LMFDB - Embedded newform 575.2.a.k.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [575,2,Mod(1,575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(575, 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("575.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 575 = 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	575.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:	$4.59139811622$
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} - 12x^{5} + 9x^{4} + 43x^{3} - 14x^{2} - 49x - 9 $ x^7 - x^6 - 12x^5 + 9x^4 + 43x^3 - 14x^2 - 49*x - 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-1.63662$ of defining polynomial
Character	$\chi$	$=$	575.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.63662 q^{2} +2.46212 q^{3} +0.678510 q^{4} +4.02954 q^{6} +4.74965 q^{7} -2.16277 q^{8} +3.06202 q^{9} +O(q^{10})$	\(q+1.63662 q^{2} +2.46212 q^{3} +0.678510 q^{4} +4.02954 q^{6} +4.74965 q^{7} -2.16277 q^{8} +3.06202 q^{9} -5.60341 q^{11} +1.67057 q^{12} -0.585596 q^{13} +7.77335 q^{14} -4.89664 q^{16} +6.12698 q^{17} +5.01134 q^{18} -6.87664 q^{19} +11.6942 q^{21} -9.17062 q^{22} -1.00000 q^{23} -5.32499 q^{24} -0.958395 q^{26} +0.152694 q^{27} +3.22268 q^{28} -0.404731 q^{29} +1.76985 q^{31} -3.68838 q^{32} -13.7962 q^{33} +10.0275 q^{34} +2.07761 q^{36} +2.95579 q^{37} -11.2544 q^{38} -1.44180 q^{39} -0.457484 q^{41} +19.1389 q^{42} -0.455669 q^{43} -3.80196 q^{44} -1.63662 q^{46} -4.23197 q^{47} -12.0561 q^{48} +15.5592 q^{49} +15.0853 q^{51} -0.397332 q^{52} +3.49673 q^{53} +0.249901 q^{54} -10.2724 q^{56} -16.9311 q^{57} -0.662389 q^{58} -5.97316 q^{59} +14.1975 q^{61} +2.89656 q^{62} +14.5435 q^{63} +3.75683 q^{64} -22.5791 q^{66} -0.518946 q^{67} +4.15722 q^{68} -2.46212 q^{69} -4.23197 q^{71} -6.62244 q^{72} -9.90404 q^{73} +4.83750 q^{74} -4.66586 q^{76} -26.6142 q^{77} -2.35968 q^{78} +3.75767 q^{79} -8.81010 q^{81} -0.748726 q^{82} -0.119403 q^{83} +7.93463 q^{84} -0.745755 q^{86} -0.996495 q^{87} +12.1189 q^{88} -10.1740 q^{89} -2.78138 q^{91} -0.678510 q^{92} +4.35757 q^{93} -6.92610 q^{94} -9.08122 q^{96} -0.0429646 q^{97} +25.4644 q^{98} -17.1577 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} + 11 q^{4} + 5 q^{6} + 3 q^{7} - 6 q^{8} + 15 q^{9}+O(q^{10}) $ 7 * q - q^2 + 11 * q^4 + 5 * q^6 + 3 * q^7 - 6 * q^8 + 15 * q^9	$ 7 q - q^{2} + 11 q^{4} + 5 q^{6} + 3 q^{7} - 6 q^{8} + 15 q^{9} - q^{11} + 6 q^{12} - 3 q^{13} + 7 q^{14} + 7 q^{16} + 10 q^{17} - 24 q^{18} + 15 q^{19} + 2 q^{21} + 21 q^{22} - 7 q^{23} + 18 q^{24} - 20 q^{26} - 11 q^{28} + 3 q^{29} + 14 q^{31} + 17 q^{32} + 6 q^{33} + 20 q^{34} - 10 q^{37} - 31 q^{38} - 8 q^{39} + 19 q^{41} + 44 q^{42} + 5 q^{43} - 3 q^{44} + q^{46} - 14 q^{47} - 27 q^{48} + 40 q^{49} + 2 q^{51} + 16 q^{52} + 4 q^{53} - q^{54} - 9 q^{56} - 4 q^{57} - 13 q^{58} - 16 q^{59} + 40 q^{61} - 12 q^{62} + 53 q^{63} - 4 q^{64} - 54 q^{66} - 4 q^{67} + 20 q^{68} - 14 q^{71} - 6 q^{72} - 3 q^{73} - 18 q^{74} + 35 q^{76} - 17 q^{77} + 23 q^{78} - q^{79} + 47 q^{81} - 22 q^{82} + 17 q^{83} - 60 q^{84} - 35 q^{86} - 56 q^{87} + 57 q^{88} + 16 q^{89} + 25 q^{91} - 11 q^{92} + 14 q^{93} + 7 q^{94} - 19 q^{96} - 24 q^{97} - 46 q^{98} - 53 q^{99}+O(q^{100}) $ 7 * q - q^2 + 11 * q^4 + 5 * q^6 + 3 * q^7 - 6 * q^8 + 15 * q^9 - q^11 + 6 * q^12 - 3 * q^13 + 7 * q^14 + 7 * q^16 + 10 * q^17 - 24 * q^18 + 15 * q^19 + 2 * q^21 + 21 * q^22 - 7 * q^23 + 18 * q^24 - 20 * q^26 - 11 * q^28 + 3 * q^29 + 14 * q^31 + 17 * q^32 + 6 * q^33 + 20 * q^34 - 10 * q^37 - 31 * q^38 - 8 * q^39 + 19 * q^41 + 44 * q^42 + 5 * q^43 - 3 * q^44 + q^46 - 14 * q^47 - 27 * q^48 + 40 * q^49 + 2 * q^51 + 16 * q^52 + 4 * q^53 - q^54 - 9 * q^56 - 4 * q^57 - 13 * q^58 - 16 * q^59 + 40 * q^61 - 12 * q^62 + 53 * q^63 - 4 * q^64 - 54 * q^66 - 4 * q^67 + 20 * q^68 - 14 * q^71 - 6 * q^72 - 3 * q^73 - 18 * q^74 + 35 * q^76 - 17 * q^77 + 23 * q^78 - q^79 + 47 * q^81 - 22 * q^82 + 17 * q^83 - 60 * q^84 - 35 * q^86 - 56 * q^87 + 57 * q^88 + 16 * q^89 + 25 * q^91 - 11 * q^92 + 14 * q^93 + 7 * q^94 - 19 * q^96 - 24 * q^97 - 46 * q^98 - 53 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.63662	1.15726	0.578631	−	0.815590i	$-0.303587\pi$
$2$	1.63662	1.15726	0.578631	+	0.815590i	$0.303587\pi$
$3$	2.46212	1.42150	0.710752	−	0.703443i	$-0.248355\pi$
$3$	2.46212	1.42150	0.710752	+	0.703443i	$0.248355\pi$
$4$	0.678510	0.339255
$5$	0	0
$5$	0	0
$6$	4.02954	1.64505
$7$	4.74965	1.79520	0.897600	−	0.440811i	$-0.145309\pi$
$7$	4.74965	1.79520	0.897600	+	0.440811i	$0.145309\pi$
$8$	−2.16277	−0.764655
$9$	3.06202	1.02067
$10$	0	0
$11$	−5.60341	−1.68949	−0.844745	−	0.535169i	$-0.820248\pi$
$11$	−5.60341	−1.68949	−0.844745	+	0.535169i	$0.820248\pi$
$12$	1.67057	0.482252
$13$	−0.585596	−0.162415	−0.0812075	−	0.996697i	$-0.525878\pi$
$13$	−0.585596	−0.162415	−0.0812075	+	0.996697i	$0.525878\pi$
$14$	7.77335	2.07752
$15$	0	0
$16$	−4.89664	−1.22416
$17$	6.12698	1.48601	0.743006	−	0.669285i	$-0.233399\pi$
$17$	6.12698	1.48601	0.743006	+	0.669285i	$0.233399\pi$
$18$	5.01134	1.18119
$19$	−6.87664	−1.57761	−0.788804	−	0.614644i	$-0.789299\pi$
$19$	−6.87664	−1.57761	−0.788804	+	0.614644i	$0.789299\pi$
$20$	0	0
$21$	11.6942	2.55188
$22$	−9.17062	−1.95518
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−5.32499	−1.08696
$25$	0	0
$26$	−0.958395	−0.187957
$27$	0.152694	0.0293860
$28$	3.22268	0.609030
$29$	−0.404731	−0.0751567	−0.0375784	−	0.999294i	$-0.511964\pi$
$29$	−0.404731	−0.0751567	−0.0375784	+	0.999294i	$0.511964\pi$
$30$	0	0
$31$	1.76985	0.317874	0.158937	−	0.987289i	$-0.449193\pi$
$31$	1.76985	0.317874	0.158937	+	0.987289i	$0.449193\pi$
$32$	−3.68838	−0.652020
$33$	−13.7962	−2.40162
$34$	10.0275	1.71970
$35$	0	0
$36$	2.07761	0.346268
$37$	2.95579	0.485929	0.242965	−	0.970035i	$-0.421880\pi$
$37$	2.95579	0.485929	0.242965	+	0.970035i	$0.421880\pi$
$38$	−11.2544	−1.82571
$39$	−1.44180	−0.230873
$40$	0	0
$41$	−0.457484	−0.0714470	−0.0357235	−	0.999362i	$-0.511374\pi$
$41$	−0.457484	−0.0714470	−0.0357235	+	0.999362i	$0.511374\pi$
$42$	19.1389	2.95320
$43$	−0.455669	−0.0694889	−0.0347445	−	0.999396i	$-0.511062\pi$
$43$	−0.455669	−0.0694889	−0.0347445	+	0.999396i	$0.511062\pi$
$44$	−3.80196	−0.573168
$45$	0	0
$46$	−1.63662	−0.241306
$47$	−4.23197	−0.617296	−0.308648	−	0.951176i	$-0.599876\pi$
$47$	−4.23197	−0.617296	−0.308648	+	0.951176i	$0.599876\pi$
$48$	−12.0561	−1.74015
$49$	15.5592	2.22274
$50$	0	0
$51$	15.0853	2.11237
$52$	−0.397332	−0.0551001
$53$	3.49673	0.480313	0.240157	−	0.970734i	$-0.422801\pi$
$53$	3.49673	0.480313	0.240157	+	0.970734i	$0.422801\pi$
$54$	0.249901	0.0340073
$55$	0	0
$56$	−10.2724	−1.37271
$57$	−16.9311	−2.24258
$58$	−0.662389	−0.0869760
$59$	−5.97316	−0.777639	−0.388819	−	0.921314i	$-0.627117\pi$
$59$	−5.97316	−0.777639	−0.388819	+	0.921314i	$0.627117\pi$
$60$	0	0
$61$	14.1975	1.81780	0.908899	−	0.417015i	$-0.136924\pi$
$61$	14.1975	1.81780	0.908899	+	0.417015i	$0.136924\pi$
$62$	2.89656	0.367864
$63$	14.5435	1.83231
$64$	3.75683	0.469604
$65$	0	0
$66$	−22.5791	−2.77930
$67$	−0.518946	−0.0633993	−0.0316997	−	0.999497i	$-0.510092\pi$
$67$	−0.518946	−0.0633993	−0.0316997	+	0.999497i	$0.510092\pi$
$68$	4.15722	0.504137
$69$	−2.46212	−0.296404
$70$	0	0
$71$	−4.23197	−0.502242	−0.251121	−	0.967956i	$-0.580799\pi$
$71$	−4.23197	−0.502242	−0.251121	+	0.967956i	$0.580799\pi$
$72$	−6.62244	−0.780462
$73$	−9.90404	−1.15918	−0.579590	−	0.814908i	$-0.696787\pi$
$73$	−9.90404	−1.15918	−0.579590	+	0.814908i	$0.696787\pi$
$74$	4.83750	0.562347
$75$	0	0
$76$	−4.66586	−0.535211
$77$	−26.6142	−3.03297
$78$	−2.35968	−0.267181
$79$	3.75767	0.422771	0.211386	−	0.977403i	$-0.432202\pi$
$79$	3.75767	0.422771	0.211386	+	0.977403i	$0.432202\pi$
$80$	0	0
$81$	−8.81010	−0.978900
$82$	−0.748726	−0.0826829
$83$	−0.119403	−0.0131061	−0.00655307	−	0.999979i	$-0.502086\pi$
$83$	−0.119403	−0.0131061	−0.00655307	+	0.999979i	$0.502086\pi$
$84$	7.93463	0.865739
$85$	0	0
$86$	−0.745755	−0.0804169
$87$	−0.996495	−0.106836
$88$	12.1189	1.29188
$89$	−10.1740	−1.07844	−0.539221	−	0.842164i	$-0.681281\pi$
$89$	−10.1740	−1.07844	−0.539221	+	0.842164i	$0.681281\pi$
$90$	0	0
$91$	−2.78138	−0.291567
$92$	−0.678510	−0.0707395
$93$	4.35757	0.451859
$94$	−6.92610	−0.714373
$95$	0	0
$96$	−9.08122	−0.926848
$97$	−0.0429646	−0.00436240	−0.00218120	−	0.999998i	$-0.500694\pi$
$97$	−0.0429646	−0.00436240	−0.00218120	+	0.999998i	$0.500694\pi$
$98$	25.4644	2.57230
$99$	−17.1577	−1.72442
$100$	0	0
$101$	−8.19407	−0.815341	−0.407670	−	0.913129i	$-0.633659\pi$
$101$	−8.19407	−0.815341	−0.407670	+	0.913129i	$0.633659\pi$
$102$	24.6889	2.44457
$103$	11.3926	1.12255	0.561275	−	0.827630i	$-0.310311\pi$
$103$	11.3926	1.12255	0.561275	+	0.827630i	$0.310311\pi$
$104$	1.26651	0.124191
$105$	0	0
$106$	5.72281	0.555848
$107$	6.60679	0.638703	0.319351	−	0.947636i	$-0.396535\pi$
$107$	6.60679	0.638703	0.319351	+	0.947636i	$0.396535\pi$
$108$	0.103604	0.00996933
$109$	−9.16599	−0.877942	−0.438971	−	0.898501i	$-0.644657\pi$
$109$	−9.16599	−0.877942	−0.438971	+	0.898501i	$0.644657\pi$
$110$	0	0
$111$	7.27751	0.690750
$112$	−23.2574	−2.19761
$113$	9.93504	0.934610	0.467305	−	0.884096i	$-0.345225\pi$
$113$	9.93504	0.934610	0.467305	+	0.884096i	$0.345225\pi$
$114$	−27.7097	−2.59525
$115$	0	0
$116$	−0.274614	−0.0254973
$117$	−1.79310	−0.165773
$118$	−9.77576	−0.899931
$119$	29.1010	2.66769
$120$	0	0
$121$	20.3982	1.85438
$122$	23.2358	2.10367
$123$	−1.12638	−0.101562
$124$	1.20086	0.107840
$125$	0	0
$126$	23.8021	2.12046
$127$	−7.69070	−0.682439	−0.341220	−	0.939984i	$-0.610840\pi$
$127$	−7.69070	−0.682439	−0.341220	+	0.939984i	$0.610840\pi$
$128$	13.5252	1.19547
$129$	−1.12191	−0.0987788
$130$	0	0
$131$	−7.03719	−0.614842	−0.307421	−	0.951574i	$-0.599466\pi$
$131$	−7.03719	−0.614842	−0.307421	+	0.951574i	$0.599466\pi$
$132$	−9.36088	−0.814760
$133$	−32.6616	−2.83212
$134$	−0.849315	−0.0733696
$135$	0	0
$136$	−13.2513	−1.13629
$137$	21.7660	1.85960	0.929798	−	0.368071i	$-0.119982\pi$
$137$	21.7660	1.85960	0.929798	+	0.368071i	$0.119982\pi$
$138$	−4.02954	−0.343017
$139$	5.59031	0.474164	0.237082	−	0.971490i	$-0.423809\pi$
$139$	5.59031	0.474164	0.237082	+	0.971490i	$0.423809\pi$
$140$	0	0
$141$	−10.4196	−0.877488
$142$	−6.92610	−0.581225
$143$	3.28133	0.274399
$144$	−14.9936	−1.24947
$145$	0	0
$146$	−16.2091	−1.34147
$147$	38.3086	3.15964
$148$	2.00553	0.164854
$149$	6.85927	0.561934	0.280967	−	0.959717i	$-0.409345\pi$
$149$	6.85927	0.561934	0.280967	+	0.959717i	$0.409345\pi$
$150$	0	0
$151$	16.6100	1.35170	0.675850	−	0.737039i	$-0.263777\pi$
$151$	16.6100	1.35170	0.675850	+	0.737039i	$0.263777\pi$
$152$	14.8726	1.20633
$153$	18.7609	1.51673
$154$	−43.5573	−3.50994
$155$	0	0
$156$	−0.978278	−0.0783249
$157$	2.53483	0.202301	0.101151	−	0.994871i	$-0.467748\pi$
$157$	2.53483	0.202301	0.101151	+	0.994871i	$0.467748\pi$
$158$	6.14987	0.489257
$159$	8.60937	0.682767
$160$	0	0
$161$	−4.74965	−0.374325
$162$	−14.4187	−1.13284
$163$	14.4841	1.13448	0.567242	−	0.823551i	$-0.308010\pi$
$163$	14.4841	1.13448	0.567242	+	0.823551i	$0.308010\pi$
$164$	−0.310407	−0.0242388
$165$	0	0
$166$	−0.195416	−0.0151672
$167$	−23.0821	−1.78615	−0.893074	−	0.449910i	$-0.851456\pi$
$167$	−23.0821	−1.78615	−0.893074	+	0.449910i	$0.851456\pi$
$168$	−25.2919	−1.95131
$169$	−12.6571	−0.973621
$170$	0	0
$171$	−21.0564	−1.61022
$172$	−0.309176	−0.0235745
$173$	−11.5532	−0.878377	−0.439188	−	0.898395i	$-0.644734\pi$
$173$	−11.5532	−0.878377	−0.439188	+	0.898395i	$0.644734\pi$
$174$	−1.63088	−0.123637
$175$	0	0
$176$	27.4379	2.06821
$177$	−14.7066	−1.10542
$178$	−16.6509	−1.24804
$179$	−15.4825	−1.15722	−0.578608	−	0.815606i	$-0.696404\pi$
$179$	−15.4825	−1.15722	−0.578608	+	0.815606i	$0.696404\pi$
$180$	0	0
$181$	6.78584	0.504388	0.252194	−	0.967677i	$-0.418848\pi$
$181$	6.78584	0.504388	0.252194	+	0.967677i	$0.418848\pi$
$182$	−4.55204	−0.337420
$183$	34.9558	2.58401
$184$	2.16277	0.159442
$185$	0	0
$186$	7.13167	0.522920
$187$	−34.3320	−2.51060
$188$	−2.87143	−0.209421
$189$	0.725243	0.0527537
$190$	0	0
$191$	−4.51027	−0.326352	−0.163176	−	0.986597i	$-0.552174\pi$
$191$	−4.51027	−0.326352	−0.163176	+	0.986597i	$0.552174\pi$
$192$	9.24975	0.667543
$193$	−6.02933	−0.434001	−0.217000	−	0.976172i	$-0.569627\pi$
$193$	−6.02933	−0.434001	−0.217000	+	0.976172i	$0.569627\pi$
$194$	−0.0703166	−0.00504844
$195$	0	0
$196$	10.5571	0.754076
$197$	−3.08922	−0.220098	−0.110049	−	0.993926i	$-0.535101\pi$
$197$	−3.08922	−0.220098	−0.110049	+	0.993926i	$0.535101\pi$
$198$	−28.0806	−1.99560
$199$	20.2062	1.43238	0.716188	−	0.697907i	$-0.245885\pi$
$199$	20.2062	1.43238	0.716188	+	0.697907i	$0.245885\pi$
$200$	0	0
$201$	−1.27771	−0.0901224
$202$	−13.4105	−0.943563
$203$	−1.92233	−0.134921
$204$	10.2356	0.716632
$205$	0	0
$206$	18.6454	1.29908
$207$	−3.06202	−0.212825
$208$	2.86745	0.198822
$209$	38.5326	2.66535
$210$	0	0
$211$	18.8595	1.29834	0.649171	−	0.760642i	$-0.275116\pi$
$211$	18.8595	1.29834	0.649171	+	0.760642i	$0.275116\pi$
$212$	2.37257	0.162949
$213$	−10.4196	−0.713939
$214$	10.8128	0.739147
$215$	0	0
$216$	−0.330242	−0.0224701
$217$	8.40617	0.570648
$218$	−15.0012	−1.01601
$219$	−24.3849	−1.64778
$220$	0	0
$221$	−3.58793	−0.241351
$222$	11.9105	0.799379
$223$	19.2794	1.29105	0.645523	−	0.763741i	$-0.276640\pi$
$223$	19.2794	1.29105	0.645523	+	0.763741i	$0.276640\pi$
$224$	−17.5185	−1.17051
$225$	0	0
$226$	16.2598	1.08159
$227$	−9.04973	−0.600652	−0.300326	−	0.953837i	$-0.597095\pi$
$227$	−9.04973	−0.600652	−0.300326	+	0.953837i	$0.597095\pi$
$228$	−11.4879	−0.760805
$229$	−16.8604	−1.11417	−0.557083	−	0.830457i	$-0.688079\pi$
$229$	−16.8604	−1.11417	−0.557083	+	0.830457i	$0.688079\pi$
$230$	0	0
$231$	−65.5273	−4.31138
$232$	0.875341	0.0574690
$233$	7.88172	0.516348	0.258174	−	0.966098i	$-0.416879\pi$
$233$	7.88172	0.516348	0.258174	+	0.966098i	$0.416879\pi$
$234$	−2.93462	−0.191842
$235$	0	0
$236$	−4.05284	−0.263818
$237$	9.25183	0.600971
$238$	47.6272	3.08721
$239$	−8.88051	−0.574433	−0.287216	−	0.957866i	$-0.592730\pi$
$239$	−8.88051	−0.574433	−0.287216	+	0.957866i	$0.592730\pi$
$240$	0	0
$241$	15.2496	0.982314	0.491157	−	0.871071i	$-0.336574\pi$
$241$	15.2496	0.982314	0.491157	+	0.871071i	$0.336574\pi$
$242$	33.3839	2.14600
$243$	−22.1496	−1.42090
$244$	9.63312	0.616697
$245$	0	0
$246$	−1.84345	−0.117534
$247$	4.02693	0.256227
$248$	−3.82778	−0.243064
$249$	−0.293983	−0.0186304
$250$	0	0
$251$	2.18525	0.137932	0.0689659	−	0.997619i	$-0.478030\pi$
$251$	2.18525	0.137932	0.0689659	+	0.997619i	$0.478030\pi$
$252$	9.86792	0.621620
$253$	5.60341	0.352283
$254$	−12.5867	−0.789761
$255$	0	0
$256$	14.6220	0.913873
$257$	29.4495	1.83701	0.918504	−	0.395411i	$-0.129398\pi$
$257$	29.4495	1.83701	0.918504	+	0.395411i	$0.129398\pi$
$258$	−1.83614	−0.114313
$259$	14.0390	0.872340
$260$	0	0
$261$	−1.23929	−0.0767104
$262$	−11.5172	−0.711533
$263$	−22.0593	−1.36024	−0.680118	−	0.733103i	$-0.738071\pi$
$263$	−22.0593	−1.36024	−0.680118	+	0.733103i	$0.738071\pi$
$264$	29.8381	1.83641
$265$	0	0
$266$	−53.4545	−3.27751
$267$	−25.0496	−1.53301
$268$	−0.352110	−0.0215085
$269$	11.1952	0.682582	0.341291	−	0.939958i	$-0.389136\pi$
$269$	11.1952	0.682582	0.341291	+	0.939958i	$0.389136\pi$
$270$	0	0
$271$	−4.61481	−0.280330	−0.140165	−	0.990128i	$-0.544763\pi$
$271$	−4.61481	−0.280330	−0.140165	+	0.990128i	$0.544763\pi$
$272$	−30.0017	−1.81912
$273$	−6.84807	−0.414464
$274$	35.6226	2.15204
$275$	0	0
$276$	−1.67057	−0.100556
$277$	25.5128	1.53291	0.766457	−	0.642296i	$-0.222018\pi$
$277$	25.5128	1.53291	0.766457	+	0.642296i	$0.222018\pi$
$278$	9.14919	0.548732
$279$	5.41931	0.324446
$280$	0	0
$281$	7.80293	0.465484	0.232742	−	0.972539i	$-0.425230\pi$
$281$	7.80293	0.465484	0.232742	+	0.972539i	$0.425230\pi$
$282$	−17.0529	−1.01548
$283$	−0.630250	−0.0374645	−0.0187322	−	0.999825i	$-0.505963\pi$
$283$	−0.630250	−0.0374645	−0.0187322	+	0.999825i	$0.505963\pi$
$284$	−2.87143	−0.170388
$285$	0	0
$286$	5.37027	0.317551
$287$	−2.17289	−0.128262
$288$	−11.2939	−0.665498
$289$	20.5399	1.20823
$290$	0	0
$291$	−0.105784	−0.00620116
$292$	−6.71998	−0.393257
$293$	28.4276	1.66076	0.830379	−	0.557199i	$-0.188124\pi$
$293$	28.4276	1.66076	0.830379	+	0.557199i	$0.188124\pi$
$294$	62.6964	3.65653
$295$	0	0
$296$	−6.39270	−0.371568
$297$	−0.855606	−0.0496473
$298$	11.2260	0.650304
$299$	0.585596	0.0338659
$300$	0	0
$301$	−2.16427	−0.124747
$302$	27.1841	1.56427
$303$	−20.1748	−1.15901
$304$	33.6724	1.93125
$305$	0	0
$306$	30.7044	1.75526
$307$	27.0544	1.54408	0.772038	−	0.635576i	$-0.219237\pi$
$307$	27.0544	1.54408	0.772038	+	0.635576i	$0.219237\pi$
$308$	−18.0580	−1.02895
$309$	28.0500	1.59571
$310$	0	0
$311$	−3.48139	−0.197411	−0.0987056	−	0.995117i	$-0.531470\pi$
$311$	−3.48139	−0.197411	−0.0987056	+	0.995117i	$0.531470\pi$
$312$	3.11829	0.176539
$313$	−9.26183	−0.523509	−0.261755	−	0.965134i	$-0.584301\pi$
$313$	−9.26183	−0.523509	−0.261755	+	0.965134i	$0.584301\pi$
$314$	4.14853	0.234115
$315$	0	0
$316$	2.54962	0.143427
$317$	−20.0425	−1.12570	−0.562848	−	0.826560i	$-0.690294\pi$
$317$	−20.0425	−1.12570	−0.562848	+	0.826560i	$0.690294\pi$
$318$	14.0902	0.790140
$319$	2.26787	0.126977
$320$	0	0
$321$	16.2667	0.907919
$322$	−7.77335	−0.433192
$323$	−42.1330	−2.34434
$324$	−5.97774	−0.332097
$325$	0	0
$326$	23.7049	1.31289
$327$	−22.5677	−1.24800
$328$	0.989434	0.0546323
$329$	−20.1004	−1.10817
$330$	0	0
$331$	−18.2598	−1.00365	−0.501825	−	0.864969i	$-0.667338\pi$
$331$	−18.2598	−1.00365	−0.501825	+	0.864969i	$0.667338\pi$
$332$	−0.0810158	−0.00444632
$333$	9.05069	0.495975
$334$	−37.7766	−2.06704
$335$	0	0
$336$	−57.2623	−3.12392
$337$	7.54119	0.410795	0.205397	−	0.978679i	$-0.434151\pi$
$337$	7.54119	0.410795	0.205397	+	0.978679i	$0.434151\pi$
$338$	−20.7148	−1.12673
$339$	24.4612	1.32855
$340$	0	0
$341$	−9.91718	−0.537046
$342$	−34.4612	−1.86345
$343$	40.6532	2.19507
$344$	0.985509	0.0531351
$345$	0	0
$346$	−18.9082	−1.01651
$347$	−3.37593	−0.181229	−0.0906146	−	0.995886i	$-0.528883\pi$
$347$	−3.37593	−0.181229	−0.0906146	+	0.995886i	$0.528883\pi$
$348$	−0.676132	−0.0362445
$349$	−13.9638	−0.747467	−0.373734	−	0.927536i	$-0.621923\pi$
$349$	−13.9638	−0.747467	−0.373734	+	0.927536i	$0.621923\pi$
$350$	0	0
$351$	−0.0894169	−0.00477272
$352$	20.6675	1.10158
$353$	−13.4541	−0.716090	−0.358045	−	0.933704i	$-0.616556\pi$
$353$	−13.4541	−0.716090	−0.358045	+	0.933704i	$0.616556\pi$
$354$	−24.0691	−1.27926
$355$	0	0
$356$	−6.90316	−0.365867
$357$	71.6502	3.79213
$358$	−25.3389	−1.33920
$359$	20.4138	1.07740	0.538699	−	0.842498i	$-0.318916\pi$
$359$	20.4138	1.07740	0.538699	+	0.842498i	$0.318916\pi$
$360$	0	0
$361$	28.2881	1.48885
$362$	11.1058	0.583709
$363$	50.2226	2.63600
$364$	−1.88719	−0.0989156
$365$	0	0
$366$	57.2092	2.99037
$367$	−25.4342	−1.32765	−0.663826	−	0.747887i	$-0.731069\pi$
$367$	−25.4342	−1.32765	−0.663826	+	0.747887i	$0.731069\pi$
$368$	4.89664	0.255255
$369$	−1.40082	−0.0729240
$370$	0	0
$371$	16.6083	0.862258
$372$	2.95666	0.153295
$373$	−32.4431	−1.67984	−0.839920	−	0.542710i	$-0.817398\pi$
$373$	−32.4431	−1.67984	−0.839920	+	0.542710i	$0.817398\pi$
$374$	−56.1882	−2.90542
$375$	0	0
$376$	9.15277	0.472018
$377$	0.237009	0.0122066
$378$	1.18694	0.0610498
$379$	−34.4815	−1.77120	−0.885598	−	0.464452i	$-0.846251\pi$
$379$	−34.4815	−1.77120	−0.885598	+	0.464452i	$0.846251\pi$
$380$	0	0
$381$	−18.9354	−0.970090
$382$	−7.38158	−0.377674
$383$	−0.645358	−0.0329762	−0.0164881	−	0.999864i	$-0.505249\pi$
$383$	−0.645358	−0.0329762	−0.0164881	+	0.999864i	$0.505249\pi$
$384$	33.3007	1.69937
$385$	0	0
$386$	−9.86769	−0.502252
$387$	−1.39527	−0.0709254
$388$	−0.0291519	−0.00147996
$389$	−17.9342	−0.909302	−0.454651	−	0.890670i	$-0.650236\pi$
$389$	−17.9342	−0.909302	−0.454651	+	0.890670i	$0.650236\pi$
$390$	0	0
$391$	−6.12698	−0.309855
$392$	−33.6510	−1.69963
$393$	−17.3264	−0.874000
$394$	−5.05587	−0.254711
$395$	0	0
$396$	−11.6417	−0.585017
$397$	−0.903231	−0.0453319	−0.0226659	−	0.999743i	$-0.507215\pi$
$397$	−0.903231	−0.0453319	−0.0226659	+	0.999743i	$0.507215\pi$
$398$	33.0697	1.65763
$399$	−80.4167	−4.02587
$400$	0	0
$401$	33.1204	1.65396	0.826978	−	0.562234i	$-0.190058\pi$
$401$	33.1204	1.65396	0.826978	+	0.562234i	$0.190058\pi$
$402$	−2.09111	−0.104295
$403$	−1.03642	−0.0516276
$404$	−5.55976	−0.276608
$405$	0	0
$406$	−3.14612	−0.156139
$407$	−16.5625	−0.820973
$408$	−32.6262	−1.61524
$409$	4.33933	0.214566	0.107283	−	0.994229i	$-0.465785\pi$
$409$	4.33933	0.214566	0.107283	+	0.994229i	$0.465785\pi$
$410$	0	0
$411$	53.5904	2.64342
$412$	7.73001	0.380830
$413$	−28.3704	−1.39602
$414$	−5.01134	−0.246294
$415$	0	0
$416$	2.15990	0.105898
$417$	13.7640	0.674026
$418$	63.0630	3.08451
$419$	−0.969259	−0.0473514	−0.0236757	−	0.999720i	$-0.507537\pi$
$419$	−0.969259	−0.0473514	−0.0236757	+	0.999720i	$0.507537\pi$
$420$	0	0
$421$	−24.9198	−1.21452	−0.607259	−	0.794504i	$-0.707731\pi$
$421$	−24.9198	−1.21452	−0.607259	+	0.794504i	$0.707731\pi$
$422$	30.8658	1.50252
$423$	−12.9584	−0.630057
$424$	−7.56264	−0.367274
$425$	0	0
$426$	−17.0529	−0.826214
$427$	67.4330	3.26331
$428$	4.48277	0.216683
$429$	8.07901	0.390059
$430$	0	0
$431$	−25.5396	−1.23020	−0.615098	−	0.788450i	$-0.710884\pi$
$431$	−25.5396	−1.23020	−0.615098	+	0.788450i	$0.710884\pi$
$432$	−0.747688	−0.0359732
$433$	9.77630	0.469819	0.234909	−	0.972017i	$-0.424521\pi$
$433$	9.77630	0.469819	0.234909	+	0.972017i	$0.424521\pi$
$434$	13.7577	0.660389
$435$	0	0
$436$	−6.21921	−0.297846
$437$	6.87664	0.328954
$438$	−39.9087	−1.90691
$439$	18.2909	0.872977	0.436489	−	0.899710i	$-0.356222\pi$
$439$	18.2909	0.872977	0.436489	+	0.899710i	$0.356222\pi$
$440$	0	0
$441$	47.6425	2.26869
$442$	−5.87207	−0.279306
$443$	35.1095	1.66810	0.834052	−	0.551686i	$-0.186015\pi$
$443$	35.1095	1.66810	0.834052	+	0.551686i	$0.186015\pi$
$444$	4.93786	0.234340
$445$	0	0
$446$	31.5530	1.49408
$447$	16.8883	0.798791
$448$	17.8436	0.843032
$449$	12.7029	0.599486	0.299743	−	0.954020i	$-0.403099\pi$
$449$	12.7029	0.599486	0.299743	+	0.954020i	$0.403099\pi$
$450$	0	0
$451$	2.56347	0.120709
$452$	6.74102	0.317071
$453$	40.8957	1.92145
$454$	−14.8109	−0.695111
$455$	0	0
$456$	36.6181	1.71480
$457$	−13.1776	−0.616422	−0.308211	−	0.951318i	$-0.599730\pi$
$457$	−13.1776	−0.616422	−0.308211	+	0.951318i	$0.599730\pi$
$458$	−27.5940	−1.28938
$459$	0.935554	0.0436679
$460$	0	0
$461$	−14.9674	−0.697101	−0.348551	−	0.937290i	$-0.613326\pi$
$461$	−14.9674	−0.697101	−0.348551	+	0.937290i	$0.613326\pi$
$462$	−107.243	−4.98940
$463$	3.82807	0.177906	0.0889528	−	0.996036i	$-0.471648\pi$
$463$	3.82807	0.177906	0.0889528	+	0.996036i	$0.471648\pi$
$464$	1.98182	0.0920039
$465$	0	0
$466$	12.8993	0.597550
$467$	−0.00337335	−0.000156100 0	−7.80501e−5	−	1.00000i	$-0.500025\pi$
$467$	−0.00337335	−0.000156100 0	−7.80501e−5		1.00000i	$0.500025\pi$
$468$	−1.21664	−0.0562391
$469$	−2.46481	−0.113814
$470$	0	0
$471$	6.24104	0.287572
$472$	12.9186	0.594625
$473$	2.55330	0.117401
$474$	15.1417	0.695481
$475$	0	0
$476$	19.7453	0.905026
$477$	10.7071	0.490243
$478$	−14.5340	−0.664769
$479$	−9.28000	−0.424014	−0.212007	−	0.977268i	$-0.568000\pi$
$479$	−9.28000	−0.424014	−0.212007	+	0.977268i	$0.568000\pi$
$480$	0	0
$481$	−1.73090	−0.0789222
$482$	24.9577	1.13679
$483$	−11.6942	−0.532104
$484$	13.8403	0.629107
$485$	0	0
$486$	−36.2503	−1.64435
$487$	23.7355	1.07556	0.537780	−	0.843085i	$-0.319263\pi$
$487$	23.7355	1.07556	0.537780	+	0.843085i	$0.319263\pi$
$488$	−30.7059	−1.38999
$489$	35.6616	1.61267
$490$	0	0
$491$	27.8337	1.25612	0.628059	−	0.778166i	$-0.283850\pi$
$491$	27.8337	1.25612	0.628059	+	0.778166i	$0.283850\pi$
$492$	−0.764259	−0.0344555
$493$	−2.47978	−0.111684
$494$	6.59053	0.296522
$495$	0	0
$496$	−8.66632	−0.389129
$497$	−20.1004	−0.901625
$498$	−0.481137	−0.0215603
$499$	−17.6150	−0.788556	−0.394278	−	0.918991i	$-0.629005\pi$
$499$	−17.6150	−0.788556	−0.394278	+	0.918991i	$0.629005\pi$
$500$	0	0
$501$	−56.8309	−2.53902
$502$	3.57641	0.159623
$503$	−19.0143	−0.847806	−0.423903	−	0.905708i	$-0.639340\pi$
$503$	−19.0143	−0.847806	−0.423903	+	0.905708i	$0.639340\pi$
$504$	−31.4543	−1.40109
$505$	0	0
$506$	9.17062	0.407684
$507$	−31.1632	−1.38401
$508$	−5.21821	−0.231521
$509$	−24.9973	−1.10799	−0.553994	−	0.832521i	$-0.686897\pi$
$509$	−24.9973	−1.10799	−0.553994	+	0.832521i	$0.686897\pi$
$510$	0	0
$511$	−47.0407	−2.08096
$512$	−3.11996	−0.137884
$513$	−1.05002	−0.0463596
$514$	48.1975	2.12590
$515$	0	0
$516$	−0.761227	−0.0335112
$517$	23.7134	1.04292
$518$	22.9764	1.00953
$519$	−28.4454	−1.24862
$520$	0	0
$521$	23.6233	1.03496	0.517478	−	0.855697i	$-0.326871\pi$
$521$	23.6233	1.03496	0.517478	+	0.855697i	$0.326871\pi$
$522$	−2.02825	−0.0887740
$523$	−7.13815	−0.312129	−0.156065	−	0.987747i	$-0.549881\pi$
$523$	−7.13815	−0.312129	−0.156065	+	0.987747i	$0.549881\pi$
$524$	−4.77480	−0.208588
$525$	0	0
$526$	−36.1026	−1.57415
$527$	10.8438	0.472365
$528$	67.5553	2.93997
$529$	1.00000	0.0434783
$530$	0	0
$531$	−18.2899	−0.793714
$532$	−22.1612	−0.960811
$533$	0.267901	0.0116041
$534$	−40.9965	−1.77409
$535$	0	0
$536$	1.12236	0.0484786
$537$	−38.1197	−1.64499
$538$	18.3222	0.789926
$539$	−87.1845	−3.75530
$540$	0	0
$541$	−20.1508	−0.866350	−0.433175	−	0.901310i	$-0.642607\pi$
$541$	−20.1508	−0.866350	−0.433175	+	0.901310i	$0.642607\pi$
$542$	−7.55267	−0.324415
$543$	16.7075	0.716989
$544$	−22.5986	−0.968909
$545$	0	0
$546$	−11.2077	−0.479643
$547$	−22.7980	−0.974772	−0.487386	−	0.873187i	$-0.662050\pi$
$547$	−22.7980	−0.974772	−0.487386	+	0.873187i	$0.662050\pi$
$548$	14.7684	0.630877
$549$	43.4729	1.85538
$550$	0	0
$551$	2.78319	0.118568
$552$	5.32499	0.226647
$553$	17.8476	0.758959
$554$	41.7546	1.77398
$555$	0	0
$556$	3.79308	0.160862
$557$	−8.36491	−0.354433	−0.177216	−	0.984172i	$-0.556709\pi$
$557$	−8.36491	−0.354433	−0.177216	+	0.984172i	$0.556709\pi$
$558$	8.86932	0.375468
$559$	0.266838	0.0112860
$560$	0	0
$561$	−84.5293	−3.56883
$562$	12.7704	0.538687
$563$	−16.6756	−0.702792	−0.351396	−	0.936227i	$-0.614293\pi$
$563$	−16.6756	−0.702792	−0.351396	+	0.936227i	$0.614293\pi$
$564$	−7.06979	−0.297692
$565$	0	0
$566$	−1.03148	−0.0433562
$567$	−41.8449	−1.75732
$568$	9.15277	0.384042
$569$	12.7803	0.535777	0.267888	−	0.963450i	$-0.413674\pi$
$569$	12.7803	0.535777	0.267888	+	0.963450i	$0.413674\pi$
$570$	0	0
$571$	−15.4483	−0.646493	−0.323246	−	0.946315i	$-0.604774\pi$
$571$	−15.4483	−0.646493	−0.323246	+	0.946315i	$0.604774\pi$
$572$	2.22641	0.0930910
$573$	−11.1048	−0.463910
$574$	−3.55619	−0.148432
$575$	0	0
$576$	11.5035	0.479312
$577$	−36.9547	−1.53845	−0.769223	−	0.638980i	$-0.779357\pi$
$577$	−36.9547	−1.53845	−0.769223	+	0.638980i	$0.779357\pi$
$578$	33.6160	1.39824
$579$	−14.8449	−0.616934
$580$	0	0
$581$	−0.567121	−0.0235281
$582$	−0.173128	−0.00717637
$583$	−19.5936	−0.811485
$584$	21.4202	0.886373
$585$	0	0
$586$	46.5250	1.92193
$587$	1.41639	0.0584606	0.0292303	−	0.999573i	$-0.490694\pi$
$587$	1.41639	0.0584606	0.0292303	+	0.999573i	$0.490694\pi$
$588$	25.9927	1.07192
$589$	−12.1706	−0.501481
$590$	0	0
$591$	−7.60603	−0.312870
$592$	−14.4735	−0.594856
$593$	−21.0358	−0.863835	−0.431918	−	0.901913i	$-0.642163\pi$
$593$	−21.0358	−0.863835	−0.431918	+	0.901913i	$0.642163\pi$
$594$	−1.40030	−0.0574549
$595$	0	0
$596$	4.65408	0.190639
$597$	49.7499	2.03613
$598$	0.958395	0.0391917
$599$	−30.9395	−1.26415	−0.632077	−	0.774905i	$-0.717798\pi$
$599$	−30.9395	−1.26415	−0.632077	+	0.774905i	$0.717798\pi$
$600$	0	0
$601$	−14.6288	−0.596720	−0.298360	−	0.954453i	$-0.596440\pi$
$601$	−14.6288	−0.596720	−0.298360	+	0.954453i	$0.596440\pi$
$602$	−3.54208	−0.144364
$603$	−1.58902	−0.0647100
$604$	11.2700	0.458571
$605$	0	0
$606$	−33.0183	−1.34128
$607$	−19.0997	−0.775233	−0.387616	−	0.921821i	$-0.626702\pi$
$607$	−19.0997	−0.775233	−0.387616	+	0.921821i	$0.626702\pi$
$608$	25.3636	1.02863
$609$	−4.73301	−0.191791
$610$	0	0
$611$	2.47822	0.100258
$612$	12.7295	0.514558
$613$	30.2834	1.22314	0.611568	−	0.791192i	$-0.290539\pi$
$613$	30.2834	1.22314	0.611568	+	0.791192i	$0.290539\pi$
$614$	44.2776	1.78690
$615$	0	0
$616$	57.5605	2.31918
$617$	−9.32654	−0.375472	−0.187736	−	0.982219i	$-0.560115\pi$
$617$	−9.32654	−0.375472	−0.187736	+	0.982219i	$0.560115\pi$
$618$	45.9070	1.84665
$619$	6.24049	0.250827	0.125413	−	0.992105i	$-0.459974\pi$
$619$	6.24049	0.250827	0.125413	+	0.992105i	$0.459974\pi$
$620$	0	0
$621$	−0.152694	−0.00612740
$622$	−5.69769	−0.228457
$623$	−48.3230	−1.93602
$624$	7.06000	0.282626
$625$	0	0
$626$	−15.1580	−0.605837
$627$	94.8717	3.78881
$628$	1.71990	0.0686316
$629$	18.1101	0.722097
$630$	0	0
$631$	44.2664	1.76222	0.881110	−	0.472912i	$-0.156797\pi$
$631$	44.2664	1.76222	0.881110	+	0.472912i	$0.156797\pi$
$632$	−8.12699	−0.323274
$633$	46.4343	1.84560
$634$	−32.8018	−1.30273
$635$	0	0
$636$	5.84154	0.231632
$637$	−9.11140	−0.361007
$638$	3.71164	0.146945
$639$	−12.9584	−0.512624
$640$	0	0
$641$	−43.9741	−1.73687	−0.868437	−	0.495799i	$-0.834875\pi$
$641$	−43.9741	−1.73687	−0.868437	+	0.495799i	$0.834875\pi$
$642$	26.6223	1.05070
$643$	−48.9040	−1.92858	−0.964292	−	0.264840i	$-0.914681\pi$
$643$	−48.9040	−1.92858	−0.964292	+	0.264840i	$0.914681\pi$
$644$	−3.22268	−0.126992
$645$	0	0
$646$	−68.9556	−2.71302
$647$	−11.0060	−0.432690	−0.216345	−	0.976317i	$-0.569414\pi$
$647$	−11.0060	−0.432690	−0.216345	+	0.976317i	$0.569414\pi$
$648$	19.0542	0.748521
$649$	33.4700	1.31381
$650$	0	0
$651$	20.6970	0.811178
$652$	9.82761	0.384879
$653$	−35.6458	−1.39493	−0.697464	−	0.716620i	$-0.745688\pi$
$653$	−35.6458	−1.39493	−0.697464	+	0.716620i	$0.745688\pi$
$654$	−36.9347	−1.44426
$655$	0	0
$656$	2.24014	0.0874627
$657$	−30.3263	−1.18314
$658$	−32.8966	−1.28244
$659$	−31.9452	−1.24441	−0.622204	−	0.782855i	$-0.713763\pi$
$659$	−31.9452	−1.24441	−0.622204	+	0.782855i	$0.713763\pi$
$660$	0	0
$661$	43.3941	1.68784	0.843918	−	0.536472i	$-0.180243\pi$
$661$	43.3941	1.68784	0.843918	+	0.536472i	$0.180243\pi$
$662$	−29.8843	−1.16149
$663$	−8.83391	−0.343081
$664$	0.258240	0.0100217
$665$	0	0
$666$	14.8125	0.573973
$667$	0.404731	0.0156713
$668$	−15.6614	−0.605959
$669$	47.4682	1.83523
$670$	0	0
$671$	−79.5541	−3.07115
$672$	−43.1326	−1.66388
$673$	−16.6011	−0.639925	−0.319963	−	0.947430i	$-0.603670\pi$
$673$	−16.6011	−0.639925	−0.319963	+	0.947430i	$0.603670\pi$
$674$	12.3420	0.475397
$675$	0	0
$676$	−8.58795	−0.330306
$677$	26.3946	1.01443	0.507213	−	0.861821i	$-0.330676\pi$
$677$	26.3946	1.01443	0.507213	+	0.861821i	$0.330676\pi$
$678$	40.0336	1.53748
$679$	−0.204067	−0.00783138
$680$	0	0
$681$	−22.2815	−0.853828
$682$	−16.2306	−0.621502
$683$	18.3432	0.701881	0.350941	−	0.936398i	$-0.385862\pi$
$683$	18.3432	0.701881	0.350941	+	0.936398i	$0.385862\pi$
$684$	−14.2870	−0.546275
$685$	0	0
$686$	66.5337	2.54027
$687$	−41.5122	−1.58379
$688$	2.23125	0.0850656
$689$	−2.04767	−0.0780101
$690$	0	0
$691$	−28.0189	−1.06589	−0.532945	−	0.846150i	$-0.678915\pi$
$691$	−28.0189	−1.06589	−0.532945	+	0.846150i	$0.678915\pi$
$692$	−7.83898	−0.297993
$693$	−81.4932	−3.09567
$694$	−5.52509	−0.209730
$695$	0	0
$696$	2.15519	0.0816923
$697$	−2.80300	−0.106171
$698$	−22.8534	−0.865015
$699$	19.4057	0.733991
$700$	0	0
$701$	34.5506	1.30496	0.652479	−	0.757807i	$-0.273729\pi$
$701$	34.5506	1.30496	0.652479	+	0.757807i	$0.273729\pi$
$702$	−0.146341	−0.00552329
$703$	−20.3259	−0.766606
$704$	−21.0510	−0.793391
$705$	0	0
$706$	−22.0192	−0.828703
$707$	−38.9190	−1.46370
$708$	−9.97857	−0.375018
$709$	31.9307	1.19918	0.599592	−	0.800306i	$-0.295329\pi$
$709$	31.9307	1.19918	0.599592	+	0.800306i	$0.295329\pi$
$710$	0	0
$711$	11.5061	0.431511
$712$	22.0041	0.824637
$713$	−1.76985	−0.0662814
$714$	117.264	4.38849
$715$	0	0
$716$	−10.5050	−0.392591
$717$	−21.8649	−0.816558
$718$	33.4095	1.24683
$719$	8.35843	0.311717	0.155858	−	0.987779i	$-0.450186\pi$
$719$	8.35843	0.311717	0.155858	+	0.987779i	$0.450186\pi$
$720$	0	0
$721$	54.1110	2.01520
$722$	46.2968	1.72299
$723$	37.5463	1.39636
$724$	4.60426	0.171116
$725$	0	0
$726$	82.1951	3.05055
$727$	−47.4874	−1.76121	−0.880606	−	0.473849i	$-0.842864\pi$
$727$	−47.4874	−1.76121	−0.880606	+	0.473849i	$0.842864\pi$
$728$	6.01548	0.222948
$729$	−28.1045	−1.04091
$730$	0	0
$731$	−2.79188	−0.103261
$732$	23.7179	0.876637
$733$	−29.0360	−1.07247	−0.536235	−	0.844069i	$-0.680154\pi$
$733$	−29.0360	−1.07247	−0.536235	+	0.844069i	$0.680154\pi$
$734$	−41.6259	−1.53644
$735$	0	0
$736$	3.68838	0.135955
$737$	2.90786	0.107113
$738$	−2.29261	−0.0843922
$739$	20.5562	0.756173	0.378087	−	0.925770i	$-0.376582\pi$
$739$	20.5562	0.756173	0.378087	+	0.925770i	$0.376582\pi$
$740$	0	0
$741$	9.91476	0.364228
$742$	27.1813	0.997859
$743$	−22.7823	−0.835802	−0.417901	−	0.908493i	$-0.637234\pi$
$743$	−22.7823	−0.835802	−0.417901	+	0.908493i	$0.637234\pi$
$744$	−9.42444	−0.345517
$745$	0	0
$746$	−53.0969	−1.94402
$747$	−0.365613	−0.0133771
$748$	−23.2946	−0.851734
$749$	31.3800	1.14660
$750$	0	0
$751$	−17.1290	−0.625048	−0.312524	−	0.949910i	$-0.601174\pi$
$751$	−17.1290	−0.625048	−0.312524	+	0.949910i	$0.601174\pi$
$752$	20.7224	0.755669
$753$	5.38034	0.196071
$754$	0.387892	0.0141262
$755$	0	0
$756$	0.492085	0.0178969
$757$	−24.0092	−0.872628	−0.436314	−	0.899794i	$-0.643716\pi$
$757$	−24.0092	−0.872628	−0.436314	+	0.899794i	$0.643716\pi$
$758$	−56.4330	−2.04974
$759$	13.7962	0.500772
$760$	0	0
$761$	27.3646	0.991965	0.495983	−	0.868332i	$-0.334808\pi$
$761$	27.3646	0.991965	0.495983	+	0.868332i	$0.334808\pi$
$762$	−30.9900	−1.12265
$763$	−43.5353	−1.57608
$764$	−3.06026	−0.110716
$765$	0	0
$766$	−1.05620	−0.0381621
$767$	3.49785	0.126300
$768$	36.0010	1.29907
$769$	47.5588	1.71501	0.857507	−	0.514473i	$-0.172012\pi$
$769$	47.5588	1.71501	0.857507	+	0.514473i	$0.172012\pi$
$770$	0	0
$771$	72.5081	2.61131
$772$	−4.09096	−0.147237
$773$	32.0301	1.15204	0.576021	−	0.817435i	$-0.304605\pi$
$773$	32.0301	1.15204	0.576021	+	0.817435i	$0.304605\pi$
$774$	−2.28352	−0.0820793
$775$	0	0
$776$	0.0929227	0.00333573
$777$	34.5656	1.24003
$778$	−29.3515	−1.05230
$779$	3.14595	0.112715
$780$	0	0
$781$	23.7134	0.848533
$782$	−10.0275	−0.358583
$783$	−0.0618000	−0.00220855
$784$	−76.1879	−2.72099
$785$	0	0
$786$	−28.3566	−1.01145
$787$	2.61899	0.0933568	0.0466784	−	0.998910i	$-0.485136\pi$
$787$	2.61899	0.0933568	0.0466784	+	0.998910i	$0.485136\pi$
$788$	−2.09607	−0.0746693
$789$	−54.3126	−1.93358
$790$	0	0
$791$	47.1880	1.67781
$792$	37.1082	1.31858
$793$	−8.31397	−0.295238
$794$	−1.47824	−0.0524609
$795$	0	0
$796$	13.7101	0.485941
$797$	−1.43475	−0.0508215	−0.0254108	−	0.999677i	$-0.508089\pi$
$797$	−1.43475	−0.0508215	−0.0254108	+	0.999677i	$0.508089\pi$
$798$	−131.611	−4.65899
$799$	−25.9292	−0.917309
$800$	0	0
$801$	−31.1530	−1.10074
$802$	54.2054	1.91406
$803$	55.4963	1.95842
$804$	−0.866935	−0.0305745
$805$	0	0
$806$	−1.69621	−0.0597466
$807$	27.5638	0.970293
$808$	17.7219	0.623455
$809$	−40.5801	−1.42672	−0.713361	−	0.700797i	$-0.752828\pi$
$809$	−40.5801	−1.42672	−0.713361	+	0.700797i	$0.752828\pi$
$810$	0	0
$811$	33.4489	1.17455	0.587275	−	0.809387i	$-0.300201\pi$
$811$	33.4489	1.17455	0.587275	+	0.809387i	$0.300201\pi$
$812$	−1.30432	−0.0457727
$813$	−11.3622	−0.398490
$814$	−27.1064	−0.950081
$815$	0	0
$816$	−73.8676	−2.58588
$817$	3.13347	0.109626
$818$	7.10182	0.248309
$819$	−8.51662	−0.297595
$820$	0	0
$821$	−30.2542	−1.05588	−0.527940	−	0.849282i	$-0.677035\pi$
$821$	−30.2542	−1.05588	−0.527940	+	0.849282i	$0.677035\pi$
$822$	87.7069	3.05913
$823$	−32.9894	−1.14994	−0.574969	−	0.818175i	$-0.694986\pi$
$823$	−32.9894	−1.14994	−0.574969	+	0.818175i	$0.694986\pi$
$824$	−24.6397	−0.858363
$825$	0	0
$826$	−46.4315	−1.61556
$827$	−14.7363	−0.512430	−0.256215	−	0.966620i	$-0.582476\pi$
$827$	−14.7363	−0.512430	−0.256215	+	0.966620i	$0.582476\pi$
$828$	−2.07761	−0.0722019
$829$	3.69888	0.128467	0.0642336	−	0.997935i	$-0.479540\pi$
$829$	3.69888	0.128467	0.0642336	+	0.997935i	$0.479540\pi$
$830$	0	0
$831$	62.8154	2.17904
$832$	−2.19998	−0.0762707
$833$	95.3310	3.30302
$834$	22.5264	0.780024
$835$	0	0
$836$	26.1447	0.904234
$837$	0.270245	0.00934105
$838$	−1.58630	−0.0547979
$839$	−26.0051	−0.897796	−0.448898	−	0.893583i	$-0.648183\pi$
$839$	−26.0051	−0.897796	−0.448898	+	0.893583i	$0.648183\pi$
$840$	0	0
$841$	−28.8362	−0.994351
$842$	−40.7842	−1.40552
$843$	19.2117	0.661687
$844$	12.7964	0.440469
$845$	0	0
$846$	−21.2078	−0.729140
$847$	96.8841	3.32898
$848$	−17.1223	−0.587981
$849$	−1.55175	−0.0532559
$850$	0	0
$851$	−2.95579	−0.101323
$852$	−7.06979	−0.242207
$853$	36.5008	1.24976	0.624882	−	0.780719i	$-0.285147\pi$
$853$	36.5008	1.24976	0.624882	+	0.780719i	$0.285147\pi$
$854$	110.362	3.77651
$855$	0	0
$856$	−14.2890	−0.488388
$857$	−20.9328	−0.715051	−0.357525	−	0.933903i	$-0.616379\pi$
$857$	−20.9328	−0.715051	−0.357525	+	0.933903i	$0.616379\pi$
$858$	13.2222	0.451400
$859$	50.5357	1.72426	0.862129	−	0.506689i	$-0.169131\pi$
$859$	50.5357	1.72426	0.862129	+	0.506689i	$0.169131\pi$
$860$	0	0
$861$	−5.34991	−0.182324
$862$	−41.7984	−1.42366
$863$	−24.6125	−0.837819	−0.418910	−	0.908028i	$-0.637588\pi$
$863$	−24.6125	−0.837819	−0.418910	+	0.908028i	$0.637588\pi$
$864$	−0.563193	−0.0191602
$865$	0	0
$866$	16.0000	0.543703
$867$	50.5717	1.71750
$868$	5.70367	0.193595
$869$	−21.0558	−0.714268
$870$	0	0
$871$	0.303892	0.0102970
$872$	19.8239	0.671323
$873$	−0.131558	−0.00445258
$874$	11.2544	0.380686
$875$	0	0
$876$	−16.5454	−0.559017
$877$	−21.2654	−0.718081	−0.359041	−	0.933322i	$-0.616896\pi$
$877$	−21.2654	−0.718081	−0.359041	+	0.933322i	$0.616896\pi$
$878$	29.9352	1.01026
$879$	69.9921	2.36077
$880$	0	0
$881$	−22.1884	−0.747547	−0.373773	−	0.927520i	$-0.621936\pi$
$881$	−22.1884	−0.747547	−0.373773	+	0.927520i	$0.621936\pi$
$882$	77.9725	2.62547
$883$	57.7070	1.94200	0.970998	−	0.239086i	$-0.0768478\pi$
$883$	57.7070	1.94200	0.970998	+	0.239086i	$0.0768478\pi$
$884$	−2.43445	−0.0818793
$885$	0	0
$886$	57.4608	1.93043
$887$	−26.0155	−0.873515	−0.436757	−	0.899579i	$-0.643873\pi$
$887$	−26.0155	−0.873515	−0.436757	+	0.899579i	$0.643873\pi$
$888$	−15.7396	−0.528186
$889$	−36.5281	−1.22511
$890$	0	0
$891$	49.3666	1.65384
$892$	13.0813	0.437993
$893$	29.1017	0.973851
$894$	27.6397	0.924410
$895$	0	0
$896$	64.2402	2.14611
$897$	1.44180	0.0481404
$898$	20.7897	0.693763
$899$	−0.716313	−0.0238904
$900$	0	0
$901$	21.4244	0.713751
$902$	4.19541	0.139692
$903$	−5.32869	−0.177328
$904$	−21.4872	−0.714654
$905$	0	0
$906$	66.9305	2.22362
$907$	−27.3456	−0.907997	−0.453998	−	0.891002i	$-0.650003\pi$
$907$	−27.3456	−0.907997	−0.453998	+	0.891002i	$0.650003\pi$
$908$	−6.14033	−0.203774
$909$	−25.0904	−0.832196
$910$	0	0
$911$	5.94055	0.196819	0.0984097	−	0.995146i	$-0.468624\pi$
$911$	5.94055	0.196819	0.0984097	+	0.995146i	$0.468624\pi$
$912$	82.9055	2.74527
$913$	0.669061	0.0221427
$914$	−21.5667	−0.713362
$915$	0	0
$916$	−11.4399	−0.377986
$917$	−33.4242	−1.10376
$918$	1.53114	0.0505352
$919$	1.33100	0.0439055	0.0219528	−	0.999759i	$-0.493012\pi$
$919$	1.33100	0.0439055	0.0219528	+	0.999759i	$0.493012\pi$
$920$	0	0
$921$	66.6111	2.19491
$922$	−24.4959	−0.806729
$923$	2.47822	0.0815716
$924$	−44.4609	−1.46266
$925$	0	0
$926$	6.26508	0.205883
$927$	34.8844	1.14576
$928$	1.49280	0.0490036
$929$	49.0281	1.60856	0.804279	−	0.594252i	$-0.202552\pi$
$929$	49.0281	1.60856	0.804279	+	0.594252i	$0.202552\pi$
$930$	0	0
$931$	−106.995	−3.50662
$932$	5.34782	0.175174
$933$	−8.57158	−0.280621
$934$	−0.00552088	−0.000180649 0
$935$	0	0
$936$	3.87807	0.126759
$937$	35.7391	1.16754	0.583772	−	0.811917i	$-0.301576\pi$
$937$	35.7391	1.16754	0.583772	+	0.811917i	$0.301576\pi$
$938$	−4.03395	−0.131713
$939$	−22.8037	−0.744170
$940$	0	0
$941$	−39.2385	−1.27914	−0.639569	−	0.768734i	$-0.720887\pi$
$941$	−39.2385	−1.27914	−0.639569	+	0.768734i	$0.720887\pi$
$942$	10.2142	0.332796
$943$	0.457484	0.0148977
$944$	29.2484	0.951955
$945$	0	0
$946$	4.17877	0.135864
$947$	0.869938	0.0282692	0.0141346	−	0.999900i	$-0.495501\pi$
$947$	0.869938	0.0282692	0.0141346	+	0.999900i	$0.495501\pi$
$948$	6.27746	0.203882
$949$	5.79976	0.188268
$950$	0	0
$951$	−49.3469	−1.60018
$952$	−62.9389	−2.03986
$953$	28.1537	0.911987	0.455994	−	0.889983i	$-0.349284\pi$
$953$	28.1537	0.911987	0.455994	+	0.889983i	$0.349284\pi$
$954$	17.5233	0.567339
$955$	0	0
$956$	−6.02551	−0.194879
$957$	5.58377	0.180498
$958$	−15.1878	−0.490695
$959$	103.381	3.33834
$960$	0	0
$961$	−27.8676	−0.898956
$962$	−2.83282	−0.0913336
$963$	20.2301	0.651907
$964$	10.3470	0.333255
$965$	0	0
$966$	−19.1389	−0.615784
$967$	21.5958	0.694473	0.347237	−	0.937778i	$-0.387120\pi$
$967$	21.5958	0.694473	0.347237	+	0.937778i	$0.387120\pi$
$968$	−44.1165	−1.41796
$969$	−103.736	−3.33249
$970$	0	0
$971$	37.6641	1.20870	0.604349	−	0.796720i	$-0.293433\pi$
$971$	37.6641	1.20870	0.604349	+	0.796720i	$0.293433\pi$
$972$	−15.0287	−0.482046
$973$	26.5520	0.851219
$974$	38.8459	1.24470
$975$	0	0
$976$	−69.5199	−2.22528
$977$	−21.8991	−0.700616	−0.350308	−	0.936635i	$-0.613923\pi$
$977$	−21.8991	−0.700616	−0.350308	+	0.936635i	$0.613923\pi$
$978$	58.3643	1.86628
$979$	57.0091	1.82202
$980$	0	0
$981$	−28.0664	−0.896092
$982$	45.5531	1.45366
$983$	−27.6246	−0.881088	−0.440544	−	0.897731i	$-0.645214\pi$
$983$	−27.6246	−0.881088	−0.440544	+	0.897731i	$0.645214\pi$
$984$	2.43610	0.0776601
$985$	0	0
$986$	−4.05845	−0.129247
$987$	−49.4894	−1.57527
$988$	2.73231	0.0869263
$989$	0.455669	0.0144894
$990$	0	0
$991$	−12.2573	−0.389365	−0.194682	−	0.980866i	$-0.562368\pi$
$991$	−12.2573	−0.389365	−0.194682	+	0.980866i	$0.562368\pi$
$992$	−6.52788	−0.207260
$993$	−44.9578	−1.42669
$994$	−32.8966	−1.04342
$995$	0	0
$996$	−0.199470	−0.00632046
$997$	2.88319	0.0913116	0.0456558	−	0.998957i	$-0.485462\pi$
$997$	2.88319	0.0913116	0.0456558	+	0.998957i	$0.485462\pi$
$998$	−28.8290	−0.912566
$999$	0.451332	0.0142795

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	575.2.a.k.1.6	✓	7
3.2	odd	2		5175.2.a.cg.1.2		7
4.3	odd	2		9200.2.a.da.1.2		7
5.2	odd	4		575.2.b.f.24.10		14
5.3	odd	4		575.2.b.f.24.5		14
5.4	even	2		575.2.a.l.1.2	yes	7
15.14	odd	2		5175.2.a.cb.1.6		7
20.19	odd	2		9200.2.a.db.1.6		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
575.2.a.k.1.6	✓	7	1.1	even	1	trivial
575.2.a.l.1.2	yes	7	5.4	even	2
575.2.b.f.24.5		14	5.3	odd	4
575.2.b.f.24.10		14	5.2	odd	4
5175.2.a.cb.1.6		7	15.14	odd	2
5175.2.a.cg.1.2		7	3.2	odd	2
9200.2.a.da.1.2		7	4.3	odd	2
9200.2.a.db.1.6		7	20.19	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:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.a (trivial)

\(f(q)\)	\(=\)	\(q+1.63662 q^{2} +2.46212 q^{3} +0.678510 q^{4} +4.02954 q^{6} +4.74965 q^{7} -2.16277 q^{8} +3.06202 q^{9} +O(q^{10})\)	\(q+1.63662 q^{2} +2.46212 q^{3} +0.678510 q^{4} +4.02954 q^{6} +4.74965 q^{7} -2.16277 q^{8} +3.06202 q^{9} -5.60341 q^{11} +1.67057 q^{12} -0.585596 q^{13} +7.77335 q^{14} -4.89664 q^{16} +6.12698 q^{17} +5.01134 q^{18} -6.87664 q^{19} +11.6942 q^{21} -9.17062 q^{22} -1.00000 q^{23} -5.32499 q^{24} -0.958395 q^{26} +0.152694 q^{27} +3.22268 q^{28} -0.404731 q^{29} +1.76985 q^{31} -3.68838 q^{32} -13.7962 q^{33} +10.0275 q^{34} +2.07761 q^{36} +2.95579 q^{37} -11.2544 q^{38} -1.44180 q^{39} -0.457484 q^{41} +19.1389 q^{42} -0.455669 q^{43} -3.80196 q^{44} -1.63662 q^{46} -4.23197 q^{47} -12.0561 q^{48} +15.5592 q^{49} +15.0853 q^{51} -0.397332 q^{52} +3.49673 q^{53} +0.249901 q^{54} -10.2724 q^{56} -16.9311 q^{57} -0.662389 q^{58} -5.97316 q^{59} +14.1975 q^{61} +2.89656 q^{62} +14.5435 q^{63} +3.75683 q^{64} -22.5791 q^{66} -0.518946 q^{67} +4.15722 q^{68} -2.46212 q^{69} -4.23197 q^{71} -6.62244 q^{72} -9.90404 q^{73} +4.83750 q^{74} -4.66586 q^{76} -26.6142 q^{77} -2.35968 q^{78} +3.75767 q^{79} -8.81010 q^{81} -0.748726 q^{82} -0.119403 q^{83} +7.93463 q^{84} -0.745755 q^{86} -0.996495 q^{87} +12.1189 q^{88} -10.1740 q^{89} -2.78138 q^{91} -0.678510 q^{92} +4.35757 q^{93} -6.92610 q^{94} -9.08122 q^{96} -0.0429646 q^{97} +25.4644 q^{98} -17.1577 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} + 11 q^{4} + 5 q^{6} + 3 q^{7} - 6 q^{8} + 15 q^{9}+O(q^{10}) \) 7 * q - q^2 + 11 * q^4 + 5 * q^6 + 3 * q^7 - 6 * q^8 + 15 * q^9	\( 7 q - q^{2} + 11 q^{4} + 5 q^{6} + 3 q^{7} - 6 q^{8} + 15 q^{9} - q^{11} + 6 q^{12} - 3 q^{13} + 7 q^{14} + 7 q^{16} + 10 q^{17} - 24 q^{18} + 15 q^{19} + 2 q^{21} + 21 q^{22} - 7 q^{23} + 18 q^{24} - 20 q^{26} - 11 q^{28} + 3 q^{29} + 14 q^{31} + 17 q^{32} + 6 q^{33} + 20 q^{34} - 10 q^{37} - 31 q^{38} - 8 q^{39} + 19 q^{41} + 44 q^{42} + 5 q^{43} - 3 q^{44} + q^{46} - 14 q^{47} - 27 q^{48} + 40 q^{49} + 2 q^{51} + 16 q^{52} + 4 q^{53} - q^{54} - 9 q^{56} - 4 q^{57} - 13 q^{58} - 16 q^{59} + 40 q^{61} - 12 q^{62} + 53 q^{63} - 4 q^{64} - 54 q^{66} - 4 q^{67} + 20 q^{68} - 14 q^{71} - 6 q^{72} - 3 q^{73} - 18 q^{74} + 35 q^{76} - 17 q^{77} + 23 q^{78} - q^{79} + 47 q^{81} - 22 q^{82} + 17 q^{83} - 60 q^{84} - 35 q^{86} - 56 q^{87} + 57 q^{88} + 16 q^{89} + 25 q^{91} - 11 q^{92} + 14 q^{93} + 7 q^{94} - 19 q^{96} - 24 q^{97} - 46 q^{98} - 53 q^{99}+O(q^{100}) \) 7 * q - q^2 + 11 * q^4 + 5 * q^6 + 3 * q^7 - 6 * q^8 + 15 * q^9 - q^11 + 6 * q^12 - 3 * q^13 + 7 * q^14 + 7 * q^16 + 10 * q^17 - 24 * q^18 + 15 * q^19 + 2 * q^21 + 21 * q^22 - 7 * q^23 + 18 * q^24 - 20 * q^26 - 11 * q^28 + 3 * q^29 + 14 * q^31 + 17 * q^32 + 6 * q^33 + 20 * q^34 - 10 * q^37 - 31 * q^38 - 8 * q^39 + 19 * q^41 + 44 * q^42 + 5 * q^43 - 3 * q^44 + q^46 - 14 * q^47 - 27 * q^48 + 40 * q^49 + 2 * q^51 + 16 * q^52 + 4 * q^53 - q^54 - 9 * q^56 - 4 * q^57 - 13 * q^58 - 16 * q^59 + 40 * q^61 - 12 * q^62 + 53 * q^63 - 4 * q^64 - 54 * q^66 - 4 * q^67 + 20 * q^68 - 14 * q^71 - 6 * q^72 - 3 * q^73 - 18 * q^74 + 35 * q^76 - 17 * q^77 + 23 * q^78 - q^79 + 47 * q^81 - 22 * q^82 + 17 * q^83 - 60 * q^84 - 35 * q^86 - 56 * q^87 + 57 * q^88 + 16 * q^89 + 25 * q^91 - 11 * q^92 + 14 * q^93 + 7 * q^94 - 19 * q^96 - 24 * q^97 - 46 * q^98 - 53 * q^99

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