LMFDB - Embedded newform 1775.4.a.g.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1775,4,Mod(1,1775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1775, 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("1775.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1775 = 5^{2} \cdot 71 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1775.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:	$104.728390260$
Analytic rank:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 9 x^{19} - 89 x^{18} + 952 x^{17} + 2911 x^{16} - 41549 x^{15} - 37799 x^{14} + \cdots - 106929408 $ x^20 - 9x^19 - 89x^18 + 952x^17 + 2911x^16 - 41549x^15 - 37799x^14 + 974485x^13 - 43478x^12 - 13402754x^11 + 6726996x^10 + 110353987x^9 - 76601582x^8 - 528296868x^7 + 380540584x^6 + 1335398700x^5 - 833784408x^4 - 1402468992x^3 + 573826752x^2 + 308840768*x - 106929408
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 355)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$0.316870$ of defining polynomial
Character	$\chi$	$=$	1775.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.316870 q^{2} +6.27919 q^{3} -7.89959 q^{4} -1.98969 q^{6} +28.3648 q^{7} +5.03811 q^{8} +12.4282 q^{9} +O(q^{10})$	\(q-0.316870 q^{2} +6.27919 q^{3} -7.89959 q^{4} -1.98969 q^{6} +28.3648 q^{7} +5.03811 q^{8} +12.4282 q^{9} -50.5142 q^{11} -49.6030 q^{12} +32.5335 q^{13} -8.98796 q^{14} +61.6003 q^{16} -7.29433 q^{17} -3.93812 q^{18} -146.330 q^{19} +178.108 q^{21} +16.0064 q^{22} +69.5381 q^{23} +31.6352 q^{24} -10.3089 q^{26} -91.4991 q^{27} -224.070 q^{28} +37.4635 q^{29} -90.3143 q^{31} -59.8242 q^{32} -317.188 q^{33} +2.31135 q^{34} -98.1776 q^{36} +235.949 q^{37} +46.3675 q^{38} +204.284 q^{39} +1.88573 q^{41} -56.4371 q^{42} -440.555 q^{43} +399.041 q^{44} -22.0346 q^{46} -125.651 q^{47} +386.800 q^{48} +461.562 q^{49} -45.8024 q^{51} -257.002 q^{52} -253.785 q^{53} +28.9934 q^{54} +142.905 q^{56} -918.830 q^{57} -11.8711 q^{58} -840.342 q^{59} +696.852 q^{61} +28.6179 q^{62} +352.523 q^{63} -473.846 q^{64} +100.507 q^{66} -472.644 q^{67} +57.6222 q^{68} +436.643 q^{69} +71.0000 q^{71} +62.6145 q^{72} -228.829 q^{73} -74.7651 q^{74} +1155.94 q^{76} -1432.83 q^{77} -64.7316 q^{78} -550.939 q^{79} -910.101 q^{81} -0.597533 q^{82} +1195.87 q^{83} -1406.98 q^{84} +139.599 q^{86} +235.240 q^{87} -254.496 q^{88} -1029.01 q^{89} +922.808 q^{91} -549.323 q^{92} -567.101 q^{93} +39.8152 q^{94} -375.647 q^{96} -367.762 q^{97} -146.255 q^{98} -627.800 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 9 q^{2} - 14 q^{3} + 99 q^{4} + 9 q^{6} - 40 q^{7} - 132 q^{8} + 236 q^{9}+O(q^{10}) $ 20 * q - 9 * q^2 - 14 * q^3 + 99 * q^4 + 9 * q^6 - 40 * q^7 - 132 * q^8 + 236 * q^9	\( 20 q - 9 q^{2} - 14 q^{3} + 99 q^{4} + 9 q^{6} - 40 q^{7} - 132 q^{8} + 236 q^{9} + 62 q^{11} - 160 q^{12} - 232 q^{13} + 56 q^{14} + 387 q^{16} - 314 q^{17} - 224 q^{18} + 54 q^{19} + 58 q^{21} + 123 q^{22} - 344 q^{23} + 419 q^{24} - 387 q^{26} - 326 q^{27} - 786 q^{28} + 748 q^{29} - 18 q^{31} - 345 q^{32} - 746 q^{33} - 142 q^{34} + 90 q^{36} - 858 q^{37} - 723 q^{38} + 210 q^{39} + 386 q^{41} + 237 q^{42} - 1210 q^{43} + 1105 q^{44} - 57 q^{46} - 320 q^{47} - 2280 q^{48} + 1576 q^{49} - 350 q^{51} - 780 q^{52} - 2066 q^{53} - 536 q^{54} + 938 q^{56} - 710 q^{57} - 1852 q^{58} + 1198 q^{59} + 284 q^{61} - 2444 q^{62} - 732 q^{63} + 1118 q^{64} - 219 q^{66} - 976 q^{67} - 2904 q^{68} + 1026 q^{69} + 1420 q^{71} - 3374 q^{72} - 4310 q^{73} + 955 q^{74} + 740 q^{76} - 5196 q^{77} - 61 q^{78} - 340 q^{79} + 2556 q^{81} - 1191 q^{82} + 354 q^{83} - 1955 q^{84} + 1248 q^{86} - 3392 q^{87} - 135 q^{88} - 1446 q^{89} - 240 q^{91} - 4114 q^{92} + 1066 q^{93} - 3985 q^{94} - 2145 q^{96} - 3282 q^{97} + 4708 q^{98} - 6506 q^{99}+O(q^{100}) \) 20 * q - 9 * q^2 - 14 * q^3 + 99 * q^4 + 9 * q^6 - 40 * q^7 - 132 * q^8 + 236 * q^9 + 62 * q^11 - 160 * q^12 - 232 * q^13 + 56 * q^14 + 387 * q^16 - 314 * q^17 - 224 * q^18 + 54 * q^19 + 58 * q^21 + 123 * q^22 - 344 * q^23 + 419 * q^24 - 387 * q^26 - 326 * q^27 - 786 * q^28 + 748 * q^29 - 18 * q^31 - 345 * q^32 - 746 * q^33 - 142 * q^34 + 90 * q^36 - 858 * q^37 - 723 * q^38 + 210 * q^39 + 386 * q^41 + 237 * q^42 - 1210 * q^43 + 1105 * q^44 - 57 * q^46 - 320 * q^47 - 2280 * q^48 + 1576 * q^49 - 350 * q^51 - 780 * q^52 - 2066 * q^53 - 536 * q^54 + 938 * q^56 - 710 * q^57 - 1852 * q^58 + 1198 * q^59 + 284 * q^61 - 2444 * q^62 - 732 * q^63 + 1118 * q^64 - 219 * q^66 - 976 * q^67 - 2904 * q^68 + 1026 * q^69 + 1420 * q^71 - 3374 * q^72 - 4310 * q^73 + 955 * q^74 + 740 * q^76 - 5196 * q^77 - 61 * q^78 - 340 * q^79 + 2556 * q^81 - 1191 * q^82 + 354 * q^83 - 1955 * q^84 + 1248 * q^86 - 3392 * q^87 - 135 * q^88 - 1446 * q^89 - 240 * q^91 - 4114 * q^92 + 1066 * q^93 - 3985 * q^94 - 2145 * q^96 - 3282 * q^97 + 4708 * q^98 - 6506 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.316870	−0.112031	−0.0560153	−	0.998430i	$-0.517840\pi$
$2$	−0.316870	−0.112031	−0.0560153	+	0.998430i	$0.517840\pi$
$3$	6.27919	1.20843	0.604215	−	0.796821i	$-0.293487\pi$
$3$	6.27919	1.20843	0.604215	+	0.796821i	$0.293487\pi$
$4$	−7.89959	−0.987449
$5$	0	0
$5$	0	0
$6$	−1.98969	−0.135381
$7$	28.3648	1.53156	0.765778	−	0.643105i	$-0.222354\pi$
$7$	28.3648	1.53156	0.765778	+	0.643105i	$0.222354\pi$
$8$	5.03811	0.222655
$9$	12.4282	0.460303
$10$	0	0
$11$	−50.5142	−1.38460	−0.692300	−	0.721610i	$-0.743402\pi$
$11$	−50.5142	−1.38460	−0.692300	+	0.721610i	$0.743402\pi$
$12$	−49.6030	−1.19326
$13$	32.5335	0.694091	0.347045	−	0.937848i	$-0.387185\pi$
$13$	32.5335	0.694091	0.347045	+	0.937848i	$0.387185\pi$
$14$	−8.98796	−0.171581
$15$	0	0
$16$	61.6003	0.962505
$17$	−7.29433	−0.104067	−0.0520334	−	0.998645i	$-0.516570\pi$
$17$	−7.29433	−0.104067	−0.0520334	+	0.998645i	$0.516570\pi$
$18$	−3.93812	−0.0515680
$19$	−146.330	−1.76686	−0.883429	−	0.468565i	$-0.844771\pi$
$19$	−146.330	−1.76686	−0.883429	+	0.468565i	$0.844771\pi$
$20$	0	0
$21$	178.108	1.85078
$22$	16.0064	0.155117
$23$	69.5381	0.630422	0.315211	−	0.949022i	$-0.397925\pi$
$23$	69.5381	0.630422	0.315211	+	0.949022i	$0.397925\pi$
$24$	31.6352	0.269063
$25$	0	0
$26$	−10.3089	−0.0777594
$27$	−91.4991	−0.652186
$28$	−224.070	−1.51233
$29$	37.4635	0.239889	0.119945	−	0.992781i	$-0.461728\pi$
$29$	37.4635	0.239889	0.119945	+	0.992781i	$0.461728\pi$
$30$	0	0
$31$	−90.3143	−0.523256	−0.261628	−	0.965169i	$-0.584259\pi$
$31$	−90.3143	−0.523256	−0.261628	+	0.965169i	$0.584259\pi$
$32$	−59.8242	−0.330485
$33$	−317.188	−1.67319
$34$	2.31135	0.0116586
$35$	0	0
$36$	−98.1776	−0.454526
$37$	235.949	1.04837	0.524185	−	0.851604i	$-0.324370\pi$
$37$	235.949	1.04837	0.524185	+	0.851604i	$0.324370\pi$
$38$	46.3675	0.197942
$39$	204.284	0.838760
$40$	0	0
$41$	1.88573	0.00718298	0.00359149	−	0.999994i	$-0.498857\pi$
$41$	1.88573	0.00718298	0.00359149	+	0.999994i	$0.498857\pi$
$42$	−56.4371	−0.207344
$43$	−440.555	−1.56242	−0.781210	−	0.624268i	$-0.785397\pi$
$43$	−440.555	−1.56242	−0.781210	+	0.624268i	$0.785397\pi$
$44$	399.041	1.36722
$45$	0	0
$46$	−22.0346	−0.0706265
$47$	−125.651	−0.389960	−0.194980	−	0.980807i	$-0.562464\pi$
$47$	−125.651	−0.389960	−0.194980	+	0.980807i	$0.562464\pi$
$48$	386.800	1.16312
$49$	461.562	1.34566
$50$	0	0
$51$	−45.8024	−0.125757
$52$	−257.002	−0.685379
$53$	−253.785	−0.657738	−0.328869	−	0.944376i	$-0.606667\pi$
$53$	−253.785	−0.657738	−0.328869	+	0.944376i	$0.606667\pi$
$54$	28.9934	0.0730647
$55$	0	0
$56$	142.905	0.341009
$57$	−918.830	−2.13512
$58$	−11.8711	−0.0268749
$59$	−840.342	−1.85429	−0.927146	−	0.374701i	$-0.877745\pi$
$59$	−840.342	−1.85429	−0.927146	+	0.374701i	$0.877745\pi$
$60$	0	0
$61$	696.852	1.46267	0.731334	−	0.682020i	$-0.238898\pi$
$61$	696.852	1.46267	0.731334	+	0.682020i	$0.238898\pi$
$62$	28.6179	0.0586206
$63$	352.523	0.704980
$64$	−473.846	−0.925481
$65$	0	0
$66$	100.507	0.187449
$67$	−472.644	−0.861831	−0.430916	−	0.902392i	$-0.641809\pi$
$67$	−472.644	−0.861831	−0.430916	+	0.902392i	$0.641809\pi$
$68$	57.6222	0.102761
$69$	436.643	0.761821
$70$	0	0
$71$	71.0000	0.118678
$71$	71.0000	0.118678
$72$	62.6145	0.102489
$73$	−228.829	−0.366882	−0.183441	−	0.983031i	$-0.558724\pi$
$73$	−228.829	−0.366882	−0.183441	+	0.983031i	$0.558724\pi$
$74$	−74.7651	−0.117450
$75$	0	0
$76$	1155.94	1.74468
$77$	−1432.83	−2.12059
$78$	−64.7316	−0.0939668
$79$	−550.939	−0.784626	−0.392313	−	0.919832i	$-0.628325\pi$
$79$	−550.939	−0.784626	−0.392313	+	0.919832i	$0.628325\pi$
$80$	0	0
$81$	−910.101	−1.24842
$82$	−0.597533	−0.000804713 0
$83$	1195.87	1.58149	0.790743	−	0.612148i	$-0.209694\pi$
$83$	1195.87	1.58149	0.790743	+	0.612148i	$0.209694\pi$
$84$	−1406.98	−1.82755
$85$	0	0
$86$	139.599	0.175039
$87$	235.240	0.289889
$88$	−254.496	−0.308288
$89$	−1029.01	−1.22555	−0.612777	−	0.790256i	$-0.709948\pi$
$89$	−1029.01	−1.22555	−0.612777	+	0.790256i	$0.709948\pi$
$90$	0	0
$91$	922.808	1.06304
$92$	−549.323	−0.622509
$93$	−567.101	−0.632318
$94$	39.8152	0.0436875
$95$	0	0
$96$	−375.647	−0.399368
$97$	−367.762	−0.384954	−0.192477	−	0.981301i	$-0.561652\pi$
$97$	−367.762	−0.384954	−0.192477	+	0.981301i	$0.561652\pi$
$98$	−146.255	−0.150755
$99$	−627.800	−0.637336
$100$	0	0
$101$	−638.154	−0.628700	−0.314350	−	0.949307i	$-0.601787\pi$
$101$	−638.154	−0.628700	−0.314350	+	0.949307i	$0.601787\pi$
$102$	14.5134	0.0140887
$103$	935.971	0.895378	0.447689	−	0.894189i	$-0.352247\pi$
$103$	935.971	0.895378	0.447689	+	0.894189i	$0.352247\pi$
$104$	163.907	0.154543
$105$	0	0
$106$	80.4171	0.0736868
$107$	1103.23	0.996759	0.498379	−	0.866959i	$-0.333929\pi$
$107$	1103.23	0.996759	0.498379	+	0.866959i	$0.333929\pi$
$108$	722.806	0.644000
$109$	−1274.15	−1.11965	−0.559824	−	0.828611i	$-0.689131\pi$
$109$	−1274.15	−1.11965	−0.559824	+	0.828611i	$0.689131\pi$
$110$	0	0
$111$	1481.57	1.26688
$112$	1747.28	1.47413
$113$	1616.79	1.34597	0.672987	−	0.739654i	$-0.265011\pi$
$113$	1616.79	1.34597	0.672987	+	0.739654i	$0.265011\pi$
$114$	291.150	0.239199
$115$	0	0
$116$	−295.946	−0.236879
$117$	404.333	0.319492
$118$	266.279	0.207737
$119$	−206.902	−0.159384
$120$	0	0
$121$	1220.68	0.917117
$122$	−220.812	−0.163863
$123$	11.8409	0.00868013
$124$	713.447	0.516689
$125$	0	0
$126$	−111.704	−0.0789793
$127$	244.433	0.170787	0.0853935	−	0.996347i	$-0.472785\pi$
$127$	244.433	0.170787	0.0853935	+	0.996347i	$0.472785\pi$
$128$	628.741	0.434167
$129$	−2766.33	−1.88808
$130$	0	0
$131$	2792.96	1.86276	0.931382	−	0.364043i	$-0.118604\pi$
$131$	2792.96	1.86276	0.931382	+	0.364043i	$0.118604\pi$
$132$	2505.66	1.65219
$133$	−4150.61	−2.70604
$134$	149.767	0.0965514
$135$	0	0
$136$	−36.7496	−0.0231710
$137$	−299.268	−0.186629	−0.0933145	−	0.995637i	$-0.529746\pi$
$137$	−299.268	−0.186629	−0.0933145	+	0.995637i	$0.529746\pi$
$138$	−138.359	−0.0853472
$139$	1359.94	0.829844	0.414922	−	0.909857i	$-0.363809\pi$
$139$	1359.94	0.829844	0.414922	+	0.909857i	$0.363809\pi$
$140$	0	0
$141$	−788.988	−0.471240
$142$	−22.4978	−0.0132956
$143$	−1643.40	−0.961038
$144$	765.580	0.443044
$145$	0	0
$146$	72.5089	0.0411019
$147$	2898.24	1.62614
$148$	−1863.90	−1.03521
$149$	−1663.60	−0.914678	−0.457339	−	0.889292i	$-0.651197\pi$
$149$	−1663.60	−0.914678	−0.457339	+	0.889292i	$0.651197\pi$
$150$	0	0
$151$	−2499.63	−1.34713	−0.673567	−	0.739127i	$-0.735239\pi$
$151$	−2499.63	−1.34713	−0.673567	+	0.739127i	$0.735239\pi$
$152$	−737.224	−0.393400
$153$	−90.6552	−0.0479022
$154$	454.020	0.237571
$155$	0	0
$156$	−1613.76	−0.828233
$157$	−3241.09	−1.64756	−0.823781	−	0.566908i	$-0.808139\pi$
$157$	−3241.09	−1.64756	−0.823781	+	0.566908i	$0.808139\pi$
$158$	174.576	0.0879021
$159$	−1593.57	−0.794830
$160$	0	0
$161$	1972.44	0.965526
$162$	288.384	0.139862
$163$	−3064.29	−1.47247	−0.736237	−	0.676724i	$-0.763399\pi$
$163$	−3064.29	−1.47247	−0.736237	+	0.676724i	$0.763399\pi$
$164$	−14.8965	−0.00709283
$165$	0	0
$166$	−378.934	−0.177175
$167$	−2590.44	−1.20032	−0.600161	−	0.799879i	$-0.704897\pi$
$167$	−2590.44	−1.20032	−0.600161	+	0.799879i	$0.704897\pi$
$168$	897.327	0.412085
$169$	−1138.57	−0.518238
$170$	0	0
$171$	−1818.61	−0.813290
$172$	3480.21	1.54281
$173$	3587.04	1.57640	0.788201	−	0.615418i	$-0.211013\pi$
$173$	3587.04	1.57640	0.788201	+	0.615418i	$0.211013\pi$
$174$	−74.5406	−0.0324765
$175$	0	0
$176$	−3111.69	−1.33268
$177$	−5276.66	−2.24078
$178$	326.061	0.137300
$179$	−1340.29	−0.559654	−0.279827	−	0.960050i	$-0.590277\pi$
$179$	−1340.29	−0.559654	−0.279827	+	0.960050i	$0.590277\pi$
$180$	0	0
$181$	993.285	0.407902	0.203951	−	0.978981i	$-0.434622\pi$
$181$	993.285	0.407902	0.203951	+	0.978981i	$0.434622\pi$
$182$	−292.410	−0.119093
$183$	4375.66	1.76753
$184$	350.341	0.140367
$185$	0	0
$186$	179.697	0.0708390
$187$	368.467	0.144091
$188$	992.595	0.385066
$189$	−2595.36	−0.998859
$190$	0	0
$191$	1605.36	0.608168	0.304084	−	0.952645i	$-0.401650\pi$
$191$	1605.36	0.608168	0.304084	+	0.952645i	$0.401650\pi$
$192$	−2975.37	−1.11838
$193$	−1762.47	−0.657335	−0.328668	−	0.944446i	$-0.606600\pi$
$193$	−1762.47	−0.657335	−0.328668	+	0.944446i	$0.606600\pi$
$194$	116.533	0.0431266
$195$	0	0
$196$	−3646.16	−1.32877
$197$	−3466.40	−1.25366	−0.626829	−	0.779157i	$-0.715648\pi$
$197$	−3466.40	−1.25366	−0.626829	+	0.779157i	$0.715648\pi$
$198$	198.931	0.0714011
$199$	−3884.74	−1.38383	−0.691915	−	0.721979i	$-0.743233\pi$
$199$	−3884.74	−1.38383	−0.691915	+	0.721979i	$0.743233\pi$
$200$	0	0
$201$	−2967.82	−1.04146
$202$	202.212	0.0704336
$203$	1062.64	0.367404
$204$	361.821	0.124179
$205$	0	0
$206$	−296.581	−0.100310
$207$	864.233	0.290185
$208$	2004.08	0.668066
$209$	7391.72	2.44639
$210$	0	0
$211$	−5597.56	−1.82631	−0.913156	−	0.407610i	$-0.866362\pi$
$211$	−5597.56	−1.82631	−0.913156	+	0.407610i	$0.866362\pi$
$212$	2004.80	0.649483
$213$	445.822	0.143414
$214$	−349.580	−0.111667
$215$	0	0
$216$	−460.983	−0.145212
$217$	−2561.75	−0.801396
$218$	403.741	0.125435
$219$	−1436.86	−0.443351
$220$	0	0
$221$	−237.310	−0.0722317
$222$	−469.464	−0.141930
$223$	1113.74	0.334446	0.167223	−	0.985919i	$-0.446520\pi$
$223$	1113.74	0.334446	0.167223	+	0.985919i	$0.446520\pi$
$224$	−1696.90	−0.506156
$225$	0	0
$226$	−512.314	−0.150790
$227$	1105.87	0.323345	0.161673	−	0.986844i	$-0.448311\pi$
$227$	1105.87	0.323345	0.161673	+	0.986844i	$0.448311\pi$
$228$	7258.39	2.10833
$229$	−259.975	−0.0750202	−0.0375101	−	0.999296i	$-0.511943\pi$
$229$	−259.975	−0.0750202	−0.0375101	+	0.999296i	$0.511943\pi$
$230$	0	0
$231$	−8996.98	−2.56259
$232$	188.745	0.0534126
$233$	−3497.60	−0.983412	−0.491706	−	0.870761i	$-0.663627\pi$
$233$	−3497.60	−0.983412	−0.491706	+	0.870761i	$0.663627\pi$
$234$	−128.121	−0.0357929
$235$	0	0
$236$	6638.36	1.83102
$237$	−3459.45	−0.948166
$238$	65.5611	0.0178559
$239$	2415.05	0.653625	0.326813	−	0.945089i	$-0.394025\pi$
$239$	2415.05	0.653625	0.326813	+	0.945089i	$0.394025\pi$
$240$	0	0
$241$	−5878.33	−1.57119	−0.785595	−	0.618741i	$-0.787643\pi$
$241$	−5878.33	−1.57119	−0.785595	+	0.618741i	$0.787643\pi$
$242$	−386.798	−0.102745
$243$	−3244.22	−0.856447
$244$	−5504.85	−1.44431
$245$	0	0
$246$	−3.75202	−0.000972440 0
$247$	−4760.62	−1.22636
$248$	−455.013	−0.116506
$249$	7509.07	1.91112
$250$	0	0
$251$	1912.94	0.481051	0.240526	−	0.970643i	$-0.422680\pi$
$251$	1912.94	0.481051	0.240526	+	0.970643i	$0.422680\pi$
$252$	−2784.79	−0.696132
$253$	−3512.66	−0.872882
$254$	−77.4537	−0.0191334
$255$	0	0
$256$	3591.54	0.876841
$257$	−4256.73	−1.03318	−0.516590	−	0.856233i	$-0.672799\pi$
$257$	−4256.73	−1.03318	−0.516590	+	0.856233i	$0.672799\pi$
$258$	876.568	0.211522
$259$	6692.64	1.60564
$260$	0	0
$261$	465.603	0.110422
$262$	−885.006	−0.208686
$263$	−4087.04	−0.958241	−0.479121	−	0.877749i	$-0.659044\pi$
$263$	−4087.04	−0.958241	−0.479121	+	0.877749i	$0.659044\pi$
$264$	−1598.03	−0.372545
$265$	0	0
$266$	1315.20	0.303159
$267$	−6461.32	−1.48100
$268$	3733.70	0.851014
$269$	−3177.67	−0.720246	−0.360123	−	0.932905i	$-0.617265\pi$
$269$	−3177.67	−0.720246	−0.360123	+	0.932905i	$0.617265\pi$
$270$	0	0
$271$	3929.49	0.880810	0.440405	−	0.897799i	$-0.354835\pi$
$271$	3929.49	0.880810	0.440405	+	0.897799i	$0.354835\pi$
$272$	−449.333	−0.100165
$273$	5794.48	1.28461
$274$	94.8290	0.0209081
$275$	0	0
$276$	−3449.30	−0.752259
$277$	7419.08	1.60928	0.804638	−	0.593766i	$-0.202360\pi$
$277$	7419.08	1.60928	0.804638	+	0.593766i	$0.202360\pi$
$278$	−430.923	−0.0929679
$279$	−1122.44	−0.240856
$280$	0	0
$281$	4965.27	1.05410	0.527052	−	0.849833i	$-0.323297\pi$
$281$	4965.27	1.05410	0.527052	+	0.849833i	$0.323297\pi$
$282$	250.007	0.0527932
$283$	3609.31	0.758132	0.379066	−	0.925370i	$-0.376245\pi$
$283$	3609.31	0.758132	0.379066	+	0.925370i	$0.376245\pi$
$284$	−560.871	−0.117189
$285$	0	0
$286$	520.746	0.107666
$287$	53.4885	0.0110011
$288$	−743.506	−0.152123
$289$	−4859.79	−0.989170
$290$	0	0
$291$	−2309.24	−0.465190
$292$	1807.65	0.362277
$293$	−4766.33	−0.950349	−0.475175	−	0.879892i	$-0.657615\pi$
$293$	−4766.33	−0.950349	−0.475175	+	0.879892i	$0.657615\pi$
$294$	−918.365	−0.182177
$295$	0	0
$296$	1188.73	0.233425
$297$	4622.00	0.903016
$298$	527.144	0.102472
$299$	2262.32	0.437570
$300$	0	0
$301$	−12496.3	−2.39293
$302$	792.059	0.150920
$303$	−4007.09	−0.759740
$304$	−9013.95	−1.70061
$305$	0	0
$306$	28.7259	0.00536651
$307$	−1554.85	−0.289055	−0.144528	−	0.989501i	$-0.546166\pi$
$307$	−1554.85	−0.289055	−0.144528	+	0.989501i	$0.546166\pi$
$308$	11318.7	2.09398
$309$	5877.14	1.08200
$310$	0	0
$311$	−1499.51	−0.273406	−0.136703	−	0.990612i	$-0.543651\pi$
$311$	−1499.51	−0.273406	−0.136703	+	0.990612i	$0.543651\pi$
$312$	1029.21	0.186754
$313$	−8397.03	−1.51638	−0.758192	−	0.652031i	$-0.773917\pi$
$313$	−8397.03	−1.51638	−0.758192	+	0.652031i	$0.773917\pi$
$314$	1027.01	0.184577
$315$	0	0
$316$	4352.19	0.774778
$317$	−3014.91	−0.534178	−0.267089	−	0.963672i	$-0.586062\pi$
$317$	−3014.91	−0.534178	−0.267089	+	0.963672i	$0.586062\pi$
$318$	504.954	0.0890453
$319$	−1892.44	−0.332151
$320$	0	0
$321$	6927.38	1.20451
$322$	−625.006	−0.108168
$323$	1067.38	0.183871
$324$	7189.43	1.23276
$325$	0	0
$326$	970.981	0.164962
$327$	−8000.64	−1.35302
$328$	9.50053	0.00159933
$329$	−3564.08	−0.597246
$330$	0	0
$331$	7905.51	1.31277	0.656384	−	0.754427i	$-0.272085\pi$
$331$	7905.51	1.31277	0.656384	+	0.754427i	$0.272085\pi$
$332$	−9446.86	−1.56164
$333$	2932.41	0.482568
$334$	820.832	0.134473
$335$	0	0
$336$	10971.5	1.78138
$337$	−3090.81	−0.499606	−0.249803	−	0.968297i	$-0.580366\pi$
$337$	−3090.81	−0.499606	−0.249803	+	0.968297i	$0.580366\pi$
$338$	360.779	0.0580585
$339$	10152.1	1.62652
$340$	0	0
$341$	4562.15	0.724500
$342$	576.264	0.0911133
$343$	3363.00	0.529402
$344$	−2219.57	−0.347881
$345$	0	0
$346$	−1136.63	−0.176605
$347$	9727.12	1.50484	0.752419	−	0.658685i	$-0.228887\pi$
$347$	9727.12	1.50484	0.752419	+	0.658685i	$0.228887\pi$
$348$	−1858.30	−0.286251
$349$	−5173.45	−0.793491	−0.396745	−	0.917929i	$-0.629860\pi$
$349$	−5173.45	−0.793491	−0.396745	+	0.917929i	$0.629860\pi$
$350$	0	0
$351$	−2976.79	−0.452676
$352$	3021.97	0.457589
$353$	6557.60	0.988742	0.494371	−	0.869251i	$-0.335398\pi$
$353$	6557.60	0.988742	0.494371	+	0.869251i	$0.335398\pi$
$354$	1672.02	0.251036
$355$	0	0
$356$	8128.72	1.21017
$357$	−1299.18	−0.192604
$358$	424.698	0.0626983
$359$	11071.7	1.62769	0.813846	−	0.581081i	$-0.197370\pi$
$359$	11071.7	1.62769	0.813846	+	0.581081i	$0.197370\pi$
$360$	0	0
$361$	14553.3	2.12179
$362$	−314.742	−0.0456975
$363$	7664.89	1.10827
$364$	−7289.80	−1.04970
$365$	0	0
$366$	−1386.52	−0.198018
$367$	1055.13	0.150074	0.0750371	−	0.997181i	$-0.476092\pi$
$367$	1055.13	0.150074	0.0750371	+	0.997181i	$0.476092\pi$
$368$	4283.57	0.606784
$369$	23.4363	0.00330635
$370$	0	0
$371$	−7198.58	−1.00736
$372$	4479.86	0.624382
$373$	−7549.83	−1.04803	−0.524015	−	0.851709i	$-0.675566\pi$
$373$	−7549.83	−1.04803	−0.524015	+	0.851709i	$0.675566\pi$
$374$	−116.756	−0.0161426
$375$	0	0
$376$	−633.045	−0.0868266
$377$	1218.82	0.166505
$378$	822.391	0.111903
$379$	8861.23	1.20098	0.600489	−	0.799633i	$-0.294973\pi$
$379$	8861.23	1.20098	0.600489	+	0.799633i	$0.294973\pi$
$380$	0	0
$381$	1534.84	0.206384
$382$	−508.692	−0.0681334
$383$	4439.20	0.592252	0.296126	−	0.955149i	$-0.404305\pi$
$383$	4439.20	0.592252	0.296126	+	0.955149i	$0.404305\pi$
$384$	3947.98	0.524661
$385$	0	0
$386$	558.476	0.0736416
$387$	−5475.31	−0.719187
$388$	2905.17	0.380123
$389$	4697.46	0.612264	0.306132	−	0.951989i	$-0.400965\pi$
$389$	4697.46	0.612264	0.306132	+	0.951989i	$0.400965\pi$
$390$	0	0
$391$	−507.234	−0.0656059
$392$	2325.40	0.299619
$393$	17537.5	2.25102
$394$	1098.40	0.140448
$395$	0	0
$396$	4959.36	0.629337
$397$	−4653.38	−0.588279	−0.294139	−	0.955763i	$-0.595033\pi$
$397$	−4653.38	−0.588279	−0.294139	+	0.955763i	$0.595033\pi$
$398$	1230.96	0.155031
$399$	−26062.5	−3.27006
$400$	0	0
$401$	−12107.8	−1.50782	−0.753908	−	0.656980i	$-0.771833\pi$
$401$	−12107.8	−1.50782	−0.753908	+	0.656980i	$0.771833\pi$
$402$	940.414	0.116676
$403$	−2938.24	−0.363187
$404$	5041.16	0.620809
$405$	0	0
$406$	−336.720	−0.0411605
$407$	−11918.8	−1.45157
$408$	−230.758	−0.0280005
$409$	−4572.66	−0.552820	−0.276410	−	0.961040i	$-0.589145\pi$
$409$	−4572.66	−0.552820	−0.276410	+	0.961040i	$0.589145\pi$
$410$	0	0
$411$	−1879.16	−0.225528
$412$	−7393.79	−0.884140
$413$	−23836.1	−2.83995
$414$	−273.850	−0.0325096
$415$	0	0
$416$	−1946.29	−0.229387
$417$	8539.30	1.00281
$418$	−2342.21	−0.274071
$419$	8568.59	0.999053	0.499527	−	0.866299i	$-0.333507\pi$
$419$	8568.59	0.999053	0.499527	+	0.866299i	$0.333507\pi$
$420$	0	0
$421$	−4973.90	−0.575803	−0.287901	−	0.957660i	$-0.592958\pi$
$421$	−4973.90	−0.575803	−0.287901	+	0.957660i	$0.592958\pi$
$422$	1773.70	0.204603
$423$	−1561.62	−0.179500
$424$	−1278.60	−0.146449
$425$	0	0
$426$	−141.268	−0.0160668
$427$	19766.1	2.24016
$428$	−8715.06	−0.984248
$429$	−10319.2	−1.16135
$430$	0	0
$431$	−7519.93	−0.840423	−0.420212	−	0.907426i	$-0.638044\pi$
$431$	−7519.93	−0.840423	−0.420212	+	0.907426i	$0.638044\pi$
$432$	−5636.38	−0.627732
$433$	10509.3	1.16639	0.583195	−	0.812332i	$-0.301802\pi$
$433$	10509.3	1.16639	0.583195	+	0.812332i	$0.301802\pi$
$434$	811.742	0.0897808
$435$	0	0
$436$	10065.3	1.10560
$437$	−10175.5	−1.11387
$438$	455.297	0.0496688
$439$	−682.186	−0.0741662	−0.0370831	−	0.999312i	$-0.511807\pi$
$439$	−682.186	−0.0741662	−0.0370831	+	0.999312i	$0.511807\pi$
$440$	0	0
$441$	5736.38	0.619413
$442$	75.1965	0.00809216
$443$	2580.52	0.276759	0.138380	−	0.990379i	$-0.455811\pi$
$443$	2580.52	0.276759	0.138380	+	0.990379i	$0.455811\pi$
$444$	−11703.8	−1.25098
$445$	0	0
$446$	−352.911	−0.0374682
$447$	−10446.0	−1.10532
$448$	−13440.6	−1.41743
$449$	−13785.0	−1.44890	−0.724448	−	0.689329i	$-0.757905\pi$
$449$	−13785.0	−1.44890	−0.724448	+	0.689329i	$0.757905\pi$
$450$	0	0
$451$	−95.2563	−0.00994556
$452$	−12772.0	−1.32908
$453$	−15695.7	−1.62792
$454$	−350.418	−0.0362245
$455$	0	0
$456$	−4629.17	−0.475396
$457$	3310.31	0.338840	0.169420	−	0.985544i	$-0.445811\pi$
$457$	3310.31	0.338840	0.169420	+	0.985544i	$0.445811\pi$
$458$	82.3783	0.00840455
$459$	667.425	0.0678708
$460$	0	0
$461$	−10738.2	−1.08487	−0.542437	−	0.840096i	$-0.682498\pi$
$461$	−10738.2	−1.08487	−0.542437	+	0.840096i	$0.682498\pi$
$462$	2850.87	0.287088
$463$	11191.2	1.12333	0.561664	−	0.827365i	$-0.310161\pi$
$463$	11191.2	1.12333	0.561664	+	0.827365i	$0.310161\pi$
$464$	2307.76	0.230895
$465$	0	0
$466$	1108.28	0.110172
$467$	976.399	0.0967503	0.0483751	−	0.998829i	$-0.484596\pi$
$467$	976.399	0.0967503	0.0483751	+	0.998829i	$0.484596\pi$
$468$	−3194.06	−0.315482
$469$	−13406.5	−1.31994
$470$	0	0
$471$	−20351.4	−1.99096
$472$	−4233.73	−0.412867
$473$	22254.3	2.16333
$474$	1096.20	0.106224
$475$	0	0
$476$	1634.44	0.157384
$477$	−3154.09	−0.302759
$478$	−765.257	−0.0732260
$479$	−7790.22	−0.743098	−0.371549	−	0.928413i	$-0.621173\pi$
$479$	−7790.22	−0.743098	−0.371549	+	0.928413i	$0.621173\pi$
$480$	0	0
$481$	7676.24	0.727664
$482$	1862.67	0.176021
$483$	12385.3	1.16677
$484$	−9642.89	−0.905606
$485$	0	0
$486$	1028.00	0.0959483
$487$	−3226.21	−0.300192	−0.150096	−	0.988671i	$-0.547958\pi$
$487$	−3226.21	−0.300192	−0.150096	+	0.988671i	$0.547958\pi$
$488$	3510.82	0.325670
$489$	−19241.2	−1.77938
$490$	0	0
$491$	−458.852	−0.0421746	−0.0210873	−	0.999778i	$-0.506713\pi$
$491$	−458.852	−0.0421746	−0.0210873	+	0.999778i	$0.506713\pi$
$492$	−93.5381	−0.00857119
$493$	−273.271	−0.0249645
$494$	1508.50	0.137390
$495$	0	0
$496$	−5563.39	−0.503636
$497$	2013.90	0.181762
$498$	−2379.40	−0.214103
$499$	−738.125	−0.0662185	−0.0331093	−	0.999452i	$-0.510541\pi$
$499$	−738.125	−0.0662185	−0.0331093	+	0.999452i	$0.510541\pi$
$500$	0	0
$501$	−16265.8	−1.45051
$502$	−606.155	−0.0538925
$503$	−17123.8	−1.51791	−0.758957	−	0.651140i	$-0.774291\pi$
$503$	−17123.8	−1.51791	−0.758957	+	0.651140i	$0.774291\pi$
$504$	1776.05	0.156967
$505$	0	0
$506$	1113.06	0.0977894
$507$	−7149.29	−0.626254
$508$	−1930.92	−0.168644
$509$	19592.6	1.70614	0.853072	−	0.521794i	$-0.174737\pi$
$509$	19592.6	1.70614	0.853072	+	0.521794i	$0.174737\pi$
$510$	0	0
$511$	−6490.68	−0.561900
$512$	−6167.98	−0.532400
$513$	13389.0	1.15232
$514$	1348.83	0.115748
$515$	0	0
$516$	21852.9	1.86438
$517$	6347.17	0.539939
$518$	−2120.70	−0.179881
$519$	22523.7	1.90497
$520$	0	0
$521$	3086.25	0.259522	0.129761	−	0.991545i	$-0.458579\pi$
$521$	3086.25	0.259522	0.129761	+	0.991545i	$0.458579\pi$
$522$	−147.536	−0.0123706
$523$	−1733.48	−0.144933	−0.0724663	−	0.997371i	$-0.523087\pi$
$523$	−1733.48	−0.144933	−0.0724663	+	0.997371i	$0.523087\pi$
$524$	−22063.3	−1.83938
$525$	0	0
$526$	1295.06	0.107352
$527$	658.782	0.0544535
$528$	−19538.9	−1.61046
$529$	−7331.45	−0.602568
$530$	0	0
$531$	−10443.9	−0.853536
$532$	32788.1	2.67208
$533$	61.3496	0.00498564
$534$	2047.40	0.165917
$535$	0	0
$536$	−2381.23	−0.191891
$537$	−8415.93	−0.676302
$538$	1006.91	0.0806895
$539$	−23315.4	−1.86321
$540$	0	0
$541$	1662.07	0.132085	0.0660424	−	0.997817i	$-0.478963\pi$
$541$	1662.07	0.132085	0.0660424	+	0.997817i	$0.478963\pi$
$542$	−1245.14	−0.0986776
$543$	6237.02	0.492921
$544$	436.377	0.0343925
$545$	0	0
$546$	−1836.10	−0.143915
$547$	9495.08	0.742194	0.371097	−	0.928594i	$-0.378982\pi$
$547$	9495.08	0.742194	0.371097	+	0.928594i	$0.378982\pi$
$548$	2364.09	0.184287
$549$	8660.60	0.673271
$550$	0	0
$551$	−5482.01	−0.423850
$552$	2199.85	0.169623
$553$	−15627.3	−1.20170
$554$	−2350.89	−0.180288
$555$	0	0
$556$	−10742.9	−0.819429
$557$	19462.4	1.48052	0.740261	−	0.672320i	$-0.234702\pi$
$557$	19462.4	1.48052	0.740261	+	0.672320i	$0.234702\pi$
$558$	355.669	0.0269833
$559$	−14332.8	−1.08446
$560$	0	0
$561$	2313.67	0.174124
$562$	−1573.35	−0.118092
$563$	2388.08	0.178767	0.0893834	−	0.995997i	$-0.471510\pi$
$563$	2388.08	0.178767	0.0893834	+	0.995997i	$0.471510\pi$
$564$	6232.69	0.465325
$565$	0	0
$566$	−1143.68	−0.0849340
$567$	−25814.8	−1.91203
$568$	357.706	0.0264243
$569$	17365.7	1.27945	0.639727	−	0.768602i	$-0.279047\pi$
$569$	17365.7	1.27945	0.639727	+	0.768602i	$0.279047\pi$
$570$	0	0
$571$	18405.5	1.34894	0.674471	−	0.738302i	$-0.264372\pi$
$571$	18405.5	1.34894	0.674471	+	0.738302i	$0.264372\pi$
$572$	12982.2	0.948976
$573$	10080.4	0.734929
$574$	−16.9489	−0.00123246
$575$	0	0
$576$	−5889.05	−0.426002
$577$	−12392.7	−0.894131	−0.447065	−	0.894501i	$-0.647531\pi$
$577$	−12392.7	−0.894131	−0.447065	+	0.894501i	$0.647531\pi$
$578$	1539.92	0.110817
$579$	−11066.9	−0.794344
$580$	0	0
$581$	33920.5	2.42213
$582$	731.731	0.0521155
$583$	12819.8	0.910704
$584$	−1152.86	−0.0816880
$585$	0	0
$586$	1510.31	0.106468
$587$	−7306.10	−0.513722	−0.256861	−	0.966448i	$-0.582688\pi$
$587$	−7306.10	−0.513722	−0.256861	+	0.966448i	$0.582688\pi$
$588$	−22894.9	−1.60573
$589$	13215.7	0.924519
$590$	0	0
$591$	−21766.2	−1.51496
$592$	14534.5	1.00906
$593$	−18344.3	−1.27034	−0.635170	−	0.772372i	$-0.719070\pi$
$593$	−18344.3	−1.27034	−0.635170	+	0.772372i	$0.719070\pi$
$594$	−1464.58	−0.101165
$595$	0	0
$596$	13141.7	0.903198
$597$	−24393.0	−1.67226
$598$	−716.862	−0.0490212
$599$	9264.73	0.631964	0.315982	−	0.948765i	$-0.397666\pi$
$599$	9264.73	0.631964	0.315982	+	0.948765i	$0.397666\pi$
$600$	0	0
$601$	7922.12	0.537687	0.268844	−	0.963184i	$-0.413359\pi$
$601$	7922.12	0.537687	0.268844	+	0.963184i	$0.413359\pi$
$602$	3959.70	0.268082
$603$	−5874.11	−0.396704
$604$	19746.1	1.33023
$605$	0	0
$606$	1269.73	0.0851141
$607$	9526.36	0.637006	0.318503	−	0.947922i	$-0.396820\pi$
$607$	9526.36	0.637006	0.318503	+	0.947922i	$0.396820\pi$
$608$	8754.04	0.583920
$609$	6672.54	0.443982
$610$	0	0
$611$	−4087.88	−0.270668
$612$	716.140	0.0473010
$613$	−15408.5	−1.01524	−0.507622	−	0.861580i	$-0.669475\pi$
$613$	−15408.5	−1.01524	−0.507622	+	0.861580i	$0.669475\pi$
$614$	492.686	0.0323830
$615$	0	0
$616$	−7218.73	−0.472160
$617$	13181.4	0.860073	0.430036	−	0.902812i	$-0.358501\pi$
$617$	13181.4	0.860073	0.430036	+	0.902812i	$0.358501\pi$
$618$	−1862.29	−0.121217
$619$	9468.93	0.614844	0.307422	−	0.951573i	$-0.400534\pi$
$619$	9468.93	0.614844	0.307422	+	0.951573i	$0.400534\pi$
$620$	0	0
$621$	−6362.68	−0.411152
$622$	475.150	0.0306299
$623$	−29187.5	−1.87701
$624$	12584.0	0.807311
$625$	0	0
$626$	2660.77	0.169881
$627$	46414.0	2.95629
$628$	25603.3	1.62688
$629$	−1721.09	−0.109100
$630$	0	0
$631$	9724.07	0.613485	0.306743	−	0.951792i	$-0.400761\pi$
$631$	9724.07	0.613485	0.306743	+	0.951792i	$0.400761\pi$
$632$	−2775.69	−0.174701
$633$	−35148.1	−2.20697
$634$	955.336	0.0598442
$635$	0	0
$636$	12588.5	0.784855
$637$	15016.3	0.934012
$638$	599.657	0.0372110
$639$	882.401	0.0546279
$640$	0	0
$641$	8046.70	0.495827	0.247914	−	0.968782i	$-0.420255\pi$
$641$	8046.70	0.495827	0.247914	+	0.968782i	$0.420255\pi$
$642$	−2195.08	−0.134942
$643$	20586.6	1.26260	0.631302	−	0.775537i	$-0.282521\pi$
$643$	20586.6	1.26260	0.631302	+	0.775537i	$0.282521\pi$
$644$	−15581.4	−0.953408
$645$	0	0
$646$	−338.219	−0.0205992
$647$	25462.4	1.54719	0.773594	−	0.633682i	$-0.218457\pi$
$647$	25462.4	1.54719	0.773594	+	0.633682i	$0.218457\pi$
$648$	−4585.19	−0.277968
$649$	42449.2	2.56745
$650$	0	0
$651$	−16085.7	−0.968431
$652$	24206.6	1.45399
$653$	−7573.48	−0.453864	−0.226932	−	0.973911i	$-0.572870\pi$
$653$	−7573.48	−0.453864	−0.226932	+	0.973911i	$0.572870\pi$
$654$	2535.16	0.151579
$655$	0	0
$656$	116.162	0.00691366
$657$	−2843.92	−0.168877
$658$	1129.35	0.0669098
$659$	19.5228	0.00115402	0.000577010	−	1.00000i	$-0.499816\pi$
$659$	19.5228	0.00115402	0.000577010		1.00000i	$0.499816\pi$
$660$	0	0
$661$	−8720.18	−0.513125	−0.256562	−	0.966528i	$-0.582590\pi$
$661$	−8720.18	−0.513125	−0.256562	+	0.966528i	$0.582590\pi$
$662$	−2505.02	−0.147070
$663$	−1490.12	−0.0872870
$664$	6024.90	0.352126
$665$	0	0
$666$	−929.195	−0.0540624
$667$	2605.14	0.151231
$668$	20463.4	1.18526
$669$	6993.37	0.404155
$670$	0	0
$671$	−35200.9	−2.02521
$672$	−10655.2	−0.611654
$673$	20070.3	1.14956	0.574778	−	0.818309i	$-0.305088\pi$
$673$	20070.3	1.14956	0.574778	+	0.818309i	$0.305088\pi$
$674$	979.387	0.0559712
$675$	0	0
$676$	8994.23	0.511734
$677$	7754.25	0.440207	0.220103	−	0.975477i	$-0.429361\pi$
$677$	7754.25	0.440207	0.220103	+	0.975477i	$0.429361\pi$
$678$	−3216.91	−0.182219
$679$	−10431.5	−0.589579
$680$	0	0
$681$	6943.98	0.390740
$682$	−1445.61	−0.0811661
$683$	−28456.1	−1.59420	−0.797102	−	0.603845i	$-0.793635\pi$
$683$	−28456.1	−1.59420	−0.797102	+	0.603845i	$0.793635\pi$
$684$	14366.3	0.803083
$685$	0	0
$686$	−1065.64	−0.0593093
$687$	−1632.43	−0.0906567
$688$	−27138.4	−1.50384
$689$	−8256.54	−0.456530
$690$	0	0
$691$	−16980.0	−0.934806	−0.467403	−	0.884044i	$-0.654810\pi$
$691$	−16980.0	−0.934806	−0.467403	+	0.884044i	$0.654810\pi$
$692$	−28336.1	−1.55662
$693$	−17807.4	−0.976115
$694$	−3082.23	−0.168588
$695$	0	0
$696$	1185.16	0.0645453
$697$	−13.7552	−0.000747509 0
$698$	1639.31	0.0888952
$699$	−21962.1	−1.18838
$700$	0	0
$701$	20805.7	1.12100	0.560499	−	0.828155i	$-0.310609\pi$
$701$	20805.7	1.12100	0.560499	+	0.828155i	$0.310609\pi$
$702$	943.256	0.0507136
$703$	−34526.3	−1.85232
$704$	23935.9	1.28142
$705$	0	0
$706$	−2077.91	−0.110769
$707$	−18101.1	−0.962889
$708$	41683.5	2.21266
$709$	−19891.2	−1.05364	−0.526820	−	0.849977i	$-0.676616\pi$
$709$	−19891.2	−1.05364	−0.526820	+	0.849977i	$0.676616\pi$
$710$	0	0
$711$	−6847.17	−0.361166
$712$	−5184.24	−0.272876
$713$	−6280.29	−0.329872
$714$	411.671	0.0215776
$715$	0	0
$716$	10587.7	0.552630
$717$	15164.5	0.789860
$718$	−3508.29	−0.182351
$719$	8228.12	0.426783	0.213392	−	0.976967i	$-0.431549\pi$
$719$	8228.12	0.426783	0.213392	+	0.976967i	$0.431549\pi$
$720$	0	0
$721$	26548.6	1.37132
$722$	−4611.52	−0.237705
$723$	−36911.1	−1.89867
$724$	−7846.55	−0.402783
$725$	0	0
$726$	−2428.78	−0.124160
$727$	24617.3	1.25585	0.627927	−	0.778272i	$-0.283903\pi$
$727$	24617.3	1.25585	0.627927	+	0.778272i	$0.283903\pi$
$728$	4649.20	0.236691
$729$	4201.68	0.213467
$730$	0	0
$731$	3213.56	0.162596
$732$	−34566.0	−1.74535
$733$	27927.4	1.40726	0.703630	−	0.710567i	$-0.251561\pi$
$733$	27927.4	1.40726	0.703630	+	0.710567i	$0.251561\pi$
$734$	−334.338	−0.0168129
$735$	0	0
$736$	−4160.06	−0.208345
$737$	23875.2	1.19329
$738$	−7.42625	−0.000370412 0
$739$	11145.2	0.554780	0.277390	−	0.960757i	$-0.410531\pi$
$739$	11145.2	0.554780	0.277390	+	0.960757i	$0.410531\pi$
$740$	0	0
$741$	−29892.8	−1.48197
$742$	2281.01	0.112855
$743$	2334.72	0.115279	0.0576396	−	0.998337i	$-0.481643\pi$
$743$	2334.72	0.115279	0.0576396	+	0.998337i	$0.481643\pi$
$744$	−2857.11	−0.140789
$745$	0	0
$746$	2392.32	0.117411
$747$	14862.4	0.727963
$748$	−2910.74	−0.142282
$749$	31292.9	1.52659
$750$	0	0
$751$	−1451.93	−0.0705484	−0.0352742	−	0.999378i	$-0.511230\pi$
$751$	−1451.93	−0.0705484	−0.0352742	+	0.999378i	$0.511230\pi$
$752$	−7740.16	−0.375339
$753$	12011.7	0.581317
$754$	−386.207	−0.0186536
$755$	0	0
$756$	20502.3	0.986323
$757$	−25545.8	−1.22652	−0.613261	−	0.789880i	$-0.710143\pi$
$757$	−25545.8	−1.22652	−0.613261	+	0.789880i	$0.710143\pi$
$758$	−2807.86	−0.134546
$759$	−22056.7	−1.05482
$760$	0	0
$761$	−18110.7	−0.862696	−0.431348	−	0.902186i	$-0.641962\pi$
$761$	−18110.7	−0.862696	−0.431348	+	0.902186i	$0.641962\pi$
$762$	−486.346	−0.0231213
$763$	−36141.1	−1.71480
$764$	−12681.7	−0.600535
$765$	0	0
$766$	−1406.65	−0.0663504
$767$	−27339.3	−1.28705
$768$	22551.9	1.05960
$769$	−5860.26	−0.274807	−0.137403	−	0.990515i	$-0.543876\pi$
$769$	−5860.26	−0.274807	−0.137403	+	0.990515i	$0.543876\pi$
$770$	0	0
$771$	−26728.8	−1.24853
$772$	13922.8	0.649085
$773$	25911.3	1.20565	0.602824	−	0.797875i	$-0.294042\pi$
$773$	25911.3	1.20565	0.602824	+	0.797875i	$0.294042\pi$
$774$	1734.96	0.0805709
$775$	0	0
$776$	−1852.82	−0.0857120
$777$	42024.3	1.94030
$778$	−1488.49	−0.0685923
$779$	−275.939	−0.0126913
$780$	0	0
$781$	−3586.51	−0.164322
$782$	160.727	0.00734987
$783$	−3427.87	−0.156452
$784$	28432.4	1.29521
$785$	0	0
$786$	−5557.12	−0.252183
$787$	39421.5	1.78555	0.892773	−	0.450507i	$-0.148757\pi$
$787$	39421.5	1.78555	0.892773	+	0.450507i	$0.148757\pi$
$788$	27383.1	1.23792
$789$	−25663.3	−1.15797
$790$	0	0
$791$	45860.0	2.06144
$792$	−3162.92	−0.141906
$793$	22671.1	1.01522
$794$	1474.52	0.0659052
$795$	0	0
$796$	30687.9	1.36646
$797$	19868.2	0.883022	0.441511	−	0.897256i	$-0.354443\pi$
$797$	19868.2	0.883022	0.441511	+	0.897256i	$0.354443\pi$
$798$	8258.42	0.366347
$799$	916.542	0.0405819
$800$	0	0
$801$	−12788.7	−0.564127
$802$	3836.60	0.168921
$803$	11559.1	0.507984
$804$	23444.6	1.02839
$805$	0	0
$806$	931.042	0.0406880
$807$	−19953.2	−0.870367
$808$	−3215.09	−0.139983
$809$	40900.3	1.77747	0.888737	−	0.458417i	$-0.151583\pi$
$809$	40900.3	1.77747	0.888737	+	0.458417i	$0.151583\pi$
$810$	0	0
$811$	26916.9	1.16545	0.582725	−	0.812669i	$-0.301986\pi$
$811$	26916.9	1.16545	0.582725	+	0.812669i	$0.301986\pi$
$812$	−8394.46	−0.362793
$813$	24674.0	1.06440
$814$	3776.70	0.162621
$815$	0	0
$816$	−2821.44	−0.121042
$817$	64466.3	2.76057
$818$	1448.94	0.0619327
$819$	11468.8	0.489320
$820$	0	0
$821$	26979.7	1.14689	0.573447	−	0.819243i	$-0.305606\pi$
$821$	26979.7	1.14689	0.573447	+	0.819243i	$0.305606\pi$
$822$	595.449	0.0252660
$823$	−10179.8	−0.431160	−0.215580	−	0.976486i	$-0.569164\pi$
$823$	−10179.8	−0.431160	−0.215580	+	0.976486i	$0.569164\pi$
$824$	4715.52	0.199360
$825$	0	0
$826$	7552.96	0.318161
$827$	−25419.2	−1.06882	−0.534409	−	0.845226i	$-0.679466\pi$
$827$	−25419.2	−1.06882	−0.534409	+	0.845226i	$0.679466\pi$
$828$	−6827.09	−0.286543
$829$	26132.7	1.09484	0.547421	−	0.836857i	$-0.315610\pi$
$829$	26132.7	1.09484	0.547421	+	0.836857i	$0.315610\pi$
$830$	0	0
$831$	46585.8	1.94470
$832$	−15415.9	−0.642367
$833$	−3366.79	−0.140039
$834$	−2705.85	−0.112345
$835$	0	0
$836$	−58391.5	−2.41569
$837$	8263.68	0.341260
$838$	−2715.13	−0.111924
$839$	−45199.3	−1.85990	−0.929948	−	0.367690i	$-0.880149\pi$
$839$	−45199.3	−1.85990	−0.929948	+	0.367690i	$0.880149\pi$
$840$	0	0
$841$	−22985.5	−0.942453
$842$	1576.08	0.0645075
$843$	31177.9	1.27381
$844$	44218.4	1.80339
$845$	0	0
$846$	494.830	0.0201095
$847$	34624.4	1.40462
$848$	−15633.3	−0.633076
$849$	22663.6	0.916150
$850$	0	0
$851$	16407.4	0.660916
$852$	−3521.81	−0.141614
$853$	−2581.44	−0.103619	−0.0518095	−	0.998657i	$-0.516499\pi$
$853$	−2581.44	−0.103619	−0.0518095	+	0.998657i	$0.516499\pi$
$854$	−6263.28	−0.250966
$855$	0	0
$856$	5558.19	0.221933
$857$	−28817.5	−1.14864	−0.574322	−	0.818630i	$-0.694734\pi$
$857$	−28817.5	−1.14864	−0.574322	+	0.818630i	$0.694734\pi$
$858$	3269.86	0.130106
$859$	37518.9	1.49025	0.745127	−	0.666923i	$-0.232389\pi$
$859$	37518.9	1.49025	0.745127	+	0.666923i	$0.232389\pi$
$860$	0	0
$861$	335.864	0.0132941
$862$	2382.84	0.0941531
$863$	21412.4	0.844598	0.422299	−	0.906457i	$-0.361223\pi$
$863$	21412.4	0.844598	0.422299	+	0.906457i	$0.361223\pi$
$864$	5473.86	0.215538
$865$	0	0
$866$	−3330.10	−0.130671
$867$	−30515.5	−1.19534
$868$	20236.8	0.791337
$869$	27830.2	1.08639
$870$	0	0
$871$	−15376.8	−0.598189
$872$	−6419.32	−0.249295
$873$	−4570.61	−0.177196
$874$	3224.31	0.124787
$875$	0	0
$876$	11350.6	0.437786
$877$	−28165.4	−1.08447	−0.542234	−	0.840228i	$-0.682421\pi$
$877$	−28165.4	−1.08447	−0.542234	+	0.840228i	$0.682421\pi$
$878$	216.164	0.00830888
$879$	−29928.7	−1.14843
$880$	0	0
$881$	33221.2	1.27043	0.635215	−	0.772335i	$-0.280911\pi$
$881$	33221.2	1.27043	0.635215	+	0.772335i	$0.280911\pi$
$882$	−1817.69	−0.0693932
$883$	−41589.4	−1.58505	−0.792523	−	0.609842i	$-0.791233\pi$
$883$	−41589.4	−1.58505	−0.792523	+	0.609842i	$0.791233\pi$
$884$	1874.65	0.0713252
$885$	0	0
$886$	−817.691	−0.0310055
$887$	33075.4	1.25204	0.626022	−	0.779805i	$-0.284682\pi$
$887$	33075.4	1.25204	0.626022	+	0.779805i	$0.284682\pi$
$888$	7464.29	0.282078
$889$	6933.31	0.261570
$890$	0	0
$891$	45973.0	1.72857
$892$	−8798.08	−0.330248
$893$	18386.5	0.689004
$894$	3310.04	0.123830
$895$	0	0
$896$	17834.1	0.664951
$897$	14205.5	0.528773
$898$	4368.06	0.162321
$899$	−3383.49	−0.125524
$900$	0	0
$901$	1851.19	0.0684486
$902$	30.1839	0.00111421
$903$	−78466.4	−2.89169
$904$	8145.58	0.299688
$905$	0	0
$906$	4973.48	0.182376
$907$	30202.5	1.10569	0.552844	−	0.833285i	$-0.313543\pi$
$907$	30202.5	1.10569	0.552844	+	0.833285i	$0.313543\pi$
$908$	−8735.94	−0.319287
$909$	−7931.10	−0.289393
$910$	0	0
$911$	24941.4	0.907074	0.453537	−	0.891237i	$-0.350162\pi$
$911$	24941.4	0.907074	0.453537	+	0.891237i	$0.350162\pi$
$912$	−56600.2	−2.05507
$913$	−60408.2	−2.18973
$914$	−1048.94	−0.0379604
$915$	0	0
$916$	2053.70	0.0740786
$917$	79221.8	2.85293
$918$	−211.487	−0.00760361
$919$	22225.7	0.797777	0.398889	−	0.916999i	$-0.369396\pi$
$919$	22225.7	0.797777	0.398889	+	0.916999i	$0.369396\pi$
$920$	0	0
$921$	−9763.20	−0.349303
$922$	3402.61	0.121539
$923$	2309.88	0.0823734
$924$	71072.5	2.53042
$925$	0	0
$926$	−3546.17	−0.125847
$927$	11632.4	0.412145
$928$	−2241.22	−0.0792798
$929$	5322.68	0.187978	0.0939889	−	0.995573i	$-0.470038\pi$
$929$	5322.68	0.187978	0.0939889	+	0.995573i	$0.470038\pi$
$930$	0	0
$931$	−67540.2	−2.37760
$932$	27629.6	0.971070
$933$	−9415.70	−0.330392
$934$	−309.392	−0.0108390
$935$	0	0
$936$	2037.07	0.0711365
$937$	−41806.5	−1.45759	−0.728793	−	0.684734i	$-0.759918\pi$
$937$	−41806.5	−1.45759	−0.728793	+	0.684734i	$0.759918\pi$
$938$	4248.11	0.147874
$939$	−52726.5	−1.83244
$940$	0	0
$941$	23455.4	0.812566	0.406283	−	0.913747i	$-0.366825\pi$
$941$	23455.4	0.812566	0.406283	+	0.913747i	$0.366825\pi$
$942$	6448.76	0.223049
$943$	131.130	0.00452831
$944$	−51765.3	−1.78476
$945$	0	0
$946$	−7051.73	−0.242359
$947$	22992.0	0.788954	0.394477	−	0.918906i	$-0.370926\pi$
$947$	22992.0	0.788954	0.394477	+	0.918906i	$0.370926\pi$
$948$	27328.2	0.936266
$949$	−7444.60	−0.254649
$950$	0	0
$951$	−18931.2	−0.645516
$952$	−1042.40	−0.0354876
$953$	4988.54	0.169564	0.0847821	−	0.996400i	$-0.472981\pi$
$953$	4988.54	0.169564	0.0847821	+	0.996400i	$0.472981\pi$
$954$	999.438	0.0339182
$955$	0	0
$956$	−19077.9	−0.645422
$957$	−11883.0	−0.401381
$958$	2468.49	0.0832497
$959$	−8488.67	−0.285833
$960$	0	0
$961$	−21634.3	−0.726203
$962$	−2432.37	−0.0815207
$963$	13711.1	0.458811
$964$	46436.4	1.55147
$965$	0	0
$966$	−3924.53	−0.130714
$967$	−13401.3	−0.445662	−0.222831	−	0.974857i	$-0.571530\pi$
$967$	−13401.3	−0.445662	−0.222831	+	0.974857i	$0.571530\pi$
$968$	6149.93	0.204201
$969$	6702.25	0.222195
$970$	0	0
$971$	4483.10	0.148166	0.0740832	−	0.997252i	$-0.476397\pi$
$971$	4483.10	0.148166	0.0740832	+	0.997252i	$0.476397\pi$
$972$	25628.0	0.845698
$973$	38574.3	1.27095
$974$	1022.29	0.0336307
$975$	0	0
$976$	42926.3	1.40783
$977$	−44077.8	−1.44337	−0.721686	−	0.692221i	$-0.756632\pi$
$977$	−44077.8	−1.44337	−0.721686	+	0.692221i	$0.756632\pi$
$978$	6096.97	0.199345
$979$	51979.4	1.69690
$980$	0	0
$981$	−15835.4	−0.515378
$982$	145.397	0.00472484
$983$	15648.1	0.507727	0.253864	−	0.967240i	$-0.418299\pi$
$983$	15648.1	0.507727	0.253864	+	0.967240i	$0.418299\pi$
$984$	59.6556	0.00193267
$985$	0	0
$986$	86.5914	0.00279679
$987$	−22379.5	−0.721730
$988$	37606.9	1.21097
$989$	−30635.4	−0.984984
$990$	0	0
$991$	−48645.9	−1.55932	−0.779661	−	0.626202i	$-0.784609\pi$
$991$	−48645.9	−1.55932	−0.779661	+	0.626202i	$0.784609\pi$
$992$	5402.98	0.172928
$993$	49640.2	1.58639
$994$	−638.145	−0.0203629
$995$	0	0
$996$	−59318.6	−1.88713
$997$	17365.8	0.551634	0.275817	−	0.961210i	$-0.411052\pi$
$997$	17365.8	0.551634	0.275817	+	0.961210i	$0.411052\pi$
$998$	233.890	0.00741849
$999$	−21589.1	−0.683733

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1775.4.a.g.1.11		20
5.4	even	2		355.4.a.d.1.10	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
355.4.a.d.1.10	✓	20	5.4	even	2
1775.4.a.g.1.11		20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1775 = 5^{2} \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1775.a (trivial)

\(f(q)\)	\(=\)	\(q-0.316870 q^{2} +6.27919 q^{3} -7.89959 q^{4} -1.98969 q^{6} +28.3648 q^{7} +5.03811 q^{8} +12.4282 q^{9} +O(q^{10})\)	\(q-0.316870 q^{2} +6.27919 q^{3} -7.89959 q^{4} -1.98969 q^{6} +28.3648 q^{7} +5.03811 q^{8} +12.4282 q^{9} -50.5142 q^{11} -49.6030 q^{12} +32.5335 q^{13} -8.98796 q^{14} +61.6003 q^{16} -7.29433 q^{17} -3.93812 q^{18} -146.330 q^{19} +178.108 q^{21} +16.0064 q^{22} +69.5381 q^{23} +31.6352 q^{24} -10.3089 q^{26} -91.4991 q^{27} -224.070 q^{28} +37.4635 q^{29} -90.3143 q^{31} -59.8242 q^{32} -317.188 q^{33} +2.31135 q^{34} -98.1776 q^{36} +235.949 q^{37} +46.3675 q^{38} +204.284 q^{39} +1.88573 q^{41} -56.4371 q^{42} -440.555 q^{43} +399.041 q^{44} -22.0346 q^{46} -125.651 q^{47} +386.800 q^{48} +461.562 q^{49} -45.8024 q^{51} -257.002 q^{52} -253.785 q^{53} +28.9934 q^{54} +142.905 q^{56} -918.830 q^{57} -11.8711 q^{58} -840.342 q^{59} +696.852 q^{61} +28.6179 q^{62} +352.523 q^{63} -473.846 q^{64} +100.507 q^{66} -472.644 q^{67} +57.6222 q^{68} +436.643 q^{69} +71.0000 q^{71} +62.6145 q^{72} -228.829 q^{73} -74.7651 q^{74} +1155.94 q^{76} -1432.83 q^{77} -64.7316 q^{78} -550.939 q^{79} -910.101 q^{81} -0.597533 q^{82} +1195.87 q^{83} -1406.98 q^{84} +139.599 q^{86} +235.240 q^{87} -254.496 q^{88} -1029.01 q^{89} +922.808 q^{91} -549.323 q^{92} -567.101 q^{93} +39.8152 q^{94} -375.647 q^{96} -367.762 q^{97} -146.255 q^{98} -627.800 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 9 q^{2} - 14 q^{3} + 99 q^{4} + 9 q^{6} - 40 q^{7} - 132 q^{8} + 236 q^{9}+O(q^{10}) \) 20 * q - 9 * q^2 - 14 * q^3 + 99 * q^4 + 9 * q^6 - 40 * q^7 - 132 * q^8 + 236 * q^9	\( 20 q - 9 q^{2} - 14 q^{3} + 99 q^{4} + 9 q^{6} - 40 q^{7} - 132 q^{8} + 236 q^{9} + 62 q^{11} - 160 q^{12} - 232 q^{13} + 56 q^{14} + 387 q^{16} - 314 q^{17} - 224 q^{18} + 54 q^{19} + 58 q^{21} + 123 q^{22} - 344 q^{23} + 419 q^{24} - 387 q^{26} - 326 q^{27} - 786 q^{28} + 748 q^{29} - 18 q^{31} - 345 q^{32} - 746 q^{33} - 142 q^{34} + 90 q^{36} - 858 q^{37} - 723 q^{38} + 210 q^{39} + 386 q^{41} + 237 q^{42} - 1210 q^{43} + 1105 q^{44} - 57 q^{46} - 320 q^{47} - 2280 q^{48} + 1576 q^{49} - 350 q^{51} - 780 q^{52} - 2066 q^{53} - 536 q^{54} + 938 q^{56} - 710 q^{57} - 1852 q^{58} + 1198 q^{59} + 284 q^{61} - 2444 q^{62} - 732 q^{63} + 1118 q^{64} - 219 q^{66} - 976 q^{67} - 2904 q^{68} + 1026 q^{69} + 1420 q^{71} - 3374 q^{72} - 4310 q^{73} + 955 q^{74} + 740 q^{76} - 5196 q^{77} - 61 q^{78} - 340 q^{79} + 2556 q^{81} - 1191 q^{82} + 354 q^{83} - 1955 q^{84} + 1248 q^{86} - 3392 q^{87} - 135 q^{88} - 1446 q^{89} - 240 q^{91} - 4114 q^{92} + 1066 q^{93} - 3985 q^{94} - 2145 q^{96} - 3282 q^{97} + 4708 q^{98} - 6506 q^{99}+O(q^{100}) \) 20 * q - 9 * q^2 - 14 * q^3 + 99 * q^4 + 9 * q^6 - 40 * q^7 - 132 * q^8 + 236 * q^9 + 62 * q^11 - 160 * q^12 - 232 * q^13 + 56 * q^14 + 387 * q^16 - 314 * q^17 - 224 * q^18 + 54 * q^19 + 58 * q^21 + 123 * q^22 - 344 * q^23 + 419 * q^24 - 387 * q^26 - 326 * q^27 - 786 * q^28 + 748 * q^29 - 18 * q^31 - 345 * q^32 - 746 * q^33 - 142 * q^34 + 90 * q^36 - 858 * q^37 - 723 * q^38 + 210 * q^39 + 386 * q^41 + 237 * q^42 - 1210 * q^43 + 1105 * q^44 - 57 * q^46 - 320 * q^47 - 2280 * q^48 + 1576 * q^49 - 350 * q^51 - 780 * q^52 - 2066 * q^53 - 536 * q^54 + 938 * q^56 - 710 * q^57 - 1852 * q^58 + 1198 * q^59 + 284 * q^61 - 2444 * q^62 - 732 * q^63 + 1118 * q^64 - 219 * q^66 - 976 * q^67 - 2904 * q^68 + 1026 * q^69 + 1420 * q^71 - 3374 * q^72 - 4310 * q^73 + 955 * q^74 + 740 * q^76 - 5196 * q^77 - 61 * q^78 - 340 * q^79 + 2556 * q^81 - 1191 * q^82 + 354 * q^83 - 1955 * q^84 + 1248 * q^86 - 3392 * q^87 - 135 * q^88 - 1446 * q^89 - 240 * q^91 - 4114 * q^92 + 1066 * q^93 - 3985 * q^94 - 2145 * q^96 - 3282 * q^97 + 4708 * q^98 - 6506 * q^99

Introduction

L-functions

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