LMFDB - Embedded newform 725.2.a.h.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,2,Mod(1,725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(725, 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("725.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.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:	$5.78915414654$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.240881.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 5x^{3} + 9x^{2} + 5x - 7 $ x^5 - 2x^4 - 5x^3 + 9x^2 + 5x - 7
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			1.5
Root			$-1.88481$ of defining polynomial
Character	$\chi$	$=$	725.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.88481 q^{2} -1.10085 q^{3} +1.55251 q^{4} -2.07489 q^{6} -1.70908 q^{7} -0.843434 q^{8} -1.78814 q^{9} +O(q^{10})$	\(q+1.88481 q^{2} -1.10085 q^{3} +1.55251 q^{4} -2.07489 q^{6} -1.70908 q^{7} -0.843434 q^{8} -1.78814 q^{9} -2.85130 q^{11} -1.70908 q^{12} -6.22128 q^{13} -3.22128 q^{14} -4.69473 q^{16} +1.40381 q^{17} -3.37030 q^{18} +6.74028 q^{19} +1.88143 q^{21} -5.37416 q^{22} -1.42153 q^{23} +0.928492 q^{24} -11.7259 q^{26} +5.27100 q^{27} -2.65336 q^{28} +1.00000 q^{29} -1.29510 q^{31} -7.16181 q^{32} +3.13884 q^{33} +2.64591 q^{34} -2.77610 q^{36} +0.989830 q^{37} +12.7042 q^{38} +6.84868 q^{39} +6.32213 q^{41} +3.54614 q^{42} -6.03720 q^{43} -4.42667 q^{44} -2.67932 q^{46} -8.97549 q^{47} +5.16818 q^{48} -4.07906 q^{49} -1.54538 q^{51} -9.65860 q^{52} -2.11288 q^{53} +9.93484 q^{54} +1.44149 q^{56} -7.42002 q^{57} +1.88481 q^{58} -10.0504 q^{59} +5.73236 q^{61} -2.44101 q^{62} +3.05606 q^{63} -4.10919 q^{64} +5.91612 q^{66} +2.45274 q^{67} +2.17943 q^{68} +1.56489 q^{69} +5.04282 q^{71} +1.50817 q^{72} -5.55668 q^{73} +1.86564 q^{74} +10.4644 q^{76} +4.87309 q^{77} +12.9085 q^{78} +9.37892 q^{79} -0.438162 q^{81} +11.9160 q^{82} -5.06744 q^{83} +2.92094 q^{84} -11.3790 q^{86} -1.10085 q^{87} +2.40488 q^{88} -1.75693 q^{89} +10.6326 q^{91} -2.20694 q^{92} +1.42570 q^{93} -16.9171 q^{94} +7.88406 q^{96} -14.6037 q^{97} -7.68825 q^{98} +5.09851 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{2} - 6 q^{3} + 4 q^{4} - q^{6} - 6 q^{7} - 3 q^{8} + 11 q^{9}+O(q^{10}) $ 5 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 - q^6 - 6 * q^7 - 3 * q^8 + 11 * q^9	$ 5 q - 2 q^{2} - 6 q^{3} + 4 q^{4} - q^{6} - 6 q^{7} - 3 q^{8} + 11 q^{9} - 2 q^{11} - 6 q^{12} - 4 q^{13} + 11 q^{14} - 10 q^{16} - 9 q^{17} + 2 q^{19} - q^{21} - 4 q^{22} - q^{23} + 13 q^{24} - 16 q^{26} - 27 q^{27} - 10 q^{28} + 5 q^{29} - q^{31} + 2 q^{32} + 7 q^{33} + 3 q^{34} - 13 q^{36} - 14 q^{37} + 3 q^{38} - 6 q^{39} + 5 q^{41} - 24 q^{42} - 28 q^{43} + 7 q^{44} - 20 q^{46} - 15 q^{47} + 26 q^{48} - 3 q^{49} + 5 q^{51} - 6 q^{52} + 8 q^{53} + 10 q^{54} - 16 q^{56} + 6 q^{57} - 2 q^{58} - 11 q^{59} - 5 q^{61} + 6 q^{62} + 5 q^{63} - 5 q^{64} - 27 q^{66} - 23 q^{67} - q^{68} - 26 q^{69} - 5 q^{71} - 3 q^{72} - 16 q^{73} + 8 q^{74} + 16 q^{76} + 30 q^{77} + 33 q^{78} - 10 q^{79} + 49 q^{81} + 19 q^{82} - 9 q^{83} + 32 q^{84} - 13 q^{86} - 6 q^{87} - 35 q^{88} - 18 q^{89} + q^{91} + 27 q^{92} - 7 q^{93} - 13 q^{94} - 38 q^{96} - 23 q^{97} - 3 q^{98} - 26 q^{99}+O(q^{100}) $ 5 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 - q^6 - 6 * q^7 - 3 * q^8 + 11 * q^9 - 2 * q^11 - 6 * q^12 - 4 * q^13 + 11 * q^14 - 10 * q^16 - 9 * q^17 + 2 * q^19 - q^21 - 4 * q^22 - q^23 + 13 * q^24 - 16 * q^26 - 27 * q^27 - 10 * q^28 + 5 * q^29 - q^31 + 2 * q^32 + 7 * q^33 + 3 * q^34 - 13 * q^36 - 14 * q^37 + 3 * q^38 - 6 * q^39 + 5 * q^41 - 24 * q^42 - 28 * q^43 + 7 * q^44 - 20 * q^46 - 15 * q^47 + 26 * q^48 - 3 * q^49 + 5 * q^51 - 6 * q^52 + 8 * q^53 + 10 * q^54 - 16 * q^56 + 6 * q^57 - 2 * q^58 - 11 * q^59 - 5 * q^61 + 6 * q^62 + 5 * q^63 - 5 * q^64 - 27 * q^66 - 23 * q^67 - q^68 - 26 * q^69 - 5 * q^71 - 3 * q^72 - 16 * q^73 + 8 * q^74 + 16 * q^76 + 30 * q^77 + 33 * q^78 - 10 * q^79 + 49 * q^81 + 19 * q^82 - 9 * q^83 + 32 * q^84 - 13 * q^86 - 6 * q^87 - 35 * q^88 - 18 * q^89 + q^91 + 27 * q^92 - 7 * q^93 - 13 * q^94 - 38 * q^96 - 23 * q^97 - 3 * q^98 - 26 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.88481	1.33276	0.666381	−	0.745611i	$-0.267842\pi$
$2$	1.88481	1.33276	0.666381	+	0.745611i	$0.267842\pi$
$3$	−1.10085	−0.635574	−0.317787	−	0.948162i	$-0.602940\pi$
$3$	−1.10085	−0.635574	−0.317787	+	0.948162i	$0.602940\pi$
$4$	1.55251	0.776255
$5$	0	0
$5$	0	0
$6$	−2.07489	−0.847069
$7$	−1.70908	−0.645970	−0.322985	−	0.946404i	$-0.604686\pi$
$7$	−1.70908	−0.645970	−0.322985	+	0.946404i	$0.604686\pi$
$8$	−0.843434	−0.298199
$9$	−1.78814	−0.596045
$10$	0	0
$11$	−2.85130	−0.859699	−0.429849	−	0.902901i	$-0.641433\pi$
$11$	−2.85130	−0.859699	−0.429849	+	0.902901i	$0.641433\pi$
$12$	−1.70908	−0.493368
$13$	−6.22128	−1.72547	−0.862737	−	0.505653i	$-0.831252\pi$
$13$	−6.22128	−1.72547	−0.862737	+	0.505653i	$0.831252\pi$
$14$	−3.22128	−0.860924
$15$	0	0
$16$	−4.69473	−1.17368
$17$	1.40381	0.340474	0.170237	−	0.985403i	$-0.445547\pi$
$17$	1.40381	0.340474	0.170237	+	0.985403i	$0.445547\pi$
$18$	−3.37030	−0.794387
$19$	6.74028	1.54633	0.773163	−	0.634207i	$-0.218673\pi$
$19$	6.74028	1.54633	0.773163	+	0.634207i	$0.218673\pi$
$20$	0	0
$21$	1.88143	0.410562
$22$	−5.37416	−1.14577
$23$	−1.42153	−0.296410	−0.148205	−	0.988957i	$-0.547349\pi$
$23$	−1.42153	−0.296410	−0.148205	+	0.988957i	$0.547349\pi$
$24$	0.928492	0.189528
$25$	0	0
$26$	−11.7259	−2.29965
$27$	5.27100	1.01441
$28$	−2.65336	−0.501437
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0	0
$31$	−1.29510	−0.232606	−0.116303	−	0.993214i	$-0.537104\pi$
$31$	−1.29510	−0.232606	−0.116303	+	0.993214i	$0.537104\pi$
$32$	−7.16181	−1.26604
$33$	3.13884	0.546403
$34$	2.64591	0.453770
$35$	0	0
$36$	−2.77610	−0.462683
$37$	0.989830	0.162727	0.0813635	−	0.996684i	$-0.474073\pi$
$37$	0.989830	0.162727	0.0813635	+	0.996684i	$0.474073\pi$
$38$	12.7042	2.06089
$39$	6.84868	1.09667
$40$	0	0
$41$	6.32213	0.987351	0.493675	−	0.869646i	$-0.335653\pi$
$41$	6.32213	0.987351	0.493675	+	0.869646i	$0.335653\pi$
$42$	3.54614	0.547181
$43$	−6.03720	−0.920665	−0.460332	−	0.887747i	$-0.652270\pi$
$43$	−6.03720	−0.920665	−0.460332	+	0.887747i	$0.652270\pi$
$44$	−4.42667	−0.667346
$45$	0	0
$46$	−2.67932	−0.395044
$47$	−8.97549	−1.30921	−0.654605	−	0.755971i	$-0.727165\pi$
$47$	−8.97549	−1.30921	−0.654605	+	0.755971i	$0.727165\pi$
$48$	5.16818	0.745963
$49$	−4.07906	−0.582723
$50$	0	0
$51$	−1.54538	−0.216396
$52$	−9.65860	−1.33941
$53$	−2.11288	−0.290227	−0.145113	−	0.989415i	$-0.546355\pi$
$53$	−2.11288	−0.290227	−0.145113	+	0.989415i	$0.546355\pi$
$54$	9.93484	1.35196
$55$	0	0
$56$	1.44149	0.192628
$57$	−7.42002	−0.982805
$58$	1.88481	0.247488
$59$	−10.0504	−1.30845	−0.654224	−	0.756301i	$-0.727005\pi$
$59$	−10.0504	−1.30845	−0.654224	+	0.756301i	$0.727005\pi$
$60$	0	0
$61$	5.73236	0.733953	0.366977	−	0.930230i	$-0.380393\pi$
$61$	5.73236	0.733953	0.366977	+	0.930230i	$0.380393\pi$
$62$	−2.44101	−0.310009
$63$	3.05606	0.385027
$64$	−4.10919	−0.513649
$65$	0	0
$66$	5.91612	0.728225
$67$	2.45274	0.299650	0.149825	−	0.988713i	$-0.452129\pi$
$67$	2.45274	0.299650	0.149825	+	0.988713i	$0.452129\pi$
$68$	2.17943	0.264294
$69$	1.56489	0.188390
$70$	0	0
$71$	5.04282	0.598473	0.299236	−	0.954179i	$-0.403268\pi$
$71$	5.04282	0.598473	0.299236	+	0.954179i	$0.403268\pi$
$72$	1.50817	0.177740
$73$	−5.55668	−0.650360	−0.325180	−	0.945652i	$-0.605425\pi$
$73$	−5.55668	−0.650360	−0.325180	+	0.945652i	$0.605425\pi$
$74$	1.86564	0.216876
$75$	0	0
$76$	10.4644	1.20034
$77$	4.87309	0.555340
$78$	12.9085	1.46160
$79$	9.37892	1.05521	0.527606	−	0.849489i	$-0.323090\pi$
$79$	9.37892	1.05521	0.527606	+	0.849489i	$0.323090\pi$
$80$	0	0
$81$	−0.438162	−0.0486846
$82$	11.9160	1.31590
$83$	−5.06744	−0.556224	−0.278112	−	0.960549i	$-0.589709\pi$
$83$	−5.06744	−0.556224	−0.278112	+	0.960549i	$0.589709\pi$
$84$	2.92094	0.318701
$85$	0	0
$86$	−11.3790	−1.22703
$87$	−1.10085	−0.118023
$88$	2.40488	0.256361
$89$	−1.75693	−0.186234	−0.0931171	−	0.995655i	$-0.529683\pi$
$89$	−1.75693	−0.186234	−0.0931171	+	0.995655i	$0.529683\pi$
$90$	0	0
$91$	10.6326	1.11460
$92$	−2.20694	−0.230089
$93$	1.42570	0.147839
$94$	−16.9171	−1.74486
$95$	0	0
$96$	7.88406	0.804663
$97$	−14.6037	−1.48278	−0.741389	−	0.671075i	$-0.765833\pi$
$97$	−14.6037	−1.48278	−0.741389	+	0.671075i	$0.765833\pi$
$98$	−7.68825	−0.776631
$99$	5.09851	0.512420
$100$	0	0
$101$	15.8868	1.58079	0.790397	−	0.612595i	$-0.209874\pi$
$101$	15.8868	1.58079	0.790397	+	0.612595i	$0.209874\pi$
$102$	−2.91275	−0.288405
$103$	−11.6322	−1.14616	−0.573079	−	0.819500i	$-0.694251\pi$
$103$	−11.6322	−1.14616	−0.573079	+	0.819500i	$0.694251\pi$
$104$	5.24724	0.514534
$105$	0	0
$106$	−3.98239	−0.386804
$107$	−13.0887	−1.26533	−0.632664	−	0.774426i	$-0.718039\pi$
$107$	−13.0887	−1.26533	−0.632664	+	0.774426i	$0.718039\pi$
$108$	8.18329	0.787437
$109$	10.5634	1.01179	0.505894	−	0.862596i	$-0.331163\pi$
$109$	10.5634	1.01179	0.505894	+	0.862596i	$0.331163\pi$
$110$	0	0
$111$	−1.08965	−0.103425
$112$	8.02365	0.758164
$113$	18.4952	1.73988	0.869940	−	0.493157i	$-0.164157\pi$
$113$	18.4952	1.73988	0.869940	+	0.493157i	$0.164157\pi$
$114$	−13.9853	−1.30985
$115$	0	0
$116$	1.55251	0.144147
$117$	11.1245	1.02846
$118$	−18.9430	−1.74385
$119$	−2.39922	−0.219936
$120$	0	0
$121$	−2.87010	−0.260918
$122$	10.8044	0.978185
$123$	−6.95970	−0.627535
$124$	−2.01065	−0.180562
$125$	0	0
$126$	5.76009	0.513150
$127$	2.95697	0.262389	0.131194	−	0.991357i	$-0.458119\pi$
$127$	2.95697	0.262389	0.131194	+	0.991357i	$0.458119\pi$
$128$	6.57858	0.581470
$129$	6.64604	0.585151
$130$	0	0
$131$	−20.9785	−1.83290	−0.916450	−	0.400150i	$-0.868958\pi$
$131$	−20.9785	−1.83290	−0.916450	+	0.400150i	$0.868958\pi$
$132$	4.87309	0.424148
$133$	−11.5197	−0.998880
$134$	4.62294	0.399362
$135$	0	0
$136$	−1.18402	−0.101529
$137$	19.5953	1.67414	0.837071	−	0.547094i	$-0.184266\pi$
$137$	19.5953	1.67414	0.837071	+	0.547094i	$0.184266\pi$
$138$	2.94952	0.251080
$139$	−21.2859	−1.80545	−0.902725	−	0.430218i	$-0.858437\pi$
$139$	−21.2859	−1.80545	−0.902725	+	0.430218i	$0.858437\pi$
$140$	0	0
$141$	9.88064	0.832100
$142$	9.50476	0.797622
$143$	17.7387	1.48339
$144$	8.39482	0.699568
$145$	0	0
$146$	−10.4733	−0.866776
$147$	4.49042	0.370364
$148$	1.53672	0.126318
$149$	−16.6123	−1.36093	−0.680466	−	0.732779i	$-0.738223\pi$
$149$	−16.6123	−1.36093	−0.680466	+	0.732779i	$0.738223\pi$
$150$	0	0
$151$	8.74718	0.711835	0.355918	−	0.934517i	$-0.384168\pi$
$151$	8.74718	0.711835	0.355918	+	0.934517i	$0.384168\pi$
$152$	−5.68498	−0.461113
$153$	−2.51020	−0.202938
$154$	9.18484	0.740136
$155$	0	0
$156$	10.6326	0.851293
$157$	20.0971	1.60392	0.801960	−	0.597378i	$-0.203791\pi$
$157$	20.0971	1.60392	0.801960	+	0.597378i	$0.203791\pi$
$158$	17.6775	1.40635
$159$	2.32596	0.184461
$160$	0	0
$161$	2.42950	0.191472
$162$	−0.825852	−0.0648850
$163$	3.21100	0.251505	0.125753	−	0.992062i	$-0.459865\pi$
$163$	3.21100	0.251505	0.125753	+	0.992062i	$0.459865\pi$
$164$	9.81517	0.766436
$165$	0	0
$166$	−9.55117	−0.741315
$167$	−6.83823	−0.529158	−0.264579	−	0.964364i	$-0.585233\pi$
$167$	−6.83823	−0.529158	−0.264579	+	0.964364i	$0.585233\pi$
$168$	−1.58686	−0.122429
$169$	25.7044	1.97726
$170$	0	0
$171$	−12.0525	−0.921681
$172$	−9.37282	−0.714671
$173$	−3.47907	−0.264509	−0.132254	−	0.991216i	$-0.542222\pi$
$173$	−3.47907	−0.264509	−0.132254	+	0.991216i	$0.542222\pi$
$174$	−2.07489	−0.157297
$175$	0	0
$176$	13.3861	1.00901
$177$	11.0639	0.831615
$178$	−3.31148	−0.248206
$179$	−23.3359	−1.74421	−0.872105	−	0.489319i	$-0.837245\pi$
$179$	−23.3359	−1.74421	−0.872105	+	0.489319i	$0.837245\pi$
$180$	0	0
$181$	−3.34240	−0.248439	−0.124219	−	0.992255i	$-0.539643\pi$
$181$	−3.34240	−0.248439	−0.124219	+	0.992255i	$0.539643\pi$
$182$	20.0405	1.48550
$183$	−6.31045	−0.466482
$184$	1.19897	0.0883891
$185$	0	0
$186$	2.68718	0.197034
$187$	−4.00268	−0.292705
$188$	−13.9345	−1.01628
$189$	−9.00855	−0.655275
$190$	0	0
$191$	4.61979	0.334276	0.167138	−	0.985934i	$-0.446547\pi$
$191$	4.61979	0.334276	0.167138	+	0.985934i	$0.446547\pi$
$192$	4.52359	0.326462
$193$	−24.9023	−1.79251	−0.896254	−	0.443542i	$-0.853722\pi$
$193$	−24.9023	−1.79251	−0.896254	+	0.443542i	$0.853722\pi$
$194$	−27.5252	−1.97619
$195$	0	0
$196$	−6.33278	−0.452342
$197$	5.96322	0.424862	0.212431	−	0.977176i	$-0.431862\pi$
$197$	5.96322	0.424862	0.212431	+	0.977176i	$0.431862\pi$
$198$	9.60972	0.682933
$199$	−19.0033	−1.34711	−0.673555	−	0.739137i	$-0.735233\pi$
$199$	−19.0033	−1.34711	−0.673555	+	0.739137i	$0.735233\pi$
$200$	0	0
$201$	−2.70009	−0.190450
$202$	29.9436	2.10682
$203$	−1.70908	−0.119954
$204$	−2.39922	−0.167979
$205$	0	0
$206$	−21.9245	−1.52755
$207$	2.54189	0.176674
$208$	29.2073	2.02516
$209$	−19.2186	−1.32938
$210$	0	0
$211$	−8.60278	−0.592240	−0.296120	−	0.955151i	$-0.595693\pi$
$211$	−8.60278	−0.592240	−0.296120	+	0.955151i	$0.595693\pi$
$212$	−3.28027	−0.225290
$213$	−5.55138	−0.380374
$214$	−24.6696	−1.68638
$215$	0	0
$216$	−4.44575	−0.302495
$217$	2.21342	0.150257
$218$	19.9100	1.34847
$219$	6.11706	0.413352
$220$	0	0
$221$	−8.73349	−0.587478
$222$	−2.05379	−0.137841
$223$	7.77513	0.520661	0.260331	−	0.965520i	$-0.416168\pi$
$223$	7.77513	0.520661	0.260331	+	0.965520i	$0.416168\pi$
$224$	12.2401	0.817825
$225$	0	0
$226$	34.8599	2.31885
$227$	11.4310	0.758699	0.379349	−	0.925253i	$-0.376148\pi$
$227$	11.4310	0.758699	0.379349	+	0.925253i	$0.376148\pi$
$228$	−11.5197	−0.762908
$229$	−6.14881	−0.406325	−0.203162	−	0.979145i	$-0.565122\pi$
$229$	−6.14881	−0.406325	−0.203162	+	0.979145i	$0.565122\pi$
$230$	0	0
$231$	−5.36452	−0.352960
$232$	−0.843434	−0.0553742
$233$	0.829745	0.0543584	0.0271792	−	0.999631i	$-0.491348\pi$
$233$	0.829745	0.0543584	0.0271792	+	0.999631i	$0.491348\pi$
$234$	20.9676	1.37069
$235$	0	0
$236$	−15.6033	−1.01569
$237$	−10.3248	−0.670665
$238$	−4.52207	−0.293122
$239$	−0.473622	−0.0306361	−0.0153180	−	0.999883i	$-0.504876\pi$
$239$	−0.473622	−0.0306361	−0.0153180	+	0.999883i	$0.504876\pi$
$240$	0	0
$241$	−22.0803	−1.42232	−0.711160	−	0.703030i	$-0.751830\pi$
$241$	−22.0803	−1.42232	−0.711160	+	0.703030i	$0.751830\pi$
$242$	−5.40958	−0.347741
$243$	−15.3307	−0.983463
$244$	8.89954	0.569735
$245$	0	0
$246$	−13.1177	−0.836355
$247$	−41.9332	−2.66815
$248$	1.09233	0.0693630
$249$	5.57848	0.353522
$250$	0	0
$251$	6.98079	0.440624	0.220312	−	0.975429i	$-0.429292\pi$
$251$	6.98079	0.440624	0.220312	+	0.975429i	$0.429292\pi$
$252$	4.74456	0.298879
$253$	4.05321	0.254823
$254$	5.57333	0.349702
$255$	0	0
$256$	20.6178	1.28861
$257$	−5.35099	−0.333785	−0.166893	−	0.985975i	$-0.553373\pi$
$257$	−5.35099	−0.333785	−0.166893	+	0.985975i	$0.553373\pi$
$258$	12.5265	0.779867
$259$	−1.69169	−0.105117
$260$	0	0
$261$	−1.78814	−0.110683
$262$	−39.5405	−2.44282
$263$	−8.56128	−0.527911	−0.263955	−	0.964535i	$-0.585027\pi$
$263$	−8.56128	−0.527911	−0.263955	+	0.964535i	$0.585027\pi$
$264$	−2.64741	−0.162937
$265$	0	0
$266$	−21.7124	−1.33127
$267$	1.93411	0.118366
$268$	3.80790	0.232604
$269$	−7.36998	−0.449356	−0.224678	−	0.974433i	$-0.572133\pi$
$269$	−7.36998	−0.449356	−0.224678	+	0.974433i	$0.572133\pi$
$270$	0	0
$271$	−5.49008	−0.333499	−0.166749	−	0.985999i	$-0.553327\pi$
$271$	−5.49008	−0.333499	−0.166749	+	0.985999i	$0.553327\pi$
$272$	−6.59051	−0.399608
$273$	−11.7049	−0.708414
$274$	36.9335	2.23123
$275$	0	0
$276$	2.42950	0.146239
$277$	24.0013	1.44210	0.721051	−	0.692882i	$-0.243659\pi$
$277$	24.0013	1.44210	0.721051	+	0.692882i	$0.243659\pi$
$278$	−40.1200	−2.40624
$279$	2.31581	0.138644
$280$	0	0
$281$	10.0364	0.598722	0.299361	−	0.954140i	$-0.403227\pi$
$281$	10.0364	0.598722	0.299361	+	0.954140i	$0.403227\pi$
$282$	18.6231	1.10899
$283$	8.41013	0.499930	0.249965	−	0.968255i	$-0.419581\pi$
$283$	8.41013	0.499930	0.249965	+	0.968255i	$0.419581\pi$
$284$	7.82903	0.464568
$285$	0	0
$286$	33.4342	1.97700
$287$	−10.8050	−0.637799
$288$	12.8063	0.754618
$289$	−15.0293	−0.884078
$290$	0	0
$291$	16.0764	0.942416
$292$	−8.62680	−0.504846
$293$	6.38571	0.373057	0.186529	−	0.982450i	$-0.440276\pi$
$293$	6.38571	0.373057	0.186529	+	0.982450i	$0.440276\pi$
$294$	8.46359	0.493607
$295$	0	0
$296$	−0.834856	−0.0485250
$297$	−15.0292	−0.872083
$298$	−31.3110	−1.81380
$299$	8.84375	0.511447
$300$	0	0
$301$	10.3180	0.594722
$302$	16.4868	0.948707
$303$	−17.4889	−1.00471
$304$	−31.6438	−1.81490
$305$	0	0
$306$	−4.73125	−0.270468
$307$	−28.7573	−1.64126	−0.820632	−	0.571458i	$-0.806378\pi$
$307$	−28.7573	−1.64126	−0.820632	+	0.571458i	$0.806378\pi$
$308$	7.56551	0.431085
$309$	12.8053	0.728468
$310$	0	0
$311$	4.20464	0.238423	0.119211	−	0.992869i	$-0.461963\pi$
$311$	4.20464	0.238423	0.119211	+	0.992869i	$0.461963\pi$
$312$	−5.77641	−0.327025
$313$	18.2272	1.03026	0.515132	−	0.857111i	$-0.327743\pi$
$313$	18.2272	1.03026	0.515132	+	0.857111i	$0.327743\pi$
$314$	37.8791	2.13764
$315$	0	0
$316$	14.5609	0.819113
$317$	−13.4593	−0.755951	−0.377975	−	0.925816i	$-0.623380\pi$
$317$	−13.4593	−0.755951	−0.377975	+	0.925816i	$0.623380\pi$
$318$	4.38400	0.245842
$319$	−2.85130	−0.159642
$320$	0	0
$321$	14.4086	0.804210
$322$	4.57915	0.255186
$323$	9.46207	0.526483
$324$	−0.680250	−0.0377917
$325$	0	0
$326$	6.05214	0.335197
$327$	−11.6287	−0.643066
$328$	−5.33230	−0.294427
$329$	15.3398	0.845710
$330$	0	0
$331$	15.2501	0.838223	0.419112	−	0.907935i	$-0.362342\pi$
$331$	15.2501	0.838223	0.419112	+	0.907935i	$0.362342\pi$
$332$	−7.86726	−0.431772
$333$	−1.76995	−0.0969927
$334$	−12.8888	−0.705242
$335$	0	0
$336$	−8.83281	−0.481870
$337$	5.07452	0.276426	0.138213	−	0.990402i	$-0.455864\pi$
$337$	5.07452	0.276426	0.138213	+	0.990402i	$0.455864\pi$
$338$	48.4479	2.63522
$339$	−20.3604	−1.10582
$340$	0	0
$341$	3.69271	0.199971
$342$	−22.7168	−1.22838
$343$	18.9350	1.02239
$344$	5.09198	0.274541
$345$	0	0
$346$	−6.55738	−0.352527
$347$	−28.0386	−1.50519	−0.752596	−	0.658482i	$-0.771199\pi$
$347$	−28.0386	−1.50519	−0.752596	+	0.658482i	$0.771199\pi$
$348$	−1.70908	−0.0916161
$349$	−27.7759	−1.48681	−0.743406	−	0.668840i	$-0.766791\pi$
$349$	−27.7759	−1.48681	−0.743406	+	0.668840i	$0.766791\pi$
$350$	0	0
$351$	−32.7924	−1.75033
$352$	20.4205	1.08841
$353$	31.4223	1.67244	0.836221	−	0.548392i	$-0.184760\pi$
$353$	31.4223	1.67244	0.836221	+	0.548392i	$0.184760\pi$
$354$	20.8534	1.10835
$355$	0	0
$356$	−2.72765	−0.144565
$357$	2.64117	0.139785
$358$	−43.9838	−2.32462
$359$	27.0194	1.42603	0.713014	−	0.701150i	$-0.247329\pi$
$359$	27.0194	1.42603	0.713014	+	0.701150i	$0.247329\pi$
$360$	0	0
$361$	26.4314	1.39113
$362$	−6.29980	−0.331110
$363$	3.15954	0.165833
$364$	16.5073	0.865217
$365$	0	0
$366$	−11.8940	−0.621709
$367$	20.3243	1.06092	0.530460	−	0.847710i	$-0.322019\pi$
$367$	20.3243	1.06092	0.530460	+	0.847710i	$0.322019\pi$
$368$	6.67371	0.347891
$369$	−11.3048	−0.588506
$370$	0	0
$371$	3.61108	0.187478
$372$	2.21342	0.114760
$373$	−15.9724	−0.827021	−0.413511	−	0.910499i	$-0.635698\pi$
$373$	−15.9724	−0.827021	−0.413511	+	0.910499i	$0.635698\pi$
$374$	−7.54429	−0.390106
$375$	0	0
$376$	7.57023	0.390405
$377$	−6.22128	−0.320412
$378$	−16.9794	−0.873326
$379$	29.4840	1.51449	0.757247	−	0.653129i	$-0.226544\pi$
$379$	29.4840	1.51449	0.757247	+	0.653129i	$0.226544\pi$
$380$	0	0
$381$	−3.25517	−0.166768
$382$	8.70742	0.445510
$383$	35.1376	1.79545	0.897723	−	0.440560i	$-0.145220\pi$
$383$	35.1376	1.79545	0.897723	+	0.440560i	$0.145220\pi$
$384$	−7.24201	−0.369567
$385$	0	0
$386$	−46.9361	−2.38899
$387$	10.7953	0.548758
$388$	−22.6724	−1.15101
$389$	28.3776	1.43880	0.719401	−	0.694595i	$-0.244417\pi$
$389$	28.3776	1.43880	0.719401	+	0.694595i	$0.244417\pi$
$390$	0	0
$391$	−1.99556	−0.100920
$392$	3.44042	0.173767
$393$	23.0941	1.16494
$394$	11.2395	0.566240
$395$	0	0
$396$	7.91549	0.397768
$397$	−24.5435	−1.23180	−0.615901	−	0.787823i	$-0.711208\pi$
$397$	−24.5435	−1.23180	−0.615901	+	0.787823i	$0.711208\pi$
$398$	−35.8176	−1.79538
$399$	12.6814	0.634863
$400$	0	0
$401$	4.95811	0.247596	0.123798	−	0.992307i	$-0.460493\pi$
$401$	4.95811	0.247596	0.123798	+	0.992307i	$0.460493\pi$
$402$	−5.08915	−0.253824
$403$	8.05717	0.401356
$404$	24.6644	1.22710
$405$	0	0
$406$	−3.22128	−0.159870
$407$	−2.82230	−0.139896
$408$	1.30342	0.0645291
$409$	−29.6350	−1.46535	−0.732677	−	0.680576i	$-0.761729\pi$
$409$	−29.6350	−1.46535	−0.732677	+	0.680576i	$0.761729\pi$
$410$	0	0
$411$	−21.5715	−1.06404
$412$	−18.0591	−0.889710
$413$	17.1769	0.845218
$414$	4.79098	0.235464
$415$	0	0
$416$	44.5557	2.18452
$417$	23.4326	1.14750
$418$	−36.2233	−1.77174
$419$	27.1403	1.32589	0.662945	−	0.748668i	$-0.269306\pi$
$419$	27.1403	1.32589	0.662945	+	0.748668i	$0.269306\pi$
$420$	0	0
$421$	−27.0310	−1.31741	−0.658705	−	0.752401i	$-0.728896\pi$
$421$	−27.0310	−1.31741	−0.658705	+	0.752401i	$0.728896\pi$
$422$	−16.2146	−0.789314
$423$	16.0494	0.780348
$424$	1.78208	0.0865454
$425$	0	0
$426$	−10.4633	−0.506948
$427$	−9.79703	−0.474112
$428$	−20.3203	−0.982217
$429$	−19.5276	−0.942803
$430$	0	0
$431$	−27.7496	−1.33665	−0.668327	−	0.743868i	$-0.732989\pi$
$431$	−27.7496	−1.33665	−0.668327	+	0.743868i	$0.732989\pi$
$432$	−24.7460	−1.19059
$433$	14.3507	0.689649	0.344825	−	0.938667i	$-0.387938\pi$
$433$	14.3507	0.689649	0.344825	+	0.938667i	$0.387938\pi$
$434$	4.17187	0.200256
$435$	0	0
$436$	16.3997	0.785405
$437$	−9.58152	−0.458346
$438$	11.5295	0.550900
$439$	19.0540	0.909398	0.454699	−	0.890645i	$-0.349747\pi$
$439$	19.0540	0.909398	0.454699	+	0.890645i	$0.349747\pi$
$440$	0	0
$441$	7.29391	0.347329
$442$	−16.4610	−0.782969
$443$	−36.2772	−1.72358	−0.861791	−	0.507263i	$-0.830657\pi$
$443$	−36.2772	−1.72358	−0.861791	+	0.507263i	$0.830657\pi$
$444$	−1.69169	−0.0802843
$445$	0	0
$446$	14.6546	0.693918
$447$	18.2876	0.864974
$448$	7.02292	0.331802
$449$	3.04282	0.143600	0.0717998	−	0.997419i	$-0.477126\pi$
$449$	3.04282	0.143600	0.0717998	+	0.997419i	$0.477126\pi$
$450$	0	0
$451$	−18.0263	−0.848825
$452$	28.7140	1.35059
$453$	−9.62931	−0.452424
$454$	21.5452	1.01117
$455$	0	0
$456$	6.25830	0.293072
$457$	24.8217	1.16111	0.580556	−	0.814220i	$-0.302835\pi$
$457$	24.8217	1.16111	0.580556	+	0.814220i	$0.302835\pi$
$458$	−11.5893	−0.541534
$459$	7.39948	0.345378
$460$	0	0
$461$	−14.1662	−0.659786	−0.329893	−	0.944018i	$-0.607013\pi$
$461$	−14.1662	−0.659786	−0.329893	+	0.944018i	$0.607013\pi$
$462$	−10.1111	−0.470411
$463$	−9.03538	−0.419910	−0.209955	−	0.977711i	$-0.567332\pi$
$463$	−9.03538	−0.419910	−0.209955	+	0.977711i	$0.567332\pi$
$464$	−4.69473	−0.217948
$465$	0	0
$466$	1.56391	0.0724468
$467$	5.28374	0.244503	0.122251	−	0.992499i	$-0.460989\pi$
$467$	5.28374	0.244503	0.122251	+	0.992499i	$0.460989\pi$
$468$	17.2709	0.798347
$469$	−4.19191	−0.193565
$470$	0	0
$471$	−22.1238	−1.01941
$472$	8.47683	0.390178
$473$	17.2139	0.791495
$474$	−19.4602	−0.893837
$475$	0	0
$476$	−3.72481	−0.170726
$477$	3.77812	0.172988
$478$	−0.892688	−0.0408306
$479$	−16.3846	−0.748634	−0.374317	−	0.927301i	$-0.622123\pi$
$479$	−16.3846	−0.748634	−0.374317	+	0.927301i	$0.622123\pi$
$480$	0	0
$481$	−6.15801	−0.280781
$482$	−41.6173	−1.89561
$483$	−2.67451	−0.121695
$484$	−4.45585	−0.202539
$485$	0	0
$486$	−28.8954	−1.31072
$487$	−2.74404	−0.124344	−0.0621722	−	0.998065i	$-0.519803\pi$
$487$	−2.74404	−0.124344	−0.0621722	+	0.998065i	$0.519803\pi$
$488$	−4.83487	−0.218864
$489$	−3.53483	−0.159850
$490$	0	0
$491$	9.46362	0.427087	0.213544	−	0.976934i	$-0.431499\pi$
$491$	9.46362	0.427087	0.213544	+	0.976934i	$0.431499\pi$
$492$	−10.8050	−0.487127
$493$	1.40381	0.0632244
$494$	−79.0361	−3.55600
$495$	0	0
$496$	6.08013	0.273006
$497$	−8.61857	−0.386595
$498$	10.5144	0.471160
$499$	−36.0076	−1.61192	−0.805960	−	0.591970i	$-0.798350\pi$
$499$	−36.0076	−1.61192	−0.805960	+	0.591970i	$0.798350\pi$
$500$	0	0
$501$	7.52784	0.336319
$502$	13.1575	0.587247
$503$	−21.6537	−0.965490	−0.482745	−	0.875761i	$-0.660360\pi$
$503$	−21.6537	−0.965490	−0.482745	+	0.875761i	$0.660360\pi$
$504$	−2.57759	−0.114815
$505$	0	0
$506$	7.63953	0.339619
$507$	−28.2966	−1.25669
$508$	4.59073	0.203681
$509$	16.5219	0.732321	0.366160	−	0.930552i	$-0.380672\pi$
$509$	16.5219	0.732321	0.366160	+	0.930552i	$0.380672\pi$
$510$	0	0
$511$	9.49679	0.420113
$512$	25.7034	1.13594
$513$	35.5281	1.56860
$514$	−10.0856	−0.444857
$515$	0	0
$516$	10.3180	0.454226
$517$	25.5918	1.12553
$518$	−3.18852	−0.140096
$519$	3.82992	0.168115
$520$	0	0
$521$	4.77373	0.209141	0.104571	−	0.994517i	$-0.466653\pi$
$521$	4.77373	0.209141	0.104571	+	0.994517i	$0.466653\pi$
$522$	−3.37030	−0.147514
$523$	−18.4589	−0.807150	−0.403575	−	0.914947i	$-0.632233\pi$
$523$	−18.4589	−0.807150	−0.403575	+	0.914947i	$0.632233\pi$
$524$	−32.5693	−1.42280
$525$	0	0
$526$	−16.1364	−0.703580
$527$	−1.81807	−0.0791963
$528$	−14.7360	−0.641303
$529$	−20.9792	−0.912141
$530$	0	0
$531$	17.9714	0.779894
$532$	−17.8844	−0.775386
$533$	−39.3318	−1.70365
$534$	3.64543	0.157753
$535$	0	0
$536$	−2.06872	−0.0893552
$537$	25.6893	1.10857
$538$	−13.8910	−0.598885
$539$	11.6306	0.500966
$540$	0	0
$541$	−43.5067	−1.87050	−0.935250	−	0.353989i	$-0.884825\pi$
$541$	−43.5067	−1.87050	−0.935250	+	0.353989i	$0.884825\pi$
$542$	−10.3478	−0.444474
$543$	3.67948	0.157901
$544$	−10.0538	−0.431054
$545$	0	0
$546$	−22.0615	−0.944147
$547$	−5.97641	−0.255533	−0.127766	−	0.991804i	$-0.540781\pi$
$547$	−5.97641	−0.255533	−0.127766	+	0.991804i	$0.540781\pi$
$548$	30.4219	1.29956
$549$	−10.2502	−0.437469
$550$	0	0
$551$	6.74028	0.287146
$552$	−1.31988	−0.0561778
$553$	−16.0293	−0.681635
$554$	45.2380	1.92198
$555$	0	0
$556$	−33.0466	−1.40149
$557$	30.0628	1.27380	0.636900	−	0.770946i	$-0.280216\pi$
$557$	30.0628	1.27380	0.636900	+	0.770946i	$0.280216\pi$
$558$	4.36486	0.184779
$559$	37.5592	1.58858
$560$	0	0
$561$	4.40634	0.186036
$562$	18.9167	0.797954
$563$	−18.5651	−0.782425	−0.391212	−	0.920300i	$-0.627944\pi$
$563$	−18.5651	−0.782425	−0.391212	+	0.920300i	$0.627944\pi$
$564$	15.3398	0.645922
$565$	0	0
$566$	15.8515	0.666288
$567$	0.748851	0.0314488
$568$	−4.25329	−0.178464
$569$	−30.6606	−1.28536	−0.642679	−	0.766135i	$-0.722177\pi$
$569$	−30.6606	−1.28536	−0.642679	+	0.766135i	$0.722177\pi$
$570$	0	0
$571$	−6.78472	−0.283932	−0.141966	−	0.989872i	$-0.545342\pi$
$571$	−6.78472	−0.283932	−0.141966	+	0.989872i	$0.545342\pi$
$572$	27.5396	1.15149
$573$	−5.08568	−0.212457
$574$	−20.3654	−0.850034
$575$	0	0
$576$	7.34779	0.306158
$577$	−27.7326	−1.15453	−0.577263	−	0.816559i	$-0.695879\pi$
$577$	−27.7326	−1.15453	−0.577263	+	0.816559i	$0.695879\pi$
$578$	−28.3274	−1.17827
$579$	27.4136	1.13927
$580$	0	0
$581$	8.66064	0.359304
$582$	30.3010	1.25602
$583$	6.02446	0.249508
$584$	4.68670	0.193937
$585$	0	0
$586$	12.0359	0.497197
$587$	16.6049	0.685359	0.342679	−	0.939452i	$-0.388666\pi$
$587$	16.6049	0.685359	0.342679	+	0.939452i	$0.388666\pi$
$588$	6.97142	0.287497
$589$	−8.72932	−0.359685
$590$	0	0
$591$	−6.56459	−0.270031
$592$	−4.64699	−0.190990
$593$	20.5406	0.843499	0.421750	−	0.906712i	$-0.361416\pi$
$593$	20.5406	0.843499	0.421750	+	0.906712i	$0.361416\pi$
$594$	−28.3272	−1.16228
$595$	0	0
$596$	−25.7908	−1.05643
$597$	20.9197	0.856188
$598$	16.6688	0.681637
$599$	31.3560	1.28117	0.640586	−	0.767886i	$-0.278691\pi$
$599$	31.3560	1.28117	0.640586	+	0.767886i	$0.278691\pi$
$600$	0	0
$601$	14.3674	0.586057	0.293029	−	0.956104i	$-0.405337\pi$
$601$	14.3674	0.586057	0.293029	+	0.956104i	$0.405337\pi$
$602$	19.4475	0.792623
$603$	−4.38583	−0.178605
$604$	13.5801	0.552566
$605$	0	0
$606$	−32.9633	−1.33904
$607$	−25.1167	−1.01945	−0.509727	−	0.860336i	$-0.670254\pi$
$607$	−25.1167	−1.01945	−0.509727	+	0.860336i	$0.670254\pi$
$608$	−48.2726	−1.95771
$609$	1.88143	0.0762394
$610$	0	0
$611$	55.8390	2.25901
$612$	−3.89711	−0.157531
$613$	36.4069	1.47046	0.735230	−	0.677818i	$-0.237074\pi$
$613$	36.4069	1.47046	0.735230	+	0.677818i	$0.237074\pi$
$614$	−54.2020	−2.18741
$615$	0	0
$616$	−4.11013	−0.165602
$617$	28.9915	1.16715	0.583576	−	0.812058i	$-0.301653\pi$
$617$	28.9915	1.16715	0.583576	+	0.812058i	$0.301653\pi$
$618$	24.1356	0.970874
$619$	−38.6097	−1.55185	−0.775927	−	0.630823i	$-0.782717\pi$
$619$	−38.6097	−1.55185	−0.775927	+	0.630823i	$0.782717\pi$
$620$	0	0
$621$	−7.49290	−0.300680
$622$	7.92494	0.317761
$623$	3.00273	0.120302
$624$	−32.1527	−1.28714
$625$	0	0
$626$	34.3549	1.37310
$627$	21.1567	0.844917
$628$	31.2009	1.24505
$629$	1.38953	0.0554043
$630$	0	0
$631$	12.4946	0.497401	0.248700	−	0.968580i	$-0.419997\pi$
$631$	12.4946	0.497401	0.248700	+	0.968580i	$0.419997\pi$
$632$	−7.91050	−0.314663
$633$	9.47034	0.376412
$634$	−25.3683	−1.00750
$635$	0	0
$636$	3.61108	0.143189
$637$	25.3770	1.00547
$638$	−5.37416	−0.212765
$639$	−9.01725	−0.356717
$640$	0	0
$641$	18.6523	0.736723	0.368361	−	0.929683i	$-0.379919\pi$
$641$	18.6523	0.736723	0.368361	+	0.929683i	$0.379919\pi$
$642$	27.1575	1.07182
$643$	−9.99161	−0.394030	−0.197015	−	0.980400i	$-0.563125\pi$
$643$	−9.99161	−0.394030	−0.197015	+	0.980400i	$0.563125\pi$
$644$	3.77183	0.148631
$645$	0	0
$646$	17.8342	0.701677
$647$	6.59170	0.259146	0.129573	−	0.991570i	$-0.458639\pi$
$647$	6.59170	0.259146	0.129573	+	0.991570i	$0.458639\pi$
$648$	0.369561	0.0145177
$649$	28.6566	1.12487
$650$	0	0
$651$	−2.43664	−0.0954993
$652$	4.98512	0.195232
$653$	47.5008	1.85885	0.929425	−	0.369011i	$-0.120304\pi$
$653$	47.5008	1.85885	0.929425	+	0.369011i	$0.120304\pi$
$654$	−21.9178	−0.857054
$655$	0	0
$656$	−29.6807	−1.15884
$657$	9.93610	0.387644
$658$	28.9126	1.12713
$659$	32.7065	1.27407	0.637033	−	0.770837i	$-0.280162\pi$
$659$	32.7065	1.27407	0.637033	+	0.770837i	$0.280162\pi$
$660$	0	0
$661$	−37.6003	−1.46248	−0.731242	−	0.682119i	$-0.761059\pi$
$661$	−37.6003	−1.46248	−0.731242	+	0.682119i	$0.761059\pi$
$662$	28.7436	1.11715
$663$	9.61424	0.373386
$664$	4.27405	0.165866
$665$	0	0
$666$	−3.33602	−0.129268
$667$	−1.42153	−0.0550419
$668$	−10.6164	−0.410762
$669$	−8.55923	−0.330919
$670$	0	0
$671$	−16.3447	−0.630979
$672$	−13.4745	−0.519788
$673$	−47.2395	−1.82095	−0.910475	−	0.413564i	$-0.864284\pi$
$673$	−47.2395	−1.82095	−0.910475	+	0.413564i	$0.864284\pi$
$674$	9.56450	0.368411
$675$	0	0
$676$	39.9063	1.53486
$677$	−17.3323	−0.666134	−0.333067	−	0.942903i	$-0.608083\pi$
$677$	−17.3323	−0.666134	−0.333067	+	0.942903i	$0.608083\pi$
$678$	−38.3754	−1.47380
$679$	24.9588	0.957830
$680$	0	0
$681$	−12.5837	−0.482209
$682$	6.96005	0.266514
$683$	−4.70774	−0.180137	−0.0900683	−	0.995936i	$-0.528709\pi$
$683$	−4.70774	−0.180137	−0.0900683	+	0.995936i	$0.528709\pi$
$684$	−18.7117	−0.715459
$685$	0	0
$686$	35.6888	1.36260
$687$	6.76890	0.258250
$688$	28.3431	1.08057
$689$	13.1449	0.500779
$690$	0	0
$691$	−2.88811	−0.109869	−0.0549345	−	0.998490i	$-0.517495\pi$
$691$	−2.88811	−0.109869	−0.0549345	+	0.998490i	$0.517495\pi$
$692$	−5.40129	−0.205326
$693$	−8.71374	−0.331008
$694$	−52.8475	−2.00606
$695$	0	0
$696$	0.928492	0.0351944
$697$	8.87506	0.336167
$698$	−52.3524	−1.98157
$699$	−0.913422	−0.0345488
$700$	0	0
$701$	39.1914	1.48024	0.740120	−	0.672475i	$-0.234769\pi$
$701$	39.1914	1.48024	0.740120	+	0.672475i	$0.234769\pi$
$702$	−61.8075	−2.33277
$703$	6.67173	0.251629
$704$	11.7165	0.441584
$705$	0	0
$706$	59.2251	2.22897
$707$	−27.1517	−1.02115
$708$	17.1769	0.645546
$709$	35.0367	1.31583	0.657915	−	0.753092i	$-0.271439\pi$
$709$	35.0367	1.31583	0.657915	+	0.753092i	$0.271439\pi$
$710$	0	0
$711$	−16.7708	−0.628954
$712$	1.48185	0.0555349
$713$	1.84102	0.0689468
$714$	4.97810	0.186301
$715$	0	0
$716$	−36.2293	−1.35395
$717$	0.521385	0.0194715
$718$	50.9264	1.90056
$719$	9.93705	0.370590	0.185295	−	0.982683i	$-0.440676\pi$
$719$	9.93705	0.370590	0.185295	+	0.982683i	$0.440676\pi$
$720$	0	0
$721$	19.8804	0.740383
$722$	49.8182	1.85404
$723$	24.3071	0.903990
$724$	−5.18912	−0.192852
$725$	0	0
$726$	5.95513	0.221015
$727$	−2.37679	−0.0881504	−0.0440752	−	0.999028i	$-0.514034\pi$
$727$	−2.37679	−0.0881504	−0.0440752	+	0.999028i	$0.514034\pi$
$728$	−8.96793	−0.332374
$729$	18.1912	0.673748
$730$	0	0
$731$	−8.47508	−0.313462
$732$	−9.79703	−0.362109
$733$	32.6214	1.20490	0.602450	−	0.798157i	$-0.294191\pi$
$733$	32.6214	1.20490	0.602450	+	0.798157i	$0.294191\pi$
$734$	38.3075	1.41396
$735$	0	0
$736$	10.1807	0.375267
$737$	−6.99349	−0.257608
$738$	−21.3075	−0.784338
$739$	16.6544	0.612642	0.306321	−	0.951928i	$-0.400902\pi$
$739$	16.6544	0.612642	0.306321	+	0.951928i	$0.400902\pi$
$740$	0	0
$741$	46.1620	1.69580
$742$	6.80620	0.249863
$743$	35.2240	1.29224	0.646121	−	0.763235i	$-0.276390\pi$
$743$	35.2240	1.29224	0.646121	+	0.763235i	$0.276390\pi$
$744$	−1.20249	−0.0440853
$745$	0	0
$746$	−30.1050	−1.10222
$747$	9.06128	0.331535
$748$	−6.21420	−0.227214
$749$	22.3695	0.817364
$750$	0	0
$751$	−46.9948	−1.71487	−0.857433	−	0.514596i	$-0.827942\pi$
$751$	−46.9948	−1.71487	−0.857433	+	0.514596i	$0.827942\pi$
$752$	42.1375	1.53660
$753$	−7.68479	−0.280049
$754$	−11.7259	−0.427034
$755$	0	0
$756$	−13.9859	−0.508661
$757$	−16.5681	−0.602179	−0.301089	−	0.953596i	$-0.597350\pi$
$757$	−16.5681	−0.602179	−0.301089	+	0.953596i	$0.597350\pi$
$758$	55.5718	2.01846
$759$	−4.46196	−0.161959
$760$	0	0
$761$	43.1593	1.56453	0.782263	−	0.622949i	$-0.214066\pi$
$761$	43.1593	1.56453	0.782263	+	0.622949i	$0.214066\pi$
$762$	−6.13538	−0.222262
$763$	−18.0536	−0.653585
$764$	7.17226	0.259483
$765$	0	0
$766$	66.2277	2.39290
$767$	62.5262	2.25769
$768$	−22.6970	−0.819007
$769$	−16.7337	−0.603434	−0.301717	−	0.953398i	$-0.597560\pi$
$769$	−16.7337	−0.603434	−0.301717	+	0.953398i	$0.597560\pi$
$770$	0	0
$771$	5.89062	0.212145
$772$	−38.6611	−1.39144
$773$	−8.41758	−0.302759	−0.151380	−	0.988476i	$-0.548372\pi$
$773$	−8.41758	−0.302759	−0.151380	+	0.988476i	$0.548372\pi$
$774$	20.3472	0.731364
$775$	0	0
$776$	12.3172	0.442163
$777$	1.86230	0.0668095
$778$	53.4864	1.91758
$779$	42.6129	1.52677
$780$	0	0
$781$	−14.3786	−0.514507
$782$	−3.76125	−0.134502
$783$	5.27100	0.188370
$784$	19.1501	0.683932
$785$	0	0
$786$	43.5280	1.55259
$787$	−50.6781	−1.80648	−0.903240	−	0.429136i	$-0.858818\pi$
$787$	−50.6781	−1.80648	−0.903240	+	0.429136i	$0.858818\pi$
$788$	9.25795	0.329801
$789$	9.42465	0.335527
$790$	0	0
$791$	−31.6097	−1.12391
$792$	−4.30026	−0.152803
$793$	−35.6626	−1.26642
$794$	−46.2598	−1.64170
$795$	0	0
$796$	−29.5028	−1.04570
$797$	21.8932	0.775498	0.387749	−	0.921765i	$-0.373253\pi$
$797$	21.8932	0.775498	0.387749	+	0.921765i	$0.373253\pi$
$798$	23.9020	0.846121
$799$	−12.5999	−0.445751
$800$	0	0
$801$	3.14163	0.111004
$802$	9.34509	0.329987
$803$	15.8438	0.559114
$804$	−4.19191	−0.147837
$805$	0	0
$806$	15.1862	0.534912
$807$	8.11323	0.285599
$808$	−13.3995	−0.471391
$809$	−8.70213	−0.305951	−0.152975	−	0.988230i	$-0.548885\pi$
$809$	−8.70213	−0.305951	−0.152975	+	0.988230i	$0.548885\pi$
$810$	0	0
$811$	39.0632	1.37170	0.685848	−	0.727745i	$-0.259431\pi$
$811$	39.0632	1.37170	0.685848	+	0.727745i	$0.259431\pi$
$812$	−2.65336	−0.0931146
$813$	6.04374	0.211963
$814$	−5.31950	−0.186448
$815$	0	0
$816$	7.25514	0.253981
$817$	−40.6925	−1.42365
$818$	−55.8563	−1.95297
$819$	−19.0126	−0.664354
$820$	0	0
$821$	16.7509	0.584612	0.292306	−	0.956325i	$-0.405577\pi$
$821$	16.7509	0.584612	0.292306	+	0.956325i	$0.405577\pi$
$822$	−40.6581	−1.41811
$823$	−38.3755	−1.33768	−0.668842	−	0.743405i	$-0.733210\pi$
$823$	−38.3755	−1.33768	−0.668842	+	0.743405i	$0.733210\pi$
$824$	9.81101	0.341783
$825$	0	0
$826$	32.3751	1.12647
$827$	−6.70137	−0.233029	−0.116515	−	0.993189i	$-0.537172\pi$
$827$	−6.70137	−0.233029	−0.116515	+	0.993189i	$0.537172\pi$
$828$	3.94631	0.137144
$829$	7.98795	0.277433	0.138716	−	0.990332i	$-0.455702\pi$
$829$	7.98795	0.277433	0.138716	+	0.990332i	$0.455702\pi$
$830$	0	0
$831$	−26.4218	−0.916562
$832$	25.5644	0.886288
$833$	−5.72622	−0.198402
$834$	44.1659	1.52934
$835$	0	0
$836$	−29.8370	−1.03193
$837$	−6.82646	−0.235957
$838$	51.1543	1.76710
$839$	−13.9407	−0.481286	−0.240643	−	0.970614i	$-0.577358\pi$
$839$	−13.9407	−0.481286	−0.240643	+	0.970614i	$0.577358\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	−50.9483	−1.75580
$843$	−11.0485	−0.380532
$844$	−13.3559	−0.459729
$845$	0	0
$846$	30.2501	1.04002
$847$	4.90521	0.168545
$848$	9.91943	0.340635
$849$	−9.25827	−0.317743
$850$	0	0
$851$	−1.40707	−0.0482339
$852$	−8.61857	−0.295267
$853$	5.78046	0.197919	0.0989597	−	0.995091i	$-0.468449\pi$
$853$	5.78046	0.197919	0.0989597	+	0.995091i	$0.468449\pi$
$854$	−18.4655	−0.631878
$855$	0	0
$856$	11.0394	0.377319
$857$	33.2410	1.13549	0.567745	−	0.823205i	$-0.307816\pi$
$857$	33.2410	1.13549	0.567745	+	0.823205i	$0.307816\pi$
$858$	−36.8059	−1.25653
$859$	1.19425	0.0407473	0.0203736	−	0.999792i	$-0.493514\pi$
$859$	1.19425	0.0407473	0.0203736	+	0.999792i	$0.493514\pi$
$860$	0	0
$861$	11.8947	0.405369
$862$	−52.3028	−1.78144
$863$	42.0216	1.43043	0.715215	−	0.698904i	$-0.246329\pi$
$863$	42.0216	1.43043	0.715215	+	0.698904i	$0.246329\pi$
$864$	−37.7499	−1.28428
$865$	0	0
$866$	27.0483	0.919138
$867$	16.5450	0.561897
$868$	3.43635	0.116637
$869$	−26.7421	−0.907164
$870$	0	0
$871$	−15.2592	−0.517037
$872$	−8.90951	−0.301714
$873$	26.1134	0.883803
$874$	−18.0593	−0.610866
$875$	0	0
$876$	9.49679	0.320867
$877$	22.8893	0.772917	0.386458	−	0.922307i	$-0.373698\pi$
$877$	22.8893	0.772917	0.386458	+	0.922307i	$0.373698\pi$
$878$	35.9132	1.21201
$879$	−7.02969	−0.237106
$880$	0	0
$881$	13.6751	0.460727	0.230363	−	0.973105i	$-0.426009\pi$
$881$	13.6751	0.460727	0.230363	+	0.973105i	$0.426009\pi$
$882$	13.7476	0.462907
$883$	−1.49072	−0.0501668	−0.0250834	−	0.999685i	$-0.507985\pi$
$883$	−1.49072	−0.0501668	−0.0250834	+	0.999685i	$0.507985\pi$
$884$	−13.5588	−0.456033
$885$	0	0
$886$	−68.3757	−2.29713
$887$	2.58705	0.0868646	0.0434323	−	0.999056i	$-0.486171\pi$
$887$	2.58705	0.0868646	0.0434323	+	0.999056i	$0.486171\pi$
$888$	0.919049	0.0308413
$889$	−5.05369	−0.169495
$890$	0	0
$891$	1.24933	0.0418541
$892$	12.0710	0.404166
$893$	−60.4973	−2.02447
$894$	34.4687	1.15280
$895$	0	0
$896$	−11.2433	−0.375612
$897$	−9.73561	−0.325063
$898$	5.73514	0.191384
$899$	−1.29510	−0.0431939
$900$	0	0
$901$	−2.96609	−0.0988146
$902$	−33.9761	−1.13128
$903$	−11.3586	−0.377990
$904$	−15.5995	−0.518831
$905$	0	0
$906$	−18.1494	−0.602974
$907$	−18.3747	−0.610121	−0.305060	−	0.952333i	$-0.598677\pi$
$907$	−18.3747	−0.610121	−0.305060	+	0.952333i	$0.598677\pi$
$908$	17.7467	0.588944
$909$	−28.4077	−0.942225
$910$	0	0
$911$	32.8875	1.08961	0.544806	−	0.838562i	$-0.316603\pi$
$911$	32.8875	1.08961	0.544806	+	0.838562i	$0.316603\pi$
$912$	34.8350	1.15350
$913$	14.4488	0.478185
$914$	46.7843	1.54749
$915$	0	0
$916$	−9.54608	−0.315412
$917$	35.8538	1.18400
$918$	13.9466	0.460307
$919$	28.2361	0.931422	0.465711	−	0.884937i	$-0.345799\pi$
$919$	28.2361	0.931422	0.465711	+	0.884937i	$0.345799\pi$
$920$	0	0
$921$	31.6573	1.04314
$922$	−26.7006	−0.879337
$923$	−31.3728	−1.03265
$924$	−8.32847	−0.273987
$925$	0	0
$926$	−17.0300	−0.559640
$927$	20.8000	0.683162
$928$	−7.16181	−0.235098
$929$	−44.5794	−1.46260	−0.731301	−	0.682055i	$-0.761087\pi$
$929$	−44.5794	−1.46260	−0.731301	+	0.682055i	$0.761087\pi$
$930$	0	0
$931$	−27.4940	−0.901080
$932$	1.28819	0.0421960
$933$	−4.62866	−0.151536
$934$	9.95886	0.325864
$935$	0	0
$936$	−9.38278	−0.306686
$937$	47.0602	1.53739	0.768695	−	0.639615i	$-0.220906\pi$
$937$	47.0602	1.53739	0.768695	+	0.639615i	$0.220906\pi$
$938$	−7.90096	−0.257976
$939$	−20.0654	−0.654809
$940$	0	0
$941$	−45.5100	−1.48358	−0.741792	−	0.670630i	$-0.766024\pi$
$941$	−45.5100	−1.48358	−0.741792	+	0.670630i	$0.766024\pi$
$942$	−41.6991	−1.35863
$943$	−8.98710	−0.292660
$944$	47.1838	1.53570
$945$	0	0
$946$	32.4449	1.05487
$947$	−9.26597	−0.301104	−0.150552	−	0.988602i	$-0.548105\pi$
$947$	−9.26597	−0.301104	−0.150552	+	0.988602i	$0.548105\pi$
$948$	−16.0293	−0.520607
$949$	34.5697	1.12218
$950$	0	0
$951$	14.8167	0.480463
$952$	2.02358	0.0655846
$953$	17.7750	0.575788	0.287894	−	0.957662i	$-0.407045\pi$
$953$	17.7750	0.575788	0.287894	+	0.957662i	$0.407045\pi$
$954$	7.12105	0.230552
$955$	0	0
$956$	−0.735303	−0.0237814
$957$	3.13884	0.101464
$958$	−30.8820	−0.997751
$959$	−33.4899	−1.08145
$960$	0	0
$961$	−29.3227	−0.945894
$962$	−11.6067	−0.374215
$963$	23.4043	0.754193
$964$	−34.2800	−1.10408
$965$	0	0
$966$	−5.04095	−0.162190
$967$	45.7913	1.47255	0.736275	−	0.676683i	$-0.236583\pi$
$967$	45.7913	1.47255	0.736275	+	0.676683i	$0.236583\pi$
$968$	2.42074	0.0778054
$969$	−10.4163	−0.334619
$970$	0	0
$971$	−14.0095	−0.449587	−0.224794	−	0.974406i	$-0.572171\pi$
$971$	−14.0095	−0.449587	−0.224794	+	0.974406i	$0.572171\pi$
$972$	−23.8010	−0.763418
$973$	36.3793	1.16627
$974$	−5.17199	−0.165721
$975$	0	0
$976$	−26.9119	−0.861428
$977$	−51.0534	−1.63334	−0.816671	−	0.577103i	$-0.804183\pi$
$977$	−51.0534	−1.63334	−0.816671	+	0.577103i	$0.804183\pi$
$978$	−6.66247	−0.213042
$979$	5.00953	0.160105
$980$	0	0
$981$	−18.8888	−0.603071
$982$	17.8371	0.569206
$983$	−4.02331	−0.128324	−0.0641618	−	0.997940i	$-0.520437\pi$
$983$	−4.02331	−0.128324	−0.0641618	+	0.997940i	$0.520437\pi$
$984$	5.87005	0.187130
$985$	0	0
$986$	2.64591	0.0842630
$987$	−16.8868	−0.537511
$988$	−65.1017	−2.07116
$989$	8.58207	0.272894
$990$	0	0
$991$	−49.5829	−1.57505	−0.787526	−	0.616282i	$-0.788638\pi$
$991$	−49.5829	−1.57505	−0.787526	+	0.616282i	$0.788638\pi$
$992$	9.27524	0.294489
$993$	−16.7881	−0.532753
$994$	−16.2444	−0.515240
$995$	0	0
$996$	8.66064	0.274423
$997$	−34.8740	−1.10447	−0.552235	−	0.833688i	$-0.686225\pi$
$997$	−34.8740	−1.10447	−0.552235	+	0.833688i	$0.686225\pi$
$998$	−67.8674	−2.14831
$999$	5.21740	0.165071

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.a.h.1.5	✓	5
3.2	odd	2		6525.2.a.bq.1.1		5
5.2	odd	4		725.2.b.f.349.9		10
5.3	odd	4		725.2.b.f.349.2		10
5.4	even	2		725.2.a.k.1.1	yes	5
15.14	odd	2		6525.2.a.bm.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
725.2.a.h.1.5	✓	5	1.1	even	1	trivial
725.2.a.k.1.1	yes	5	5.4	even	2
725.2.b.f.349.2		10	5.3	odd	4
725.2.b.f.349.9		10	5.2	odd	4
6525.2.a.bm.1.5		5	15.14	odd	2
6525.2.a.bq.1.1		5	3.2	odd	2

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.a (trivial)

\(f(q)\)	\(=\)	\(q+1.88481 q^{2} -1.10085 q^{3} +1.55251 q^{4} -2.07489 q^{6} -1.70908 q^{7} -0.843434 q^{8} -1.78814 q^{9} +O(q^{10})\)	\(q+1.88481 q^{2} -1.10085 q^{3} +1.55251 q^{4} -2.07489 q^{6} -1.70908 q^{7} -0.843434 q^{8} -1.78814 q^{9} -2.85130 q^{11} -1.70908 q^{12} -6.22128 q^{13} -3.22128 q^{14} -4.69473 q^{16} +1.40381 q^{17} -3.37030 q^{18} +6.74028 q^{19} +1.88143 q^{21} -5.37416 q^{22} -1.42153 q^{23} +0.928492 q^{24} -11.7259 q^{26} +5.27100 q^{27} -2.65336 q^{28} +1.00000 q^{29} -1.29510 q^{31} -7.16181 q^{32} +3.13884 q^{33} +2.64591 q^{34} -2.77610 q^{36} +0.989830 q^{37} +12.7042 q^{38} +6.84868 q^{39} +6.32213 q^{41} +3.54614 q^{42} -6.03720 q^{43} -4.42667 q^{44} -2.67932 q^{46} -8.97549 q^{47} +5.16818 q^{48} -4.07906 q^{49} -1.54538 q^{51} -9.65860 q^{52} -2.11288 q^{53} +9.93484 q^{54} +1.44149 q^{56} -7.42002 q^{57} +1.88481 q^{58} -10.0504 q^{59} +5.73236 q^{61} -2.44101 q^{62} +3.05606 q^{63} -4.10919 q^{64} +5.91612 q^{66} +2.45274 q^{67} +2.17943 q^{68} +1.56489 q^{69} +5.04282 q^{71} +1.50817 q^{72} -5.55668 q^{73} +1.86564 q^{74} +10.4644 q^{76} +4.87309 q^{77} +12.9085 q^{78} +9.37892 q^{79} -0.438162 q^{81} +11.9160 q^{82} -5.06744 q^{83} +2.92094 q^{84} -11.3790 q^{86} -1.10085 q^{87} +2.40488 q^{88} -1.75693 q^{89} +10.6326 q^{91} -2.20694 q^{92} +1.42570 q^{93} -16.9171 q^{94} +7.88406 q^{96} -14.6037 q^{97} -7.68825 q^{98} +5.09851 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} - 6 q^{3} + 4 q^{4} - q^{6} - 6 q^{7} - 3 q^{8} + 11 q^{9}+O(q^{10}) \) 5 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 - q^6 - 6 * q^7 - 3 * q^8 + 11 * q^9	\( 5 q - 2 q^{2} - 6 q^{3} + 4 q^{4} - q^{6} - 6 q^{7} - 3 q^{8} + 11 q^{9} - 2 q^{11} - 6 q^{12} - 4 q^{13} + 11 q^{14} - 10 q^{16} - 9 q^{17} + 2 q^{19} - q^{21} - 4 q^{22} - q^{23} + 13 q^{24} - 16 q^{26} - 27 q^{27} - 10 q^{28} + 5 q^{29} - q^{31} + 2 q^{32} + 7 q^{33} + 3 q^{34} - 13 q^{36} - 14 q^{37} + 3 q^{38} - 6 q^{39} + 5 q^{41} - 24 q^{42} - 28 q^{43} + 7 q^{44} - 20 q^{46} - 15 q^{47} + 26 q^{48} - 3 q^{49} + 5 q^{51} - 6 q^{52} + 8 q^{53} + 10 q^{54} - 16 q^{56} + 6 q^{57} - 2 q^{58} - 11 q^{59} - 5 q^{61} + 6 q^{62} + 5 q^{63} - 5 q^{64} - 27 q^{66} - 23 q^{67} - q^{68} - 26 q^{69} - 5 q^{71} - 3 q^{72} - 16 q^{73} + 8 q^{74} + 16 q^{76} + 30 q^{77} + 33 q^{78} - 10 q^{79} + 49 q^{81} + 19 q^{82} - 9 q^{83} + 32 q^{84} - 13 q^{86} - 6 q^{87} - 35 q^{88} - 18 q^{89} + q^{91} + 27 q^{92} - 7 q^{93} - 13 q^{94} - 38 q^{96} - 23 q^{97} - 3 q^{98} - 26 q^{99}+O(q^{100}) \) 5 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 - q^6 - 6 * q^7 - 3 * q^8 + 11 * q^9 - 2 * q^11 - 6 * q^12 - 4 * q^13 + 11 * q^14 - 10 * q^16 - 9 * q^17 + 2 * q^19 - q^21 - 4 * q^22 - q^23 + 13 * q^24 - 16 * q^26 - 27 * q^27 - 10 * q^28 + 5 * q^29 - q^31 + 2 * q^32 + 7 * q^33 + 3 * q^34 - 13 * q^36 - 14 * q^37 + 3 * q^38 - 6 * q^39 + 5 * q^41 - 24 * q^42 - 28 * q^43 + 7 * q^44 - 20 * q^46 - 15 * q^47 + 26 * q^48 - 3 * q^49 + 5 * q^51 - 6 * q^52 + 8 * q^53 + 10 * q^54 - 16 * q^56 + 6 * q^57 - 2 * q^58 - 11 * q^59 - 5 * q^61 + 6 * q^62 + 5 * q^63 - 5 * q^64 - 27 * q^66 - 23 * q^67 - q^68 - 26 * q^69 - 5 * q^71 - 3 * q^72 - 16 * q^73 + 8 * q^74 + 16 * q^76 + 30 * q^77 + 33 * q^78 - 10 * q^79 + 49 * q^81 + 19 * q^82 - 9 * q^83 + 32 * q^84 - 13 * q^86 - 6 * q^87 - 35 * q^88 - 18 * q^89 + q^91 + 27 * q^92 - 7 * q^93 - 13 * q^94 - 38 * q^96 - 23 * q^97 - 3 * q^98 - 26 * q^99

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