LMFDB - Embedded newform 775.2.a.h.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(1,775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(775, 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("775.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.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:	$6.18840615665$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.144209.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 6x^{3} - x^{2} + 6x - 1 $ x^5 - 6x^3 - x^2 + 6x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.177477$ of defining polynomial
Character	$\chi$	$=$	775.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.264183 q^{2} -2.96850 q^{3} -1.93021 q^{4} -0.784228 q^{6} +2.14598 q^{7} -1.03829 q^{8} +5.81200 q^{9} +O(q^{10})$	\(q+0.264183 q^{2} -2.96850 q^{3} -1.93021 q^{4} -0.784228 q^{6} +2.14598 q^{7} -1.03829 q^{8} +5.81200 q^{9} +1.13359 q^{11} +5.72982 q^{12} -0.737342 q^{13} +0.566932 q^{14} +3.58611 q^{16} -2.91329 q^{17} +1.53543 q^{18} +6.85889 q^{19} -6.37034 q^{21} +0.299476 q^{22} -7.06380 q^{23} +3.08218 q^{24} -0.194793 q^{26} -8.34744 q^{27} -4.14218 q^{28} -7.65851 q^{29} -1.00000 q^{31} +3.02398 q^{32} -3.36507 q^{33} -0.769643 q^{34} -11.2184 q^{36} -5.57905 q^{37} +1.81200 q^{38} +2.18880 q^{39} +3.02250 q^{41} -1.68294 q^{42} -3.79962 q^{43} -2.18807 q^{44} -1.86614 q^{46} -7.55794 q^{47} -10.6454 q^{48} -2.39477 q^{49} +8.64812 q^{51} +1.42322 q^{52} +10.9820 q^{53} -2.20525 q^{54} -2.22816 q^{56} -20.3606 q^{57} -2.02325 q^{58} -9.35603 q^{59} -8.38726 q^{61} -0.264183 q^{62} +12.4724 q^{63} -6.37334 q^{64} -0.888995 q^{66} +13.8863 q^{67} +5.62326 q^{68} +20.9689 q^{69} -10.3298 q^{71} -6.03457 q^{72} -5.10463 q^{73} -1.47389 q^{74} -13.2391 q^{76} +2.43267 q^{77} +0.578244 q^{78} +5.76964 q^{79} +7.34337 q^{81} +0.798495 q^{82} +1.01132 q^{83} +12.2961 q^{84} -1.00379 q^{86} +22.7343 q^{87} -1.17700 q^{88} -6.78423 q^{89} -1.58232 q^{91} +13.6346 q^{92} +2.96850 q^{93} -1.99668 q^{94} -8.97669 q^{96} -15.3051 q^{97} -0.632659 q^{98} +6.58844 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 4 q^{2} - 3 q^{3} + 6 q^{4} - q^{6} - 2 q^{7} - 9 q^{8} + 6 q^{9}+O(q^{10}) $ 5 * q - 4 * q^2 - 3 * q^3 + 6 * q^4 - q^6 - 2 * q^7 - 9 * q^8 + 6 * q^9	$ 5 q - 4 q^{2} - 3 q^{3} + 6 q^{4} - q^{6} - 2 q^{7} - 9 q^{8} + 6 q^{9} - 2 q^{11} - 5 q^{12} - 4 q^{13} + 2 q^{14} + 4 q^{16} - 19 q^{17} - 5 q^{18} + 8 q^{19} - 15 q^{21} + 10 q^{22} - 12 q^{23} + 26 q^{24} - 16 q^{26} - 6 q^{27} - 6 q^{28} + 6 q^{29} - 5 q^{31} - 7 q^{32} - 3 q^{33} + 31 q^{34} - 13 q^{36} - 16 q^{37} - 14 q^{38} - 13 q^{39} - 2 q^{41} + 22 q^{42} - q^{43} - 4 q^{44} - 11 q^{46} - 8 q^{47} - 31 q^{48} - 9 q^{49} + 5 q^{51} + 26 q^{52} - 3 q^{53} + 10 q^{54} - 9 q^{56} - 14 q^{57} - 5 q^{58} - 4 q^{59} - 5 q^{61} + 4 q^{62} + 26 q^{63} - 5 q^{64} - 25 q^{66} - 13 q^{67} - 30 q^{68} + 10 q^{69} + 6 q^{71} - 2 q^{72} - 19 q^{73} + 4 q^{74} - 5 q^{76} - 23 q^{77} + 38 q^{78} - 6 q^{79} - 7 q^{81} + 27 q^{82} - 18 q^{83} - 15 q^{84} - 7 q^{86} + 5 q^{87} + q^{88} - 31 q^{89} + 8 q^{91} + 16 q^{92} + 3 q^{93} - 14 q^{94} + 10 q^{96} + q^{97} - 10 q^{98} - 33 q^{99}+O(q^{100}) $ 5 * q - 4 * q^2 - 3 * q^3 + 6 * q^4 - q^6 - 2 * q^7 - 9 * q^8 + 6 * q^9 - 2 * q^11 - 5 * q^12 - 4 * q^13 + 2 * q^14 + 4 * q^16 - 19 * q^17 - 5 * q^18 + 8 * q^19 - 15 * q^21 + 10 * q^22 - 12 * q^23 + 26 * q^24 - 16 * q^26 - 6 * q^27 - 6 * q^28 + 6 * q^29 - 5 * q^31 - 7 * q^32 - 3 * q^33 + 31 * q^34 - 13 * q^36 - 16 * q^37 - 14 * q^38 - 13 * q^39 - 2 * q^41 + 22 * q^42 - q^43 - 4 * q^44 - 11 * q^46 - 8 * q^47 - 31 * q^48 - 9 * q^49 + 5 * q^51 + 26 * q^52 - 3 * q^53 + 10 * q^54 - 9 * q^56 - 14 * q^57 - 5 * q^58 - 4 * q^59 - 5 * q^61 + 4 * q^62 + 26 * q^63 - 5 * q^64 - 25 * q^66 - 13 * q^67 - 30 * q^68 + 10 * q^69 + 6 * q^71 - 2 * q^72 - 19 * q^73 + 4 * q^74 - 5 * q^76 - 23 * q^77 + 38 * q^78 - 6 * q^79 - 7 * q^81 + 27 * q^82 - 18 * q^83 - 15 * q^84 - 7 * q^86 + 5 * q^87 + q^88 - 31 * q^89 + 8 * q^91 + 16 * q^92 + 3 * q^93 - 14 * q^94 + 10 * q^96 + q^97 - 10 * q^98 - 33 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.264183	0.186806	0.0934029	−	0.995628i	$-0.470226\pi$
$2$	0.264183	0.186806	0.0934029	+	0.995628i	$0.470226\pi$
$3$	−2.96850	−1.71387	−0.856933	−	0.515428i	$-0.827633\pi$
$3$	−2.96850	−1.71387	−0.856933	+	0.515428i	$0.827633\pi$
$4$	−1.93021	−0.965104
$5$	0	0
$5$	0	0
$6$	−0.784228	−0.320160
$7$	2.14598	0.811104	0.405552	−	0.914072i	$-0.367079\pi$
$7$	2.14598	0.811104	0.405552	+	0.914072i	$0.367079\pi$
$8$	−1.03829	−0.367093
$9$	5.81200	1.93733
$10$	0	0
$11$	1.13359	0.341791	0.170895	−	0.985289i	$-0.445334\pi$
$11$	1.13359	0.341791	0.170895	+	0.985289i	$0.445334\pi$
$12$	5.72982	1.65406
$13$	−0.737342	−0.204502	−0.102251	−	0.994759i	$-0.532604\pi$
$13$	−0.737342	−0.204502	−0.102251	+	0.994759i	$0.532604\pi$
$14$	0.566932	0.151519
$15$	0	0
$16$	3.58611	0.896529
$17$	−2.91329	−0.706578	−0.353289	−	0.935514i	$-0.614937\pi$
$17$	−2.91329	−0.706578	−0.353289	+	0.935514i	$0.614937\pi$
$18$	1.53543	0.361905
$19$	6.85889	1.57354	0.786769	−	0.617248i	$-0.211753\pi$
$19$	6.85889	1.57354	0.786769	+	0.617248i	$0.211753\pi$
$20$	0	0
$21$	−6.37034	−1.39012
$22$	0.299476	0.0638485
$23$	−7.06380	−1.47290	−0.736452	−	0.676490i	$-0.763500\pi$
$23$	−7.06380	−1.47290	−0.736452	+	0.676490i	$0.763500\pi$
$24$	3.08218	0.629147
$25$	0	0
$26$	−0.194793	−0.0382021
$27$	−8.34744	−1.60646
$28$	−4.14218	−0.782799
$29$	−7.65851	−1.42215	−0.711074	−	0.703117i	$-0.751791\pi$
$29$	−7.65851	−1.42215	−0.711074	+	0.703117i	$0.751791\pi$
$30$	0	0
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	3.02398	0.534569
$33$	−3.36507	−0.585784
$34$	−0.769643	−0.131993
$35$	0	0
$36$	−11.2184	−1.86973
$37$	−5.57905	−0.917190	−0.458595	−	0.888645i	$-0.651647\pi$
$37$	−5.57905	−0.917190	−0.458595	+	0.888645i	$0.651647\pi$
$38$	1.81200	0.293946
$39$	2.18880	0.350489
$40$	0	0
$41$	3.02250	0.472036	0.236018	−	0.971749i	$-0.424158\pi$
$41$	3.02250	0.472036	0.236018	+	0.971749i	$0.424158\pi$
$42$	−1.68294	−0.259683
$43$	−3.79962	−0.579436	−0.289718	−	0.957112i	$-0.593562\pi$
$43$	−3.79962	−0.579436	−0.289718	+	0.957112i	$0.593562\pi$
$44$	−2.18807	−0.329864
$45$	0	0
$46$	−1.86614	−0.275147
$47$	−7.55794	−1.10244	−0.551219	−	0.834360i	$-0.685837\pi$
$47$	−7.55794	−1.10244	−0.551219	+	0.834360i	$0.685837\pi$
$48$	−10.6454	−1.53653
$49$	−2.39477	−0.342111
$50$	0	0
$51$	8.64812	1.21098
$52$	1.42322	0.197365
$53$	10.9820	1.50849	0.754244	−	0.656594i	$-0.228003\pi$
$53$	10.9820	1.50849	0.754244	+	0.656594i	$0.228003\pi$
$54$	−2.20525	−0.300097
$55$	0	0
$56$	−2.22816	−0.297750
$57$	−20.3606	−2.69683
$58$	−2.02325	−0.265666
$59$	−9.35603	−1.21805	−0.609026	−	0.793151i	$-0.708439\pi$
$59$	−9.35603	−1.21805	−0.609026	+	0.793151i	$0.708439\pi$
$60$	0	0
$61$	−8.38726	−1.07388	−0.536939	−	0.843621i	$-0.680419\pi$
$61$	−8.38726	−1.07388	−0.536939	+	0.843621i	$0.680419\pi$
$62$	−0.264183	−0.0335513
$63$	12.4724	1.57138
$64$	−6.37334	−0.796668
$65$	0	0
$66$	−0.888995	−0.109428
$67$	13.8863	1.69648	0.848238	−	0.529615i	$-0.177663\pi$
$67$	13.8863	1.69648	0.848238	+	0.529615i	$0.177663\pi$
$68$	5.62326	0.681921
$69$	20.9689	2.52436
$70$	0	0
$71$	−10.3298	−1.22592	−0.612961	−	0.790113i	$-0.710022\pi$
$71$	−10.3298	−1.22592	−0.612961	+	0.790113i	$0.710022\pi$
$72$	−6.03457	−0.711181
$73$	−5.10463	−0.597452	−0.298726	−	0.954339i	$-0.596562\pi$
$73$	−5.10463	−0.597452	−0.298726	+	0.954339i	$0.596562\pi$
$74$	−1.47389	−0.171336
$75$	0	0
$76$	−13.2391	−1.51863
$77$	2.43267	0.277228
$78$	0.578244	0.0654733
$79$	5.76964	0.649136	0.324568	−	0.945862i	$-0.394781\pi$
$79$	5.76964	0.649136	0.324568	+	0.945862i	$0.394781\pi$
$80$	0	0
$81$	7.34337	0.815930
$82$	0.798495	0.0881790
$83$	1.01132	0.111007	0.0555036	−	0.998458i	$-0.482324\pi$
$83$	1.01132	0.111007	0.0555036	+	0.998458i	$0.482324\pi$
$84$	12.2961	1.34161
$85$	0	0
$86$	−1.00379	−0.108242
$87$	22.7343	2.43737
$88$	−1.17700	−0.125469
$89$	−6.78423	−0.719127	−0.359563	−	0.933121i	$-0.617074\pi$
$89$	−6.78423	−0.719127	−0.359563	+	0.933121i	$0.617074\pi$
$90$	0	0
$91$	−1.58232	−0.165872
$92$	13.6346	1.42151
$93$	2.96850	0.307819
$94$	−1.99668	−0.205942
$95$	0	0
$96$	−8.97669	−0.916180
$97$	−15.3051	−1.55400	−0.777001	−	0.629499i	$-0.783260\pi$
$97$	−15.3051	−1.55400	−0.777001	+	0.629499i	$0.783260\pi$
$98$	−0.632659	−0.0639082
$99$	6.58844	0.662163
$100$	0	0
$101$	18.4020	1.83106	0.915532	−	0.402245i	$-0.131770\pi$
$101$	18.4020	1.83106	0.915532	+	0.402245i	$0.131770\pi$
$102$	2.28469	0.226218
$103$	3.20925	0.316216	0.158108	−	0.987422i	$-0.449461\pi$
$103$	3.20925	0.316216	0.158108	+	0.987422i	$0.449461\pi$
$104$	0.765578	0.0750711
$105$	0	0
$106$	2.90125	0.281794
$107$	4.18235	0.404323	0.202161	−	0.979352i	$-0.435203\pi$
$107$	4.18235	0.404323	0.202161	+	0.979352i	$0.435203\pi$
$108$	16.1123	1.55041
$109$	−14.8656	−1.42386	−0.711931	−	0.702250i	$-0.752179\pi$
$109$	−14.8656	−1.42386	−0.711931	+	0.702250i	$0.752179\pi$
$110$	0	0
$111$	16.5614	1.57194
$112$	7.69573	0.727178
$113$	−10.8709	−1.02265	−0.511326	−	0.859387i	$-0.670845\pi$
$113$	−10.8709	−1.02265	−0.511326	+	0.859387i	$0.670845\pi$
$114$	−5.37893	−0.503783
$115$	0	0
$116$	14.7825	1.37252
$117$	−4.28543	−0.396188
$118$	−2.47171	−0.227539
$119$	−6.25187	−0.573108
$120$	0	0
$121$	−9.71497	−0.883179
$122$	−2.21577	−0.200607
$123$	−8.97231	−0.809006
$124$	1.93021	0.173338
$125$	0	0
$126$	3.29501	0.293543
$127$	4.22557	0.374959	0.187479	−	0.982269i	$-0.439968\pi$
$127$	4.22557	0.374959	0.187479	+	0.982269i	$0.439968\pi$
$128$	−7.73169	−0.683391
$129$	11.2792	0.993075
$130$	0	0
$131$	6.59896	0.576554	0.288277	−	0.957547i	$-0.406918\pi$
$131$	6.59896	0.576554	0.288277	+	0.957547i	$0.406918\pi$
$132$	6.49528	0.565342
$133$	14.7190	1.27630
$134$	3.66852	0.316912
$135$	0	0
$136$	3.02486	0.259379
$137$	−22.0518	−1.88401	−0.942004	−	0.335601i	$-0.891061\pi$
$137$	−22.0518	−1.88401	−0.942004	+	0.335601i	$0.891061\pi$
$138$	5.53963	0.471565
$139$	11.2326	0.952739	0.476369	−	0.879245i	$-0.341953\pi$
$139$	11.2326	0.952739	0.476369	+	0.879245i	$0.341953\pi$
$140$	0	0
$141$	22.4357	1.88943
$142$	−2.72896	−0.229009
$143$	−0.835845	−0.0698969
$144$	20.8425	1.73688
$145$	0	0
$146$	−1.34856	−0.111607
$147$	7.10889	0.586331
$148$	10.7687	0.885183
$149$	−14.2166	−1.16467	−0.582334	−	0.812950i	$-0.697860\pi$
$149$	−14.2166	−1.16467	−0.582334	+	0.812950i	$0.697860\pi$
$150$	0	0
$151$	18.5380	1.50860	0.754302	−	0.656528i	$-0.227976\pi$
$151$	18.5380	1.50860	0.754302	+	0.656528i	$0.227976\pi$
$152$	−7.12155	−0.577634
$153$	−16.9321	−1.36888
$154$	0.642669	0.0517878
$155$	0	0
$156$	−4.22484	−0.338258
$157$	14.5650	1.16241	0.581207	−	0.813756i	$-0.302581\pi$
$157$	14.5650	1.16241	0.581207	+	0.813756i	$0.302581\pi$
$158$	1.52424	0.121262
$159$	−32.6000	−2.58535
$160$	0	0
$161$	−15.1588	−1.19468
$162$	1.94000	0.152420
$163$	−3.82214	−0.299373	−0.149687	−	0.988733i	$-0.547827\pi$
$163$	−3.82214	−0.299373	−0.149687	+	0.988733i	$0.547827\pi$
$164$	−5.83406	−0.455563
$165$	0	0
$166$	0.267175	0.0207368
$167$	11.5390	0.892916	0.446458	−	0.894805i	$-0.352685\pi$
$167$	11.5390	0.892916	0.446458	+	0.894805i	$0.352685\pi$
$168$	6.61429	0.510304
$169$	−12.4563	−0.958179
$170$	0	0
$171$	39.8639	3.04847
$172$	7.33405	0.559216
$173$	−5.70512	−0.433752	−0.216876	−	0.976199i	$-0.569587\pi$
$173$	−5.70512	−0.433752	−0.216876	+	0.976199i	$0.569587\pi$
$174$	6.00602	0.455315
$175$	0	0
$176$	4.06519	0.306425
$177$	27.7734	2.08758
$178$	−1.79228	−0.134337
$179$	−12.0891	−0.903580	−0.451790	−	0.892124i	$-0.649214\pi$
$179$	−12.0891	−0.903580	−0.451790	+	0.892124i	$0.649214\pi$
$180$	0	0
$181$	−23.0801	−1.71553	−0.857766	−	0.514040i	$-0.828148\pi$
$181$	−23.0801	−1.71553	−0.857766	+	0.514040i	$0.828148\pi$
$182$	−0.418022	−0.0309859
$183$	24.8976	1.84048
$184$	7.33430	0.540692
$185$	0	0
$186$	0.784228	0.0575024
$187$	−3.30249	−0.241502
$188$	14.5884	1.06397
$189$	−17.9134	−1.30301
$190$	0	0
$191$	3.50613	0.253695	0.126847	−	0.991922i	$-0.459514\pi$
$191$	3.50613	0.253695	0.126847	+	0.991922i	$0.459514\pi$
$192$	18.9193	1.36538
$193$	−2.19838	−0.158243	−0.0791216	−	0.996865i	$-0.525212\pi$
$193$	−2.19838	−0.158243	−0.0791216	+	0.996865i	$0.525212\pi$
$194$	−4.04336	−0.290297
$195$	0	0
$196$	4.62241	0.330172
$197$	−10.4883	−0.747259	−0.373629	−	0.927578i	$-0.621887\pi$
$197$	−10.4883	−0.747259	−0.373629	+	0.927578i	$0.621887\pi$
$198$	1.74056	0.123696
$199$	−13.4959	−0.956697	−0.478349	−	0.878170i	$-0.658764\pi$
$199$	−13.4959	−0.956697	−0.478349	+	0.878170i	$0.658764\pi$
$200$	0	0
$201$	−41.2214	−2.90753
$202$	4.86149	0.342053
$203$	−16.4350	−1.15351
$204$	−16.6927	−1.16872
$205$	0	0
$206$	0.847829	0.0590710
$207$	−41.0548	−2.85351
$208$	−2.64419	−0.183342
$209$	7.77519	0.537821
$210$	0	0
$211$	−13.2300	−0.910793	−0.455397	−	0.890289i	$-0.650503\pi$
$211$	−13.2300	−0.910793	−0.455397	+	0.890289i	$0.650503\pi$
$212$	−21.1975	−1.45585
$213$	30.6640	2.10107
$214$	1.10491	0.0755298
$215$	0	0
$216$	8.66710	0.589721
$217$	−2.14598	−0.145679
$218$	−3.92723	−0.265986
$219$	15.1531	1.02395
$220$	0	0
$221$	2.14809	0.144496
$222$	4.37525	0.293647
$223$	15.2035	1.01810	0.509051	−	0.860736i	$-0.329996\pi$
$223$	15.2035	1.01810	0.509051	+	0.860736i	$0.329996\pi$
$224$	6.48940	0.433591
$225$	0	0
$226$	−2.87192	−0.191037
$227$	−1.51386	−0.100479	−0.0502393	−	0.998737i	$-0.515998\pi$
$227$	−1.51386	−0.100479	−0.0502393	+	0.998737i	$0.515998\pi$
$228$	39.3002	2.60272
$229$	8.55623	0.565412	0.282706	−	0.959207i	$-0.408768\pi$
$229$	8.55623	0.565412	0.282706	+	0.959207i	$0.408768\pi$
$230$	0	0
$231$	−7.22137	−0.475131
$232$	7.95179	0.522060
$233$	−29.0101	−1.90051	−0.950257	−	0.311468i	$-0.899179\pi$
$233$	−29.0101	−1.90051	−0.950257	+	0.311468i	$0.899179\pi$
$234$	−1.13214	−0.0740102
$235$	0	0
$236$	18.0591	1.17555
$237$	−17.1272	−1.11253
$238$	−1.65164	−0.107060
$239$	−13.2639	−0.857971	−0.428986	−	0.903311i	$-0.641129\pi$
$239$	−13.2639	−0.857971	−0.428986	+	0.903311i	$0.641129\pi$
$240$	0	0
$241$	−4.69319	−0.302315	−0.151157	−	0.988510i	$-0.548300\pi$
$241$	−4.69319	−0.302315	−0.151157	+	0.988510i	$0.548300\pi$
$242$	−2.56653	−0.164983
$243$	3.24350	0.208071
$244$	16.1891	1.03640
$245$	0	0
$246$	−2.37033	−0.151127
$247$	−5.05735	−0.321791
$248$	1.03829	0.0659318
$249$	−3.00211	−0.190251
$250$	0	0
$251$	2.03024	0.128148	0.0640739	−	0.997945i	$-0.479591\pi$
$251$	2.03024	0.128148	0.0640739	+	0.997945i	$0.479591\pi$
$252$	−24.0744	−1.51654
$253$	−8.00747	−0.503425
$254$	1.11632	0.0700444
$255$	0	0
$256$	10.7041	0.669007
$257$	−6.81919	−0.425369	−0.212685	−	0.977121i	$-0.568221\pi$
$257$	−6.81919	−0.425369	−0.212685	+	0.977121i	$0.568221\pi$
$258$	2.97977	0.185512
$259$	−11.9725	−0.743936
$260$	0	0
$261$	−44.5113	−2.75518
$262$	1.74333	0.107704
$263$	0.818007	0.0504404	0.0252202	−	0.999682i	$-0.491971\pi$
$263$	0.818007	0.0504404	0.0252202	+	0.999682i	$0.491971\pi$
$264$	3.49394	0.215037
$265$	0	0
$266$	3.88852	0.238421
$267$	20.1390	1.23249
$268$	−26.8034	−1.63728
$269$	1.10427	0.0673285	0.0336642	−	0.999433i	$-0.489282\pi$
$269$	1.10427	0.0673285	0.0336642	+	0.999433i	$0.489282\pi$
$270$	0	0
$271$	5.42896	0.329786	0.164893	−	0.986311i	$-0.447272\pi$
$271$	5.42896	0.329786	0.164893	+	0.986311i	$0.447272\pi$
$272$	−10.4474	−0.633467
$273$	4.69712	0.284283
$274$	−5.82570	−0.351944
$275$	0	0
$276$	−40.4743	−2.43627
$277$	18.9283	1.13729	0.568646	−	0.822583i	$-0.307468\pi$
$277$	18.9283	1.13729	0.568646	+	0.822583i	$0.307468\pi$
$278$	2.96747	0.177977
$279$	−5.81200	−0.347956
$280$	0	0
$281$	9.85285	0.587772	0.293886	−	0.955841i	$-0.405051\pi$
$281$	9.85285	0.587772	0.293886	+	0.955841i	$0.405051\pi$
$282$	5.92715	0.352956
$283$	31.7526	1.88750	0.943748	−	0.330666i	$-0.107273\pi$
$283$	31.7526	1.88750	0.943748	+	0.330666i	$0.107273\pi$
$284$	19.9387	1.18314
$285$	0	0
$286$	−0.220816	−0.0130571
$287$	6.48623	0.382870
$288$	17.5754	1.03564
$289$	−8.51272	−0.500748
$290$	0	0
$291$	45.4334	2.66335
$292$	9.85300	0.576603
$293$	19.1975	1.12153	0.560766	−	0.827974i	$-0.310507\pi$
$293$	19.1975	1.12153	0.560766	+	0.827974i	$0.310507\pi$
$294$	1.87805	0.109530
$295$	0	0
$296$	5.79269	0.336694
$297$	−9.46259	−0.549075
$298$	−3.75578	−0.217566
$299$	5.20843	0.301212
$300$	0	0
$301$	−8.15390	−0.469983
$302$	4.89744	0.281816
$303$	−54.6263	−3.13820
$304$	24.5968	1.41072
$305$	0	0
$306$	−4.47317	−0.255714
$307$	−25.2908	−1.44342	−0.721710	−	0.692196i	$-0.756643\pi$
$307$	−25.2908	−1.44342	−0.721710	+	0.692196i	$0.756643\pi$
$308$	−4.69555	−0.267554
$309$	−9.52665	−0.541952
$310$	0	0
$311$	−9.49162	−0.538220	−0.269110	−	0.963109i	$-0.586730\pi$
$311$	−9.49162	−0.538220	−0.269110	+	0.963109i	$0.586730\pi$
$312$	−2.27262	−0.128662
$313$	19.2026	1.08539	0.542696	−	0.839929i	$-0.317403\pi$
$313$	19.2026	1.08539	0.542696	+	0.839929i	$0.317403\pi$
$314$	3.84783	0.217146
$315$	0	0
$316$	−11.1366	−0.626483
$317$	6.76462	0.379939	0.189969	−	0.981790i	$-0.439161\pi$
$317$	6.76462	0.379939	0.189969	+	0.981790i	$0.439161\pi$
$318$	−8.61236	−0.482957
$319$	−8.68162	−0.486078
$320$	0	0
$321$	−12.4153	−0.692955
$322$	−4.00469	−0.223173
$323$	−19.9820	−1.11183
$324$	−14.1742	−0.787457
$325$	0	0
$326$	−1.00975	−0.0559247
$327$	44.1284	2.44031
$328$	−3.13825	−0.173281
$329$	−16.2192	−0.894192
$330$	0	0
$331$	−27.1257	−1.49096	−0.745481	−	0.666527i	$-0.767780\pi$
$331$	−27.1257	−1.49096	−0.745481	+	0.666527i	$0.767780\pi$
$332$	−1.95206	−0.107133
$333$	−32.4254	−1.77690
$334$	3.04841	0.166802
$335$	0	0
$336$	−22.8448	−1.24628
$337$	28.0407	1.52747	0.763737	−	0.645527i	$-0.223362\pi$
$337$	28.0407	1.52747	0.763737	+	0.645527i	$0.223362\pi$
$338$	−3.29075	−0.178993
$339$	32.2704	1.75269
$340$	0	0
$341$	−1.13359	−0.0613875
$342$	10.5314	0.569471
$343$	−20.1610	−1.08859
$344$	3.94512	0.212707
$345$	0	0
$346$	−1.50720	−0.0810274
$347$	−19.2914	−1.03561	−0.517807	−	0.855497i	$-0.673252\pi$
$347$	−19.2914	−1.03561	−0.517807	+	0.855497i	$0.673252\pi$
$348$	−43.8819	−2.35232
$349$	20.8611	1.11667	0.558336	−	0.829615i	$-0.311440\pi$
$349$	20.8611	1.11667	0.558336	+	0.829615i	$0.311440\pi$
$350$	0	0
$351$	6.15491	0.328525
$352$	3.42796	0.182711
$353$	14.3753	0.765123	0.382561	−	0.923930i	$-0.375042\pi$
$353$	14.3753	0.765123	0.382561	+	0.923930i	$0.375042\pi$
$354$	7.33726	0.389971
$355$	0	0
$356$	13.0950	0.694032
$357$	18.5587	0.982230
$358$	−3.19373	−0.168794
$359$	21.2523	1.12165	0.560827	−	0.827933i	$-0.310483\pi$
$359$	21.2523	1.12165	0.560827	+	0.827933i	$0.310483\pi$
$360$	0	0
$361$	28.0444	1.47602
$362$	−6.09738	−0.320471
$363$	28.8389	1.51365
$364$	3.05421	0.160084
$365$	0	0
$366$	6.57752	0.343813
$367$	−0.665621	−0.0347451	−0.0173726	−	0.999849i	$-0.505530\pi$
$367$	−0.665621	−0.0347451	−0.0173726	+	0.999849i	$0.505530\pi$
$368$	−25.3316	−1.32050
$369$	17.5668	0.914491
$370$	0	0
$371$	23.5671	1.22354
$372$	−5.72982	−0.297078
$373$	18.6381	0.965045	0.482522	−	0.875884i	$-0.339721\pi$
$373$	18.6381	0.965045	0.482522	+	0.875884i	$0.339721\pi$
$374$	−0.872462	−0.0451139
$375$	0	0
$376$	7.84736	0.404697
$377$	5.64694	0.290832
$378$	−4.73242	−0.243410
$379$	−14.5982	−0.749861	−0.374931	−	0.927053i	$-0.622333\pi$
$379$	−14.5982	−0.749861	−0.374931	+	0.927053i	$0.622333\pi$
$380$	0	0
$381$	−12.5436	−0.642629
$382$	0.926261	0.0473917
$383$	2.77909	0.142005	0.0710024	−	0.997476i	$-0.477380\pi$
$383$	2.77909	0.142005	0.0710024	+	0.997476i	$0.477380\pi$
$384$	22.9515	1.17124
$385$	0	0
$386$	−0.580776	−0.0295607
$387$	−22.0834	−1.12256
$388$	29.5421	1.49977
$389$	37.9321	1.92323	0.961616	−	0.274398i	$-0.0884785\pi$
$389$	37.9321	1.92323	0.961616	+	0.274398i	$0.0884785\pi$
$390$	0	0
$391$	20.5789	1.04072
$392$	2.48648	0.125586
$393$	−19.5890	−0.988136
$394$	−2.77083	−0.139592
$395$	0	0
$396$	−12.7171	−0.639056
$397$	−10.3664	−0.520277	−0.260138	−	0.965571i	$-0.583768\pi$
$397$	−10.3664	−0.520277	−0.260138	+	0.965571i	$0.583768\pi$
$398$	−3.56538	−0.178717
$399$	−43.6935	−2.18741
$400$	0	0
$401$	−12.3610	−0.617279	−0.308640	−	0.951179i	$-0.599874\pi$
$401$	−12.3610	−0.617279	−0.308640	+	0.951179i	$0.599874\pi$
$402$	−10.8900	−0.543144
$403$	0.737342	0.0367296
$404$	−35.5196	−1.76717
$405$	0	0
$406$	−4.34185	−0.215482
$407$	−6.32437	−0.313487
$408$	−8.97929	−0.444541
$409$	33.8499	1.67377	0.836885	−	0.547379i	$-0.184375\pi$
$409$	33.8499	1.67377	0.836885	+	0.547379i	$0.184375\pi$
$410$	0	0
$411$	65.4607	3.22894
$412$	−6.19451	−0.305182
$413$	−20.0778	−0.987966
$414$	−10.8460	−0.533052
$415$	0	0
$416$	−2.22971	−0.109320
$417$	−33.3441	−1.63287
$418$	2.05407	0.100468
$419$	24.9078	1.21682	0.608412	−	0.793621i	$-0.291807\pi$
$419$	24.9078	1.21682	0.608412	+	0.793621i	$0.291807\pi$
$420$	0	0
$421$	7.03930	0.343074	0.171537	−	0.985178i	$-0.445127\pi$
$421$	7.03930	0.343074	0.171537	+	0.985178i	$0.445127\pi$
$422$	−3.49515	−0.170141
$423$	−43.9268	−2.13579
$424$	−11.4025	−0.553755
$425$	0	0
$426$	8.10092	0.392491
$427$	−17.9989	−0.871027
$428$	−8.07279	−0.390213
$429$	2.48121	0.119794
$430$	0	0
$431$	−6.94074	−0.334324	−0.167162	−	0.985929i	$-0.553460\pi$
$431$	−6.94074	−0.334324	−0.167162	+	0.985929i	$0.553460\pi$
$432$	−29.9349	−1.44024
$433$	−16.2700	−0.781885	−0.390943	−	0.920415i	$-0.627851\pi$
$433$	−16.2700	−0.781885	−0.390943	+	0.920415i	$0.627851\pi$
$434$	−0.566932	−0.0272136
$435$	0	0
$436$	28.6936	1.37417
$437$	−48.4498	−2.31767
$438$	4.00320	0.191280
$439$	13.1144	0.625916	0.312958	−	0.949767i	$-0.398680\pi$
$439$	13.1144	0.625916	0.312958	+	0.949767i	$0.398680\pi$
$440$	0	0
$441$	−13.9184	−0.662783
$442$	0.567490	0.0269927
$443$	26.3432	1.25160	0.625801	−	0.779983i	$-0.284772\pi$
$443$	26.3432	1.25160	0.625801	+	0.779983i	$0.284772\pi$
$444$	−31.9670	−1.51708
$445$	0	0
$446$	4.01651	0.190187
$447$	42.2019	1.99608
$448$	−13.6771	−0.646181
$449$	−12.8845	−0.608058	−0.304029	−	0.952663i	$-0.598332\pi$
$449$	−12.8845	−0.608058	−0.304029	+	0.952663i	$0.598332\pi$
$450$	0	0
$451$	3.42629	0.161338
$452$	20.9832	0.986965
$453$	−55.0302	−2.58554
$454$	−0.399937	−0.0187700
$455$	0	0
$456$	21.1403	0.989987
$457$	0.122280	0.00572001	0.00286000	−	0.999996i	$-0.499090\pi$
$457$	0.122280	0.00572001	0.00286000	+	0.999996i	$0.499090\pi$
$458$	2.26041	0.105622
$459$	24.3185	1.13509
$460$	0	0
$461$	−23.2014	−1.08060	−0.540298	−	0.841474i	$-0.681689\pi$
$461$	−23.2014	−1.08060	−0.540298	+	0.841474i	$0.681689\pi$
$462$	−1.90776	−0.0887573
$463$	3.99507	0.185667	0.0928333	−	0.995682i	$-0.470408\pi$
$463$	3.99507	0.185667	0.0928333	+	0.995682i	$0.470408\pi$
$464$	−27.4643	−1.27500
$465$	0	0
$466$	−7.66397	−0.355027
$467$	−38.5295	−1.78293	−0.891467	−	0.453085i	$-0.850323\pi$
$467$	−38.5295	−1.78293	−0.891467	+	0.453085i	$0.850323\pi$
$468$	8.27177	0.382363
$469$	29.7996	1.37602
$470$	0	0
$471$	−43.2362	−1.99222
$472$	9.71431	0.447138
$473$	−4.30722	−0.198046
$474$	−4.52472	−0.207827
$475$	0	0
$476$	12.0674	0.553108
$477$	63.8272	2.92245
$478$	−3.50410	−0.160274
$479$	−4.15155	−0.189689	−0.0948445	−	0.995492i	$-0.530235\pi$
$479$	−4.15155	−0.189689	−0.0948445	+	0.995492i	$0.530235\pi$
$480$	0	0
$481$	4.11366	0.187567
$482$	−1.23986	−0.0564741
$483$	44.9988	2.04752
$484$	18.7519	0.852359
$485$	0	0
$486$	0.856878	0.0388688
$487$	1.26418	0.0572856	0.0286428	−	0.999590i	$-0.490881\pi$
$487$	1.26418	0.0572856	0.0286428	+	0.999590i	$0.490881\pi$
$488$	8.70844	0.394213
$489$	11.3460	0.513086
$490$	0	0
$491$	−36.5423	−1.64913	−0.824565	−	0.565767i	$-0.808580\pi$
$491$	−36.5423	−1.64913	−0.824565	+	0.565767i	$0.808580\pi$
$492$	17.3184	0.780774
$493$	22.3115	1.00486
$494$	−1.33607	−0.0601124
$495$	0	0
$496$	−3.58611	−0.161021
$497$	−22.1675	−0.994350
$498$	−0.793108	−0.0355400
$499$	−15.7894	−0.706831	−0.353416	−	0.935466i	$-0.614980\pi$
$499$	−15.7894	−0.706831	−0.353416	+	0.935466i	$0.614980\pi$
$500$	0	0
$501$	−34.2536	−1.53034
$502$	0.536356	0.0239388
$503$	−18.5564	−0.827390	−0.413695	−	0.910416i	$-0.635762\pi$
$503$	−18.5564	−0.827390	−0.413695	+	0.910416i	$0.635762\pi$
$504$	−12.9501	−0.576842
$505$	0	0
$506$	−2.11544	−0.0940427
$507$	36.9766	1.64219
$508$	−8.15623	−0.361874
$509$	23.0935	1.02360	0.511801	−	0.859104i	$-0.328978\pi$
$509$	23.0935	1.02360	0.511801	+	0.859104i	$0.328978\pi$
$510$	0	0
$511$	−10.9544	−0.484596
$512$	18.2912	0.808366
$513$	−57.2541	−2.52783
$514$	−1.80151	−0.0794614
$515$	0	0
$516$	−21.7711	−0.958421
$517$	−8.56762	−0.376803
$518$	−3.16294	−0.138972
$519$	16.9357	0.743393
$520$	0	0
$521$	36.7618	1.61056	0.805281	−	0.592893i	$-0.202014\pi$
$521$	36.7618	1.61056	0.805281	+	0.592893i	$0.202014\pi$
$522$	−11.7591	−0.514683
$523$	31.7538	1.38850	0.694249	−	0.719735i	$-0.255737\pi$
$523$	31.7538	1.38850	0.694249	+	0.719735i	$0.255737\pi$
$524$	−12.7374	−0.556434
$525$	0	0
$526$	0.216104	0.00942256
$527$	2.91329	0.126905
$528$	−12.0675	−0.525172
$529$	26.8973	1.16945
$530$	0	0
$531$	−54.3773	−2.35977
$532$	−28.4108	−1.23176
$533$	−2.22862	−0.0965322
$534$	5.32038	0.230235
$535$	0	0
$536$	−14.4180	−0.622764
$537$	35.8865	1.54862
$538$	0.291729	0.0125773
$539$	−2.71470	−0.116930
$540$	0	0
$541$	19.0037	0.817034	0.408517	−	0.912751i	$-0.366046\pi$
$541$	19.0037	0.817034	0.408517	+	0.912751i	$0.366046\pi$
$542$	1.43424	0.0616058
$543$	68.5134	2.94019
$544$	−8.80974	−0.377715
$545$	0	0
$546$	1.24090	0.0531056
$547$	3.98428	0.170356	0.0851778	−	0.996366i	$-0.472854\pi$
$547$	3.98428	0.170356	0.0851778	+	0.996366i	$0.472854\pi$
$548$	42.5645	1.81826
$549$	−48.7468	−2.08046
$550$	0	0
$551$	−52.5288	−2.23780
$552$	−21.7719	−0.926674
$553$	12.3815	0.526516
$554$	5.00054	0.212453
$555$	0	0
$556$	−21.6813	−0.919492
$557$	−41.8896	−1.77492	−0.887460	−	0.460885i	$-0.847532\pi$
$557$	−41.8896	−1.77492	−0.887460	+	0.460885i	$0.847532\pi$
$558$	−1.53543	−0.0650001
$559$	2.80162	0.118496
$560$	0	0
$561$	9.80344	0.413902
$562$	2.60296	0.109799
$563$	−13.4064	−0.565010	−0.282505	−	0.959266i	$-0.591165\pi$
$563$	−13.4064	−0.565010	−0.282505	+	0.959266i	$0.591165\pi$
$564$	−43.3056	−1.82350
$565$	0	0
$566$	8.38850	0.352595
$567$	15.7587	0.661804
$568$	10.7254	0.450027
$569$	−3.75926	−0.157597	−0.0787983	−	0.996891i	$-0.525108\pi$
$569$	−3.75926	−0.157597	−0.0787983	+	0.996891i	$0.525108\pi$
$570$	0	0
$571$	−10.0725	−0.421521	−0.210761	−	0.977538i	$-0.567594\pi$
$571$	−10.0725	−0.421521	−0.210761	+	0.977538i	$0.567594\pi$
$572$	1.61335	0.0674577
$573$	−10.4080	−0.434799
$574$	1.71355	0.0715223
$575$	0	0
$576$	−37.0419	−1.54341
$577$	−15.5629	−0.647894	−0.323947	−	0.946075i	$-0.605010\pi$
$577$	−15.5629	−0.647894	−0.323947	+	0.946075i	$0.605010\pi$
$578$	−2.24892	−0.0935426
$579$	6.52591	0.271207
$580$	0	0
$581$	2.17028	0.0900383
$582$	12.0027	0.497529
$583$	12.4491	0.515588
$584$	5.30011	0.219320
$585$	0	0
$586$	5.07167	0.209509
$587$	−20.9217	−0.863531	−0.431765	−	0.901986i	$-0.642109\pi$
$587$	−20.9217	−0.863531	−0.431765	+	0.901986i	$0.642109\pi$
$588$	−13.7216	−0.565871
$589$	−6.85889	−0.282616
$590$	0	0
$591$	31.1345	1.28070
$592$	−20.0071	−0.822287
$593$	−13.9196	−0.571610	−0.285805	−	0.958288i	$-0.592261\pi$
$593$	−13.9196	−0.571610	−0.285805	+	0.958288i	$0.592261\pi$
$594$	−2.49986	−0.102570
$595$	0	0
$596$	27.4409	1.12402
$597$	40.0625	1.63965
$598$	1.37598	0.0562680
$599$	−20.1940	−0.825104	−0.412552	−	0.910934i	$-0.635362\pi$
$599$	−20.1940	−0.825104	−0.412552	+	0.910934i	$0.635362\pi$
$600$	0	0
$601$	−14.5143	−0.592049	−0.296025	−	0.955180i	$-0.595661\pi$
$601$	−14.5143	−0.592049	−0.296025	+	0.955180i	$0.595661\pi$
$602$	−2.15412	−0.0877955
$603$	80.7070	3.28664
$604$	−35.7822	−1.45596
$605$	0	0
$606$	−14.4313	−0.586233
$607$	36.6572	1.48787	0.743934	−	0.668253i	$-0.232958\pi$
$607$	36.6572	1.48787	0.743934	+	0.668253i	$0.232958\pi$
$608$	20.7411	0.841165
$609$	48.7873	1.97696
$610$	0	0
$611$	5.57278	0.225451
$612$	32.6824	1.32111
$613$	−10.3229	−0.416938	−0.208469	−	0.978029i	$-0.566848\pi$
$613$	−10.3229	−0.416938	−0.208469	+	0.978029i	$0.566848\pi$
$614$	−6.68139	−0.269639
$615$	0	0
$616$	−2.52582	−0.101768
$617$	−23.3921	−0.941729	−0.470865	−	0.882206i	$-0.656058\pi$
$617$	−23.3921	−0.941729	−0.470865	+	0.882206i	$0.656058\pi$
$618$	−2.51678	−0.101240
$619$	31.4862	1.26554	0.632769	−	0.774340i	$-0.281918\pi$
$619$	31.4862	1.26554	0.632769	+	0.774340i	$0.281918\pi$
$620$	0	0
$621$	58.9646	2.36617
$622$	−2.50753	−0.100543
$623$	−14.5588	−0.583286
$624$	7.84929	0.314223
$625$	0	0
$626$	5.07299	0.202758
$627$	−23.0807	−0.921752
$628$	−28.1135	−1.12185
$629$	16.2534	0.648066
$630$	0	0
$631$	−16.6711	−0.663668	−0.331834	−	0.943338i	$-0.607667\pi$
$631$	−16.6711	−0.663668	−0.331834	+	0.943338i	$0.607667\pi$
$632$	−5.99059	−0.238293
$633$	39.2734	1.56098
$634$	1.78710	0.0709747
$635$	0	0
$636$	62.9247	2.49513
$637$	1.76577	0.0699622
$638$	−2.29354	−0.0908021
$639$	−60.0368	−2.37502
$640$	0	0
$641$	−42.2037	−1.66695	−0.833473	−	0.552560i	$-0.813651\pi$
$641$	−42.2037	−1.66695	−0.833473	+	0.552560i	$0.813651\pi$
$642$	−3.27991	−0.129448
$643$	30.9789	1.22169	0.610845	−	0.791751i	$-0.290830\pi$
$643$	30.9789	1.22169	0.610845	+	0.791751i	$0.290830\pi$
$644$	29.2596	1.15299
$645$	0	0
$646$	−5.27890	−0.207695
$647$	−8.32177	−0.327163	−0.163581	−	0.986530i	$-0.552305\pi$
$647$	−8.32177	−0.327163	−0.163581	+	0.986530i	$0.552305\pi$
$648$	−7.62458	−0.299522
$649$	−10.6059	−0.416319
$650$	0	0
$651$	6.37034	0.249673
$652$	7.37753	0.288926
$653$	18.7569	0.734012	0.367006	−	0.930218i	$-0.380383\pi$
$653$	18.7569	0.734012	0.367006	+	0.930218i	$0.380383\pi$
$654$	11.6580	0.455863
$655$	0	0
$656$	10.8390	0.423194
$657$	−29.6682	−1.15746
$658$	−4.28483	−0.167040
$659$	−25.3896	−0.989037	−0.494518	−	0.869167i	$-0.664656\pi$
$659$	−25.3896	−0.989037	−0.494518	+	0.869167i	$0.664656\pi$
$660$	0	0
$661$	−3.43376	−0.133558	−0.0667789	−	0.997768i	$-0.521272\pi$
$661$	−3.43376	−0.133558	−0.0667789	+	0.997768i	$0.521272\pi$
$662$	−7.16615	−0.278520
$663$	−6.37662	−0.247647
$664$	−1.05005	−0.0407499
$665$	0	0
$666$	−8.56626	−0.331936
$667$	54.0982	2.09469
$668$	−22.2727	−0.861756
$669$	−45.1317	−1.74489
$670$	0	0
$671$	−9.50773	−0.367042
$672$	−19.2638	−0.743117
$673$	8.30298	0.320056	0.160028	−	0.987112i	$-0.448842\pi$
$673$	8.30298	0.320056	0.160028	+	0.987112i	$0.448842\pi$
$674$	7.40788	0.285341
$675$	0	0
$676$	24.0433	0.924742
$677$	6.44471	0.247690	0.123845	−	0.992302i	$-0.460477\pi$
$677$	6.44471	0.247690	0.123845	+	0.992302i	$0.460477\pi$
$678$	8.52529	0.327412
$679$	−32.8445	−1.26046
$680$	0	0
$681$	4.49390	0.172207
$682$	−0.299476	−0.0114675
$683$	44.0122	1.68408	0.842040	−	0.539416i	$-0.181355\pi$
$683$	44.0122	1.68408	0.842040	+	0.539416i	$0.181355\pi$
$684$	−76.9456	−2.94209
$685$	0	0
$686$	−5.32619	−0.203355
$687$	−25.3992	−0.969040
$688$	−13.6259	−0.519481
$689$	−8.09746	−0.308489
$690$	0	0
$691$	23.7146	0.902146	0.451073	−	0.892487i	$-0.351041\pi$
$691$	23.7146	0.902146	0.451073	+	0.892487i	$0.351041\pi$
$692$	11.0121	0.418616
$693$	14.1387	0.537083
$694$	−5.09645	−0.193459
$695$	0	0
$696$	−23.6049	−0.894741
$697$	−8.80544	−0.333530
$698$	5.51116	0.208601
$699$	86.1165	3.25722
$700$	0	0
$701$	47.7474	1.80340	0.901698	−	0.432366i	$-0.142321\pi$
$701$	47.7474	1.80340	0.901698	+	0.432366i	$0.142321\pi$
$702$	1.62602	0.0613703
$703$	−38.2661	−1.44323
$704$	−7.22478	−0.272294
$705$	0	0
$706$	3.79773	0.142929
$707$	39.4902	1.48518
$708$	−53.6084	−2.01473
$709$	18.8673	0.708576	0.354288	−	0.935136i	$-0.384723\pi$
$709$	18.8673	0.708576	0.354288	+	0.935136i	$0.384723\pi$
$710$	0	0
$711$	33.5332	1.25759
$712$	7.04403	0.263986
$713$	7.06380	0.264541
$714$	4.90289	0.183486
$715$	0	0
$716$	23.3344	0.872049
$717$	39.3739	1.47045
$718$	5.61450	0.209531
$719$	2.09269	0.0780440	0.0390220	−	0.999238i	$-0.487576\pi$
$719$	2.09269	0.0780440	0.0390220	+	0.999238i	$0.487576\pi$
$720$	0	0
$721$	6.88697	0.256484
$722$	7.40885	0.275729
$723$	13.9317	0.518127
$724$	44.5494	1.65567
$725$	0	0
$726$	7.61875	0.282758
$727$	11.5637	0.428872	0.214436	−	0.976738i	$-0.431209\pi$
$727$	11.5637	0.428872	0.214436	+	0.976738i	$0.431209\pi$
$728$	1.64291	0.0608904
$729$	−31.6584	−1.17254
$730$	0	0
$731$	11.0694	0.409417
$732$	−48.0575	−1.77626
$733$	−19.6851	−0.727087	−0.363544	−	0.931577i	$-0.618433\pi$
$733$	−19.6851	−0.727087	−0.363544	+	0.931577i	$0.618433\pi$
$734$	−0.175846	−0.00649059
$735$	0	0
$736$	−21.3608	−0.787369
$737$	15.7414	0.579840
$738$	4.64085	0.170832
$739$	−1.35449	−0.0498258	−0.0249129	−	0.999690i	$-0.507931\pi$
$739$	−1.35449	−0.0498258	−0.0249129	+	0.999690i	$0.507931\pi$
$740$	0	0
$741$	15.0127	0.551507
$742$	6.22602	0.228564
$743$	28.3972	1.04179	0.520895	−	0.853621i	$-0.325598\pi$
$743$	28.3972	1.04179	0.520895	+	0.853621i	$0.325598\pi$
$744$	−3.08218	−0.112998
$745$	0	0
$746$	4.92387	0.180276
$747$	5.87781	0.215058
$748$	6.37449	0.233074
$749$	8.97523	0.327948
$750$	0	0
$751$	16.4155	0.599010	0.299505	−	0.954095i	$-0.403178\pi$
$751$	16.4155	0.599010	0.299505	+	0.954095i	$0.403178\pi$
$752$	−27.1036	−0.988368
$753$	−6.02678	−0.219628
$754$	1.49183	0.0543291
$755$	0	0
$756$	34.5766	1.25754
$757$	19.3374	0.702829	0.351415	−	0.936220i	$-0.385701\pi$
$757$	19.3374	0.702829	0.351415	+	0.936220i	$0.385701\pi$
$758$	−3.85661	−0.140078
$759$	23.7702	0.862803
$760$	0	0
$761$	21.6923	0.786346	0.393173	−	0.919464i	$-0.371377\pi$
$761$	21.6923	0.786346	0.393173	+	0.919464i	$0.371377\pi$
$762$	−3.31381	−0.120047
$763$	−31.9012	−1.15490
$764$	−6.76756	−0.244842
$765$	0	0
$766$	0.734188	0.0265273
$767$	6.89859	0.249094
$768$	−31.7752	−1.14659
$769$	−23.6351	−0.852305	−0.426153	−	0.904651i	$-0.640131\pi$
$769$	−23.6351	−0.852305	−0.426153	+	0.904651i	$0.640131\pi$
$770$	0	0
$771$	20.2428	0.729026
$772$	4.24334	0.152721
$773$	−3.67852	−0.132307	−0.0661536	−	0.997809i	$-0.521073\pi$
$773$	−3.67852	−0.132307	−0.0661536	+	0.997809i	$0.521073\pi$
$774$	−5.83406	−0.209701
$775$	0	0
$776$	15.8913	0.570463
$777$	35.5404	1.27501
$778$	10.0210	0.359271
$779$	20.7310	0.742766
$780$	0	0
$781$	−11.7098	−0.419009
$782$	5.43661	0.194413
$783$	63.9289	2.28463
$784$	−8.58793	−0.306712
$785$	0	0
$786$	−5.17509	−0.184589
$787$	−3.62197	−0.129109	−0.0645547	−	0.997914i	$-0.520563\pi$
$787$	−3.62197	−0.129109	−0.0645547	+	0.997914i	$0.520563\pi$
$788$	20.2445	0.721182
$789$	−2.42825	−0.0864481
$790$	0	0
$791$	−23.3288	−0.829477
$792$	−6.84074	−0.243075
$793$	6.18427	0.219610
$794$	−2.73864	−0.0971907
$795$	0	0
$796$	26.0498	0.923312
$797$	4.34495	0.153906	0.0769529	−	0.997035i	$-0.475481\pi$
$797$	4.34495	0.153906	0.0769529	+	0.997035i	$0.475481\pi$
$798$	−11.5431	−0.408621
$799$	22.0185	0.778958
$800$	0	0
$801$	−39.4300	−1.39319
$802$	−3.26557	−0.115311
$803$	−5.78658	−0.204204
$804$	79.5658	2.80607
$805$	0	0
$806$	0.194793	0.00686130
$807$	−3.27802	−0.115392
$808$	−19.1067	−0.672170
$809$	−8.74314	−0.307392	−0.153696	−	0.988118i	$-0.549118\pi$
$809$	−8.74314	−0.307392	−0.153696	+	0.988118i	$0.549118\pi$
$810$	0	0
$811$	28.7426	1.00929	0.504644	−	0.863328i	$-0.331624\pi$
$811$	28.7426	1.00929	0.504644	+	0.863328i	$0.331624\pi$
$812$	31.7229	1.11326
$813$	−16.1159	−0.565208
$814$	−1.67079	−0.0585612
$815$	0	0
$816$	31.0131	1.08568
$817$	−26.0612	−0.911764
$818$	8.94257	0.312670
$819$	−9.19645	−0.321350
$820$	0	0
$821$	53.2555	1.85863	0.929315	−	0.369288i	$-0.120398\pi$
$821$	53.2555	1.85863	0.929315	+	0.369288i	$0.120398\pi$
$822$	17.2936	0.603184
$823$	22.7844	0.794213	0.397106	−	0.917773i	$-0.370014\pi$
$823$	22.7844	0.794213	0.397106	+	0.917773i	$0.370014\pi$
$824$	−3.33214	−0.116081
$825$	0	0
$826$	−5.30423	−0.184558
$827$	12.7870	0.444648	0.222324	−	0.974973i	$-0.428636\pi$
$827$	12.7870	0.444648	0.222324	+	0.974973i	$0.428636\pi$
$828$	79.2443	2.75393
$829$	5.19645	0.180480	0.0902400	−	0.995920i	$-0.471237\pi$
$829$	5.19645	0.180480	0.0902400	+	0.995920i	$0.471237\pi$
$830$	0	0
$831$	−56.1887	−1.94916
$832$	4.69933	0.162920
$833$	6.97668	0.241728
$834$	−8.80894	−0.305029
$835$	0	0
$836$	−15.0077	−0.519053
$837$	8.34744	0.288530
$838$	6.58021	0.227310
$839$	−6.70333	−0.231425	−0.115712	−	0.993283i	$-0.536915\pi$
$839$	−6.70333	−0.231425	−0.115712	+	0.993283i	$0.536915\pi$
$840$	0	0
$841$	29.6527	1.02251
$842$	1.85966	0.0640882
$843$	−29.2482	−1.00736
$844$	25.5367	0.879010
$845$	0	0
$846$	−11.6047	−0.398978
$847$	−20.8481	−0.716350
$848$	39.3826	1.35240
$849$	−94.2576	−3.23491
$850$	0	0
$851$	39.4093	1.35093
$852$	−59.1879	−2.02775
$853$	−7.30984	−0.250284	−0.125142	−	0.992139i	$-0.539939\pi$
$853$	−7.30984	−0.250284	−0.125142	+	0.992139i	$0.539939\pi$
$854$	−4.75500	−0.162713
$855$	0	0
$856$	−4.34251	−0.148424
$857$	24.4667	0.835768	0.417884	−	0.908500i	$-0.362772\pi$
$857$	24.4667	0.835768	0.417884	+	0.908500i	$0.362772\pi$
$858$	0.655493	0.0223782
$859$	−35.9327	−1.22601	−0.613005	−	0.790079i	$-0.710039\pi$
$859$	−35.9327	−1.22601	−0.613005	+	0.790079i	$0.710039\pi$
$860$	0	0
$861$	−19.2544	−0.656188
$862$	−1.83363	−0.0624535
$863$	−14.7380	−0.501686	−0.250843	−	0.968028i	$-0.580708\pi$
$863$	−14.7380	−0.501686	−0.250843	+	0.968028i	$0.580708\pi$
$864$	−25.2425	−0.858767
$865$	0	0
$866$	−4.29826	−0.146061
$867$	25.2700	0.858215
$868$	4.14218	0.140595
$869$	6.54042	0.221869
$870$	0	0
$871$	−10.2389	−0.346933
$872$	15.4348	0.522689
$873$	−88.9536	−3.01062
$874$	−12.7996	−0.432954
$875$	0	0
$876$	−29.2487	−0.988221
$877$	1.10555	0.0373317	0.0186658	−	0.999826i	$-0.494058\pi$
$877$	1.10555	0.0373317	0.0186658	+	0.999826i	$0.494058\pi$
$878$	3.46460	0.116925
$879$	−56.9879	−1.92215
$880$	0	0
$881$	−4.50629	−0.151821	−0.0759104	−	0.997115i	$-0.524186\pi$
$881$	−4.50629	−0.151821	−0.0759104	+	0.997115i	$0.524186\pi$
$882$	−3.67702	−0.123812
$883$	−22.1741	−0.746218	−0.373109	−	0.927787i	$-0.621708\pi$
$883$	−22.1741	−0.746218	−0.373109	+	0.927787i	$0.621708\pi$
$884$	−4.14627	−0.139454
$885$	0	0
$886$	6.95942	0.233806
$887$	27.5123	0.923773	0.461887	−	0.886939i	$-0.347173\pi$
$887$	27.5123	0.923773	0.461887	+	0.886939i	$0.347173\pi$
$888$	−17.1956	−0.577047
$889$	9.06798	0.304130
$890$	0	0
$891$	8.32439	0.278878
$892$	−29.3459	−0.982575
$893$	−51.8391	−1.73473
$894$	11.1490	0.372880
$895$	0	0
$896$	−16.5920	−0.554301
$897$	−15.4612	−0.516236
$898$	−3.40387	−0.113589
$899$	7.65851	0.255425
$900$	0	0
$901$	−31.9937	−1.06586
$902$	0.905167	0.0301388
$903$	24.2049	0.805487
$904$	11.2872	0.375408
$905$	0	0
$906$	−14.5380	−0.482994
$907$	−5.13775	−0.170596	−0.0852982	−	0.996355i	$-0.527184\pi$
$907$	−5.13775	−0.170596	−0.0852982	+	0.996355i	$0.527184\pi$
$908$	2.92207	0.0969722
$909$	106.952	3.54738
$910$	0	0
$911$	−24.8391	−0.822957	−0.411478	−	0.911420i	$-0.634987\pi$
$911$	−24.8391	−0.822957	−0.411478	+	0.911420i	$0.634987\pi$
$912$	−73.0155	−2.41779
$913$	1.14643	0.0379412
$914$	0.0323043	0.00106853
$915$	0	0
$916$	−16.5153	−0.545681
$917$	14.1612	0.467645
$918$	6.42455	0.212042
$919$	−24.2553	−0.800108	−0.400054	−	0.916492i	$-0.631009\pi$
$919$	−24.2553	−0.800108	−0.400054	+	0.916492i	$0.631009\pi$
$920$	0	0
$921$	75.0756	2.47383
$922$	−6.12942	−0.201862
$923$	7.61659	0.250703
$924$	13.9387	0.458551
$925$	0	0
$926$	1.05543	0.0346836
$927$	18.6521	0.612617
$928$	−23.1592	−0.760237
$929$	20.3390	0.667301	0.333650	−	0.942697i	$-0.391719\pi$
$929$	20.3390	0.667301	0.333650	+	0.942697i	$0.391719\pi$
$930$	0	0
$931$	−16.4255	−0.538324
$932$	55.9955	1.83419
$933$	28.1759	0.922437
$934$	−10.1789	−0.333062
$935$	0	0
$936$	4.44954	0.145438
$937$	−56.2552	−1.83778	−0.918888	−	0.394518i	$-0.870912\pi$
$937$	−56.2552	−1.83778	−0.918888	+	0.394518i	$0.870912\pi$
$938$	7.87256	0.257048
$939$	−57.0028	−1.86022
$940$	0	0
$941$	34.4730	1.12379	0.561894	−	0.827210i	$-0.310073\pi$
$941$	34.4730	1.12379	0.561894	+	0.827210i	$0.310073\pi$
$942$	−11.4223	−0.372158
$943$	−21.3504	−0.695263
$944$	−33.5518	−1.09202
$945$	0	0
$946$	−1.13789	−0.0369961
$947$	−39.4986	−1.28353	−0.641766	−	0.766901i	$-0.721798\pi$
$947$	−39.4986	−1.28353	−0.641766	+	0.766901i	$0.721798\pi$
$948$	33.0590	1.07371
$949$	3.76386	0.122180
$950$	0	0
$951$	−20.0808	−0.651164
$952$	6.49128	0.210384
$953$	21.9633	0.711462	0.355731	−	0.934588i	$-0.384232\pi$
$953$	21.9633	0.711462	0.355731	+	0.934588i	$0.384232\pi$
$954$	16.8621	0.545930
$955$	0	0
$956$	25.6021	0.828031
$957$	25.7714	0.833072
$958$	−1.09677	−0.0354350
$959$	−47.3226	−1.52813
$960$	0	0
$961$	1.00000	0.0322581
$962$	1.08676	0.0350386
$963$	24.3078	0.783308
$964$	9.05882	0.291765
$965$	0	0
$966$	11.8879	0.382488
$967$	−40.1621	−1.29153	−0.645763	−	0.763538i	$-0.723461\pi$
$967$	−40.1621	−1.29153	−0.645763	+	0.763538i	$0.723461\pi$
$968$	10.0870	0.324208
$969$	59.3165	1.90552
$970$	0	0
$971$	−57.3568	−1.84067	−0.920333	−	0.391136i	$-0.872082\pi$
$971$	−57.3568	−1.84067	−0.920333	+	0.391136i	$0.872082\pi$
$972$	−6.26062	−0.200810
$973$	24.1050	0.772770
$974$	0.333976	0.0107013
$975$	0	0
$976$	−30.0777	−0.962762
$977$	−13.1468	−0.420605	−0.210302	−	0.977636i	$-0.567445\pi$
$977$	−13.1468	−0.420605	−0.210302	+	0.977636i	$0.567445\pi$
$978$	2.99743	0.0958473
$979$	−7.69055	−0.245791
$980$	0	0
$981$	−86.3986	−2.75850
$982$	−9.65385	−0.308067
$983$	1.42361	0.0454062	0.0227031	−	0.999742i	$-0.492773\pi$
$983$	1.42361	0.0454062	0.0227031	+	0.999742i	$0.492773\pi$
$984$	9.31590	0.296980
$985$	0	0
$986$	5.89432	0.187713
$987$	48.1466	1.53252
$988$	9.76172	0.310562
$989$	26.8397	0.853454
$990$	0	0
$991$	2.78624	0.0885077	0.0442539	−	0.999020i	$-0.485909\pi$
$991$	2.78624	0.0885077	0.0442539	+	0.999020i	$0.485909\pi$
$992$	−3.02398	−0.0960115
$993$	80.5226	2.55531
$994$	−5.85629	−0.185750
$995$	0	0
$996$	5.79470	0.183612
$997$	22.0927	0.699684	0.349842	−	0.936809i	$-0.386235\pi$
$997$	22.0927	0.699684	0.349842	+	0.936809i	$0.386235\pi$
$998$	−4.17130	−0.132040
$999$	46.5707	1.47343

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.a.h.1.4	✓	5
3.2	odd	2		6975.2.a.by.1.2		5
5.2	odd	4		775.2.b.g.249.6		10
5.3	odd	4		775.2.b.g.249.5		10
5.4	even	2		775.2.a.k.1.2	yes	5
15.14	odd	2		6975.2.a.bp.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
775.2.a.h.1.4	✓	5	1.1	even	1	trivial
775.2.a.k.1.2	yes	5	5.4	even	2
775.2.b.g.249.5		10	5.3	odd	4
775.2.b.g.249.6		10	5.2	odd	4
6975.2.a.bp.1.4		5	15.14	odd	2
6975.2.a.by.1.2		5	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.a (trivial)

\(f(q)\)	\(=\)	\(q+0.264183 q^{2} -2.96850 q^{3} -1.93021 q^{4} -0.784228 q^{6} +2.14598 q^{7} -1.03829 q^{8} +5.81200 q^{9} +O(q^{10})\)	\(q+0.264183 q^{2} -2.96850 q^{3} -1.93021 q^{4} -0.784228 q^{6} +2.14598 q^{7} -1.03829 q^{8} +5.81200 q^{9} +1.13359 q^{11} +5.72982 q^{12} -0.737342 q^{13} +0.566932 q^{14} +3.58611 q^{16} -2.91329 q^{17} +1.53543 q^{18} +6.85889 q^{19} -6.37034 q^{21} +0.299476 q^{22} -7.06380 q^{23} +3.08218 q^{24} -0.194793 q^{26} -8.34744 q^{27} -4.14218 q^{28} -7.65851 q^{29} -1.00000 q^{31} +3.02398 q^{32} -3.36507 q^{33} -0.769643 q^{34} -11.2184 q^{36} -5.57905 q^{37} +1.81200 q^{38} +2.18880 q^{39} +3.02250 q^{41} -1.68294 q^{42} -3.79962 q^{43} -2.18807 q^{44} -1.86614 q^{46} -7.55794 q^{47} -10.6454 q^{48} -2.39477 q^{49} +8.64812 q^{51} +1.42322 q^{52} +10.9820 q^{53} -2.20525 q^{54} -2.22816 q^{56} -20.3606 q^{57} -2.02325 q^{58} -9.35603 q^{59} -8.38726 q^{61} -0.264183 q^{62} +12.4724 q^{63} -6.37334 q^{64} -0.888995 q^{66} +13.8863 q^{67} +5.62326 q^{68} +20.9689 q^{69} -10.3298 q^{71} -6.03457 q^{72} -5.10463 q^{73} -1.47389 q^{74} -13.2391 q^{76} +2.43267 q^{77} +0.578244 q^{78} +5.76964 q^{79} +7.34337 q^{81} +0.798495 q^{82} +1.01132 q^{83} +12.2961 q^{84} -1.00379 q^{86} +22.7343 q^{87} -1.17700 q^{88} -6.78423 q^{89} -1.58232 q^{91} +13.6346 q^{92} +2.96850 q^{93} -1.99668 q^{94} -8.97669 q^{96} -15.3051 q^{97} -0.632659 q^{98} +6.58844 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 4 q^{2} - 3 q^{3} + 6 q^{4} - q^{6} - 2 q^{7} - 9 q^{8} + 6 q^{9}+O(q^{10}) \) 5 * q - 4 * q^2 - 3 * q^3 + 6 * q^4 - q^6 - 2 * q^7 - 9 * q^8 + 6 * q^9	\( 5 q - 4 q^{2} - 3 q^{3} + 6 q^{4} - q^{6} - 2 q^{7} - 9 q^{8} + 6 q^{9} - 2 q^{11} - 5 q^{12} - 4 q^{13} + 2 q^{14} + 4 q^{16} - 19 q^{17} - 5 q^{18} + 8 q^{19} - 15 q^{21} + 10 q^{22} - 12 q^{23} + 26 q^{24} - 16 q^{26} - 6 q^{27} - 6 q^{28} + 6 q^{29} - 5 q^{31} - 7 q^{32} - 3 q^{33} + 31 q^{34} - 13 q^{36} - 16 q^{37} - 14 q^{38} - 13 q^{39} - 2 q^{41} + 22 q^{42} - q^{43} - 4 q^{44} - 11 q^{46} - 8 q^{47} - 31 q^{48} - 9 q^{49} + 5 q^{51} + 26 q^{52} - 3 q^{53} + 10 q^{54} - 9 q^{56} - 14 q^{57} - 5 q^{58} - 4 q^{59} - 5 q^{61} + 4 q^{62} + 26 q^{63} - 5 q^{64} - 25 q^{66} - 13 q^{67} - 30 q^{68} + 10 q^{69} + 6 q^{71} - 2 q^{72} - 19 q^{73} + 4 q^{74} - 5 q^{76} - 23 q^{77} + 38 q^{78} - 6 q^{79} - 7 q^{81} + 27 q^{82} - 18 q^{83} - 15 q^{84} - 7 q^{86} + 5 q^{87} + q^{88} - 31 q^{89} + 8 q^{91} + 16 q^{92} + 3 q^{93} - 14 q^{94} + 10 q^{96} + q^{97} - 10 q^{98} - 33 q^{99}+O(q^{100}) \) 5 * q - 4 * q^2 - 3 * q^3 + 6 * q^4 - q^6 - 2 * q^7 - 9 * q^8 + 6 * q^9 - 2 * q^11 - 5 * q^12 - 4 * q^13 + 2 * q^14 + 4 * q^16 - 19 * q^17 - 5 * q^18 + 8 * q^19 - 15 * q^21 + 10 * q^22 - 12 * q^23 + 26 * q^24 - 16 * q^26 - 6 * q^27 - 6 * q^28 + 6 * q^29 - 5 * q^31 - 7 * q^32 - 3 * q^33 + 31 * q^34 - 13 * q^36 - 16 * q^37 - 14 * q^38 - 13 * q^39 - 2 * q^41 + 22 * q^42 - q^43 - 4 * q^44 - 11 * q^46 - 8 * q^47 - 31 * q^48 - 9 * q^49 + 5 * q^51 + 26 * q^52 - 3 * q^53 + 10 * q^54 - 9 * q^56 - 14 * q^57 - 5 * q^58 - 4 * q^59 - 5 * q^61 + 4 * q^62 + 26 * q^63 - 5 * q^64 - 25 * q^66 - 13 * q^67 - 30 * q^68 + 10 * q^69 + 6 * q^71 - 2 * q^72 - 19 * q^73 + 4 * q^74 - 5 * q^76 - 23 * q^77 + 38 * q^78 - 6 * q^79 - 7 * q^81 + 27 * q^82 - 18 * q^83 - 15 * q^84 - 7 * q^86 + 5 * q^87 + q^88 - 31 * q^89 + 8 * q^91 + 16 * q^92 + 3 * q^93 - 14 * q^94 + 10 * q^96 + q^97 - 10 * q^98 - 33 * q^99

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