LMFDB - Embedded newform 245.4.a.m.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,4,Mod(1,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("245.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	245.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:	$14.4554679514$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 37x^{3} + 21x^{2} + 288x + 64 $ x^5 - x^4 - 37x^3 + 21x^2 + 288*x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 35)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$5.20362$ of defining polynomial
Character	$\chi$	$=$	245.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.20362 q^{2} +4.90652 q^{3} +19.0777 q^{4} -5.00000 q^{5} +25.5317 q^{6} +57.6442 q^{8} -2.92609 q^{9} +O(q^{10})$	\(q+5.20362 q^{2} +4.90652 q^{3} +19.0777 q^{4} -5.00000 q^{5} +25.5317 q^{6} +57.6442 q^{8} -2.92609 q^{9} -26.0181 q^{10} +56.6772 q^{11} +93.6051 q^{12} -43.4297 q^{13} -24.5326 q^{15} +147.337 q^{16} -39.8387 q^{17} -15.2263 q^{18} +52.3880 q^{19} -95.3885 q^{20} +294.927 q^{22} -53.5158 q^{23} +282.832 q^{24} +25.0000 q^{25} -225.992 q^{26} -146.833 q^{27} +49.6376 q^{29} -127.658 q^{30} -73.7860 q^{31} +305.533 q^{32} +278.087 q^{33} -207.305 q^{34} -55.8231 q^{36} -307.079 q^{37} +272.607 q^{38} -213.089 q^{39} -288.221 q^{40} +292.064 q^{41} -365.956 q^{43} +1081.27 q^{44} +14.6305 q^{45} -278.476 q^{46} -442.452 q^{47} +722.912 q^{48} +130.091 q^{50} -195.469 q^{51} -828.539 q^{52} +25.7711 q^{53} -764.063 q^{54} -283.386 q^{55} +257.043 q^{57} +258.295 q^{58} +376.601 q^{59} -468.025 q^{60} +632.575 q^{61} -383.955 q^{62} +411.183 q^{64} +217.149 q^{65} +1447.06 q^{66} +511.098 q^{67} -760.030 q^{68} -262.576 q^{69} +134.881 q^{71} -168.672 q^{72} +409.415 q^{73} -1597.92 q^{74} +122.663 q^{75} +999.443 q^{76} -1108.83 q^{78} -926.848 q^{79} -736.685 q^{80} -641.433 q^{81} +1519.79 q^{82} +296.372 q^{83} +199.193 q^{85} -1904.30 q^{86} +243.548 q^{87} +3267.11 q^{88} +488.781 q^{89} +76.1315 q^{90} -1020.96 q^{92} -362.032 q^{93} -2302.35 q^{94} -261.940 q^{95} +1499.10 q^{96} -475.907 q^{97} -165.843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{2} - 8 q^{3} + 35 q^{4} - 25 q^{5} + 16 q^{6} + 33 q^{8} + 81 q^{9}+O(q^{10}) $ 5 * q + q^2 - 8 * q^3 + 35 * q^4 - 25 * q^5 + 16 * q^6 + 33 * q^8 + 81 * q^9	\( 5 q + q^{2} - 8 q^{3} + 35 q^{4} - 25 q^{5} + 16 q^{6} + 33 q^{8} + 81 q^{9} - 5 q^{10} + 47 q^{11} - 98 q^{12} + q^{13} + 40 q^{15} + 171 q^{16} - 2 q^{17} - 51 q^{18} - 21 q^{19} - 175 q^{20} + 523 q^{22} + 201 q^{23} + 848 q^{24} + 125 q^{25} - 47 q^{26} - 518 q^{27} + 190 q^{29} - 80 q^{30} + 388 q^{31} - 95 q^{32} - 262 q^{33} + 130 q^{34} + 1229 q^{36} - 145 q^{37} + 835 q^{38} + 14 q^{39} - 165 q^{40} - 281 q^{41} + 568 q^{43} + 1091 q^{44} - 405 q^{45} + 337 q^{46} - 473 q^{47} + 70 q^{48} + 25 q^{50} + 732 q^{51} - 379 q^{52} + 351 q^{53} - 774 q^{54} - 235 q^{55} + 954 q^{57} + 1818 q^{58} + 708 q^{59} + 490 q^{60} + 1944 q^{61} + 448 q^{62} - 125 q^{64} - 5 q^{65} + 1482 q^{66} + 1118 q^{67} - 3118 q^{68} + 374 q^{69} + 864 q^{71} - 2219 q^{72} - 1652 q^{73} - 3285 q^{74} - 200 q^{75} + 691 q^{76} - 5574 q^{78} + 218 q^{79} - 855 q^{80} - 455 q^{81} + 1027 q^{82} - 1502 q^{83} + 10 q^{85} - 4264 q^{86} + 390 q^{87} + 2131 q^{88} + 2322 q^{89} + 255 q^{90} - 2957 q^{92} - 2288 q^{93} - 2677 q^{94} + 105 q^{95} + 4592 q^{96} + 598 q^{97} + 35 q^{99}+O(q^{100}) \) 5 * q + q^2 - 8 * q^3 + 35 * q^4 - 25 * q^5 + 16 * q^6 + 33 * q^8 + 81 * q^9 - 5 * q^10 + 47 * q^11 - 98 * q^12 + q^13 + 40 * q^15 + 171 * q^16 - 2 * q^17 - 51 * q^18 - 21 * q^19 - 175 * q^20 + 523 * q^22 + 201 * q^23 + 848 * q^24 + 125 * q^25 - 47 * q^26 - 518 * q^27 + 190 * q^29 - 80 * q^30 + 388 * q^31 - 95 * q^32 - 262 * q^33 + 130 * q^34 + 1229 * q^36 - 145 * q^37 + 835 * q^38 + 14 * q^39 - 165 * q^40 - 281 * q^41 + 568 * q^43 + 1091 * q^44 - 405 * q^45 + 337 * q^46 - 473 * q^47 + 70 * q^48 + 25 * q^50 + 732 * q^51 - 379 * q^52 + 351 * q^53 - 774 * q^54 - 235 * q^55 + 954 * q^57 + 1818 * q^58 + 708 * q^59 + 490 * q^60 + 1944 * q^61 + 448 * q^62 - 125 * q^64 - 5 * q^65 + 1482 * q^66 + 1118 * q^67 - 3118 * q^68 + 374 * q^69 + 864 * q^71 - 2219 * q^72 - 1652 * q^73 - 3285 * q^74 - 200 * q^75 + 691 * q^76 - 5574 * q^78 + 218 * q^79 - 855 * q^80 - 455 * q^81 + 1027 * q^82 - 1502 * q^83 + 10 * q^85 - 4264 * q^86 + 390 * q^87 + 2131 * q^88 + 2322 * q^89 + 255 * q^90 - 2957 * q^92 - 2288 * q^93 - 2677 * q^94 + 105 * q^95 + 4592 * q^96 + 598 * q^97 + 35 * 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 $

$2$	5.20362	1.83976	0.919879	−	0.392201i	$-0.128286\pi$
$2$	5.20362	1.83976	0.919879	+	0.392201i	$0.128286\pi$
$3$	4.90652	0.944260	0.472130	−	0.881529i	$-0.343485\pi$
$3$	4.90652	0.944260	0.472130	+	0.881529i	$0.343485\pi$
$4$	19.0777	2.38471
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	25.5317	1.73721
$7$	0	0
$7$	0	0
$8$	57.6442	2.54754
$9$	−2.92609	−0.108374
$10$	−26.0181	−0.822765
$11$	56.6772	1.55353	0.776764	−	0.629792i	$-0.216860\pi$
$11$	56.6772	1.55353	0.776764	+	0.629792i	$0.216860\pi$
$12$	93.6051	2.25179
$13$	−43.4297	−0.926556	−0.463278	−	0.886213i	$-0.653327\pi$
$13$	−43.4297	−0.926556	−0.463278	+	0.886213i	$0.653327\pi$
$14$	0	0
$15$	−24.5326	−0.422286
$16$	147.337	2.30214
$17$	−39.8387	−0.568370	−0.284185	−	0.958769i	$-0.591723\pi$
$17$	−39.8387	−0.568370	−0.284185	+	0.958769i	$0.591723\pi$
$18$	−15.2263	−0.199382
$19$	52.3880	0.632560	0.316280	−	0.948666i	$-0.397566\pi$
$19$	52.3880	0.632560	0.316280	+	0.948666i	$0.397566\pi$
$20$	−95.3885	−1.06648
$21$	0	0
$22$	294.927	2.85812
$23$	−53.5158	−0.485166	−0.242583	−	0.970131i	$-0.577995\pi$
$23$	−53.5158	−0.485166	−0.242583	+	0.970131i	$0.577995\pi$
$24$	282.832	2.40554
$25$	25.0000	0.200000
$26$	−225.992	−1.70464
$27$	−146.833	−1.04659
$28$	0	0
$29$	49.6376	0.317844	0.158922	−	0.987291i	$-0.449198\pi$
$29$	49.6376	0.317844	0.158922	+	0.987291i	$0.449198\pi$
$30$	−127.658	−0.776904
$31$	−73.7860	−0.427496	−0.213748	−	0.976889i	$-0.568567\pi$
$31$	−73.7860	−0.427496	−0.213748	+	0.976889i	$0.568567\pi$
$32$	305.533	1.68785
$33$	278.087	1.46693
$34$	−207.305	−1.04566
$35$	0	0
$36$	−55.8231	−0.258440
$37$	−307.079	−1.36442	−0.682210	−	0.731157i	$-0.738981\pi$
$37$	−307.079	−1.36442	−0.682210	+	0.731157i	$0.738981\pi$
$38$	272.607	1.16376
$39$	−213.089	−0.874910
$40$	−288.221	−1.13929
$41$	292.064	1.11251	0.556254	−	0.831012i	$-0.312238\pi$
$41$	292.064	1.11251	0.556254	+	0.831012i	$0.312238\pi$
$42$	0	0
$43$	−365.956	−1.29786	−0.648928	−	0.760850i	$-0.724783\pi$
$43$	−365.956	−1.29786	−0.648928	+	0.760850i	$0.724783\pi$
$44$	1081.27	3.70472
$45$	14.6305	0.0484663
$46$	−278.476	−0.892588
$47$	−442.452	−1.37315	−0.686577	−	0.727057i	$-0.740888\pi$
$47$	−442.452	−1.37315	−0.686577	+	0.727057i	$0.740888\pi$
$48$	722.912	2.17382
$49$	0	0
$50$	130.091	0.367952
$51$	−195.469	−0.536689
$52$	−828.539	−2.20957
$53$	25.7711	0.0667913	0.0333957	−	0.999442i	$-0.489368\pi$
$53$	25.7711	0.0667913	0.0333957	+	0.999442i	$0.489368\pi$
$54$	−764.063	−1.92548
$55$	−283.386	−0.694759
$56$	0	0
$57$	257.043	0.597300
$58$	258.295	0.584756
$59$	376.601	0.831004	0.415502	−	0.909592i	$-0.363606\pi$
$59$	376.601	0.831004	0.415502	+	0.909592i	$0.363606\pi$
$60$	−468.025	−1.00703
$61$	632.575	1.32775	0.663876	−	0.747843i	$-0.268910\pi$
$61$	632.575	1.32775	0.663876	+	0.747843i	$0.268910\pi$
$62$	−383.955	−0.786489
$63$	0	0
$64$	411.183	0.803092
$65$	217.149	0.414369
$66$	1447.06	2.69880
$67$	511.098	0.931949	0.465974	−	0.884798i	$-0.345704\pi$
$67$	511.098	0.931949	0.465974	+	0.884798i	$0.345704\pi$
$68$	−760.030	−1.35540
$69$	−262.576	−0.458123
$70$	0	0
$71$	134.881	0.225457	0.112728	−	0.993626i	$-0.464041\pi$
$71$	134.881	0.225457	0.112728	+	0.993626i	$0.464041\pi$
$72$	−168.672	−0.276086
$73$	409.415	0.656417	0.328208	−	0.944605i	$-0.393555\pi$
$73$	409.415	0.656417	0.328208	+	0.944605i	$0.393555\pi$
$74$	−1597.92	−2.51020
$75$	122.663	0.188852
$76$	999.443	1.50847
$77$	0	0
$78$	−1108.83	−1.60962
$79$	−926.848	−1.31998	−0.659991	−	0.751274i	$-0.729440\pi$
$79$	−926.848	−1.31998	−0.659991	+	0.751274i	$0.729440\pi$
$80$	−736.685	−1.02955
$81$	−641.433	−0.879881
$82$	1519.79	2.04675
$83$	296.372	0.391940	0.195970	−	0.980610i	$-0.437214\pi$
$83$	296.372	0.391940	0.195970	+	0.980610i	$0.437214\pi$
$84$	0	0
$85$	199.193	0.254183
$86$	−1904.30	−2.38774
$87$	243.548	0.300127
$88$	3267.11	3.95767
$89$	488.781	0.582143	0.291071	−	0.956701i	$-0.405988\pi$
$89$	488.781	0.582143	0.291071	+	0.956701i	$0.405988\pi$
$90$	76.1315	0.0891662
$91$	0	0
$92$	−1020.96	−1.15698
$93$	−362.032	−0.403667
$94$	−2302.35	−2.52627
$95$	−261.940	−0.282889
$96$	1499.10	1.59377
$97$	−475.907	−0.498155	−0.249077	−	0.968484i	$-0.580127\pi$
$97$	−475.907	−0.498155	−0.249077	+	0.968484i	$0.580127\pi$
$98$	0	0
$99$	−165.843	−0.168362
$100$	476.943	0.476943
$101$	77.5809	0.0764315	0.0382158	−	0.999270i	$-0.487833\pi$
$101$	77.5809	0.0764315	0.0382158	+	0.999270i	$0.487833\pi$
$102$	−1017.15	−0.987379
$103$	1137.77	1.08843	0.544214	−	0.838947i	$-0.316828\pi$
$103$	1137.77	1.08843	0.544214	+	0.838947i	$0.316828\pi$
$104$	−2503.47	−2.36044
$105$	0	0
$106$	134.103	0.122880
$107$	75.1405	0.0678888	0.0339444	−	0.999424i	$-0.489193\pi$
$107$	75.1405	0.0678888	0.0339444	+	0.999424i	$0.489193\pi$
$108$	−2801.23	−2.49582
$109$	82.9346	0.0728780	0.0364390	−	0.999336i	$-0.488399\pi$
$109$	82.9346	0.0728780	0.0364390	+	0.999336i	$0.488399\pi$
$110$	−1474.63	−1.27819
$111$	−1506.69	−1.28837
$112$	0	0
$113$	714.602	0.594903	0.297452	−	0.954737i	$-0.403863\pi$
$113$	714.602	0.594903	0.297452	+	0.954737i	$0.403863\pi$
$114$	1337.55	1.09889
$115$	267.579	0.216973
$116$	946.971	0.757966
$117$	127.079	0.100414
$118$	1959.69	1.52885
$119$	0	0
$120$	−1414.16	−1.07579
$121$	1881.30	1.41345
$122$	3291.68	2.44274
$123$	1433.02	1.05050
$124$	−1407.67	−1.01945
$125$	−125.000	−0.0894427
$126$	0	0
$127$	1881.66	1.31473	0.657363	−	0.753574i	$-0.271672\pi$
$127$	1881.66	1.31473	0.657363	+	0.753574i	$0.271672\pi$
$128$	−304.624	−0.210353
$129$	−1795.57	−1.22551
$130$	1129.96	0.762338
$131$	183.909	0.122658	0.0613289	−	0.998118i	$-0.480466\pi$
$131$	183.909	0.122658	0.0613289	+	0.998118i	$0.480466\pi$
$132$	5305.27	3.49822
$133$	0	0
$134$	2659.56	1.71456
$135$	734.164	0.468050
$136$	−2296.47	−1.44794
$137$	887.747	0.553616	0.276808	−	0.960925i	$-0.410723\pi$
$137$	887.747	0.553616	0.276808	+	0.960925i	$0.410723\pi$
$138$	−1366.35	−0.842835
$139$	−2335.25	−1.42499	−0.712495	−	0.701678i	$-0.752435\pi$
$139$	−2335.25	−1.42499	−0.712495	+	0.701678i	$0.752435\pi$
$140$	0	0
$141$	−2170.90	−1.29661
$142$	701.870	0.414786
$143$	−2461.47	−1.43943
$144$	−431.122	−0.249492
$145$	−248.188	−0.142144
$146$	2130.44	1.20765
$147$	0	0
$148$	−5858.36	−3.25375
$149$	−2403.07	−1.32126	−0.660629	−	0.750712i	$-0.729711\pi$
$149$	−2403.07	−1.32126	−0.660629	+	0.750712i	$0.729711\pi$
$150$	638.292	0.347442
$151$	1234.38	0.665246	0.332623	−	0.943060i	$-0.392066\pi$
$151$	1234.38	0.665246	0.332623	+	0.943060i	$0.392066\pi$
$152$	3019.86	1.61147
$153$	116.572	0.0615965
$154$	0	0
$155$	368.930	0.191182
$156$	−4065.24	−2.08641
$157$	1432.49	0.728185	0.364092	−	0.931363i	$-0.381379\pi$
$157$	1432.49	0.728185	0.364092	+	0.931363i	$0.381379\pi$
$158$	−4822.97	−2.42845
$159$	126.447	0.0630683
$160$	−1527.67	−0.754829
$161$	0	0
$162$	−3337.78	−1.61877
$163$	−860.830	−0.413653	−0.206826	−	0.978378i	$-0.566314\pi$
$163$	−860.830	−0.413653	−0.206826	+	0.978378i	$0.566314\pi$
$164$	5571.92	2.65301
$165$	−1390.44	−0.656033
$166$	1542.21	0.721076
$167$	−1346.77	−0.624049	−0.312024	−	0.950074i	$-0.601007\pi$
$167$	−1346.77	−0.624049	−0.312024	+	0.950074i	$0.601007\pi$
$168$	0	0
$169$	−310.861	−0.141493
$170$	1036.53	0.467635
$171$	−153.292	−0.0685529
$172$	−6981.61	−3.09502
$173$	−2610.49	−1.14724	−0.573618	−	0.819123i	$-0.694461\pi$
$173$	−2610.49	−1.14724	−0.573618	+	0.819123i	$0.694461\pi$
$174$	1267.33	0.552161
$175$	0	0
$176$	8350.65	3.57644
$177$	1847.80	0.784683
$178$	2543.43	1.07100
$179$	1350.45	0.563895	0.281947	−	0.959430i	$-0.409020\pi$
$179$	1350.45	0.563895	0.281947	+	0.959430i	$0.409020\pi$
$180$	279.116	0.115578
$181$	2846.61	1.16899	0.584493	−	0.811399i	$-0.301293\pi$
$181$	2846.61	1.16899	0.584493	+	0.811399i	$0.301293\pi$
$182$	0	0
$183$	3103.74	1.25374
$184$	−3084.87	−1.23598
$185$	1535.40	0.610187
$186$	−1883.88	−0.742650
$187$	−2257.94	−0.882980
$188$	−8440.97	−3.27458
$189$	0	0
$190$	−1363.04	−0.520448
$191$	4203.49	1.59243	0.796215	−	0.605014i	$-0.206832\pi$
$191$	4203.49	1.59243	0.796215	+	0.605014i	$0.206832\pi$
$192$	2017.48	0.758327
$193$	138.585	0.0516867	0.0258434	−	0.999666i	$-0.491773\pi$
$193$	138.585	0.0516867	0.0258434	+	0.999666i	$0.491773\pi$
$194$	−2476.44	−0.916485
$195$	1065.44	0.391272
$196$	0	0
$197$	1473.76	0.532998	0.266499	−	0.963835i	$-0.414133\pi$
$197$	1473.76	0.532998	0.266499	+	0.963835i	$0.414133\pi$
$198$	−862.983	−0.309745
$199$	−3609.60	−1.28582	−0.642909	−	0.765943i	$-0.722273\pi$
$199$	−3609.60	−1.28582	−0.642909	+	0.765943i	$0.722273\pi$
$200$	1441.10	0.509507
$201$	2507.71	0.880002
$202$	403.702	0.140616
$203$	0	0
$204$	−3729.10	−1.27985
$205$	−1460.32	−0.497529
$206$	5920.54	2.00244
$207$	156.592	0.0525793
$208$	−6398.80	−2.13306
$209$	2969.20	0.982699
$210$	0	0
$211$	1782.00	0.581412	0.290706	−	0.956812i	$-0.406110\pi$
$211$	1782.00	0.581412	0.290706	+	0.956812i	$0.406110\pi$
$212$	491.654	0.159278
$213$	661.796	0.212890
$214$	391.003	0.124899
$215$	1829.78	0.580419
$216$	−8464.06	−2.66623
$217$	0	0
$218$	431.561	0.134078
$219$	2008.80	0.619828
$220$	−5406.35	−1.65680
$221$	1730.18	0.526627
$222$	−7840.24	−2.37028
$223$	5258.44	1.57906	0.789532	−	0.613709i	$-0.210323\pi$
$223$	5258.44	1.57906	0.789532	+	0.613709i	$0.210323\pi$
$224$	0	0
$225$	−73.1524	−0.0216748
$226$	3718.52	1.09448
$227$	−6707.86	−1.96130	−0.980652	−	0.195758i	$-0.937283\pi$
$227$	−6707.86	−1.96130	−0.980652	+	0.195758i	$0.937283\pi$
$228$	4903.78	1.42439
$229$	1200.25	0.346353	0.173177	−	0.984891i	$-0.444597\pi$
$229$	1200.25	0.346353	0.173177	+	0.984891i	$0.444597\pi$
$230$	1392.38	0.399178
$231$	0	0
$232$	2861.32	0.809719
$233$	6351.42	1.78582	0.892909	−	0.450237i	$-0.148661\pi$
$233$	6351.42	1.78582	0.892909	+	0.450237i	$0.148661\pi$
$234$	661.273	0.184738
$235$	2212.26	0.614093
$236$	7184.67	1.98171
$237$	−4547.59	−1.24640
$238$	0	0
$239$	−3003.73	−0.812951	−0.406475	−	0.913662i	$-0.633242\pi$
$239$	−3003.73	−0.812951	−0.406475	+	0.913662i	$0.633242\pi$
$240$	−3614.56	−0.972161
$241$	5692.32	1.52147	0.760736	−	0.649062i	$-0.224838\pi$
$241$	5692.32	1.52147	0.760736	+	0.649062i	$0.224838\pi$
$242$	9789.59	2.60041
$243$	817.284	0.215756
$244$	12068.1	3.16631
$245$	0	0
$246$	7456.89	1.93266
$247$	−2275.20	−0.586102
$248$	−4253.34	−1.08906
$249$	1454.15	0.370093
$250$	−650.453	−0.164553
$251$	6973.37	1.75361	0.876803	−	0.480850i	$-0.159672\pi$
$251$	6973.37	1.75361	0.876803	+	0.480850i	$0.159672\pi$
$252$	0	0
$253$	−3033.12	−0.753719
$254$	9791.44	2.41878
$255$	977.346	0.240015
$256$	−4874.61	−1.19009
$257$	3091.81	0.750435	0.375217	−	0.926937i	$-0.377568\pi$
$257$	3091.81	0.750435	0.375217	+	0.926937i	$0.377568\pi$
$258$	−9343.48	−2.25465
$259$	0	0
$260$	4142.69	0.988150
$261$	−145.244	−0.0344459
$262$	956.992	0.225661
$263$	1984.83	0.465360	0.232680	−	0.972553i	$-0.425251\pi$
$263$	1984.83	0.465360	0.232680	+	0.972553i	$0.425251\pi$
$264$	16030.1	3.73707
$265$	−128.856	−0.0298700
$266$	0	0
$267$	2398.21	0.549694
$268$	9750.58	2.22243
$269$	6180.74	1.40092	0.700458	−	0.713694i	$-0.252979\pi$
$269$	6180.74	1.40092	0.700458	+	0.713694i	$0.252979\pi$
$270$	3820.32	0.861100
$271$	−6118.99	−1.37159	−0.685797	−	0.727793i	$-0.740546\pi$
$271$	−6118.99	−1.37159	−0.685797	+	0.727793i	$0.740546\pi$
$272$	−5869.71	−1.30847
$273$	0	0
$274$	4619.50	1.01852
$275$	1416.93	0.310706
$276$	−5009.35	−1.09249
$277$	3294.84	0.714685	0.357342	−	0.933973i	$-0.383683\pi$
$277$	3294.84	0.714685	0.357342	+	0.933973i	$0.383683\pi$
$278$	−12151.8	−2.62164
$279$	215.905	0.0463294
$280$	0	0
$281$	−4604.53	−0.977521	−0.488760	−	0.872418i	$-0.662551\pi$
$281$	−4604.53	−0.977521	−0.488760	+	0.872418i	$0.662551\pi$
$282$	−11296.5	−2.38546
$283$	−1219.55	−0.256166	−0.128083	−	0.991763i	$-0.540882\pi$
$283$	−1219.55	−0.256166	−0.128083	+	0.991763i	$0.540882\pi$
$284$	2573.22	0.537649
$285$	−1285.21	−0.267121
$286$	−12808.6	−2.64821
$287$	0	0
$288$	−894.019	−0.182919
$289$	−3325.88	−0.676955
$290$	−1291.48	−0.261511
$291$	−2335.04	−0.470387
$292$	7810.70	1.56537
$293$	−8434.81	−1.68180	−0.840899	−	0.541192i	$-0.817973\pi$
$293$	−8434.81	−1.68180	−0.840899	+	0.541192i	$0.817973\pi$
$294$	0	0
$295$	−1883.00	−0.371636
$296$	−17701.3	−3.47591
$297$	−8322.07	−1.62591
$298$	−12504.7	−2.43080
$299$	2324.18	0.449534
$300$	2340.13	0.450358
$301$	0	0
$302$	6423.23	1.22389
$303$	380.652	0.0721712
$304$	7718.69	1.45624
$305$	−3162.87	−0.593789
$306$	606.595	0.113323
$307$	846.546	0.157378	0.0786888	−	0.996899i	$-0.474927\pi$
$307$	846.546	0.157378	0.0786888	+	0.996899i	$0.474927\pi$
$308$	0	0
$309$	5582.50	1.02776
$310$	1919.77	0.351729
$311$	1961.59	0.357657	0.178829	−	0.983880i	$-0.442769\pi$
$311$	1961.59	0.357657	0.178829	+	0.983880i	$0.442769\pi$
$312$	−12283.3	−2.22886
$313$	6529.96	1.17922	0.589609	−	0.807689i	$-0.299282\pi$
$313$	6529.96	1.17922	0.589609	+	0.807689i	$0.299282\pi$
$314$	7454.13	1.33968
$315$	0	0
$316$	−17682.1	−3.14778
$317$	−7690.53	−1.36260	−0.681298	−	0.732006i	$-0.738584\pi$
$317$	−7690.53	−1.36260	−0.681298	+	0.732006i	$0.738584\pi$
$318$	657.980	0.116031
$319$	2813.32	0.493779
$320$	−2055.91	−0.359153
$321$	368.678	0.0641047
$322$	0	0
$323$	−2087.07	−0.359528
$324$	−12237.1	−2.09826
$325$	−1085.74	−0.185311
$326$	−4479.43	−0.761021
$327$	406.920	0.0688157
$328$	16835.8	2.83415
$329$	0	0
$330$	−7235.31	−1.20694
$331$	6526.27	1.08373	0.541867	−	0.840464i	$-0.317718\pi$
$331$	6526.27	1.08373	0.541867	+	0.840464i	$0.317718\pi$
$332$	5654.09	0.934665
$333$	898.543	0.147867
$334$	−7008.08	−1.14810
$335$	−2555.49	−0.416780
$336$	0	0
$337$	1217.56	0.196809	0.0984047	−	0.995146i	$-0.468626\pi$
$337$	1217.56	0.196809	0.0984047	+	0.995146i	$0.468626\pi$
$338$	−1617.60	−0.260314
$339$	3506.20	0.561743
$340$	3800.15	0.606153
$341$	−4181.98	−0.664127
$342$	−797.675	−0.126121
$343$	0	0
$344$	−21095.3	−3.30634
$345$	1312.88	0.204879
$346$	−13584.0	−2.11064
$347$	−8429.29	−1.30406	−0.652029	−	0.758194i	$-0.726082\pi$
$347$	−8429.29	−1.30406	−0.652029	+	0.758194i	$0.726082\pi$
$348$	4646.33	0.715716
$349$	−135.644	−0.0208047	−0.0104023	−	0.999946i	$-0.503311\pi$
$349$	−135.644	−0.0208047	−0.0104023	+	0.999946i	$0.503311\pi$
$350$	0	0
$351$	6376.91	0.969727
$352$	17316.8	2.62212
$353$	2324.14	0.350429	0.175215	−	0.984530i	$-0.443938\pi$
$353$	2324.14	0.350429	0.175215	+	0.984530i	$0.443938\pi$
$354$	9615.24	1.44363
$355$	−674.405	−0.100827
$356$	9324.82	1.38824
$357$	0	0
$358$	7027.22	1.03743
$359$	−5327.30	−0.783187	−0.391594	−	0.920138i	$-0.628076\pi$
$359$	−5327.30	−0.783187	−0.391594	+	0.920138i	$0.628076\pi$
$360$	843.362	0.123470
$361$	−4114.50	−0.599868
$362$	14812.7	2.15065
$363$	9230.64	1.33466
$364$	0	0
$365$	−2047.08	−0.293559
$366$	16150.7	2.30658
$367$	−7291.62	−1.03711	−0.518555	−	0.855044i	$-0.673530\pi$
$367$	−7291.62	−1.03711	−0.518555	+	0.855044i	$0.673530\pi$
$368$	−7884.86	−1.11692
$369$	−854.608	−0.120567
$370$	7989.62	1.12260
$371$	0	0
$372$	−6906.75	−0.962629
$373$	−1661.50	−0.230642	−0.115321	−	0.993328i	$-0.536790\pi$
$373$	−1661.50	−0.230642	−0.115321	+	0.993328i	$0.536790\pi$
$374$	−11749.5	−1.62447
$375$	−613.315	−0.0844571
$376$	−25504.8	−3.49816
$377$	−2155.75	−0.294500
$378$	0	0
$379$	409.820	0.0555436	0.0277718	−	0.999614i	$-0.491159\pi$
$379$	409.820	0.0555436	0.0277718	+	0.999614i	$0.491159\pi$
$380$	−4997.21	−0.674610
$381$	9232.39	1.24144
$382$	21873.4	2.92969
$383$	−10941.2	−1.45971	−0.729853	−	0.683604i	$-0.760412\pi$
$383$	−10941.2	−1.45971	−0.729853	+	0.683604i	$0.760412\pi$
$384$	−1494.64	−0.198628
$385$	0	0
$386$	721.142	0.0950911
$387$	1070.82	0.140654
$388$	−9079.21	−1.18796
$389$	−6236.80	−0.812900	−0.406450	−	0.913673i	$-0.633234\pi$
$389$	−6236.80	−0.812900	−0.406450	+	0.913673i	$0.633234\pi$
$390$	5544.16	0.719845
$391$	2132.00	0.275754
$392$	0	0
$393$	902.351	0.115821
$394$	7668.87	0.980589
$395$	4634.24	0.590314
$396$	−3163.90	−0.401495
$397$	−11447.8	−1.44723	−0.723614	−	0.690205i	$-0.757520\pi$
$397$	−11447.8	−1.44723	−0.723614	+	0.690205i	$0.757520\pi$
$398$	−18783.0	−2.36559
$399$	0	0
$400$	3683.43	0.460428
$401$	−9233.47	−1.14987	−0.574935	−	0.818199i	$-0.694973\pi$
$401$	−9233.47	−1.14987	−0.574935	+	0.818199i	$0.694973\pi$
$402$	13049.2	1.61899
$403$	3204.51	0.396099
$404$	1480.06	0.182267
$405$	3207.17	0.393495
$406$	0	0
$407$	−17404.4	−2.11966
$408$	−11267.7	−1.36724
$409$	−4435.14	−0.536195	−0.268097	−	0.963392i	$-0.586395\pi$
$409$	−4435.14	−0.536195	−0.268097	+	0.963392i	$0.586395\pi$
$410$	−7598.97	−0.915332
$411$	4355.75	0.522757
$412$	21706.1	2.59559
$413$	0	0
$414$	814.847	0.0967332
$415$	−1481.86	−0.175281
$416$	−13269.2	−1.56389
$417$	−11458.0	−1.34556
$418$	15450.6	1.80793
$419$	−6434.23	−0.750197	−0.375099	−	0.926985i	$-0.622391\pi$
$419$	−6434.23	−0.750197	−0.375099	+	0.926985i	$0.622391\pi$
$420$	0	0
$421$	−9442.51	−1.09311	−0.546556	−	0.837423i	$-0.684061\pi$
$421$	−9442.51	−1.09311	−0.546556	+	0.837423i	$0.684061\pi$
$422$	9272.86	1.06966
$423$	1294.66	0.148814
$424$	1485.56	0.170153
$425$	−995.967	−0.113674
$426$	3443.74	0.391666
$427$	0	0
$428$	1433.51	0.161895
$429$	−12077.3	−1.35920
$430$	9521.50	1.06783
$431$	−2241.20	−0.250475	−0.125238	−	0.992127i	$-0.539969\pi$
$431$	−2241.20	−0.250475	−0.125238	+	0.992127i	$0.539969\pi$
$432$	−21633.9	−2.40940
$433$	−14181.1	−1.57391	−0.786954	−	0.617012i	$-0.788343\pi$
$433$	−14181.1	−1.57391	−0.786954	+	0.617012i	$0.788343\pi$
$434$	0	0
$435$	−1217.74	−0.134221
$436$	1582.20	0.173793
$437$	−2803.59	−0.306896
$438$	10453.1	1.14033
$439$	8692.64	0.945051	0.472525	−	0.881317i	$-0.343343\pi$
$439$	8692.64	0.945051	0.472525	+	0.881317i	$0.343343\pi$
$440$	−16335.5	−1.76992
$441$	0	0
$442$	9003.22	0.968867
$443$	−9393.70	−1.00747	−0.503734	−	0.863859i	$-0.668041\pi$
$443$	−9393.70	−1.00747	−0.503734	+	0.863859i	$0.668041\pi$
$444$	−28744.2	−3.07238
$445$	−2443.91	−0.260342
$446$	27362.9	2.90510
$447$	−11790.7	−1.24761
$448$	0	0
$449$	9511.86	0.999761	0.499880	−	0.866094i	$-0.333377\pi$
$449$	9511.86	0.999761	0.499880	+	0.866094i	$0.333377\pi$
$450$	−380.657	−0.0398764
$451$	16553.4	1.72831
$452$	13633.0	1.41867
$453$	6056.49	0.628165
$454$	−34905.2	−3.60833
$455$	0	0
$456$	14817.0	1.52165
$457$	−1367.21	−0.139946	−0.0699732	−	0.997549i	$-0.522291\pi$
$457$	−1367.21	−0.139946	−0.0699732	+	0.997549i	$0.522291\pi$
$458$	6245.66	0.637206
$459$	5849.63	0.594852
$460$	5104.79	0.517418
$461$	8760.60	0.885080	0.442540	−	0.896749i	$-0.354078\pi$
$461$	8760.60	0.885080	0.442540	+	0.896749i	$0.354078\pi$
$462$	0	0
$463$	10357.4	1.03963	0.519817	−	0.854278i	$-0.326000\pi$
$463$	10357.4	1.03963	0.519817	+	0.854278i	$0.326000\pi$
$464$	7313.45	0.731721
$465$	1810.16	0.180525
$466$	33050.4	3.28547
$467$	−8499.74	−0.842229	−0.421115	−	0.907007i	$-0.638361\pi$
$467$	−8499.74	−0.842229	−0.421115	+	0.907007i	$0.638361\pi$
$468$	2424.38	0.239460
$469$	0	0
$470$	11511.8	1.12978
$471$	7028.53	0.687596
$472$	21708.8	2.11701
$473$	−20741.4	−2.01626
$474$	−23664.0	−2.29308
$475$	1309.70	0.126512
$476$	0	0
$477$	−75.4088	−0.00723843
$478$	−15630.3	−1.49563
$479$	−722.973	−0.0689634	−0.0344817	−	0.999405i	$-0.510978\pi$
$479$	−722.973	−0.0689634	−0.0344817	+	0.999405i	$0.510978\pi$
$480$	−7495.52	−0.712754
$481$	13336.4	1.26421
$482$	29620.7	2.79914
$483$	0	0
$484$	35890.9	3.37067
$485$	2379.53	0.222782
$486$	4252.84	0.396940
$487$	2307.31	0.214690	0.107345	−	0.994222i	$-0.465765\pi$
$487$	2307.31	0.214690	0.107345	+	0.994222i	$0.465765\pi$
$488$	36464.3	3.38250
$489$	−4223.67	−0.390595
$490$	0	0
$491$	−8668.77	−0.796774	−0.398387	−	0.917217i	$-0.630430\pi$
$491$	−8668.77	−0.796774	−0.398387	+	0.917217i	$0.630430\pi$
$492$	27338.7	2.50513
$493$	−1977.50	−0.180653
$494$	−11839.3	−1.07829
$495$	829.214	0.0752937
$496$	−10871.4	−0.984155
$497$	0	0
$498$	7566.87	0.680883
$499$	19921.7	1.78721	0.893606	−	0.448852i	$-0.148167\pi$
$499$	19921.7	1.78721	0.893606	+	0.448852i	$0.148167\pi$
$500$	−2384.71	−0.213295
$501$	−6607.95	−0.589264
$502$	36286.8	3.22621
$503$	17007.8	1.50763	0.753817	−	0.657084i	$-0.228210\pi$
$503$	17007.8	1.50763	0.753817	+	0.657084i	$0.228210\pi$
$504$	0	0
$505$	−387.904	−0.0341812
$506$	−15783.2	−1.38666
$507$	−1525.24	−0.133606
$508$	35897.7	3.13524
$509$	−18465.0	−1.60795	−0.803977	−	0.594661i	$-0.797286\pi$
$509$	−18465.0	−1.60795	−0.803977	+	0.594661i	$0.797286\pi$
$510$	5085.74	0.441569
$511$	0	0
$512$	−22928.6	−1.97913
$513$	−7692.28	−0.662032
$514$	16088.6	1.38062
$515$	−5688.86	−0.486760
$516$	−34255.4	−2.92250
$517$	−25076.9	−2.13323
$518$	0	0
$519$	−12808.4	−1.08329
$520$	12517.3	1.05562
$521$	−4335.85	−0.364601	−0.182300	−	0.983243i	$-0.558354\pi$
$521$	−4335.85	−0.364601	−0.182300	+	0.983243i	$0.558354\pi$
$522$	−755.796	−0.0633722
$523$	−8373.20	−0.700066	−0.350033	−	0.936737i	$-0.613830\pi$
$523$	−8373.20	−0.700066	−0.350033	+	0.936737i	$0.613830\pi$
$524$	3508.56	0.292504
$525$	0	0
$526$	10328.3	0.856150
$527$	2939.54	0.242976
$528$	40972.6	3.37709
$529$	−9303.06	−0.764614
$530$	−670.517	−0.0549536
$531$	−1101.97	−0.0900591
$532$	0	0
$533$	−12684.3	−1.03080
$534$	12479.4	1.01130
$535$	−375.702	−0.0303608
$536$	29461.8	2.37417
$537$	6625.99	0.532463
$538$	32162.2	2.57735
$539$	0	0
$540$	14006.2	1.11617
$541$	11875.0	0.943707	0.471853	−	0.881677i	$-0.343585\pi$
$541$	11875.0	0.943707	0.471853	+	0.881677i	$0.343585\pi$
$542$	−31840.9	−2.52340
$543$	13966.9	1.10383
$544$	−12172.0	−0.959323
$545$	−414.673	−0.0325920
$546$	0	0
$547$	25018.5	1.95560	0.977802	−	0.209532i	$-0.0671939\pi$
$547$	25018.5	1.95560	0.977802	+	0.209532i	$0.0671939\pi$
$548$	16936.2	1.32021
$549$	−1850.97	−0.143894
$550$	7373.17	0.571623
$551$	2600.41	0.201055
$552$	−15136.0	−1.16708
$553$	0	0
$554$	17145.1	1.31485
$555$	7533.45	0.576175
$556$	−44551.2	−3.39819
$557$	−3952.18	−0.300645	−0.150323	−	0.988637i	$-0.548031\pi$
$557$	−3952.18	−0.300645	−0.150323	+	0.988637i	$0.548031\pi$
$558$	1123.49	0.0852348
$559$	15893.4	1.20254
$560$	0	0
$561$	−11078.6	−0.833762
$562$	−23960.3	−1.79840
$563$	319.466	0.0239146	0.0119573	−	0.999929i	$-0.496194\pi$
$563$	319.466	0.0239146	0.0119573	+	0.999929i	$0.496194\pi$
$564$	−41415.7	−3.09205
$565$	−3573.01	−0.266049
$566$	−6346.09	−0.471283
$567$	0	0
$568$	7775.10	0.574359
$569$	−24250.9	−1.78673	−0.893366	−	0.449329i	$-0.851663\pi$
$569$	−24250.9	−1.78673	−0.893366	+	0.449329i	$0.851663\pi$
$570$	−6687.77	−0.491438
$571$	−2827.47	−0.207226	−0.103613	−	0.994618i	$-0.533040\pi$
$571$	−2827.47	−0.207226	−0.103613	+	0.994618i	$0.533040\pi$
$572$	−46959.2	−3.43263
$573$	20624.5	1.50367
$574$	0	0
$575$	−1337.89	−0.0970332
$576$	−1203.16	−0.0870341
$577$	18260.2	1.31748	0.658738	−	0.752373i	$-0.271091\pi$
$577$	18260.2	1.31748	0.658738	+	0.752373i	$0.271091\pi$
$578$	−17306.6	−1.24543
$579$	679.967	0.0488057
$580$	−4734.85	−0.338973
$581$	0	0
$582$	−12150.7	−0.865400
$583$	1460.64	0.103762
$584$	23600.4	1.67225
$585$	−635.397	−0.0449067
$586$	−43891.6	−3.09410
$587$	7749.13	0.544873	0.272437	−	0.962174i	$-0.412170\pi$
$587$	7749.13	0.544873	0.272437	+	0.962174i	$0.412170\pi$
$588$	0	0
$589$	−3865.50	−0.270416
$590$	−9798.44	−0.683721
$591$	7231.00	0.503289
$592$	−45244.1	−3.14109
$593$	−634.663	−0.0439502	−0.0219751	−	0.999759i	$-0.506995\pi$
$593$	−634.663	−0.0439502	−0.0219751	+	0.999759i	$0.506995\pi$
$594$	−43304.9	−2.99128
$595$	0	0
$596$	−45845.1	−3.15082
$597$	−17710.6	−1.21415
$598$	12094.1	0.827033
$599$	8637.48	0.589178	0.294589	−	0.955624i	$-0.404817\pi$
$599$	8637.48	0.589178	0.294589	+	0.955624i	$0.404817\pi$
$600$	7070.80	0.481107
$601$	−19947.7	−1.35388	−0.676941	−	0.736037i	$-0.736695\pi$
$601$	−19947.7	−1.35388	−0.676941	+	0.736037i	$0.736695\pi$
$602$	0	0
$603$	−1495.52	−0.100999
$604$	23549.1	1.58642
$605$	−9406.51	−0.632114
$606$	1980.77	0.132778
$607$	1237.17	0.0827268	0.0413634	−	0.999144i	$-0.486830\pi$
$607$	1237.17	0.0827268	0.0413634	+	0.999144i	$0.486830\pi$
$608$	16006.3	1.06766
$609$	0	0
$610$	−16458.4	−1.09243
$611$	19215.6	1.27230
$612$	2223.92	0.146890
$613$	17527.6	1.15487	0.577434	−	0.816438i	$-0.304054\pi$
$613$	17527.6	1.15487	0.577434	+	0.816438i	$0.304054\pi$
$614$	4405.11	0.289537
$615$	−7165.10	−0.469796
$616$	0	0
$617$	18508.3	1.20764	0.603821	−	0.797120i	$-0.293644\pi$
$617$	18508.3	1.20764	0.603821	+	0.797120i	$0.293644\pi$
$618$	29049.2	1.89083
$619$	−6029.84	−0.391534	−0.195767	−	0.980650i	$-0.562720\pi$
$619$	−6029.84	−0.391534	−0.195767	+	0.980650i	$0.562720\pi$
$620$	7038.34	0.455914
$621$	7857.88	0.507771
$622$	10207.4	0.658003
$623$	0	0
$624$	−31395.8	−2.01417
$625$	625.000	0.0400000
$626$	33979.5	2.16948
$627$	14568.4	0.927923
$628$	27328.6	1.73651
$629$	12233.6	0.775495
$630$	0	0
$631$	5728.80	0.361426	0.180713	−	0.983536i	$-0.442160\pi$
$631$	5728.80	0.361426	0.180713	+	0.983536i	$0.442160\pi$
$632$	−53427.4	−3.36270
$633$	8743.41	0.549004
$634$	−40018.6	−2.50685
$635$	−9408.29	−0.587963
$636$	2412.31	0.150400
$637$	0	0
$638$	14639.4	0.908434
$639$	−394.674	−0.0244336
$640$	1523.12	0.0940727
$641$	−1875.82	−0.115586	−0.0577930	−	0.998329i	$-0.518406\pi$
$641$	−1875.82	−0.115586	−0.0577930	+	0.998329i	$0.518406\pi$
$642$	1918.46	0.117937
$643$	−20619.9	−1.26465	−0.632325	−	0.774703i	$-0.717899\pi$
$643$	−20619.9	−1.26465	−0.632325	+	0.774703i	$0.717899\pi$
$644$	0	0
$645$	8977.86	0.548066
$646$	−10860.3	−0.661445
$647$	−11527.1	−0.700431	−0.350216	−	0.936669i	$-0.613892\pi$
$647$	−11527.1	−0.700431	−0.350216	+	0.936669i	$0.613892\pi$
$648$	−36974.9	−2.24153
$649$	21344.7	1.29099
$650$	−5649.80	−0.340928
$651$	0	0
$652$	−16422.6	−0.986443
$653$	−4516.21	−0.270648	−0.135324	−	0.990801i	$-0.543208\pi$
$653$	−4516.21	−0.270648	−0.135324	+	0.990801i	$0.543208\pi$
$654$	2117.46	0.126604
$655$	−919.544	−0.0548543
$656$	43031.9	2.56115
$657$	−1197.99	−0.0711384
$658$	0	0
$659$	−27663.5	−1.63523	−0.817615	−	0.575766i	$-0.804704\pi$
$659$	−27663.5	−1.63523	−0.817615	+	0.575766i	$0.804704\pi$
$660$	−26526.3	−1.56445
$661$	−31510.8	−1.85421	−0.927103	−	0.374807i	$-0.877709\pi$
$661$	−31510.8	−1.85421	−0.927103	+	0.374807i	$0.877709\pi$
$662$	33960.3	1.99381
$663$	8489.17	0.497273
$664$	17084.1	0.998482
$665$	0	0
$666$	4675.68	0.272040
$667$	−2656.39	−0.154207
$668$	−25693.3	−1.48818
$669$	25800.6	1.49105
$670$	−13297.8	−0.766775
$671$	35852.5	2.06270
$672$	0	0
$673$	−9072.58	−0.519647	−0.259823	−	0.965656i	$-0.583664\pi$
$673$	−9072.58	−0.519647	−0.259823	+	0.965656i	$0.583664\pi$
$674$	6335.73	0.362082
$675$	−3670.82	−0.209319
$676$	−5930.51	−0.337421
$677$	−24997.7	−1.41911	−0.709557	−	0.704648i	$-0.751105\pi$
$677$	−24997.7	−1.41911	−0.709557	+	0.704648i	$0.751105\pi$
$678$	18245.0	1.03347
$679$	0	0
$680$	11482.3	0.647541
$681$	−32912.2	−1.85198
$682$	−21761.5	−1.22183
$683$	−13261.8	−0.742970	−0.371485	−	0.928439i	$-0.621151\pi$
$683$	−13261.8	−0.742970	−0.371485	+	0.928439i	$0.621151\pi$
$684$	−2924.46	−0.163479
$685$	−4438.74	−0.247585
$686$	0	0
$687$	5889.06	0.327047
$688$	−53918.9	−2.98785
$689$	−1119.23	−0.0618859
$690$	6831.74	0.376927
$691$	−24643.5	−1.35671	−0.678353	−	0.734736i	$-0.737306\pi$
$691$	−24643.5	−1.35671	−0.678353	+	0.734736i	$0.737306\pi$
$692$	−49802.2	−2.73583
$693$	0	0
$694$	−43862.8	−2.39915
$695$	11676.3	0.637275
$696$	14039.1	0.764585
$697$	−11635.5	−0.632316
$698$	−705.838	−0.0382756
$699$	31163.4	1.68628
$700$	0	0
$701$	20723.2	1.11656	0.558278	−	0.829654i	$-0.311462\pi$
$701$	20723.2	1.11656	0.558278	+	0.829654i	$0.311462\pi$
$702$	33183.0	1.78406
$703$	−16087.3	−0.863076
$704$	23304.7	1.24763
$705$	10854.5	0.579864
$706$	12094.0	0.644705
$707$	0	0
$708$	35251.7	1.87124
$709$	25935.8	1.37382	0.686910	−	0.726743i	$-0.258967\pi$
$709$	25935.8	1.37382	0.686910	+	0.726743i	$0.258967\pi$
$710$	−3509.35	−0.185498
$711$	2712.04	0.143051
$712$	28175.4	1.48303
$713$	3948.72	0.207406
$714$	0	0
$715$	12307.4	0.643733
$716$	25763.4	1.34473
$717$	−14737.9	−0.767637
$718$	−27721.3	−1.44088
$719$	−13653.7	−0.708201	−0.354101	−	0.935207i	$-0.615213\pi$
$719$	−13653.7	−0.708201	−0.354101	+	0.935207i	$0.615213\pi$
$720$	2155.61	0.111576
$721$	0	0
$722$	−21410.3	−1.10361
$723$	27929.5	1.43666
$724$	54306.7	2.78770
$725$	1240.94	0.0635687
$726$	48032.8	2.45546
$727$	17709.4	0.903448	0.451724	−	0.892158i	$-0.350809\pi$
$727$	17709.4	0.903448	0.451724	+	0.892158i	$0.350809\pi$
$728$	0	0
$729$	21328.7	1.08361
$730$	−10652.2	−0.540077
$731$	14579.2	0.737663
$732$	59212.2	2.98982
$733$	11873.5	0.598303	0.299152	−	0.954206i	$-0.403296\pi$
$733$	11873.5	0.598303	0.299152	+	0.954206i	$0.403296\pi$
$734$	−37942.9	−1.90803
$735$	0	0
$736$	−16350.8	−0.818886
$737$	28967.6	1.44781
$738$	−4447.06	−0.221814
$739$	31302.7	1.55817	0.779087	−	0.626916i	$-0.215683\pi$
$739$	31302.7	1.55817	0.779087	+	0.626916i	$0.215683\pi$
$740$	29291.8	1.45512
$741$	−11163.3	−0.553433
$742$	0	0
$743$	−10385.8	−0.512808	−0.256404	−	0.966570i	$-0.582538\pi$
$743$	−10385.8	−0.512808	−0.256404	+	0.966570i	$0.582538\pi$
$744$	−20869.1	−1.02836
$745$	12015.4	0.590885
$746$	−8645.83	−0.424325
$747$	−867.212	−0.0424761
$748$	−43076.4	−2.10565
$749$	0	0
$750$	−3191.46	−0.155381
$751$	16571.3	0.805185	0.402593	−	0.915379i	$-0.368109\pi$
$751$	16571.3	0.805185	0.402593	+	0.915379i	$0.368109\pi$
$752$	−65189.6	−3.16120
$753$	34214.9	1.65586
$754$	−11217.7	−0.541809
$755$	−6171.88	−0.297507
$756$	0	0
$757$	16463.8	0.790473	0.395236	−	0.918579i	$-0.370663\pi$
$757$	16463.8	0.790473	0.395236	+	0.918579i	$0.370663\pi$
$758$	2132.55	0.102187
$759$	−14882.1	−0.711706
$760$	−15099.3	−0.720671
$761$	16421.9	0.782251	0.391126	−	0.920337i	$-0.372086\pi$
$761$	16421.9	0.782251	0.391126	+	0.920337i	$0.372086\pi$
$762$	48041.9	2.28395
$763$	0	0
$764$	80193.0	3.79749
$765$	−582.859	−0.0275468
$766$	−56933.7	−2.68551
$767$	−16355.7	−0.769972
$768$	−23917.4	−1.12375
$769$	17603.4	0.825479	0.412739	−	0.910849i	$-0.364572\pi$
$769$	17603.4	0.825479	0.412739	+	0.910849i	$0.364572\pi$
$770$	0	0
$771$	15170.0	0.708605
$772$	2643.87	0.123258
$773$	15908.3	0.740210	0.370105	−	0.928990i	$-0.379322\pi$
$773$	15908.3	0.740210	0.370105	+	0.928990i	$0.379322\pi$
$774$	5572.16	0.258769
$775$	−1844.65	−0.0854991
$776$	−27433.3	−1.26907
$777$	0	0
$778$	−32454.0	−1.49554
$779$	15300.7	0.703727
$780$	20326.2	0.933070
$781$	7644.67	0.350253
$782$	11094.1	0.507321
$783$	−7288.43	−0.332653
$784$	0	0
$785$	−7162.44	−0.325654
$786$	4695.50	0.213082
$787$	18988.9	0.860076	0.430038	−	0.902811i	$-0.358500\pi$
$787$	18988.9	0.860076	0.430038	+	0.902811i	$0.358500\pi$
$788$	28115.9	1.27105
$789$	9738.58	0.439420
$790$	24114.8	1.08603
$791$	0	0
$792$	−9559.87	−0.428908
$793$	−27472.5	−1.23024
$794$	−59570.1	−2.66255
$795$	−632.233	−0.0282050
$796$	−68862.8	−3.06630
$797$	−33731.8	−1.49917	−0.749586	−	0.661906i	$-0.769748\pi$
$797$	−33731.8	−1.49917	−0.749586	+	0.661906i	$0.769748\pi$
$798$	0	0
$799$	17626.7	0.780460
$800$	7638.33	0.337570
$801$	−1430.22	−0.0630890
$802$	−48047.5	−2.11548
$803$	23204.5	1.01976
$804$	47841.4	2.09855
$805$	0	0
$806$	16675.0	0.728726
$807$	30325.9	1.32283
$808$	4472.09	0.194712
$809$	26643.7	1.15790	0.578950	−	0.815363i	$-0.303463\pi$
$809$	26643.7	1.15790	0.578950	+	0.815363i	$0.303463\pi$
$810$	16688.9	0.723936
$811$	15678.2	0.678835	0.339418	−	0.940636i	$-0.389770\pi$
$811$	15678.2	0.678835	0.339418	+	0.940636i	$0.389770\pi$
$812$	0	0
$813$	−30022.9	−1.29514
$814$	−90565.8	−3.89967
$815$	4304.15	0.184991
$816$	−28799.8	−1.23553
$817$	−19171.7	−0.820972
$818$	−23078.8	−0.986469
$819$	0	0
$820$	−27859.6	−1.18646
$821$	−10133.8	−0.430784	−0.215392	−	0.976528i	$-0.569103\pi$
$821$	−10133.8	−0.430784	−0.215392	+	0.976528i	$0.569103\pi$
$822$	22665.7	0.961747
$823$	−14062.7	−0.595618	−0.297809	−	0.954626i	$-0.596256\pi$
$823$	−14062.7	−0.595618	−0.297809	+	0.954626i	$0.596256\pi$
$824$	65586.0	2.77281
$825$	6952.19	0.293387
$826$	0	0
$827$	−13697.4	−0.575942	−0.287971	−	0.957639i	$-0.592981\pi$
$827$	−13697.4	−0.575942	−0.287971	+	0.957639i	$0.592981\pi$
$828$	2987.42	0.125387
$829$	17554.9	0.735475	0.367737	−	0.929930i	$-0.380133\pi$
$829$	17554.9	0.735475	0.367737	+	0.929930i	$0.380133\pi$
$830$	−7711.04	−0.322475
$831$	16166.2	0.674848
$832$	−17857.6	−0.744110
$833$	0	0
$834$	−59622.9	−2.47551
$835$	6733.85	0.279083
$836$	56645.6	2.34345
$837$	10834.2	0.447414
$838$	−33481.3	−1.38018
$839$	1415.03	0.0582268	0.0291134	−	0.999576i	$-0.490732\pi$
$839$	1415.03	0.0582268	0.0291134	+	0.999576i	$0.490732\pi$
$840$	0	0
$841$	−21925.1	−0.898975
$842$	−49135.3	−2.01106
$843$	−22592.2	−0.923033
$844$	33996.5	1.38650
$845$	1554.30	0.0632778
$846$	6736.90	0.273782
$847$	0	0
$848$	3797.05	0.153763
$849$	−5983.75	−0.241887
$850$	−5182.64	−0.209133
$851$	16433.6	0.661970
$852$	12625.5	0.507681
$853$	−16014.1	−0.642804	−0.321402	−	0.946943i	$-0.604154\pi$
$853$	−16014.1	−0.642804	−0.321402	+	0.946943i	$0.604154\pi$
$854$	0	0
$855$	766.461	0.0306578
$856$	4331.41	0.172949
$857$	43497.4	1.73377	0.866886	−	0.498506i	$-0.166118\pi$
$857$	43497.4	1.73377	0.866886	+	0.498506i	$0.166118\pi$
$858$	−62845.5	−2.50059
$859$	25278.6	1.00407	0.502034	−	0.864848i	$-0.332585\pi$
$859$	25278.6	1.00407	0.502034	+	0.864848i	$0.332585\pi$
$860$	34908.0	1.38413
$861$	0	0
$862$	−11662.4	−0.460814
$863$	−15407.8	−0.607748	−0.303874	−	0.952712i	$-0.598280\pi$
$863$	−15407.8	−0.607748	−0.303874	+	0.952712i	$0.598280\pi$
$864$	−44862.3	−1.76649
$865$	13052.5	0.513060
$866$	−73793.3	−2.89561
$867$	−16318.5	−0.639221
$868$	0	0
$869$	−52531.1	−2.05063
$870$	−6336.65	−0.246934
$871$	−22196.8	−0.863503
$872$	4780.70	0.185659
$873$	1392.55	0.0539870
$874$	−14588.8	−0.564615
$875$	0	0
$876$	38323.3	1.47811
$877$	32788.6	1.26248	0.631238	−	0.775589i	$-0.282547\pi$
$877$	32788.6	1.26248	0.631238	+	0.775589i	$0.282547\pi$
$878$	45233.2	1.73867
$879$	−41385.5	−1.58805
$880$	−41753.2	−1.59943
$881$	−30457.9	−1.16476	−0.582379	−	0.812918i	$-0.697878\pi$
$881$	−30457.9	−1.16476	−0.582379	+	0.812918i	$0.697878\pi$
$882$	0	0
$883$	37997.3	1.44814	0.724071	−	0.689725i	$-0.242269\pi$
$883$	37997.3	1.44814	0.724071	+	0.689725i	$0.242269\pi$
$884$	33007.9	1.25585
$885$	−9238.99	−0.350921
$886$	−48881.3	−1.85350
$887$	5.59606	0.000211835 0	0.000105917	−	1.00000i	$-0.499966\pi$
$887$	5.59606	0.000211835 0	0.000105917		1.00000i	$0.499966\pi$
$888$	−86851.9	−3.28216
$889$	0	0
$890$	−12717.2	−0.478967
$891$	−36354.6	−1.36692
$892$	100319.	3.76561
$893$	−23179.2	−0.868602
$894$	−61354.5	−2.29530
$895$	−6752.24	−0.252181
$896$	0	0
$897$	11403.6	0.424476
$898$	49496.2	1.83932
$899$	−3662.56	−0.135877
$900$	−1395.58	−0.0516881
$901$	−1026.69	−0.0379622
$902$	86137.6	3.17968
$903$	0	0
$904$	41192.6	1.51554
$905$	−14233.0	−0.522787
$906$	31515.7	1.15567
$907$	−7723.31	−0.282744	−0.141372	−	0.989957i	$-0.545151\pi$
$907$	−7723.31	−0.282744	−0.141372	+	0.989957i	$0.545151\pi$
$908$	−127970.	−4.67715
$909$	−227.009	−0.00828318
$910$	0	0
$911$	6805.43	0.247502	0.123751	−	0.992313i	$-0.460508\pi$
$911$	6805.43	0.247502	0.123751	+	0.992313i	$0.460508\pi$
$912$	37871.9	1.37507
$913$	16797.5	0.608890
$914$	−7114.46	−0.257468
$915$	−15518.7	−0.560691
$916$	22898.0	0.825953
$917$	0	0
$918$	30439.3	1.09438
$919$	−45180.2	−1.62172	−0.810858	−	0.585243i	$-0.800999\pi$
$919$	−45180.2	−1.62172	−0.810858	+	0.585243i	$0.800999\pi$
$920$	15424.4	0.552746
$921$	4153.59	0.148605
$922$	45586.9	1.62833
$923$	−5857.84	−0.208898
$924$	0	0
$925$	−7676.98	−0.272884
$926$	53896.1	1.91267
$927$	−3329.23	−0.117957
$928$	15165.9	0.536472
$929$	5192.22	0.183370	0.0916852	−	0.995788i	$-0.470775\pi$
$929$	5192.22	0.183370	0.0916852	+	0.995788i	$0.470775\pi$
$930$	9419.40	0.332123
$931$	0	0
$932$	121171.	4.25866
$933$	9624.56	0.337721
$934$	−44229.4	−1.54950
$935$	11289.7	0.394880
$936$	7325.39	0.255810
$937$	−7107.58	−0.247806	−0.123903	−	0.992294i	$-0.539541\pi$
$937$	−7107.58	−0.247806	−0.123903	+	0.992294i	$0.539541\pi$
$938$	0	0
$939$	32039.4	1.11349
$940$	42204.8	1.46444
$941$	−43663.0	−1.51262	−0.756309	−	0.654214i	$-0.773000\pi$
$941$	−43663.0	−1.51262	−0.756309	+	0.654214i	$0.773000\pi$
$942$	36573.8	1.26501
$943$	−15630.1	−0.539751
$944$	55487.2	1.91309
$945$	0	0
$946$	−107930.	−3.70943
$947$	15442.1	0.529884	0.264942	−	0.964264i	$-0.414647\pi$
$947$	15442.1	0.529884	0.264942	+	0.964264i	$0.414647\pi$
$948$	−86757.6	−2.97232
$949$	−17780.8	−0.608207
$950$	6815.19	0.232751
$951$	−37733.7	−1.28664
$952$	0	0
$953$	44561.5	1.51468	0.757339	−	0.653022i	$-0.226499\pi$
$953$	44561.5	1.51468	0.757339	+	0.653022i	$0.226499\pi$
$954$	−392.399	−0.0133170
$955$	−21017.5	−0.712157
$956$	−57304.3	−1.93865
$957$	13803.6	0.466256
$958$	−3762.08	−0.126876
$959$	0	0
$960$	−10087.4	−0.339134
$961$	−24346.6	−0.817247
$962$	69397.4	2.32584
$963$	−219.868	−0.00735737
$964$	108596.	3.62827
$965$	−692.923	−0.0231150
$966$	0	0
$967$	−34733.3	−1.15506	−0.577532	−	0.816368i	$-0.695984\pi$
$967$	−34733.3	−1.15506	−0.577532	+	0.816368i	$0.695984\pi$
$968$	108446.	3.60082
$969$	−10240.2	−0.339488
$970$	12382.2	0.409864
$971$	−17710.3	−0.585325	−0.292662	−	0.956216i	$-0.594541\pi$
$971$	−17710.3	−0.585325	−0.292662	+	0.956216i	$0.594541\pi$
$972$	15591.9	0.514517
$973$	0	0
$974$	12006.4	0.394979
$975$	−5327.21	−0.174982
$976$	93201.7	3.05667
$977$	−57557.4	−1.88477	−0.942387	−	0.334524i	$-0.891425\pi$
$977$	−57557.4	−1.88477	−0.942387	+	0.334524i	$0.891425\pi$
$978$	−21978.4	−0.718601
$979$	27702.7	0.904375
$980$	0	0
$981$	−242.675	−0.00789806
$982$	−45109.0	−1.46587
$983$	−24988.8	−0.810802	−0.405401	−	0.914139i	$-0.632868\pi$
$983$	−24988.8	−0.810802	−0.405401	+	0.914139i	$0.632868\pi$
$984$	82605.2	2.67618
$985$	−7368.78	−0.238364
$986$	−10290.1	−0.332358
$987$	0	0
$988$	−43405.5	−1.39769
$989$	19584.5	0.629676
$990$	4314.92	0.138522
$991$	61573.2	1.97370	0.986850	−	0.161637i	$-0.0516775\pi$
$991$	61573.2	1.97370	0.986850	+	0.161637i	$0.0516775\pi$
$992$	−22544.1	−0.721548
$993$	32021.2	1.02333
$994$	0	0
$995$	18048.0	0.575035
$996$	27741.9	0.882566
$997$	−9393.19	−0.298380	−0.149190	−	0.988809i	$-0.547667\pi$
$997$	−9393.19	−0.298380	−0.149190	+	0.988809i	$0.547667\pi$
$998$	103665.	3.28804
$999$	45089.3	1.42799

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.4.a.m.1.5		5
3.2	odd	2		2205.4.a.bu.1.1		5
5.4	even	2		1225.4.a.bg.1.1		5
7.2	even	3		35.4.e.c.11.1	✓	10
7.3	odd	6		245.4.e.o.226.1		10
7.4	even	3		35.4.e.c.16.1	yes	10
7.5	odd	6		245.4.e.o.116.1		10
7.6	odd	2		245.4.a.n.1.5		5
21.2	odd	6		315.4.j.g.46.5		10
21.11	odd	6		315.4.j.g.226.5		10
21.20	even	2		2205.4.a.bt.1.1		5
28.11	odd	6		560.4.q.n.401.4		10
28.23	odd	6		560.4.q.n.81.4		10
35.2	odd	12		175.4.k.d.74.10		20
35.4	even	6		175.4.e.d.51.5		10
35.9	even	6		175.4.e.d.151.5		10
35.18	odd	12		175.4.k.d.149.10		20
35.23	odd	12		175.4.k.d.74.1		20
35.32	odd	12		175.4.k.d.149.1		20
35.34	odd	2		1225.4.a.bf.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.e.c.11.1	✓	10	7.2	even	3
35.4.e.c.16.1	yes	10	7.4	even	3
175.4.e.d.51.5		10	35.4	even	6
175.4.e.d.151.5		10	35.9	even	6
175.4.k.d.74.1		20	35.23	odd	12
175.4.k.d.74.10		20	35.2	odd	12
175.4.k.d.149.1		20	35.32	odd	12
175.4.k.d.149.10		20	35.18	odd	12
245.4.a.m.1.5		5	1.1	even	1	trivial
245.4.a.n.1.5		5	7.6	odd	2
245.4.e.o.116.1		10	7.5	odd	6
245.4.e.o.226.1		10	7.3	odd	6
315.4.j.g.46.5		10	21.2	odd	6
315.4.j.g.226.5		10	21.11	odd	6
560.4.q.n.81.4		10	28.23	odd	6
560.4.q.n.401.4		10	28.11	odd	6
1225.4.a.bf.1.1		5	35.34	odd	2
1225.4.a.bg.1.1		5	5.4	even	2
2205.4.a.bt.1.1		5	21.20	even	2
2205.4.a.bu.1.1		5	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	245.a (trivial)

\(f(q)\)	\(=\)	\(q+5.20362 q^{2} +4.90652 q^{3} +19.0777 q^{4} -5.00000 q^{5} +25.5317 q^{6} +57.6442 q^{8} -2.92609 q^{9} +O(q^{10})\)	\(q+5.20362 q^{2} +4.90652 q^{3} +19.0777 q^{4} -5.00000 q^{5} +25.5317 q^{6} +57.6442 q^{8} -2.92609 q^{9} -26.0181 q^{10} +56.6772 q^{11} +93.6051 q^{12} -43.4297 q^{13} -24.5326 q^{15} +147.337 q^{16} -39.8387 q^{17} -15.2263 q^{18} +52.3880 q^{19} -95.3885 q^{20} +294.927 q^{22} -53.5158 q^{23} +282.832 q^{24} +25.0000 q^{25} -225.992 q^{26} -146.833 q^{27} +49.6376 q^{29} -127.658 q^{30} -73.7860 q^{31} +305.533 q^{32} +278.087 q^{33} -207.305 q^{34} -55.8231 q^{36} -307.079 q^{37} +272.607 q^{38} -213.089 q^{39} -288.221 q^{40} +292.064 q^{41} -365.956 q^{43} +1081.27 q^{44} +14.6305 q^{45} -278.476 q^{46} -442.452 q^{47} +722.912 q^{48} +130.091 q^{50} -195.469 q^{51} -828.539 q^{52} +25.7711 q^{53} -764.063 q^{54} -283.386 q^{55} +257.043 q^{57} +258.295 q^{58} +376.601 q^{59} -468.025 q^{60} +632.575 q^{61} -383.955 q^{62} +411.183 q^{64} +217.149 q^{65} +1447.06 q^{66} +511.098 q^{67} -760.030 q^{68} -262.576 q^{69} +134.881 q^{71} -168.672 q^{72} +409.415 q^{73} -1597.92 q^{74} +122.663 q^{75} +999.443 q^{76} -1108.83 q^{78} -926.848 q^{79} -736.685 q^{80} -641.433 q^{81} +1519.79 q^{82} +296.372 q^{83} +199.193 q^{85} -1904.30 q^{86} +243.548 q^{87} +3267.11 q^{88} +488.781 q^{89} +76.1315 q^{90} -1020.96 q^{92} -362.032 q^{93} -2302.35 q^{94} -261.940 q^{95} +1499.10 q^{96} -475.907 q^{97} -165.843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} - 8 q^{3} + 35 q^{4} - 25 q^{5} + 16 q^{6} + 33 q^{8} + 81 q^{9}+O(q^{10}) \) 5 * q + q^2 - 8 * q^3 + 35 * q^4 - 25 * q^5 + 16 * q^6 + 33 * q^8 + 81 * q^9	\( 5 q + q^{2} - 8 q^{3} + 35 q^{4} - 25 q^{5} + 16 q^{6} + 33 q^{8} + 81 q^{9} - 5 q^{10} + 47 q^{11} - 98 q^{12} + q^{13} + 40 q^{15} + 171 q^{16} - 2 q^{17} - 51 q^{18} - 21 q^{19} - 175 q^{20} + 523 q^{22} + 201 q^{23} + 848 q^{24} + 125 q^{25} - 47 q^{26} - 518 q^{27} + 190 q^{29} - 80 q^{30} + 388 q^{31} - 95 q^{32} - 262 q^{33} + 130 q^{34} + 1229 q^{36} - 145 q^{37} + 835 q^{38} + 14 q^{39} - 165 q^{40} - 281 q^{41} + 568 q^{43} + 1091 q^{44} - 405 q^{45} + 337 q^{46} - 473 q^{47} + 70 q^{48} + 25 q^{50} + 732 q^{51} - 379 q^{52} + 351 q^{53} - 774 q^{54} - 235 q^{55} + 954 q^{57} + 1818 q^{58} + 708 q^{59} + 490 q^{60} + 1944 q^{61} + 448 q^{62} - 125 q^{64} - 5 q^{65} + 1482 q^{66} + 1118 q^{67} - 3118 q^{68} + 374 q^{69} + 864 q^{71} - 2219 q^{72} - 1652 q^{73} - 3285 q^{74} - 200 q^{75} + 691 q^{76} - 5574 q^{78} + 218 q^{79} - 855 q^{80} - 455 q^{81} + 1027 q^{82} - 1502 q^{83} + 10 q^{85} - 4264 q^{86} + 390 q^{87} + 2131 q^{88} + 2322 q^{89} + 255 q^{90} - 2957 q^{92} - 2288 q^{93} - 2677 q^{94} + 105 q^{95} + 4592 q^{96} + 598 q^{97} + 35 q^{99}+O(q^{100}) \) 5 * q + q^2 - 8 * q^3 + 35 * q^4 - 25 * q^5 + 16 * q^6 + 33 * q^8 + 81 * q^9 - 5 * q^10 + 47 * q^11 - 98 * q^12 + q^13 + 40 * q^15 + 171 * q^16 - 2 * q^17 - 51 * q^18 - 21 * q^19 - 175 * q^20 + 523 * q^22 + 201 * q^23 + 848 * q^24 + 125 * q^25 - 47 * q^26 - 518 * q^27 + 190 * q^29 - 80 * q^30 + 388 * q^31 - 95 * q^32 - 262 * q^33 + 130 * q^34 + 1229 * q^36 - 145 * q^37 + 835 * q^38 + 14 * q^39 - 165 * q^40 - 281 * q^41 + 568 * q^43 + 1091 * q^44 - 405 * q^45 + 337 * q^46 - 473 * q^47 + 70 * q^48 + 25 * q^50 + 732 * q^51 - 379 * q^52 + 351 * q^53 - 774 * q^54 - 235 * q^55 + 954 * q^57 + 1818 * q^58 + 708 * q^59 + 490 * q^60 + 1944 * q^61 + 448 * q^62 - 125 * q^64 - 5 * q^65 + 1482 * q^66 + 1118 * q^67 - 3118 * q^68 + 374 * q^69 + 864 * q^71 - 2219 * q^72 - 1652 * q^73 - 3285 * q^74 - 200 * q^75 + 691 * q^76 - 5574 * q^78 + 218 * q^79 - 855 * q^80 - 455 * q^81 + 1027 * q^82 - 1502 * q^83 + 10 * q^85 - 4264 * q^86 + 390 * q^87 + 2131 * q^88 + 2322 * q^89 + 255 * q^90 - 2957 * q^92 - 2288 * q^93 - 2677 * q^94 + 105 * q^95 + 4592 * q^96 + 598 * q^97 + 35 * q^99

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