	0.187437
$934$	58.3130	1.90806
$935$	0	0
$936$	95.7625	3.13009
$937$	3.55974	0.116292	0.0581459	−	0.998308i	$-0.481481\pi$
$937$	3.55974	0.116292	0.0581459	+	0.998308i	$0.481481\pi$
$938$	50.7729	1.65779
$939$	−4.02009	−0.131191
$940$	0	0
$941$	−48.6506	−1.58596	−0.792982	−	0.609245i	$-0.791473\pi$
$941$	−48.6506	−1.58596	−0.792982	+	0.609245i	$0.791473\pi$
$942$	−3.73749	−0.121774
$943$	−2.69796	−0.0878577
$944$	−64.9081	−2.11258
$945$	0	0
$946$	1.14223	0.0371371
$947$	27.2253	0.884703	0.442351	−	0.896842i	$-0.354144\pi$
$947$	27.2253	0.884703	0.442351	+	0.896842i	$0.354144\pi$
$948$	−11.9801	−0.389097
$949$	−52.0202	−1.68865
$950$	0	0
$951$	2.09168	0.0678274
$952$	154.716	5.01439
$953$	29.2162	0.946406	0.473203	−	0.880953i	$-0.343098\pi$
$953$	29.2162	0.946406	0.473203	+	0.880953i	$0.343098\pi$
$954$	106.826	3.45863
$955$	0	0
$956$	3.59976	0.116425
$957$	−0.255026	−0.00824382
$958$	−92.7676	−2.99719
$959$	−41.5126	−1.34051
$960$	0	0
$961$	−22.2848	−0.718865
$962$	105.540	3.40274
$963$	40.7956	1.31462
$964$	57.3496	1.84710
$965$	0	0
$966$	9.02005	0.290215
$967$	37.1947	1.19610	0.598051	−	0.801458i	$-0.295942\pi$
$967$	37.1947	1.19610	0.598051	+	0.801458i	$0.295942\pi$
$968$	101.358	3.25778
$969$	5.03672	0.161803
$970$	0	0
$971$	−33.6880	−1.08110	−0.540550	−	0.841312i	$-0.681784\pi$
$971$	−33.6880	−1.08110	−0.540550	+	0.841312i	$0.681784\pi$
$972$	28.2641	0.906572
$973$	7.20791	0.231075
$974$	35.8000	1.14711
$975$	0	0
$976$	171.060	5.47549
$977$	8.61387	0.275582	0.137791	−	0.990461i	$-0.456000\pi$
$977$	8.61387	0.275582	0.137791	+	0.990461i	$0.456000\pi$
$978$	7.76115	0.248174
$979$	2.08181	0.0665350
$980$	0	0
$981$	5.80946	0.185482
$982$	9.20926	0.293879
$983$	21.5448	0.687174	0.343587	−	0.939121i	$-0.388358\pi$
$983$	21.5448	0.687174	0.343587	+	0.939121i	$0.388358\pi$
$984$	−0.852508	−0.0271770
$985$	0	0
$986$	−48.1433	−1.53320
$987$	3.84670	0.122442
$988$	−84.8536	−2.69955
$989$	5.80728	0.184661
$990$	0	0
$991$	−52.8980	−1.68036	−0.840180	−	0.542308i	$-0.817551\pi$
$991$	−52.8980	−1.68036	−0.840180	+	0.542308i	$0.817551\pi$
$992$	62.7372	1.99191
$993$	0.131590	0.00417588
$994$	−0.358481	−0.0113703
$995$	0	0
$996$	10.9018	0.345437
$997$	−8.98160	−0.284450	−0.142225	−	0.989834i	$-0.545426\pi$
$997$	−8.98160	−0.284450	−0.142225	+	0.989834i	$0.545426\pi$
$998$	−56.0449	−1.77407
$999$	13.0956	0.414328

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1075.2.a.p.1.1		6
3.2	odd	2		9675.2.a.cl.1.6		6
5.2	odd	4		1075.2.b.k.474.1		12
5.3	odd	4		1075.2.b.k.474.12		12
5.4	even	2		215.2.a.d.1.6	✓	6
15.14	odd	2		1935.2.a.z.1.1		6
20.19	odd	2		3440.2.a.x.1.5		6
215.214	odd	2		9245.2.a.n.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
215.2.a.d.1.6	✓	6	5.4	even	2
1075.2.a.p.1.1		6	1.1	even	1	trivial
1075.2.b.k.474.1		12	5.2	odd	4
1075.2.b.k.474.12		12	5.3	odd	4
1935.2.a.z.1.1		6	15.14	odd	2
3440.2.a.x.1.5		6	20.19	odd	2
9245.2.a.n.1.1		6	215.214	odd	2
9675.2.a.cl.1.6		6	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:	\( N \)	\(=\)	\( 1075 = 5^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1075.a (trivial)

\(f(q)\)	\(=\)	\(q-2.72658 q^{2} +0.195967 q^{3} +5.43426 q^{4} -0.534322 q^{6} +2.90692 q^{7} -9.36379 q^{8} -2.96160 q^{9} +O(q^{10})\)	\(q-2.72658 q^{2} +0.195967 q^{3} +5.43426 q^{4} -0.534322 q^{6} +2.90692 q^{7} -9.36379 q^{8} -2.96160 q^{9} +0.418923 q^{11} +1.06494 q^{12} +3.45317 q^{13} -7.92596 q^{14} +14.6626 q^{16} -5.68396 q^{17} +8.07504 q^{18} -4.52181 q^{19} +0.569662 q^{21} -1.14223 q^{22} -5.80728 q^{23} -1.83500 q^{24} -9.41535 q^{26} -1.16828 q^{27} +15.7970 q^{28} -3.10646 q^{29} -2.95215 q^{31} -21.2514 q^{32} +0.0820953 q^{33} +15.4978 q^{34} -16.0941 q^{36} -11.2093 q^{37} +12.3291 q^{38} +0.676708 q^{39} +0.464582 q^{41} -1.55323 q^{42} -1.00000 q^{43} +2.27654 q^{44} +15.8340 q^{46} +6.75261 q^{47} +2.87340 q^{48} +1.45018 q^{49} -1.11387 q^{51} +18.7654 q^{52} +13.2292 q^{53} +3.18541 q^{54} -27.2198 q^{56} -0.886128 q^{57} +8.47003 q^{58} -4.42676 q^{59} +11.6664 q^{61} +8.04928 q^{62} -8.60913 q^{63} +28.6183 q^{64} -0.223840 q^{66} -6.40590 q^{67} -30.8881 q^{68} -1.13804 q^{69} +0.0452288 q^{71} +27.7318 q^{72} -15.0645 q^{73} +30.5632 q^{74} -24.5727 q^{76} +1.21778 q^{77} -1.84510 q^{78} -11.2496 q^{79} +8.65585 q^{81} -1.26672 q^{82} +10.2370 q^{83} +3.09569 q^{84} +2.72658 q^{86} -0.608765 q^{87} -3.92271 q^{88} +4.96944 q^{89} +10.0381 q^{91} -31.5583 q^{92} -0.578525 q^{93} -18.4116 q^{94} -4.16457 q^{96} -2.50160 q^{97} -3.95405 q^{98} -1.24068 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 4 q^{3} + 7 q^{4} - 8 q^{7} - 9 q^{8} + 8 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - 4 * q^3 + 7 * q^4 - 8 * q^7 - 9 * q^8 + 8 * q^9	\( 6 q - 3 q^{2} - 4 q^{3} + 7 q^{4} - 8 q^{7} - 9 q^{8} + 8 q^{9} - 5 q^{12} - 6 q^{13} - 4 q^{14} + 5 q^{16} - 6 q^{17} + 11 q^{18} + 6 q^{19} - 12 q^{21} + q^{22} - 32 q^{26} - 10 q^{27} + 10 q^{28} - 10 q^{29} - 11 q^{32} - 6 q^{33} + 14 q^{34} - 41 q^{36} - 28 q^{37} + 6 q^{38} + 8 q^{39} - 6 q^{41} - 5 q^{42} - 6 q^{43} + 4 q^{44} - 8 q^{46} + 6 q^{47} + 32 q^{48} + 20 q^{49} - 8 q^{51} + 16 q^{52} + 4 q^{53} - 5 q^{54} - 35 q^{56} - 4 q^{57} + 26 q^{58} - 20 q^{59} - 8 q^{61} - 2 q^{62} + 2 q^{63} + 17 q^{64} - 35 q^{66} - 22 q^{67} - 22 q^{68} - 42 q^{69} + 8 q^{71} + 2 q^{72} - 34 q^{73} + 45 q^{74} - 16 q^{76} - 8 q^{77} + 26 q^{78} - 16 q^{79} + 46 q^{81} - 22 q^{82} + 14 q^{83} + 37 q^{84} + 3 q^{86} + 2 q^{87} - 20 q^{88} + 24 q^{91} - 46 q^{92} - 30 q^{93} + 12 q^{94} - 23 q^{96} - 34 q^{97} - 32 q^{98} - 16 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 4 * q^3 + 7 * q^4 - 8 * q^7 - 9 * q^8 + 8 * q^9 - 5 * q^12 - 6 * q^13 - 4 * q^14 + 5 * q^16 - 6 * q^17 + 11 * q^18 + 6 * q^19 - 12 * q^21 + q^22 - 32 * q^26 - 10 * q^27 + 10 * q^28 - 10 * q^29 - 11 * q^32 - 6 * q^33 + 14 * q^34 - 41 * q^36 - 28 * q^37 + 6 * q^38 + 8 * q^39 - 6 * q^41 - 5 * q^42 - 6 * q^43 + 4 * q^44 - 8 * q^46 + 6 * q^47 + 32 * q^48 + 20 * q^49 - 8 * q^51 + 16 * q^52 + 4 * q^53 - 5 * q^54 - 35 * q^56 - 4 * q^57 + 26 * q^58 - 20 * q^59 - 8 * q^61 - 2 * q^62 + 2 * q^63 + 17 * q^64 - 35 * q^66 - 22 * q^67 - 22 * q^68 - 42 * q^69 + 8 * q^71 + 2 * q^72 - 34 * q^73 + 45 * q^74 - 16 * q^76 - 8 * q^77 + 26 * q^78 - 16 * q^79 + 46 * q^81 - 22 * q^82 + 14 * q^83 + 37 * q^84 + 3 * q^86 + 2 * q^87 - 20 * q^88 + 24 * q^91 - 46 * q^92 - 30 * q^93 + 12 * q^94 - 23 * q^96 - 34 * q^97 - 32 * q^98 - 16 * q^99

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