LMFDB - Embedded newform 4375.2.a.o.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4375,2,Mod(1,4375)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4375, 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("4375.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4375 = 5^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4375.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:	$34.9345508843$
Analytic rank:	$1$
Dimension:	$28$
Twist minimal:	no (minimal twist has level 175)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	4375.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.198876 q^{2} -1.54520 q^{3} -1.96045 q^{4} +0.307303 q^{6} +1.00000 q^{7} +0.787638 q^{8} -0.612360 q^{9} +O(q^{10})$	\(q-0.198876 q^{2} -1.54520 q^{3} -1.96045 q^{4} +0.307303 q^{6} +1.00000 q^{7} +0.787638 q^{8} -0.612360 q^{9} +3.14562 q^{11} +3.02928 q^{12} -6.50036 q^{13} -0.198876 q^{14} +3.76425 q^{16} +2.85384 q^{17} +0.121784 q^{18} -3.43490 q^{19} -1.54520 q^{21} -0.625589 q^{22} +0.580225 q^{23} -1.21706 q^{24} +1.29277 q^{26} +5.58182 q^{27} -1.96045 q^{28} +1.11204 q^{29} -1.92597 q^{31} -2.32390 q^{32} -4.86062 q^{33} -0.567561 q^{34} +1.20050 q^{36} -2.52448 q^{37} +0.683119 q^{38} +10.0444 q^{39} +5.15481 q^{41} +0.307303 q^{42} +3.23994 q^{43} -6.16683 q^{44} -0.115393 q^{46} -3.54129 q^{47} -5.81652 q^{48} +1.00000 q^{49} -4.40975 q^{51} +12.7436 q^{52} +0.713940 q^{53} -1.11009 q^{54} +0.787638 q^{56} +5.30760 q^{57} -0.221157 q^{58} +10.6183 q^{59} +8.53936 q^{61} +0.383030 q^{62} -0.612360 q^{63} -7.06634 q^{64} +0.966660 q^{66} -15.2464 q^{67} -5.59481 q^{68} -0.896563 q^{69} -11.8070 q^{71} -0.482318 q^{72} -1.87075 q^{73} +0.502059 q^{74} +6.73394 q^{76} +3.14562 q^{77} -1.99758 q^{78} +8.48593 q^{79} -6.78794 q^{81} -1.02517 q^{82} +11.9004 q^{83} +3.02928 q^{84} -0.644347 q^{86} -1.71832 q^{87} +2.47761 q^{88} +16.7559 q^{89} -6.50036 q^{91} -1.13750 q^{92} +2.97601 q^{93} +0.704278 q^{94} +3.59088 q^{96} +10.0125 q^{97} -0.198876 q^{98} -1.92625 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 8 q^{2} - 8 q^{3} + 24 q^{4} + 28 q^{7} - 24 q^{8} + 22 q^{9}+O(q^{10}) $ 28 * q - 8 * q^2 - 8 * q^3 + 24 * q^4 + 28 * q^7 - 24 * q^8 + 22 * q^9	$ 28 q - 8 q^{2} - 8 q^{3} + 24 q^{4} + 28 q^{7} - 24 q^{8} + 22 q^{9} - 16 q^{11} - 24 q^{12} - 16 q^{13} - 8 q^{14} + 24 q^{16} - 40 q^{17} - 24 q^{18} + 4 q^{19} - 8 q^{21} - 16 q^{22} - 32 q^{23} + 14 q^{24} + 6 q^{26} - 32 q^{27} + 24 q^{28} - 24 q^{29} + 6 q^{31} - 56 q^{32} - 28 q^{33} + 18 q^{36} - 32 q^{37} - 40 q^{38} - 28 q^{39} + 2 q^{41} - 16 q^{43} - 26 q^{44} - 12 q^{46} - 26 q^{47} - 46 q^{48} + 28 q^{49} - 22 q^{51} - 28 q^{52} - 60 q^{53} + 38 q^{54} - 24 q^{56} - 76 q^{57} - 16 q^{58} + 8 q^{59} + 18 q^{61} - 34 q^{62} + 22 q^{63} + 28 q^{64} + 38 q^{66} - 24 q^{67} - 62 q^{68} + 14 q^{69} - 54 q^{71} - 40 q^{72} - 46 q^{73} - 30 q^{74} + 26 q^{76} - 16 q^{77} - 32 q^{78} - 30 q^{79} + 4 q^{81} - 22 q^{82} - 60 q^{83} - 24 q^{84} - 10 q^{86} - 18 q^{87} - 16 q^{88} + 6 q^{89} - 16 q^{91} - 72 q^{92} - 48 q^{93} + 86 q^{94} + 106 q^{96} - 70 q^{97} - 8 q^{98} - 30 q^{99}+O(q^{100}) $ 28 * q - 8 * q^2 - 8 * q^3 + 24 * q^4 + 28 * q^7 - 24 * q^8 + 22 * q^9 - 16 * q^11 - 24 * q^12 - 16 * q^13 - 8 * q^14 + 24 * q^16 - 40 * q^17 - 24 * q^18 + 4 * q^19 - 8 * q^21 - 16 * q^22 - 32 * q^23 + 14 * q^24 + 6 * q^26 - 32 * q^27 + 24 * q^28 - 24 * q^29 + 6 * q^31 - 56 * q^32 - 28 * q^33 + 18 * q^36 - 32 * q^37 - 40 * q^38 - 28 * q^39 + 2 * q^41 - 16 * q^43 - 26 * q^44 - 12 * q^46 - 26 * q^47 - 46 * q^48 + 28 * q^49 - 22 * q^51 - 28 * q^52 - 60 * q^53 + 38 * q^54 - 24 * q^56 - 76 * q^57 - 16 * q^58 + 8 * q^59 + 18 * q^61 - 34 * q^62 + 22 * q^63 + 28 * q^64 + 38 * q^66 - 24 * q^67 - 62 * q^68 + 14 * q^69 - 54 * q^71 - 40 * q^72 - 46 * q^73 - 30 * q^74 + 26 * q^76 - 16 * q^77 - 32 * q^78 - 30 * q^79 + 4 * q^81 - 22 * q^82 - 60 * q^83 - 24 * q^84 - 10 * q^86 - 18 * q^87 - 16 * q^88 + 6 * q^89 - 16 * q^91 - 72 * q^92 - 48 * q^93 + 86 * q^94 + 106 * q^96 - 70 * q^97 - 8 * q^98 - 30 * 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 $

$2$	−0.198876	−0.140627	−0.0703133	−	0.997525i	$-0.522400\pi$
$2$	−0.198876	−0.140627	−0.0703133	+	0.997525i	$0.522400\pi$
$3$	−1.54520	−0.892121	−0.446061	−	0.895003i	$-0.647173\pi$
$3$	−1.54520	−0.892121	−0.446061	+	0.895003i	$0.647173\pi$
$4$	−1.96045	−0.980224
$5$	0	0
$5$	0	0
$6$	0.307303	0.125456
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0.787638	0.278472
$9$	−0.612360	−0.204120
$10$	0	0
$11$	3.14562	0.948441	0.474221	−	0.880406i	$-0.342730\pi$
$11$	3.14562	0.948441	0.474221	+	0.880406i	$0.342730\pi$
$12$	3.02928	0.874479
$13$	−6.50036	−1.80288	−0.901438	−	0.432908i	$-0.857488\pi$
$13$	−6.50036	−1.80288	−0.901438	+	0.432908i	$0.857488\pi$
$14$	−0.198876	−0.0531519
$15$	0	0
$16$	3.76425	0.941064
$17$	2.85384	0.692158	0.346079	−	0.938205i	$-0.387513\pi$
$17$	2.85384	0.692158	0.346079	+	0.938205i	$0.387513\pi$
$18$	0.121784	0.0287047
$19$	−3.43490	−0.788020	−0.394010	−	0.919106i	$-0.628912\pi$
$19$	−3.43490	−0.788020	−0.394010	+	0.919106i	$0.628912\pi$
$20$	0	0
$21$	−1.54520	−0.337190
$22$	−0.625589	−0.133376
$23$	0.580225	0.120985	0.0604926	−	0.998169i	$-0.480733\pi$
$23$	0.580225	0.120985	0.0604926	+	0.998169i	$0.480733\pi$
$24$	−1.21706	−0.248431
$25$	0	0
$26$	1.29277	0.253532
$27$	5.58182	1.07422
$28$	−1.96045	−0.370490
$29$	1.11204	0.206500	0.103250	−	0.994655i	$-0.467076\pi$
$29$	1.11204	0.206500	0.103250	+	0.994655i	$0.467076\pi$
$30$	0	0
$31$	−1.92597	−0.345915	−0.172957	−	0.984929i	$-0.555332\pi$
$31$	−1.92597	−0.345915	−0.172957	+	0.984929i	$0.555332\pi$
$32$	−2.32390	−0.410811
$33$	−4.86062	−0.846125
$34$	−0.567561	−0.0973359
$35$	0	0
$36$	1.20050	0.200083
$37$	−2.52448	−0.415022	−0.207511	−	0.978233i	$-0.566536\pi$
$37$	−2.52448	−0.415022	−0.207511	+	0.978233i	$0.566536\pi$
$38$	0.683119	0.110817
$39$	10.0444	1.60838
$40$	0	0
$41$	5.15481	0.805046	0.402523	−	0.915410i	$-0.368133\pi$
$41$	5.15481	0.805046	0.402523	+	0.915410i	$0.368133\pi$
$42$	0.307303	0.0474179
$43$	3.23994	0.494086	0.247043	−	0.969004i	$-0.420541\pi$
$43$	3.23994	0.494086	0.247043	+	0.969004i	$0.420541\pi$
$44$	−6.16683	−0.929685
$45$	0	0
$46$	−0.115393	−0.0170138
$47$	−3.54129	−0.516550	−0.258275	−	0.966071i	$-0.583154\pi$
$47$	−3.54129	−0.516550	−0.258275	+	0.966071i	$0.583154\pi$
$48$	−5.81652	−0.839543
$49$	1.00000	0.142857
$50$	0	0
$51$	−4.40975	−0.617489
$52$	12.7436	1.76722
$53$	0.713940	0.0980672	0.0490336	−	0.998797i	$-0.484386\pi$
$53$	0.713940	0.0980672	0.0490336	+	0.998797i	$0.484386\pi$
$54$	−1.11009	−0.151064
$55$	0	0
$56$	0.787638	0.105253
$57$	5.30760	0.703009
$58$	−0.221157	−0.0290394
$59$	10.6183	1.38238	0.691192	−	0.722672i	$-0.257086\pi$
$59$	10.6183	1.38238	0.691192	+	0.722672i	$0.257086\pi$
$60$	0	0
$61$	8.53936	1.09335	0.546677	−	0.837344i	$-0.315893\pi$
$61$	8.53936	1.09335	0.546677	+	0.837344i	$0.315893\pi$
$62$	0.383030	0.0486448
$63$	−0.612360	−0.0771501
$64$	−7.06634	−0.883293
$65$	0	0
$66$	0.966660	0.118988
$67$	−15.2464	−1.86264	−0.931320	−	0.364202i	$-0.881342\pi$
$67$	−15.2464	−1.86264	−0.931320	+	0.364202i	$0.881342\pi$
$68$	−5.59481	−0.678470
$69$	−0.896563	−0.107934
$70$	0	0
$71$	−11.8070	−1.40123	−0.700616	−	0.713539i	$-0.747091\pi$
$71$	−11.8070	−1.40123	−0.700616	+	0.713539i	$0.747091\pi$
$72$	−0.482318	−0.0568417
$73$	−1.87075	−0.218955	−0.109477	−	0.993989i	$-0.534918\pi$
$73$	−1.87075	−0.218955	−0.109477	+	0.993989i	$0.534918\pi$
$74$	0.502059	0.0583631
$75$	0	0
$76$	6.73394	0.772436
$77$	3.14562	0.358477
$78$	−1.99758	−0.226182
$79$	8.48593	0.954741	0.477371	−	0.878702i	$-0.341590\pi$
$79$	8.48593	0.954741	0.477371	+	0.878702i	$0.341590\pi$
$80$	0	0
$81$	−6.78794	−0.754215
$82$	−1.02517	−0.113211
$83$	11.9004	1.30623	0.653117	−	0.757257i	$-0.273461\pi$
$83$	11.9004	1.30623	0.653117	+	0.757257i	$0.273461\pi$
$84$	3.02928	0.330522
$85$	0	0
$86$	−0.644347	−0.0694817
$87$	−1.71832	−0.184223
$88$	2.47761	0.264115
$89$	16.7559	1.77612	0.888059	−	0.459729i	$-0.152053\pi$
$89$	16.7559	1.77612	0.888059	+	0.459729i	$0.152053\pi$
$90$	0	0
$91$	−6.50036	−0.681423
$92$	−1.13750	−0.118593
$93$	2.97601	0.308598
$94$	0.704278	0.0726407
$95$	0	0
$96$	3.59088	0.366493
$97$	10.0125	1.01661	0.508306	−	0.861177i	$-0.330272\pi$
$97$	10.0125	1.01661	0.508306	+	0.861177i	$0.330272\pi$
$98$	−0.198876	−0.0200895
$99$	−1.92625	−0.193596
$100$	0	0
$101$	18.6057	1.85133	0.925667	−	0.378339i	$-0.123505\pi$
$101$	18.6057	1.85133	0.925667	+	0.378339i	$0.123505\pi$
$102$	0.876995	0.0868354
$103$	−6.82241	−0.672232	−0.336116	−	0.941821i	$-0.609113\pi$
$103$	−6.82241	−0.672232	−0.336116	+	0.941821i	$0.609113\pi$
$104$	−5.11994	−0.502051
$105$	0	0
$106$	−0.141986	−0.0137909
$107$	11.2305	1.08570	0.542848	−	0.839831i	$-0.317346\pi$
$107$	11.2305	1.08570	0.542848	+	0.839831i	$0.317346\pi$
$108$	−10.9429	−1.05298
$109$	−18.0473	−1.72862	−0.864309	−	0.502961i	$-0.832244\pi$
$109$	−18.0473	−1.72862	−0.864309	+	0.502961i	$0.832244\pi$
$110$	0	0
$111$	3.90082	0.370250
$112$	3.76425	0.355689
$113$	−10.9086	−1.02620	−0.513098	−	0.858330i	$-0.671502\pi$
$113$	−10.9086	−1.02620	−0.513098	+	0.858330i	$0.671502\pi$
$114$	−1.05556	−0.0988618
$115$	0	0
$116$	−2.18009	−0.202416
$117$	3.98056	0.368003
$118$	−2.11172	−0.194400
$119$	2.85384	0.261611
$120$	0	0
$121$	−1.10505	−0.100459
$122$	−1.69827	−0.153755
$123$	−7.96520	−0.718198
$124$	3.77577	0.339074
$125$	0	0
$126$	0.121784	0.0108494
$127$	−12.4530	−1.10503	−0.552514	−	0.833504i	$-0.686331\pi$
$127$	−12.4530	−1.10503	−0.552514	+	0.833504i	$0.686331\pi$
$128$	6.05312	0.535025
$129$	−5.00636	−0.440785
$130$	0	0
$131$	−2.48876	−0.217444	−0.108722	−	0.994072i	$-0.534676\pi$
$131$	−2.48876	−0.217444	−0.108722	+	0.994072i	$0.534676\pi$
$132$	9.52899	0.829392
$133$	−3.43490	−0.297844
$134$	3.03214	0.261937
$135$	0	0
$136$	2.24780	0.192747
$137$	−10.1074	−0.863531	−0.431765	−	0.901986i	$-0.642109\pi$
$137$	−10.1074	−0.863531	−0.431765	+	0.901986i	$0.642109\pi$
$138$	0.178305	0.0151783
$139$	−18.4047	−1.56107	−0.780535	−	0.625112i	$-0.785053\pi$
$139$	−18.4047	−1.56107	−0.780535	+	0.625112i	$0.785053\pi$
$140$	0	0
$141$	5.47200	0.460825
$142$	2.34813	0.197050
$143$	−20.4477	−1.70992
$144$	−2.30508	−0.192090
$145$	0	0
$146$	0.372047	0.0307909
$147$	−1.54520	−0.127446
$148$	4.94911	0.406815
$149$	20.1992	1.65479	0.827393	−	0.561623i	$-0.189823\pi$
$149$	20.1992	1.65479	0.827393	+	0.561623i	$0.189823\pi$
$150$	0	0
$151$	11.8668	0.965706	0.482853	−	0.875701i	$-0.339601\pi$
$151$	11.8668	0.965706	0.482853	+	0.875701i	$0.339601\pi$
$152$	−2.70546	−0.219442
$153$	−1.74758	−0.141283
$154$	−0.625589	−0.0504114
$155$	0	0
$156$	−19.6914	−1.57658
$157$	−16.5799	−1.32322	−0.661608	−	0.749850i	$-0.730126\pi$
$157$	−16.5799	−1.32322	−0.661608	+	0.749850i	$0.730126\pi$
$158$	−1.68765	−0.134262
$159$	−1.10318	−0.0874879
$160$	0	0
$161$	0.580225	0.0457281
$162$	1.34996	0.106063
$163$	−19.3232	−1.51351	−0.756756	−	0.653698i	$-0.773217\pi$
$163$	−19.3232	−1.51351	−0.756756	+	0.653698i	$0.773217\pi$
$164$	−10.1057	−0.789125
$165$	0	0
$166$	−2.36670	−0.183691
$167$	1.53236	0.118578	0.0592888	−	0.998241i	$-0.481117\pi$
$167$	1.53236	0.118578	0.0592888	+	0.998241i	$0.481117\pi$
$168$	−1.21706	−0.0938981
$169$	29.2547	2.25036
$170$	0	0
$171$	2.10339	0.160851
$172$	−6.35174	−0.484316
$173$	4.62352	0.351520	0.175760	−	0.984433i	$-0.443762\pi$
$173$	4.62352	0.351520	0.175760	+	0.984433i	$0.443762\pi$
$174$	0.341732	0.0259066
$175$	0	0
$176$	11.8409	0.892544
$177$	−16.4074	−1.23325
$178$	−3.33234	−0.249770
$179$	1.84119	0.137617	0.0688084	−	0.997630i	$-0.478080\pi$
$179$	1.84119	0.137617	0.0688084	+	0.997630i	$0.478080\pi$
$180$	0	0
$181$	−2.09911	−0.156026	−0.0780129	−	0.996952i	$-0.524858\pi$
$181$	−2.09911	−0.156026	−0.0780129	+	0.996952i	$0.524858\pi$
$182$	1.29277	0.0958262
$183$	−13.1950	−0.975403
$184$	0.457008	0.0336910
$185$	0	0
$186$	−0.591857	−0.0433971
$187$	8.97712	0.656472
$188$	6.94252	0.506335
$189$	5.58182	0.406017
$190$	0	0
$191$	21.0450	1.52276	0.761380	−	0.648306i	$-0.224522\pi$
$191$	21.0450	1.52276	0.761380	+	0.648306i	$0.224522\pi$
$192$	10.9189	0.788004
$193$	−22.4099	−1.61310	−0.806548	−	0.591168i	$-0.798667\pi$
$193$	−22.4099	−1.61310	−0.806548	+	0.591168i	$0.798667\pi$
$194$	−1.99124	−0.142963
$195$	0	0
$196$	−1.96045	−0.140032
$197$	−12.4075	−0.884000	−0.442000	−	0.897015i	$-0.645731\pi$
$197$	−12.4075	−0.884000	−0.442000	+	0.897015i	$0.645731\pi$
$198$	0.383086	0.0272247
$199$	−16.7681	−1.18866	−0.594329	−	0.804222i	$-0.702582\pi$
$199$	−16.7681	−1.18866	−0.594329	+	0.804222i	$0.702582\pi$
$200$	0	0
$201$	23.5587	1.66170
$202$	−3.70022	−0.260347
$203$	1.11204	0.0780496
$204$	8.64510	0.605278
$205$	0	0
$206$	1.35681	0.0945338
$207$	−0.355306	−0.0246955
$208$	−24.4690	−1.69662
$209$	−10.8049	−0.747391
$210$	0	0
$211$	−9.19189	−0.632796	−0.316398	−	0.948627i	$-0.602473\pi$
$211$	−9.19189	−0.632796	−0.316398	+	0.948627i	$0.602473\pi$
$212$	−1.39964	−0.0961279
$213$	18.2441	1.25007
$214$	−2.23348	−0.152678
$215$	0	0
$216$	4.39645	0.299141
$217$	−1.92597	−0.130743
$218$	3.58918	0.243090
$219$	2.89068	0.195334
$220$	0	0
$221$	−18.5510	−1.24788
$222$	−0.775781	−0.0520670
$223$	−18.3193	−1.22675	−0.613374	−	0.789793i	$-0.710188\pi$
$223$	−18.3193	−1.22675	−0.613374	+	0.789793i	$0.710188\pi$
$224$	−2.32390	−0.155272
$225$	0	0
$226$	2.16946	0.144311
$227$	−17.2104	−1.14230	−0.571148	−	0.820847i	$-0.693502\pi$
$227$	−17.2104	−1.14230	−0.571148	+	0.820847i	$0.693502\pi$
$228$	−10.4053	−0.689107
$229$	2.35494	0.155619	0.0778094	−	0.996968i	$-0.475207\pi$
$229$	2.35494	0.155619	0.0778094	+	0.996968i	$0.475207\pi$
$230$	0	0
$231$	−4.86062	−0.319805
$232$	0.875882	0.0575045
$233$	−1.39104	−0.0911301	−0.0455651	−	0.998961i	$-0.514509\pi$
$233$	−1.39104	−0.0911301	−0.0455651	+	0.998961i	$0.514509\pi$
$234$	−0.791638	−0.0517510
$235$	0	0
$236$	−20.8166	−1.35505
$237$	−13.1124	−0.851745
$238$	−0.567561	−0.0367895
$239$	−10.5032	−0.679397	−0.339698	−	0.940534i	$-0.610325\pi$
$239$	−10.5032	−0.679397	−0.339698	+	0.940534i	$0.610325\pi$
$240$	0	0
$241$	−12.7941	−0.824139	−0.412069	−	0.911152i	$-0.635194\pi$
$241$	−12.7941	−0.824139	−0.412069	+	0.911152i	$0.635194\pi$
$242$	0.219768	0.0141272
$243$	−6.25673	−0.401370
$244$	−16.7410	−1.07173
$245$	0	0
$246$	1.58409	0.100998
$247$	22.3281	1.42070
$248$	−1.51697	−0.0963277
$249$	−18.3884	−1.16532
$250$	0	0
$251$	−12.7027	−0.801789	−0.400894	−	0.916124i	$-0.631301\pi$
$251$	−12.7027	−0.801789	−0.400894	+	0.916124i	$0.631301\pi$
$252$	1.20050	0.0756244
$253$	1.82517	0.114747
$254$	2.47661	0.155396
$255$	0	0
$256$	12.9289	0.808054
$257$	−20.2119	−1.26079	−0.630393	−	0.776276i	$-0.717106\pi$
$257$	−20.2119	−1.26079	−0.630393	+	0.776276i	$0.717106\pi$
$258$	0.995644	0.0619861
$259$	−2.52448	−0.156864
$260$	0	0
$261$	−0.680966	−0.0421507
$262$	0.494955	0.0305784
$263$	1.60161	0.0987597	0.0493798	−	0.998780i	$-0.484276\pi$
$263$	1.60161	0.0987597	0.0493798	+	0.998780i	$0.484276\pi$
$264$	−3.82841	−0.235622
$265$	0	0
$266$	0.683119	0.0418847
$267$	−25.8912	−1.58451
$268$	29.8897	1.82580
$269$	19.6982	1.20102	0.600511	−	0.799616i	$-0.294964\pi$
$269$	19.6982	1.20102	0.600511	+	0.799616i	$0.294964\pi$
$270$	0	0
$271$	−26.6623	−1.61962	−0.809811	−	0.586691i	$-0.800430\pi$
$271$	−26.6623	−1.61962	−0.809811	+	0.586691i	$0.800430\pi$
$272$	10.7426	0.651365
$273$	10.0444	0.607912
$274$	2.01011	0.121435
$275$	0	0
$276$	1.75767	0.105799
$277$	−3.39817	−0.204176	−0.102088	−	0.994775i	$-0.532552\pi$
$277$	−3.39817	−0.204176	−0.102088	+	0.994775i	$0.532552\pi$
$278$	3.66026	0.219528
$279$	1.17939	0.0706081
$280$	0	0
$281$	−33.1362	−1.97674	−0.988371	−	0.152060i	$-0.951409\pi$
$281$	−33.1362	−1.97674	−0.988371	+	0.152060i	$0.951409\pi$
$282$	−1.08825	−0.0648043
$283$	8.82375	0.524518	0.262259	−	0.964998i	$-0.415533\pi$
$283$	8.82375	0.524518	0.262259	+	0.964998i	$0.415533\pi$
$284$	23.1470	1.37352
$285$	0	0
$286$	4.06656	0.240461
$287$	5.15481	0.304279
$288$	1.42306	0.0838547
$289$	−8.85558	−0.520917
$290$	0	0
$291$	−15.4712	−0.906941
$292$	3.66751	0.214625
$293$	−16.0205	−0.935929	−0.467965	−	0.883747i	$-0.655013\pi$
$293$	−16.0205	−0.935929	−0.467965	+	0.883747i	$0.655013\pi$
$294$	0.307303	0.0179223
$295$	0	0
$296$	−1.98838	−0.115572
$297$	17.5583	1.01884
$298$	−4.01714	−0.232707
$299$	−3.77167	−0.218122
$300$	0	0
$301$	3.23994	0.186747
$302$	−2.36002	−0.135804
$303$	−28.7495	−1.65161
$304$	−12.9298	−0.741577
$305$	0	0
$306$	0.347551	0.0198682
$307$	13.9199	0.794452	0.397226	−	0.917721i	$-0.369973\pi$
$307$	13.9199	0.794452	0.397226	+	0.917721i	$0.369973\pi$
$308$	−6.16683	−0.351388
$309$	10.5420	0.599713
$310$	0	0
$311$	21.1766	1.20082	0.600408	−	0.799693i	$-0.295005\pi$
$311$	21.1766	1.20082	0.600408	+	0.799693i	$0.295005\pi$
$312$	7.91132	0.447890
$313$	−11.9008	−0.672670	−0.336335	−	0.941742i	$-0.609188\pi$
$313$	−11.9008	−0.672670	−0.336335	+	0.941742i	$0.609188\pi$
$314$	3.29734	0.186079
$315$	0	0
$316$	−16.6362	−0.935861
$317$	15.8125	0.888121	0.444061	−	0.895997i	$-0.353537\pi$
$317$	15.8125	0.888121	0.444061	+	0.895997i	$0.353537\pi$
$318$	0.219396	0.0123031
$319$	3.49805	0.195853
$320$	0	0
$321$	−17.3534	−0.968573
$322$	−0.115393	−0.00643059
$323$	−9.80266	−0.545435
$324$	13.3074	0.739300
$325$	0	0
$326$	3.84293	0.212840
$327$	27.8867	1.54214
$328$	4.06012	0.224183
$329$	−3.54129	−0.195238
$330$	0	0
$331$	0.500197	0.0274933	0.0137467	−	0.999906i	$-0.495624\pi$
$331$	0.500197	0.0274933	0.0137467	+	0.999906i	$0.495624\pi$
$332$	−23.3300	−1.28040
$333$	1.54589	0.0847143
$334$	−0.304750	−0.0166752
$335$	0	0
$336$	−5.81652	−0.317317
$337$	−16.0496	−0.874278	−0.437139	−	0.899394i	$-0.644008\pi$
$337$	−16.0496	−0.874278	−0.437139	+	0.899394i	$0.644008\pi$
$338$	−5.81806	−0.316461
$339$	16.8560	0.915492
$340$	0	0
$341$	−6.05838	−0.328080
$342$	−0.418315	−0.0226199
$343$	1.00000	0.0539949
$344$	2.55190	0.137589
$345$	0	0
$346$	−0.919508	−0.0494331
$347$	−29.7249	−1.59571	−0.797857	−	0.602846i	$-0.794033\pi$
$347$	−29.7249	−1.59571	−0.797857	+	0.602846i	$0.794033\pi$
$348$	3.36867	0.180580
$349$	4.77252	0.255467	0.127734	−	0.991809i	$-0.459230\pi$
$349$	4.77252	0.255467	0.127734	+	0.991809i	$0.459230\pi$
$350$	0	0
$351$	−36.2838	−1.93669
$352$	−7.31011	−0.389630
$353$	14.8852	0.792259	0.396129	−	0.918195i	$-0.370353\pi$
$353$	14.8852	0.792259	0.396129	+	0.918195i	$0.370353\pi$
$354$	3.26303	0.173428
$355$	0	0
$356$	−32.8490	−1.74099
$357$	−4.40975	−0.233389
$358$	−0.366168	−0.0193526
$359$	−1.51887	−0.0801630	−0.0400815	−	0.999196i	$-0.512762\pi$
$359$	−1.51887	−0.0801630	−0.0400815	+	0.999196i	$0.512762\pi$
$360$	0	0
$361$	−7.20147	−0.379025
$362$	0.417463	0.0219414
$363$	1.70752	0.0896217
$364$	12.7436	0.667947
$365$	0	0
$366$	2.62417	0.137168
$367$	1.12114	0.0585233	0.0292616	−	0.999572i	$-0.490684\pi$
$367$	1.12114	0.0585233	0.0292616	+	0.999572i	$0.490684\pi$
$368$	2.18411	0.113855
$369$	−3.15660	−0.164326
$370$	0	0
$371$	0.713940	0.0370659
$372$	−5.83431	−0.302495
$373$	−20.7026	−1.07194	−0.535970	−	0.844237i	$-0.680054\pi$
$373$	−20.7026	−1.07194	−0.535970	+	0.844237i	$0.680054\pi$
$374$	−1.78533	−0.0923174
$375$	0	0
$376$	−2.78926	−0.143845
$377$	−7.22864	−0.372294
$378$	−1.11009	−0.0570968
$379$	11.1139	0.570883	0.285441	−	0.958396i	$-0.407860\pi$
$379$	11.1139	0.570883	0.285441	+	0.958396i	$0.407860\pi$
$380$	0	0
$381$	19.2424	0.985818
$382$	−4.18534	−0.214140
$383$	21.8921	1.11863	0.559317	−	0.828954i	$-0.311063\pi$
$383$	21.8921	1.11863	0.559317	+	0.828954i	$0.311063\pi$
$384$	−9.35328	−0.477307
$385$	0	0
$386$	4.45678	0.226844
$387$	−1.98401	−0.100853
$388$	−19.6289	−0.996507
$389$	−32.5289	−1.64928	−0.824639	−	0.565659i	$-0.808622\pi$
$389$	−32.5289	−1.64928	−0.824639	+	0.565659i	$0.808622\pi$
$390$	0	0
$391$	1.65587	0.0837410
$392$	0.787638	0.0397817
$393$	3.84563	0.193986
$394$	2.46756	0.124314
$395$	0	0
$396$	3.77632	0.189767
$397$	8.31695	0.417416	0.208708	−	0.977978i	$-0.433074\pi$
$397$	8.31695	0.417416	0.208708	+	0.977978i	$0.433074\pi$
$398$	3.33477	0.167157
$399$	5.30760	0.265712
$400$	0	0
$401$	0.343282	0.0171427	0.00857134	−	0.999963i	$-0.497272\pi$
$401$	0.343282	0.0171427	0.00857134	+	0.999963i	$0.497272\pi$
$402$	−4.68526	−0.233679
$403$	12.5195	0.623642
$404$	−36.4755	−1.81472
$405$	0	0
$406$	−0.221157	−0.0109759
$407$	−7.94107	−0.393624
$408$	−3.47329	−0.171954
$409$	−16.8994	−0.835619	−0.417810	−	0.908535i	$-0.637202\pi$
$409$	−16.8994	−0.835619	−0.417810	+	0.908535i	$0.637202\pi$
$410$	0	0
$411$	15.6179	0.770374
$412$	13.3750	0.658938
$413$	10.6183	0.522492
$414$	0.0706619	0.00347285
$415$	0	0
$416$	15.1062	0.740641
$417$	28.4390	1.39266
$418$	2.14884	0.105103
$419$	−27.4236	−1.33973	−0.669864	−	0.742484i	$-0.733648\pi$
$419$	−27.4236	−1.33973	−0.669864	+	0.742484i	$0.733648\pi$
$420$	0	0
$421$	12.4449	0.606529	0.303264	−	0.952906i	$-0.401923\pi$
$421$	12.4449	0.606529	0.303264	+	0.952906i	$0.401923\pi$
$422$	1.82805	0.0889879
$423$	2.16854	0.105438
$424$	0.562327	0.0273090
$425$	0	0
$426$	−3.62832	−0.175793
$427$	8.53936	0.413249
$428$	−22.0169	−1.06423
$429$	31.5958	1.52546
$430$	0	0
$431$	−18.0815	−0.870955	−0.435477	−	0.900200i	$-0.643420\pi$
$431$	−18.0815	−0.870955	−0.435477	+	0.900200i	$0.643420\pi$
$432$	21.0114	1.01091
$433$	15.8655	0.762447	0.381223	−	0.924483i	$-0.375503\pi$
$433$	15.8655	0.762447	0.381223	+	0.924483i	$0.375503\pi$
$434$	0.383030	0.0183860
$435$	0	0
$436$	35.3808	1.69443
$437$	−1.99301	−0.0953388
$438$	−0.574887	−0.0274692
$439$	20.7802	0.991784	0.495892	−	0.868384i	$-0.334841\pi$
$439$	20.7802	0.991784	0.495892	+	0.868384i	$0.334841\pi$
$440$	0	0
$441$	−0.612360	−0.0291600
$442$	3.68935	0.175485
$443$	17.1519	0.814913	0.407456	−	0.913225i	$-0.366416\pi$
$443$	17.1519	0.814913	0.407456	+	0.913225i	$0.366416\pi$
$444$	−7.64737	−0.362928
$445$	0	0
$446$	3.64326	0.172513
$447$	−31.2118	−1.47627
$448$	−7.06634	−0.333853
$449$	−40.9515	−1.93262	−0.966311	−	0.257378i	$-0.917141\pi$
$449$	−40.9515	−1.93262	−0.966311	+	0.257378i	$0.917141\pi$
$450$	0	0
$451$	16.2151	0.763538
$452$	21.3858	1.00590
$453$	−18.3366	−0.861527
$454$	3.42274	0.160637
$455$	0	0
$456$	4.18047	0.195769
$457$	−2.15047	−0.100595	−0.0502974	−	0.998734i	$-0.516017\pi$
$457$	−2.15047	−0.100595	−0.0502974	+	0.998734i	$0.516017\pi$
$458$	−0.468341	−0.0218841
$459$	15.9296	0.743531
$460$	0	0
$461$	−18.7347	−0.872564	−0.436282	−	0.899810i	$-0.643705\pi$
$461$	−18.7347	−0.872564	−0.436282	+	0.899810i	$0.643705\pi$
$462$	0.966660	0.0449731
$463$	−9.36691	−0.435317	−0.217659	−	0.976025i	$-0.569842\pi$
$463$	−9.36691	−0.435317	−0.217659	+	0.976025i	$0.569842\pi$
$464$	4.18599	0.194330
$465$	0	0
$466$	0.276645	0.0128153
$467$	17.2041	0.796110	0.398055	−	0.917362i	$-0.369685\pi$
$467$	17.2041	0.796110	0.398055	+	0.917362i	$0.369685\pi$
$468$	−7.80368	−0.360725
$469$	−15.2464	−0.704012
$470$	0	0
$471$	25.6192	1.18047
$472$	8.36337	0.384955
$473$	10.1916	0.468612
$474$	2.60775	0.119778
$475$	0	0
$476$	−5.59481	−0.256438
$477$	−0.437188	−0.0200175
$478$	2.08884	0.0955413
$479$	−1.59621	−0.0729326	−0.0364663	−	0.999335i	$-0.511610\pi$
$479$	−1.59621	−0.0729326	−0.0364663	+	0.999335i	$0.511610\pi$
$480$	0	0
$481$	16.4100	0.748233
$482$	2.54444	0.115896
$483$	−0.896563	−0.0407950
$484$	2.16639	0.0984724
$485$	0	0
$486$	1.24431	0.0564432
$487$	36.9348	1.67367	0.836837	−	0.547452i	$-0.184402\pi$
$487$	36.9348	1.67367	0.836837	+	0.547452i	$0.184402\pi$
$488$	6.72593	0.304468
$489$	29.8582	1.35024
$490$	0	0
$491$	14.2365	0.642482	0.321241	−	0.946997i	$-0.395900\pi$
$491$	14.2365	0.642482	0.321241	+	0.946997i	$0.395900\pi$
$492$	15.6154	0.703995
$493$	3.17358	0.142931
$494$	−4.44052	−0.199789
$495$	0	0
$496$	−7.24985	−0.325528
$497$	−11.8070	−0.529616
$498$	3.65702	0.163875
$499$	8.62876	0.386276	0.193138	−	0.981172i	$-0.438133\pi$
$499$	8.62876	0.386276	0.193138	+	0.981172i	$0.438133\pi$
$500$	0	0
$501$	−2.36780	−0.105786
$502$	2.52627	0.112753
$503$	5.62923	0.250995	0.125498	−	0.992094i	$-0.459947\pi$
$503$	5.62923	0.250995	0.125498	+	0.992094i	$0.459947\pi$
$504$	−0.482318	−0.0214842
$505$	0	0
$506$	−0.362983	−0.0161365
$507$	−45.2044	−2.00760
$508$	24.4135	1.08317
$509$	16.2973	0.722367	0.361184	−	0.932495i	$-0.382373\pi$
$509$	16.2973	0.722367	0.361184	+	0.932495i	$0.382373\pi$
$510$	0	0
$511$	−1.87075	−0.0827571
$512$	−14.6775	−0.648659
$513$	−19.1730	−0.846507
$514$	4.01967	0.177300
$515$	0	0
$516$	9.81470	0.432068
$517$	−11.1396	−0.489918
$518$	0.502059	0.0220592
$519$	−7.14427	−0.313598
$520$	0	0
$521$	0.236310	0.0103529	0.00517647	−	0.999987i	$-0.498352\pi$
$521$	0.236310	0.0103529	0.00517647	+	0.999987i	$0.498352\pi$
$522$	0.135428	0.00592752
$523$	7.67311	0.335522	0.167761	−	0.985828i	$-0.446346\pi$
$523$	7.67311	0.335522	0.167761	+	0.985828i	$0.446346\pi$
$524$	4.87909	0.213144
$525$	0	0
$526$	−0.318522	−0.0138882
$527$	−5.49642	−0.239428
$528$	−18.2966	−0.796257
$529$	−22.6633	−0.985363
$530$	0	0
$531$	−6.50221	−0.282172
$532$	6.73394	0.291953
$533$	−33.5081	−1.45140
$534$	5.14913	0.222825
$535$	0	0
$536$	−12.0086	−0.518693
$537$	−2.84500	−0.122771
$538$	−3.91751	−0.168896
$539$	3.14562	0.135492
$540$	0	0
$541$	1.32136	0.0568097	0.0284049	−	0.999597i	$-0.490957\pi$
$541$	1.32136	0.0568097	0.0284049	+	0.999597i	$0.490957\pi$
$542$	5.30250	0.227762
$543$	3.24355	0.139194
$544$	−6.63204	−0.284346
$545$	0	0
$546$	−1.99758	−0.0854886
$547$	−34.5160	−1.47580	−0.737898	−	0.674912i	$-0.764182\pi$
$547$	−34.5160	−1.47580	−0.737898	+	0.674912i	$0.764182\pi$
$548$	19.8150	0.846454
$549$	−5.22916	−0.223175
$550$	0	0
$551$	−3.81973	−0.162726
$552$	−0.706168	−0.0300565
$553$	8.48593	0.360858
$554$	0.675815	0.0287126
$555$	0	0
$556$	36.0815	1.53020
$557$	39.5507	1.67582	0.837909	−	0.545810i	$-0.183778\pi$
$557$	39.5507	1.67582	0.837909	+	0.545810i	$0.183778\pi$
$558$	−0.234552	−0.00992938
$559$	−21.0608	−0.890777
$560$	0	0
$561$	−13.8714	−0.585652
$562$	6.59001	0.277983
$563$	4.88107	0.205713	0.102856	−	0.994696i	$-0.467202\pi$
$563$	4.88107	0.205713	0.102856	+	0.994696i	$0.467202\pi$
$564$	−10.7276	−0.451712
$565$	0	0
$566$	−1.75483	−0.0737611
$567$	−6.78794	−0.285067
$568$	−9.29963	−0.390204
$569$	−10.2000	−0.427605	−0.213802	−	0.976877i	$-0.568585\pi$
$569$	−10.2000	−0.427605	−0.213802	+	0.976877i	$0.568585\pi$
$570$	0	0
$571$	12.3743	0.517848	0.258924	−	0.965898i	$-0.416632\pi$
$571$	12.3743	0.517848	0.258924	+	0.965898i	$0.416632\pi$
$572$	40.0867	1.67611
$573$	−32.5186	−1.35849
$574$	−1.02517	−0.0427897
$575$	0	0
$576$	4.32714	0.180298
$577$	−25.2484	−1.05111	−0.525553	−	0.850761i	$-0.676141\pi$
$577$	−25.2484	−1.05111	−0.525553	+	0.850761i	$0.676141\pi$
$578$	1.76116	0.0732547
$579$	34.6277	1.43908
$580$	0	0
$581$	11.9004	0.493710
$582$	3.07686	0.127540
$583$	2.24579	0.0930110
$584$	−1.47347	−0.0609728
$585$	0	0
$586$	3.18610	0.131617
$587$	25.3415	1.04595	0.522977	−	0.852347i	$-0.324821\pi$
$587$	25.3415	1.04595	0.522977	+	0.852347i	$0.324821\pi$
$588$	3.02928	0.124926
$589$	6.61552	0.272588
$590$	0	0
$591$	19.1721	0.788635
$592$	−9.50279	−0.390562
$593$	22.4503	0.921924	0.460962	−	0.887420i	$-0.347505\pi$
$593$	22.4503	0.921924	0.460962	+	0.887420i	$0.347505\pi$
$594$	−3.49192	−0.143275
$595$	0	0
$596$	−39.5996	−1.62206
$597$	25.9100	1.06043
$598$	0.750096	0.0306737
$599$	−19.6210	−0.801691	−0.400845	−	0.916146i	$-0.631284\pi$
$599$	−19.6210	−0.801691	−0.400845	+	0.916146i	$0.631284\pi$
$600$	0	0
$601$	−10.6423	−0.434109	−0.217055	−	0.976159i	$-0.569645\pi$
$601$	−10.6423	−0.434109	−0.217055	+	0.976159i	$0.569645\pi$
$602$	−0.644347	−0.0262616
$603$	9.33626	0.380202
$604$	−23.2642	−0.946608
$605$	0	0
$606$	5.71758	0.232261
$607$	−0.0394412	−0.00160087	−0.000800435	−	1.00000i	$-0.500255\pi$
$607$	−0.0394412	−0.00160087	−0.000800435		1.00000i	$0.500255\pi$
$608$	7.98235	0.323727
$609$	−1.71832	−0.0696297
$610$	0	0
$611$	23.0197	0.931276
$612$	3.42604	0.138489
$613$	13.5769	0.548366	0.274183	−	0.961677i	$-0.411593\pi$
$613$	13.5769	0.548366	0.274183	+	0.961677i	$0.411593\pi$
$614$	−2.76834	−0.111721
$615$	0	0
$616$	2.47761	0.0998259
$617$	−42.7519	−1.72113	−0.860564	−	0.509342i	$-0.829889\pi$
$617$	−42.7519	−1.72113	−0.860564	+	0.509342i	$0.829889\pi$
$618$	−2.09655	−0.0843356
$619$	−1.73516	−0.0697421	−0.0348711	−	0.999392i	$-0.511102\pi$
$619$	−1.73516	−0.0697421	−0.0348711	+	0.999392i	$0.511102\pi$
$620$	0	0
$621$	3.23871	0.129965
$622$	−4.21153	−0.168867
$623$	16.7559	0.671310
$624$	37.8095	1.51359
$625$	0	0
$626$	2.36678	0.0945954
$627$	16.6957	0.666763
$628$	32.5039	1.29705
$629$	−7.20447	−0.287261
$630$	0	0
$631$	12.2039	0.485832	0.242916	−	0.970047i	$-0.421896\pi$
$631$	12.2039	0.485832	0.242916	+	0.970047i	$0.421896\pi$
$632$	6.68384	0.265869
$633$	14.2033	0.564530
$634$	−3.14474	−0.124893
$635$	0	0
$636$	2.16273	0.0857577
$637$	−6.50036	−0.257554
$638$	−0.695678	−0.0275422
$639$	7.23012	0.286019
$640$	0	0
$641$	−6.23057	−0.246093	−0.123046	−	0.992401i	$-0.539266\pi$
$641$	−6.23057	−0.246093	−0.123046	+	0.992401i	$0.539266\pi$
$642$	3.45118	0.136207
$643$	11.8383	0.466857	0.233429	−	0.972374i	$-0.425005\pi$
$643$	11.8383	0.466857	0.233429	+	0.972374i	$0.425005\pi$
$644$	−1.13750	−0.0448238
$645$	0	0
$646$	1.94951	0.0767026
$647$	4.04918	0.159190	0.0795948	−	0.996827i	$-0.474637\pi$
$647$	4.04918	0.159190	0.0795948	+	0.996827i	$0.474637\pi$
$648$	−5.34644	−0.210028
$649$	33.4011	1.31111
$650$	0	0
$651$	2.97601	0.116639
$652$	37.8822	1.48358
$653$	21.4037	0.837590	0.418795	−	0.908081i	$-0.362453\pi$
$653$	21.4037	0.837590	0.418795	+	0.908081i	$0.362453\pi$
$654$	−5.54599	−0.216865
$655$	0	0
$656$	19.4040	0.757599
$657$	1.14557	0.0446930
$658$	0.704278	0.0274556
$659$	15.2236	0.593028	0.296514	−	0.955028i	$-0.404176\pi$
$659$	15.2236	0.593028	0.296514	+	0.955028i	$0.404176\pi$
$660$	0	0
$661$	−12.4913	−0.485857	−0.242928	−	0.970044i	$-0.578108\pi$
$661$	−12.4913	−0.485857	−0.242928	+	0.970044i	$0.578108\pi$
$662$	−0.0994773	−0.00386629
$663$	28.6650	1.11326
$664$	9.37317	0.363750
$665$	0	0
$666$	−0.307441	−0.0119131
$667$	0.645231	0.0249835
$668$	−3.00411	−0.116233
$669$	28.3069	1.09441
$670$	0	0
$671$	26.8616	1.03698
$672$	3.59088	0.138521
$673$	16.3626	0.630732	0.315366	−	0.948970i	$-0.397873\pi$
$673$	16.3626	0.630732	0.315366	+	0.948970i	$0.397873\pi$
$674$	3.19188	0.122947
$675$	0	0
$676$	−57.3524	−2.20586
$677$	22.2709	0.855940	0.427970	−	0.903793i	$-0.359229\pi$
$677$	22.2709	0.855940	0.427970	+	0.903793i	$0.359229\pi$
$678$	−3.35225	−0.128742
$679$	10.0125	0.384243
$680$	0	0
$681$	26.5935	1.01907
$682$	1.20487	0.0461368
$683$	−10.1184	−0.387168	−0.193584	−	0.981084i	$-0.562011\pi$
$683$	−10.1184	−0.387168	−0.193584	+	0.981084i	$0.562011\pi$
$684$	−4.12359	−0.157670
$685$	0	0
$686$	−0.198876	−0.00759312
$687$	−3.63885	−0.138831
$688$	12.1960	0.464967
$689$	−4.64087	−0.176803
$690$	0	0
$691$	13.4910	0.513223	0.256612	−	0.966515i	$-0.417394\pi$
$691$	13.4910	0.513223	0.256612	+	0.966515i	$0.417394\pi$
$692$	−9.06418	−0.344568
$693$	−1.92625	−0.0731723
$694$	5.91156	0.224400
$695$	0	0
$696$	−1.35341	−0.0513010
$697$	14.7110	0.557219
$698$	−0.949140	−0.0359255
$699$	2.14944	0.0812991
$700$	0	0
$701$	12.7883	0.483007	0.241503	−	0.970400i	$-0.422360\pi$
$701$	12.7883	0.483007	0.241503	+	0.970400i	$0.422360\pi$
$702$	7.21598	0.272350
$703$	8.67133	0.327046
$704$	−22.2281	−0.837751
$705$	0	0
$706$	−2.96031	−0.111413
$707$	18.6057	0.699739
$708$	32.1658	1.20886
$709$	−25.0093	−0.939243	−0.469622	−	0.882868i	$-0.655610\pi$
$709$	−25.0093	−0.939243	−0.469622	+	0.882868i	$0.655610\pi$
$710$	0	0
$711$	−5.19644	−0.194882
$712$	13.1976	0.494600
$713$	−1.11750	−0.0418506
$714$	0.876995	0.0328207
$715$	0	0
$716$	−3.60955	−0.134895
$717$	16.2296	0.606104
$718$	0.302067	0.0112731
$719$	7.27771	0.271413	0.135706	−	0.990749i	$-0.456670\pi$
$719$	7.27771	0.271413	0.135706	+	0.990749i	$0.456670\pi$
$720$	0	0
$721$	−6.82241	−0.254080
$722$	1.43220	0.0533010
$723$	19.7694	0.735232
$724$	4.11520	0.152940
$725$	0	0
$726$	−0.339585	−0.0126032
$727$	23.2476	0.862207	0.431103	−	0.902303i	$-0.358124\pi$
$727$	23.2476	0.862207	0.431103	+	0.902303i	$0.358124\pi$
$728$	−5.11994	−0.189757
$729$	30.0317	1.11229
$730$	0	0
$731$	9.24628	0.341986
$732$	25.8681	0.956114
$733$	−35.1536	−1.29843	−0.649214	−	0.760606i	$-0.724902\pi$
$733$	−35.1536	−1.29843	−0.649214	+	0.760606i	$0.724902\pi$
$734$	−0.222969	−0.00822993
$735$	0	0
$736$	−1.34838	−0.0497021
$737$	−47.9593	−1.76660
$738$	0.627771	0.0231086
$739$	17.5121	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$739$	17.5121	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$740$	0	0
$741$	−34.5013	−1.26744
$742$	−0.141986	−0.00521246
$743$	12.5993	0.462223	0.231111	−	0.972927i	$-0.425764\pi$
$743$	12.5993	0.462223	0.231111	+	0.972927i	$0.425764\pi$
$744$	2.34402	0.0859359
$745$	0	0
$746$	4.11725	0.150743
$747$	−7.28730	−0.266628
$748$	−17.5992	−0.643489
$749$	11.2305	0.410355
$750$	0	0
$751$	9.86802	0.360089	0.180045	−	0.983658i	$-0.442376\pi$
$751$	9.86802	0.360089	0.180045	+	0.983658i	$0.442376\pi$
$752$	−13.3303	−0.486107
$753$	19.6282	0.715293
$754$	1.43760	0.0523544
$755$	0	0
$756$	−10.9429	−0.397988
$757$	37.0730	1.34744	0.673721	−	0.738986i	$-0.264695\pi$
$757$	37.0730	1.34744	0.673721	+	0.738986i	$0.264695\pi$
$758$	−2.21029	−0.0802813
$759$	−2.82025	−0.102369
$760$	0	0
$761$	−29.5304	−1.07047	−0.535237	−	0.844702i	$-0.679778\pi$
$761$	−29.5304	−1.07047	−0.535237	+	0.844702i	$0.679778\pi$
$762$	−3.82685	−0.138632
$763$	−18.0473	−0.653356
$764$	−41.2575	−1.49265
$765$	0	0
$766$	−4.35382	−0.157310
$767$	−69.0227	−2.49227
$768$	−19.9777	−0.720882
$769$	−25.2768	−0.911503	−0.455752	−	0.890107i	$-0.650629\pi$
$769$	−25.2768	−0.911503	−0.455752	+	0.890107i	$0.650629\pi$
$770$	0	0
$771$	31.2315	1.12477
$772$	43.9334	1.58120
$773$	−4.28572	−0.154147	−0.0770734	−	0.997025i	$-0.524558\pi$
$773$	−4.28572	−0.154147	−0.0770734	+	0.997025i	$0.524558\pi$
$774$	0.394572	0.0141826
$775$	0	0
$776$	7.88620	0.283098
$777$	3.90082	0.139941
$778$	6.46921	0.231932
$779$	−17.7062	−0.634392
$780$	0	0
$781$	−37.1403	−1.32899
$782$	−0.329313	−0.0117762
$783$	6.20718	0.221827
$784$	3.76425	0.134438
$785$	0	0
$786$	−0.764804	−0.0272797
$787$	−45.7560	−1.63103	−0.815513	−	0.578738i	$-0.803545\pi$
$787$	−45.7560	−1.63103	−0.815513	+	0.578738i	$0.803545\pi$
$788$	24.3243	0.866518
$789$	−2.47481	−0.0881056
$790$	0	0
$791$	−10.9086	−0.387866
$792$	−1.51719	−0.0539110
$793$	−55.5089	−1.97118
$794$	−1.65404	−0.0586998
$795$	0	0
$796$	32.8730	1.16515
$797$	−26.6677	−0.944619	−0.472310	−	0.881433i	$-0.656580\pi$
$797$	−26.6677	−0.944619	−0.472310	+	0.881433i	$0.656580\pi$
$798$	−1.05556	−0.0373662
$799$	−10.1063	−0.357535
$800$	0	0
$801$	−10.2606	−0.362541
$802$	−0.0682705	−0.00241072
$803$	−5.88467	−0.207666
$804$	−46.1856	−1.62884
$805$	0	0
$806$	−2.48983	−0.0877006
$807$	−30.4377	−1.07146
$808$	14.6545	0.515545
$809$	−8.97961	−0.315706	−0.157853	−	0.987463i	$-0.550457\pi$
$809$	−8.97961	−0.315706	−0.157853	+	0.987463i	$0.550457\pi$
$810$	0	0
$811$	−31.1919	−1.09530	−0.547648	−	0.836709i	$-0.684477\pi$
$811$	−31.1919	−1.09530	−0.547648	+	0.836709i	$0.684477\pi$
$812$	−2.18009	−0.0765061
$813$	41.1986	1.44490
$814$	1.57929	0.0553540
$815$	0	0
$816$	−16.5994	−0.581097
$817$	−11.1289	−0.389350
$818$	3.36088	0.117510
$819$	3.98056	0.139092
$820$	0	0
$821$	20.3391	0.709840	0.354920	−	0.934897i	$-0.384508\pi$
$821$	20.3391	0.709840	0.354920	+	0.934897i	$0.384508\pi$
$822$	−3.10603	−0.108335
$823$	13.9779	0.487238	0.243619	−	0.969871i	$-0.421665\pi$
$823$	13.9779	0.487238	0.243619	+	0.969871i	$0.421665\pi$
$824$	−5.37359	−0.187198
$825$	0	0
$826$	−2.11172	−0.0734762
$827$	−34.2086	−1.18955	−0.594775	−	0.803892i	$-0.702759\pi$
$827$	−34.2086	−1.18955	−0.594775	+	0.803892i	$0.702759\pi$
$828$	0.696560	0.0242071
$829$	44.5213	1.54629	0.773144	−	0.634230i	$-0.218683\pi$
$829$	44.5213	1.54629	0.773144	+	0.634230i	$0.218683\pi$
$830$	0	0
$831$	5.25085	0.182150
$832$	45.9338	1.59247
$833$	2.85384	0.0988798
$834$	−5.65583	−0.195846
$835$	0	0
$836$	21.1824	0.732610
$837$	−10.7504	−0.371589
$838$	5.45389	0.188401
$839$	−35.1670	−1.21410	−0.607050	−	0.794664i	$-0.707647\pi$
$839$	−35.1670	−1.21410	−0.607050	+	0.794664i	$0.707647\pi$
$840$	0	0
$841$	−27.7634	−0.957358
$842$	−2.47500	−0.0852941
$843$	51.2021	1.76349
$844$	18.0202	0.620282
$845$	0	0
$846$	−0.431271	−0.0148274
$847$	−1.10505	−0.0379700
$848$	2.68745	0.0922875
$849$	−13.6345	−0.467933
$850$	0	0
$851$	−1.46477	−0.0502116
$852$	−35.7667	−1.22535
$853$	−18.1232	−0.620527	−0.310264	−	0.950651i	$-0.600417\pi$
$853$	−18.1232	−0.620527	−0.310264	+	0.950651i	$0.600417\pi$
$854$	−1.69827	−0.0581138
$855$	0	0
$856$	8.84560	0.302336
$857$	−34.1832	−1.16767	−0.583837	−	0.811871i	$-0.698449\pi$
$857$	−34.1832	−1.16767	−0.583837	+	0.811871i	$0.698449\pi$
$858$	−6.28364	−0.214520
$859$	−20.5259	−0.700336	−0.350168	−	0.936687i	$-0.613875\pi$
$859$	−20.5259	−0.700336	−0.350168	+	0.936687i	$0.613875\pi$
$860$	0	0
$861$	−7.96520	−0.271453
$862$	3.59598	0.122479
$863$	29.3628	0.999521	0.499761	−	0.866164i	$-0.333421\pi$
$863$	29.3628	0.999521	0.499761	+	0.866164i	$0.333421\pi$
$864$	−12.9716	−0.441301
$865$	0	0
$866$	−3.15527	−0.107220
$867$	13.6836	0.464721
$868$	3.77577	0.128158
$869$	26.6935	0.905516
$870$	0	0
$871$	99.1069	3.35811
$872$	−14.2147	−0.481372
$873$	−6.13123	−0.207511
$874$	0.396363	0.0134072
$875$	0	0
$876$	−5.66703	−0.191471
$877$	28.9755	0.978431	0.489216	−	0.872163i	$-0.337283\pi$
$877$	28.9755	0.978431	0.489216	+	0.872163i	$0.337283\pi$
$878$	−4.13268	−0.139471
$879$	24.7549	0.834962
$880$	0	0
$881$	51.3985	1.73166	0.865830	−	0.500339i	$-0.166791\pi$
$881$	51.3985	1.73166	0.865830	+	0.500339i	$0.166791\pi$
$882$	0.121784	0.00410067
$883$	24.7561	0.833110	0.416555	−	0.909110i	$-0.363237\pi$
$883$	24.7561	0.833110	0.416555	+	0.909110i	$0.363237\pi$
$884$	36.3683	1.22320
$885$	0	0
$886$	−3.41111	−0.114598
$887$	−25.2045	−0.846283	−0.423142	−	0.906064i	$-0.639073\pi$
$887$	−25.2045	−0.846283	−0.423142	+	0.906064i	$0.639073\pi$
$888$	3.07244	0.103104
$889$	−12.4530	−0.417661
$890$	0	0
$891$	−21.3523	−0.715329
$892$	35.9140	1.20249
$893$	12.1640	0.407052
$894$	6.20729	0.207603
$895$	0	0
$896$	6.05312	0.202221
$897$	5.82799	0.194591
$898$	8.14428	0.271778
$899$	−2.14175	−0.0714314
$900$	0	0
$901$	2.03747	0.0678781
$902$	−3.22479	−0.107374
$903$	−5.00636	−0.166601
$904$	−8.59205	−0.285767
$905$	0	0
$906$	3.64670	0.121154
$907$	−9.04710	−0.300404	−0.150202	−	0.988655i	$-0.547992\pi$
$907$	−9.04710	−0.300404	−0.150202	+	0.988655i	$0.547992\pi$
$908$	33.7401	1.11971
$909$	−11.3934	−0.377894
$910$	0	0
$911$	−6.10647	−0.202316	−0.101158	−	0.994870i	$-0.532255\pi$
$911$	−6.10647	−0.202316	−0.101158	+	0.994870i	$0.532255\pi$
$912$	19.9792	0.661576
$913$	37.4340	1.23889
$914$	0.427677	0.0141463
$915$	0	0
$916$	−4.61674	−0.152541
$917$	−2.48876	−0.0821861
$918$	−3.16802	−0.104560
$919$	−3.09363	−0.102049	−0.0510247	−	0.998697i	$-0.516249\pi$
$919$	−3.09363	−0.102049	−0.0510247	+	0.998697i	$0.516249\pi$
$920$	0	0
$921$	−21.5091	−0.708747
$922$	3.72589	0.122706
$923$	76.7497	2.52625
$924$	9.52899	0.313481
$925$	0	0
$926$	1.86285	0.0612172
$927$	4.17777	0.137216
$928$	−2.58426	−0.0848324
$929$	−8.94574	−0.293500	−0.146750	−	0.989174i	$-0.546881\pi$
$929$	−8.94574	−0.293500	−0.146750	+	0.989174i	$0.546881\pi$
$930$	0	0
$931$	−3.43490	−0.112574
$932$	2.72706	0.0893280
$933$	−32.7221	−1.07127
$934$	−3.42148	−0.111954
$935$	0	0
$936$	3.13524	0.102479
$937$	17.4848	0.571203	0.285602	−	0.958348i	$-0.407807\pi$
$937$	17.4848	0.571203	0.285602	+	0.958348i	$0.407807\pi$
$938$	3.03214	0.0990028
$939$	18.3890	0.600104
$940$	0	0
$941$	43.5546	1.41984	0.709920	−	0.704283i	$-0.248731\pi$
$941$	43.5546	1.41984	0.709920	+	0.704283i	$0.248731\pi$
$942$	−5.09504	−0.166005
$943$	2.99095	0.0973987
$944$	39.9699	1.30091
$945$	0	0
$946$	−2.02687	−0.0658993
$947$	−52.0634	−1.69183	−0.845916	−	0.533316i	$-0.820946\pi$
$947$	−52.0634	−1.69183	−0.845916	+	0.533316i	$0.820946\pi$
$948$	25.7063	0.834901
$949$	12.1606	0.394748
$950$	0	0
$951$	−24.4335	−0.792312
$952$	2.24780	0.0728515
$953$	14.0278	0.454404	0.227202	−	0.973848i	$-0.427042\pi$
$953$	14.0278	0.454404	0.227202	+	0.973848i	$0.427042\pi$
$954$	0.0869463	0.00281499
$955$	0	0
$956$	20.5910	0.665961
$957$	−5.40518	−0.174725
$958$	0.317448	0.0102563
$959$	−10.1074	−0.326384
$960$	0	0
$961$	−27.2906	−0.880343
$962$	−3.26356	−0.105222
$963$	−6.87713	−0.221612
$964$	25.0821	0.807841
$965$	0	0
$966$	0.178305	0.00573687
$967$	−18.8223	−0.605284	−0.302642	−	0.953104i	$-0.597869\pi$
$967$	−18.8223	−0.605284	−0.302642	+	0.953104i	$0.597869\pi$
$968$	−0.870380	−0.0279751
$969$	15.1471	0.486594
$970$	0	0
$971$	18.7463	0.601598	0.300799	−	0.953688i	$-0.402747\pi$
$971$	18.7463	0.601598	0.300799	+	0.953688i	$0.402747\pi$
$972$	12.2660	0.393432
$973$	−18.4047	−0.590029
$974$	−7.34544	−0.235363
$975$	0	0
$976$	32.1443	1.02891
$977$	−45.5183	−1.45626	−0.728130	−	0.685440i	$-0.759610\pi$
$977$	−45.5183	−1.45626	−0.728130	+	0.685440i	$0.759610\pi$
$978$	−5.93808	−0.189879
$979$	52.7077	1.68454
$980$	0	0
$981$	11.0514	0.352845
$982$	−2.83129	−0.0903501
$983$	−11.4203	−0.364252	−0.182126	−	0.983275i	$-0.558298\pi$
$983$	−11.4203	−0.364252	−0.182126	+	0.983275i	$0.558298\pi$
$984$	−6.27370	−0.199998
$985$	0	0
$986$	−0.631148	−0.0200999
$987$	5.47200	0.174176
$988$	−43.7731	−1.39261
$989$	1.87990	0.0597772
$990$	0	0
$991$	8.94815	0.284247	0.142124	−	0.989849i	$-0.454607\pi$
$991$	8.94815	0.284247	0.142124	+	0.989849i	$0.454607\pi$
$992$	4.47576	0.142106
$993$	−0.772905	−0.0245274
$994$	2.34813	0.0744781
$995$	0	0
$996$	36.0495	1.14227
$997$	36.0047	1.14028	0.570140	−	0.821547i	$-0.306889\pi$
$997$	36.0047	1.14028	0.570140	+	0.821547i	$0.306889\pi$
$998$	−1.71605	−0.0543207
$999$	−14.0912	−0.445825

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4375.2.a.o.1.16		28
5.4	even	2		4375.2.a.p.1.13		28
25.3	odd	20		175.2.n.a.134.8	yes	56
25.4	even	10		875.2.h.d.701.8		56
25.6	even	5		875.2.h.e.176.7		56
25.8	odd	20		875.2.n.c.449.7		56
25.17	odd	20		175.2.n.a.64.8	✓	56
25.19	even	10		875.2.h.d.176.8		56
25.21	even	5		875.2.h.e.701.7		56
25.22	odd	20		875.2.n.c.799.7		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.n.a.64.8	✓	56	25.17	odd	20
175.2.n.a.134.8	yes	56	25.3	odd	20
875.2.h.d.176.8		56	25.19	even	10
875.2.h.d.701.8		56	25.4	even	10
875.2.h.e.176.7		56	25.6	even	5
875.2.h.e.701.7		56	25.21	even	5
875.2.n.c.449.7		56	25.8	odd	20
875.2.n.c.799.7		56	25.22	odd	20
4375.2.a.o.1.16		28	1.1	even	1	trivial
4375.2.a.p.1.13		28	5.4	even	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:	\( N \)	\(=\)	\( 4375 = 5^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4375.a (trivial)

\(f(q)\)	\(=\)	\(q-0.198876 q^{2} -1.54520 q^{3} -1.96045 q^{4} +0.307303 q^{6} +1.00000 q^{7} +0.787638 q^{8} -0.612360 q^{9} +O(q^{10})\)	\(q-0.198876 q^{2} -1.54520 q^{3} -1.96045 q^{4} +0.307303 q^{6} +1.00000 q^{7} +0.787638 q^{8} -0.612360 q^{9} +3.14562 q^{11} +3.02928 q^{12} -6.50036 q^{13} -0.198876 q^{14} +3.76425 q^{16} +2.85384 q^{17} +0.121784 q^{18} -3.43490 q^{19} -1.54520 q^{21} -0.625589 q^{22} +0.580225 q^{23} -1.21706 q^{24} +1.29277 q^{26} +5.58182 q^{27} -1.96045 q^{28} +1.11204 q^{29} -1.92597 q^{31} -2.32390 q^{32} -4.86062 q^{33} -0.567561 q^{34} +1.20050 q^{36} -2.52448 q^{37} +0.683119 q^{38} +10.0444 q^{39} +5.15481 q^{41} +0.307303 q^{42} +3.23994 q^{43} -6.16683 q^{44} -0.115393 q^{46} -3.54129 q^{47} -5.81652 q^{48} +1.00000 q^{49} -4.40975 q^{51} +12.7436 q^{52} +0.713940 q^{53} -1.11009 q^{54} +0.787638 q^{56} +5.30760 q^{57} -0.221157 q^{58} +10.6183 q^{59} +8.53936 q^{61} +0.383030 q^{62} -0.612360 q^{63} -7.06634 q^{64} +0.966660 q^{66} -15.2464 q^{67} -5.59481 q^{68} -0.896563 q^{69} -11.8070 q^{71} -0.482318 q^{72} -1.87075 q^{73} +0.502059 q^{74} +6.73394 q^{76} +3.14562 q^{77} -1.99758 q^{78} +8.48593 q^{79} -6.78794 q^{81} -1.02517 q^{82} +11.9004 q^{83} +3.02928 q^{84} -0.644347 q^{86} -1.71832 q^{87} +2.47761 q^{88} +16.7559 q^{89} -6.50036 q^{91} -1.13750 q^{92} +2.97601 q^{93} +0.704278 q^{94} +3.59088 q^{96} +10.0125 q^{97} -0.198876 q^{98} -1.92625 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 8 q^{2} - 8 q^{3} + 24 q^{4} + 28 q^{7} - 24 q^{8} + 22 q^{9}+O(q^{10}) \) 28 * q - 8 * q^2 - 8 * q^3 + 24 * q^4 + 28 * q^7 - 24 * q^8 + 22 * q^9	\( 28 q - 8 q^{2} - 8 q^{3} + 24 q^{4} + 28 q^{7} - 24 q^{8} + 22 q^{9} - 16 q^{11} - 24 q^{12} - 16 q^{13} - 8 q^{14} + 24 q^{16} - 40 q^{17} - 24 q^{18} + 4 q^{19} - 8 q^{21} - 16 q^{22} - 32 q^{23} + 14 q^{24} + 6 q^{26} - 32 q^{27} + 24 q^{28} - 24 q^{29} + 6 q^{31} - 56 q^{32} - 28 q^{33} + 18 q^{36} - 32 q^{37} - 40 q^{38} - 28 q^{39} + 2 q^{41} - 16 q^{43} - 26 q^{44} - 12 q^{46} - 26 q^{47} - 46 q^{48} + 28 q^{49} - 22 q^{51} - 28 q^{52} - 60 q^{53} + 38 q^{54} - 24 q^{56} - 76 q^{57} - 16 q^{58} + 8 q^{59} + 18 q^{61} - 34 q^{62} + 22 q^{63} + 28 q^{64} + 38 q^{66} - 24 q^{67} - 62 q^{68} + 14 q^{69} - 54 q^{71} - 40 q^{72} - 46 q^{73} - 30 q^{74} + 26 q^{76} - 16 q^{77} - 32 q^{78} - 30 q^{79} + 4 q^{81} - 22 q^{82} - 60 q^{83} - 24 q^{84} - 10 q^{86} - 18 q^{87} - 16 q^{88} + 6 q^{89} - 16 q^{91} - 72 q^{92} - 48 q^{93} + 86 q^{94} + 106 q^{96} - 70 q^{97} - 8 q^{98} - 30 q^{99}+O(q^{100}) \) 28 * q - 8 * q^2 - 8 * q^3 + 24 * q^4 + 28 * q^7 - 24 * q^8 + 22 * q^9 - 16 * q^11 - 24 * q^12 - 16 * q^13 - 8 * q^14 + 24 * q^16 - 40 * q^17 - 24 * q^18 + 4 * q^19 - 8 * q^21 - 16 * q^22 - 32 * q^23 + 14 * q^24 + 6 * q^26 - 32 * q^27 + 24 * q^28 - 24 * q^29 + 6 * q^31 - 56 * q^32 - 28 * q^33 + 18 * q^36 - 32 * q^37 - 40 * q^38 - 28 * q^39 + 2 * q^41 - 16 * q^43 - 26 * q^44 - 12 * q^46 - 26 * q^47 - 46 * q^48 + 28 * q^49 - 22 * q^51 - 28 * q^52 - 60 * q^53 + 38 * q^54 - 24 * q^56 - 76 * q^57 - 16 * q^58 + 8 * q^59 + 18 * q^61 - 34 * q^62 + 22 * q^63 + 28 * q^64 + 38 * q^66 - 24 * q^67 - 62 * q^68 + 14 * q^69 - 54 * q^71 - 40 * q^72 - 46 * q^73 - 30 * q^74 + 26 * q^76 - 16 * q^77 - 32 * q^78 - 30 * q^79 + 4 * q^81 - 22 * q^82 - 60 * q^83 - 24 * q^84 - 10 * q^86 - 18 * q^87 - 16 * q^88 + 6 * q^89 - 16 * q^91 - 72 * q^92 - 48 * q^93 + 86 * q^94 + 106 * q^96 - 70 * q^97 - 8 * q^98 - 30 * q^99

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