LMFDB - Embedded newform 2303.4.a.h.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2303,4,Mod(1,2303)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2303, 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("2303.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2303 = 7^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2303.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:	$135.881398743$
Analytic rank:	$0$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	2303.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.77029 q^{2} +0.853932 q^{3} +6.21511 q^{4} -1.45940 q^{5} -3.21958 q^{6} +6.72955 q^{8} -26.2708 q^{9} +O(q^{10})$	\(q-3.77029 q^{2} +0.853932 q^{3} +6.21511 q^{4} -1.45940 q^{5} -3.21958 q^{6} +6.72955 q^{8} -26.2708 q^{9} +5.50238 q^{10} +47.6033 q^{11} +5.30729 q^{12} +57.4768 q^{13} -1.24623 q^{15} -75.0933 q^{16} +123.083 q^{17} +99.0486 q^{18} -139.724 q^{19} -9.07036 q^{20} -179.478 q^{22} +64.5635 q^{23} +5.74658 q^{24} -122.870 q^{25} -216.704 q^{26} -45.4897 q^{27} +217.903 q^{29} +4.69866 q^{30} +25.7417 q^{31} +229.287 q^{32} +40.6500 q^{33} -464.057 q^{34} -163.276 q^{36} +232.129 q^{37} +526.802 q^{38} +49.0813 q^{39} -9.82114 q^{40} +458.304 q^{41} +211.144 q^{43} +295.860 q^{44} +38.3397 q^{45} -243.423 q^{46} +47.0000 q^{47} -64.1246 q^{48} +463.256 q^{50} +105.104 q^{51} +357.224 q^{52} +99.6033 q^{53} +171.509 q^{54} -69.4724 q^{55} -119.315 q^{57} -821.558 q^{58} +69.8931 q^{59} -7.74548 q^{60} -230.922 q^{61} -97.0538 q^{62} -263.734 q^{64} -83.8818 q^{65} -153.262 q^{66} -1025.46 q^{67} +764.972 q^{68} +55.1329 q^{69} -81.9115 q^{71} -176.791 q^{72} -221.056 q^{73} -875.196 q^{74} -104.923 q^{75} -868.403 q^{76} -185.051 q^{78} +171.890 q^{79} +109.591 q^{80} +670.466 q^{81} -1727.94 q^{82} +111.310 q^{83} -179.627 q^{85} -796.077 q^{86} +186.074 q^{87} +320.349 q^{88} +467.622 q^{89} -144.552 q^{90} +401.270 q^{92} +21.9817 q^{93} -177.204 q^{94} +203.914 q^{95} +195.796 q^{96} -860.280 q^{97} -1250.58 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9}+O(q^{10}) $ 35 * q + 5 * q^2 + 12 * q^3 + 139 * q^4 + 20 * q^5 + 24 * q^6 + 39 * q^8 + 303 * q^9	\( 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9} + 100 q^{10} + 40 q^{11} + 144 q^{12} + 328 q^{13} + 20 q^{15} + 643 q^{16} + 152 q^{17} + 51 q^{18} + 266 q^{19} + 1064 q^{20} - 168 q^{22} - 134 q^{23} + 288 q^{24} + 1137 q^{25} + 156 q^{26} + 672 q^{27} + 248 q^{29} - 216 q^{30} + 276 q^{31} + 347 q^{32} + 1056 q^{33} + 908 q^{34} + 909 q^{36} - 418 q^{37} + 164 q^{38} - 548 q^{39} + 1200 q^{40} + 918 q^{41} + 608 q^{43} + 1288 q^{44} + 876 q^{45} - 972 q^{46} + 1645 q^{47} + 1252 q^{48} - 367 q^{50} - 464 q^{51} + 3798 q^{52} - 218 q^{53} - 744 q^{54} + 1004 q^{55} - 436 q^{57} - 1270 q^{58} + 3760 q^{59} - 424 q^{60} + 956 q^{61} + 84 q^{62} + 2189 q^{64} - 596 q^{65} + 5500 q^{66} - 476 q^{67} + 256 q^{68} + 444 q^{69} + 852 q^{71} - 883 q^{72} + 6250 q^{73} + 1366 q^{74} - 2568 q^{75} + 1742 q^{76} - 1460 q^{78} + 632 q^{79} + 10124 q^{80} + 1267 q^{81} + 792 q^{82} + 796 q^{83} - 1228 q^{85} - 2864 q^{86} + 8360 q^{87} - 50 q^{88} + 908 q^{89} - 1858 q^{90} + 1696 q^{92} + 644 q^{93} + 235 q^{94} + 1320 q^{95} + 2688 q^{96} + 6184 q^{97} - 1812 q^{99}+O(q^{100}) \) 35 * q + 5 * q^2 + 12 * q^3 + 139 * q^4 + 20 * q^5 + 24 * q^6 + 39 * q^8 + 303 * q^9 + 100 * q^10 + 40 * q^11 + 144 * q^12 + 328 * q^13 + 20 * q^15 + 643 * q^16 + 152 * q^17 + 51 * q^18 + 266 * q^19 + 1064 * q^20 - 168 * q^22 - 134 * q^23 + 288 * q^24 + 1137 * q^25 + 156 * q^26 + 672 * q^27 + 248 * q^29 - 216 * q^30 + 276 * q^31 + 347 * q^32 + 1056 * q^33 + 908 * q^34 + 909 * q^36 - 418 * q^37 + 164 * q^38 - 548 * q^39 + 1200 * q^40 + 918 * q^41 + 608 * q^43 + 1288 * q^44 + 876 * q^45 - 972 * q^46 + 1645 * q^47 + 1252 * q^48 - 367 * q^50 - 464 * q^51 + 3798 * q^52 - 218 * q^53 - 744 * q^54 + 1004 * q^55 - 436 * q^57 - 1270 * q^58 + 3760 * q^59 - 424 * q^60 + 956 * q^61 + 84 * q^62 + 2189 * q^64 - 596 * q^65 + 5500 * q^66 - 476 * q^67 + 256 * q^68 + 444 * q^69 + 852 * q^71 - 883 * q^72 + 6250 * q^73 + 1366 * q^74 - 2568 * q^75 + 1742 * q^76 - 1460 * q^78 + 632 * q^79 + 10124 * q^80 + 1267 * q^81 + 792 * q^82 + 796 * q^83 - 1228 * q^85 - 2864 * q^86 + 8360 * q^87 - 50 * q^88 + 908 * q^89 - 1858 * q^90 + 1696 * q^92 + 644 * q^93 + 235 * q^94 + 1320 * q^95 + 2688 * q^96 + 6184 * q^97 - 1812 * 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 $

$2$	−3.77029	−1.33300	−0.666500	−	0.745505i	$-0.732208\pi$
$2$	−3.77029	−1.33300	−0.666500	+	0.745505i	$0.732208\pi$
$3$	0.853932	0.164339	0.0821697	−	0.996618i	$-0.473815\pi$
$3$	0.853932	0.164339	0.0821697	+	0.996618i	$0.473815\pi$
$4$	6.21511	0.776889
$5$	−1.45940	−0.130533	−0.0652666	−	0.997868i	$-0.520790\pi$
$5$	−1.45940	−0.130533	−0.0652666	+	0.997868i	$0.520790\pi$
$6$	−3.21958	−0.219064
$7$	0	0
$7$	0	0
$8$	6.72955	0.297407
$9$	−26.2708	−0.972993
$10$	5.50238	0.174001
$11$	47.6033	1.30481	0.652406	−	0.757870i	$-0.273760\pi$
$11$	47.6033	1.30481	0.652406	+	0.757870i	$0.273760\pi$
$12$	5.30729	0.127673
$13$	57.4768	1.22624	0.613122	−	0.789988i	$-0.289913\pi$
$13$	57.4768	1.22624	0.613122	+	0.789988i	$0.289913\pi$
$14$	0	0
$15$	−1.24623	−0.0214517
$16$	−75.0933	−1.17333
$17$	123.083	1.75599	0.877997	−	0.478666i	$-0.158880\pi$
$17$	123.083	1.75599	0.877997	+	0.478666i	$0.158880\pi$
$18$	99.0486	1.29700
$19$	−139.724	−1.68710	−0.843552	−	0.537048i	$-0.819539\pi$
$19$	−139.724	−1.68710	−0.843552	+	0.537048i	$0.819539\pi$
$20$	−9.07036	−0.101410
$21$	0	0
$22$	−179.478	−1.73931
$23$	64.5635	0.585323	0.292661	−	0.956216i	$-0.405459\pi$
$23$	64.5635	0.585323	0.292661	+	0.956216i	$0.405459\pi$
$24$	5.74658	0.0488757
$25$	−122.870	−0.982961
$26$	−216.704	−1.63458
$27$	−45.4897	−0.324240
$28$	0	0
$29$	217.903	1.39530	0.697648	−	0.716441i	$-0.254230\pi$
$29$	217.903	1.39530	0.697648	+	0.716441i	$0.254230\pi$
$30$	4.69866	0.0285952
$31$	25.7417	0.149140	0.0745701	−	0.997216i	$-0.476242\pi$
$31$	25.7417	0.149140	0.0745701	+	0.997216i	$0.476242\pi$
$32$	229.287	1.26665
$33$	40.6500	0.214432
$34$	−464.057	−2.34074
$35$	0	0
$36$	−163.276	−0.755907
$37$	232.129	1.03140	0.515700	−	0.856769i	$-0.327532\pi$
$37$	232.129	1.03140	0.515700	+	0.856769i	$0.327532\pi$
$38$	526.802	2.24891
$39$	49.0813	0.201520
$40$	−9.82114	−0.0388215
$41$	458.304	1.74573	0.872867	−	0.487958i	$-0.162258\pi$
$41$	458.304	1.74573	0.872867	+	0.487958i	$0.162258\pi$
$42$	0	0
$43$	211.144	0.748819	0.374410	−	0.927263i	$-0.377845\pi$
$43$	211.144	0.748819	0.374410	+	0.927263i	$0.377845\pi$
$44$	295.860	1.01369
$45$	38.3397	0.127008
$46$	−243.423	−0.780236
$47$	47.0000	0.145865
$47$	47.0000	0.145865
$48$	−64.1246	−0.192825
$49$	0	0
$50$	463.256	1.31029
$51$	105.104	0.288579
$52$	357.224	0.952656
$53$	99.6033	0.258143	0.129071	−	0.991635i	$-0.458800\pi$
$53$	99.6033	0.258143	0.129071	+	0.991635i	$0.458800\pi$
$54$	171.509	0.432212
$55$	−69.4724	−0.170321
$56$	0	0
$57$	−119.315	−0.277258
$58$	−821.558	−1.85993
$59$	69.8931	0.154225	0.0771127	−	0.997022i	$-0.475430\pi$
$59$	69.8931	0.154225	0.0771127	+	0.997022i	$0.475430\pi$
$60$	−7.74548	−0.0166656
$61$	−230.922	−0.484697	−0.242349	−	0.970189i	$-0.577918\pi$
$61$	−230.922	−0.484697	−0.242349	+	0.970189i	$0.577918\pi$
$62$	−97.0538	−0.198804
$63$	0	0
$64$	−263.734	−0.515106
$65$	−83.8818	−0.160066
$66$	−153.262	−0.285838
$67$	−1025.46	−1.86984	−0.934922	−	0.354852i	$-0.884531\pi$
$67$	−1025.46	−1.86984	−0.934922	+	0.354852i	$0.884531\pi$
$68$	764.972	1.36421
$69$	55.1329	0.0961916
$70$	0	0
$71$	−81.9115	−0.136917	−0.0684585	−	0.997654i	$-0.521808\pi$
$71$	−81.9115	−0.136917	−0.0684585	+	0.997654i	$0.521808\pi$
$72$	−176.791	−0.289375
$73$	−221.056	−0.354419	−0.177210	−	0.984173i	$-0.556707\pi$
$73$	−221.056	−0.354419	−0.177210	+	0.984173i	$0.556707\pi$
$74$	−875.196	−1.37486
$75$	−104.923	−0.161539
$76$	−868.403	−1.31069
$77$	0	0
$78$	−185.051	−0.268627
$79$	171.890	0.244799	0.122400	−	0.992481i	$-0.460941\pi$
$79$	171.890	0.244799	0.122400	+	0.992481i	$0.460941\pi$
$80$	109.591	0.153159
$81$	670.466	0.919707
$82$	−1727.94	−2.32706
$83$	111.310	0.147203	0.0736017	−	0.997288i	$-0.476551\pi$
$83$	111.310	0.147203	0.0736017	+	0.997288i	$0.476551\pi$
$84$	0	0
$85$	−179.627	−0.229215
$86$	−796.077	−0.998176
$87$	186.074	0.229302
$88$	320.349	0.388060
$89$	467.622	0.556942	0.278471	−	0.960445i	$-0.410172\pi$
$89$	467.622	0.556942	0.278471	+	0.960445i	$0.410172\pi$
$90$	−144.552	−0.169301
$91$	0	0
$92$	401.270	0.454731
$93$	21.9817	0.0245096
$94$	−177.204	−0.194438
$95$	203.914	0.220223
$96$	195.796	0.208160
$97$	−860.280	−0.900497	−0.450248	−	0.892903i	$-0.648665\pi$
$97$	−860.280	−0.900497	−0.450248	+	0.892903i	$0.648665\pi$
$98$	0	0
$99$	−1250.58	−1.26957
$100$	−763.652	−0.763652
$101$	964.735	0.950443	0.475221	−	0.879866i	$-0.342368\pi$
$101$	964.735	0.950443	0.475221	+	0.879866i	$0.342368\pi$
$102$	−396.274	−0.384676
$103$	270.787	0.259043	0.129522	−	0.991577i	$-0.458656\pi$
$103$	270.787	0.259043	0.129522	+	0.991577i	$0.458656\pi$
$104$	386.793	0.364694
$105$	0	0
$106$	−375.534	−0.344104
$107$	112.756	0.101874	0.0509370	−	0.998702i	$-0.483779\pi$
$107$	112.756	0.101874	0.0509370	+	0.998702i	$0.483779\pi$
$108$	−282.723	−0.251899
$109$	1921.53	1.68852	0.844261	−	0.535932i	$-0.180040\pi$
$109$	1921.53	1.68852	0.844261	+	0.535932i	$0.180040\pi$
$110$	261.931	0.227038
$111$	198.223	0.169500
$112$	0	0
$113$	1216.31	1.01258	0.506289	−	0.862364i	$-0.331017\pi$
$113$	1216.31	1.01258	0.506289	+	0.862364i	$0.331017\pi$
$114$	449.853	0.369584
$115$	−94.2243	−0.0764040
$116$	1354.29	1.08399
$117$	−1509.96	−1.19313
$118$	−263.517	−0.205583
$119$	0	0
$120$	−8.38659	−0.00637989
$121$	935.070	0.702532
$122$	870.643	0.646101
$123$	391.361	0.286893
$124$	159.988	0.115865
$125$	361.743	0.258842
$126$	0	0
$127$	−1153.79	−0.806159	−0.403079	−	0.915165i	$-0.632060\pi$
$127$	−1153.79	−0.806159	−0.403079	+	0.915165i	$0.632060\pi$
$128$	−839.943	−0.580010
$129$	180.303	0.123060
$130$	316.259	0.213367
$131$	−1279.18	−0.853146	−0.426573	−	0.904453i	$-0.640279\pi$
$131$	−1279.18	−0.853146	−0.426573	+	0.904453i	$0.640279\pi$
$132$	252.644	0.166590
$133$	0	0
$134$	3866.28	2.49250
$135$	66.3878	0.0423241
$136$	828.290	0.522245
$137$	−2260.00	−1.40938	−0.704688	−	0.709517i	$-0.748913\pi$
$137$	−2260.00	−1.40938	−0.704688	+	0.709517i	$0.748913\pi$
$138$	−207.867	−0.128223
$139$	−3115.11	−1.90087	−0.950433	−	0.310930i	$-0.899359\pi$
$139$	−3115.11	−1.90087	−0.950433	+	0.310930i	$0.899359\pi$
$140$	0	0
$141$	40.1348	0.0239714
$142$	308.830	0.182510
$143$	2736.08	1.60002
$144$	1972.76	1.14164
$145$	−318.009	−0.182132
$146$	833.445	0.472441
$147$	0	0
$148$	1442.71	0.801284
$149$	1786.58	0.982297	0.491149	−	0.871076i	$-0.336577\pi$
$149$	1786.58	0.982297	0.491149	+	0.871076i	$0.336577\pi$
$150$	395.590	0.215332
$151$	−940.930	−0.507098	−0.253549	−	0.967323i	$-0.581598\pi$
$151$	−940.930	−0.507098	−0.253549	+	0.967323i	$0.581598\pi$
$152$	−940.282	−0.501756
$153$	−3233.48	−1.70857
$154$	0	0
$155$	−37.5676	−0.0194677
$156$	305.046	0.156559
$157$	2744.47	1.39511	0.697556	−	0.716530i	$-0.254271\pi$
$157$	2744.47	1.39511	0.697556	+	0.716530i	$0.254271\pi$
$158$	−648.075	−0.326317
$159$	85.0545	0.0424230
$160$	−334.623	−0.165339
$161$	0	0
$162$	−2527.86	−1.22597
$163$	−1941.40	−0.932896	−0.466448	−	0.884549i	$-0.654466\pi$
$163$	−1941.40	−0.932896	−0.466448	+	0.884549i	$0.654466\pi$
$164$	2848.41	1.35624
$165$	−59.3247	−0.0279904
$166$	−419.672	−0.196222
$167$	−1127.38	−0.522390	−0.261195	−	0.965286i	$-0.584116\pi$
$167$	−1127.38	−0.522390	−0.261195	+	0.965286i	$0.584116\pi$
$168$	0	0
$169$	1106.58	0.503677
$170$	677.247	0.305544
$171$	3670.67	1.64154
$172$	1312.29	0.581749
$173$	757.241	0.332786	0.166393	−	0.986060i	$-0.446788\pi$
$173$	757.241	0.332786	0.166393	+	0.986060i	$0.446788\pi$
$174$	−701.555	−0.305660
$175$	0	0
$176$	−3574.68	−1.53098
$177$	59.6839	0.0253453
$178$	−1763.07	−0.742404
$179$	−2841.28	−1.18641	−0.593205	−	0.805052i	$-0.702138\pi$
$179$	−2841.28	−1.18641	−0.593205	+	0.805052i	$0.702138\pi$
$180$	238.286	0.0986709
$181$	−2685.08	−1.10265	−0.551327	−	0.834289i	$-0.685878\pi$
$181$	−2685.08	−1.10265	−0.551327	+	0.834289i	$0.685878\pi$
$182$	0	0
$183$	−197.192	−0.0796548
$184$	434.484	0.174079
$185$	−338.771	−0.134632
$186$	−82.8774	−0.0326713
$187$	5859.13	2.29124
$188$	292.110	0.113321
$189$	0	0
$190$	−768.817	−0.293557
$191$	3064.93	1.16110	0.580552	−	0.814223i	$-0.302837\pi$
$191$	3064.93	1.16110	0.580552	+	0.814223i	$0.302837\pi$
$192$	−225.211	−0.0846521
$193$	801.213	0.298822	0.149411	−	0.988775i	$-0.452262\pi$
$193$	801.213	0.298822	0.149411	+	0.988775i	$0.452262\pi$
$194$	3243.51	1.20036
$195$	−71.6294	−0.0263051
$196$	0	0
$197$	946.372	0.342265	0.171133	−	0.985248i	$-0.445257\pi$
$197$	946.372	0.342265	0.171133	+	0.985248i	$0.445257\pi$
$198$	4715.04	1.69234
$199$	−3901.14	−1.38967	−0.694835	−	0.719169i	$-0.744522\pi$
$199$	−3901.14	−1.38967	−0.694835	+	0.719169i	$0.744522\pi$
$200$	−826.861	−0.292340
$201$	−875.672	−0.307289
$202$	−3637.33	−1.26694
$203$	0	0
$204$	653.234	0.224194
$205$	−668.851	−0.227876
$206$	−1020.95	−0.345305
$207$	−1696.14	−0.569515
$208$	−4316.12	−1.43879
$209$	−6651.33	−2.20135
$210$	0	0
$211$	1367.57	0.446196	0.223098	−	0.974796i	$-0.428383\pi$
$211$	1367.57	0.446196	0.223098	+	0.974796i	$0.428383\pi$
$212$	619.046	0.200548
$213$	−69.9468	−0.0225008
$214$	−425.122	−0.135798
$215$	−308.145	−0.0977457
$216$	−306.125	−0.0964313
$217$	0	0
$218$	−7244.72	−2.25080
$219$	−188.767	−0.0582450
$220$	−431.779	−0.132321
$221$	7074.38	2.15328
$222$	−747.358	−0.225943
$223$	3047.59	0.915166	0.457583	−	0.889167i	$-0.348715\pi$
$223$	3047.59	0.915166	0.457583	+	0.889167i	$0.348715\pi$
$224$	0	0
$225$	3227.90	0.956414
$226$	−4585.86	−1.34977
$227$	−4071.42	−1.19044	−0.595220	−	0.803563i	$-0.702935\pi$
$227$	−4071.42	−1.19044	−0.595220	+	0.803563i	$0.702935\pi$
$228$	−741.557	−0.215398
$229$	−2949.03	−0.850992	−0.425496	−	0.904960i	$-0.639900\pi$
$229$	−2949.03	−0.850992	−0.425496	+	0.904960i	$0.639900\pi$
$230$	355.253	0.101847
$231$	0	0
$232$	1466.39	0.414971
$233$	482.840	0.135759	0.0678796	−	0.997694i	$-0.478377\pi$
$233$	482.840	0.135759	0.0678796	+	0.997694i	$0.478377\pi$
$234$	5692.99	1.59044
$235$	−68.5920	−0.0190402
$236$	434.393	0.119816
$237$	146.782	0.0402301
$238$	0	0
$239$	956.110	0.258768	0.129384	−	0.991595i	$-0.458700\pi$
$239$	956.110	0.258768	0.129384	+	0.991595i	$0.458700\pi$
$240$	93.5837	0.0251700
$241$	6307.25	1.68583	0.842916	−	0.538045i	$-0.180837\pi$
$241$	6307.25	1.68583	0.842916	+	0.538045i	$0.180837\pi$
$242$	−3525.49	−0.936475
$243$	1800.75	0.475384
$244$	−1435.21	−0.376556
$245$	0	0
$246$	−1475.55	−0.382428
$247$	−8030.90	−2.06880
$248$	173.230	0.0443553
$249$	95.0514	0.0241913
$250$	−1363.88	−0.345036
$251$	−346.427	−0.0871167	−0.0435583	−	0.999051i	$-0.513869\pi$
$251$	−346.427	−0.0871167	−0.0435583	+	0.999051i	$0.513869\pi$
$252$	0	0
$253$	3073.43	0.763736
$254$	4350.12	1.07461
$255$	−153.389	−0.0376691
$256$	5276.71	1.28826
$257$	−7108.32	−1.72531	−0.862655	−	0.505793i	$-0.831200\pi$
$257$	−7108.32	−1.72531	−0.862655	+	0.505793i	$0.831200\pi$
$258$	−679.796	−0.164040
$259$	0	0
$260$	−521.335	−0.124353
$261$	−5724.49	−1.35761
$262$	4822.87	1.13724
$263$	−6952.34	−1.63004	−0.815018	−	0.579436i	$-0.803273\pi$
$263$	−6952.34	−1.63004	−0.815018	+	0.579436i	$0.803273\pi$
$264$	273.556	0.0637735
$265$	−145.362	−0.0336962
$266$	0	0
$267$	399.318	0.0915276
$268$	−6373.33	−1.45266
$269$	7228.04	1.63830	0.819148	−	0.573582i	$-0.194447\pi$
$269$	7228.04	1.63830	0.819148	+	0.573582i	$0.194447\pi$
$270$	−250.302	−0.0564180
$271$	4538.67	1.01736	0.508681	−	0.860955i	$-0.330133\pi$
$271$	4538.67	1.01736	0.508681	+	0.860955i	$0.330133\pi$
$272$	−9242.67	−2.06036
$273$	0	0
$274$	8520.85	1.87870
$275$	−5849.02	−1.28258
$276$	342.657	0.0747302
$277$	−815.102	−0.176804	−0.0884021	−	0.996085i	$-0.528176\pi$
$277$	−815.102	−0.176804	−0.0884021	+	0.996085i	$0.528176\pi$
$278$	11744.9	2.53385
$279$	−676.255	−0.145112
$280$	0	0
$281$	2824.21	0.599567	0.299784	−	0.954007i	$-0.403086\pi$
$281$	2824.21	0.599567	0.299784	+	0.954007i	$0.403086\pi$
$282$	−151.320	−0.0319538
$283$	−7149.98	−1.50184	−0.750922	−	0.660391i	$-0.770391\pi$
$283$	−7149.98	−1.50184	−0.750922	+	0.660391i	$0.770391\pi$
$284$	−509.089	−0.106369
$285$	174.129	0.0361913
$286$	−10315.8	−2.13282
$287$	0	0
$288$	−6023.56	−1.23244
$289$	10236.3	2.08352
$290$	1198.99	0.242782
$291$	−734.621	−0.147987
$292$	−1373.89	−0.275344
$293$	1310.74	0.261345	0.130673	−	0.991426i	$-0.458286\pi$
$293$	1310.74	0.261345	0.130673	+	0.991426i	$0.458286\pi$
$294$	0	0
$295$	−102.002	−0.0201315
$296$	1562.13	0.306746
$297$	−2165.46	−0.423072
$298$	−6735.93	−1.30940
$299$	3710.90	0.717749
$300$	−652.107	−0.125498
$301$	0	0
$302$	3547.58	0.675961
$303$	823.818	0.156195
$304$	10492.4	1.97953
$305$	337.008	0.0632690
$306$	12191.2	2.27752
$307$	−373.688	−0.0694706	−0.0347353	−	0.999397i	$-0.511059\pi$
$307$	−373.688	−0.0694706	−0.0347353	+	0.999397i	$0.511059\pi$
$308$	0	0
$309$	231.234	0.0425710
$310$	141.641	0.0259505
$311$	6419.45	1.17046	0.585231	−	0.810867i	$-0.301004\pi$
$311$	6419.45	1.17046	0.585231	+	0.810867i	$0.301004\pi$
$312$	330.295	0.0599335
$313$	5448.69	0.983957	0.491978	−	0.870607i	$-0.336274\pi$
$313$	5448.69	0.983957	0.491978	+	0.870607i	$0.336274\pi$
$314$	−10347.5	−1.85968
$315$	0	0
$316$	1068.32	0.190182
$317$	3604.16	0.638579	0.319290	−	0.947657i	$-0.396556\pi$
$317$	3604.16	0.638579	0.319290	+	0.947657i	$0.396556\pi$
$318$	−320.680	−0.0565499
$319$	10372.9	1.82060
$320$	384.895	0.0672383
$321$	96.2858	0.0167419
$322$	0	0
$323$	−17197.6	−2.96254
$324$	4167.02	0.714510
$325$	−7062.18	−1.20535
$326$	7319.64	1.24355
$327$	1640.85	0.277491
$328$	3084.18	0.519194
$329$	0	0
$330$	223.672	0.0373113
$331$	−3042.76	−0.505272	−0.252636	−	0.967561i	$-0.581297\pi$
$331$	−3042.76	−0.505272	−0.252636	+	0.967561i	$0.581297\pi$
$332$	691.806	0.114361
$333$	−6098.22	−1.00355
$334$	4250.54	0.696345
$335$	1496.56	0.244077
$336$	0	0
$337$	−5469.88	−0.884165	−0.442082	−	0.896974i	$-0.645760\pi$
$337$	−5469.88	−0.884165	−0.442082	+	0.896974i	$0.645760\pi$
$338$	−4172.12	−0.671401
$339$	1038.65	0.166406
$340$	−1116.40	−0.178075
$341$	1225.39	0.194600
$342$	−13839.5	−2.18817
$343$	0	0
$344$	1420.91	0.222704
$345$	−80.4612	−0.0125562
$346$	−2855.02	−0.443604
$347$	5174.34	0.800499	0.400250	−	0.916406i	$-0.368923\pi$
$347$	5174.34	0.800499	0.400250	+	0.916406i	$0.368923\pi$
$348$	1156.47	0.178142
$349$	6221.32	0.954210	0.477105	−	0.878846i	$-0.341686\pi$
$349$	6221.32	0.954210	0.477105	+	0.878846i	$0.341686\pi$
$350$	0	0
$351$	−2614.60	−0.397598
$352$	10914.8	1.65273
$353$	−4386.49	−0.661386	−0.330693	−	0.943738i	$-0.607282\pi$
$353$	−4386.49	−0.661386	−0.330693	+	0.943738i	$0.607282\pi$
$354$	−225.026	−0.0337853
$355$	119.542	0.0178722
$356$	2906.33	0.432682
$357$	0	0
$358$	10712.5	1.58148
$359$	906.201	0.133224	0.0666121	−	0.997779i	$-0.478781\pi$
$359$	906.201	0.133224	0.0666121	+	0.997779i	$0.478781\pi$
$360$	258.009	0.0377730
$361$	12663.9	1.84632
$362$	10123.5	1.46984
$363$	798.486	0.115454
$364$	0	0
$365$	322.610	0.0462634
$366$	743.471	0.106180
$367$	3843.34	0.546650	0.273325	−	0.961922i	$-0.411877\pi$
$367$	3843.34	0.546650	0.273325	+	0.961922i	$0.411877\pi$
$368$	−4848.29	−0.686778
$369$	−12040.0	−1.69859
$370$	1277.26	0.179464
$371$	0	0
$372$	136.619	0.0190412
$373$	2350.31	0.326258	0.163129	−	0.986605i	$-0.447841\pi$
$373$	2350.31	0.326258	0.163129	+	0.986605i	$0.447841\pi$
$374$	−22090.6	−3.05422
$375$	308.904	0.0425379
$376$	316.289	0.0433813
$377$	12524.4	1.71097
$378$	0	0
$379$	−2204.69	−0.298806	−0.149403	−	0.988776i	$-0.547735\pi$
$379$	−2204.69	−0.298806	−0.149403	+	0.988776i	$0.547735\pi$
$380$	1267.35	0.171089
$381$	−985.257	−0.132484
$382$	−11555.7	−1.54775
$383$	10192.4	1.35981	0.679906	−	0.733299i	$-0.262021\pi$
$383$	10192.4	1.35981	0.679906	+	0.733299i	$0.262021\pi$
$384$	−717.255	−0.0953184
$385$	0	0
$386$	−3020.81	−0.398329
$387$	−5546.93	−0.728596
$388$	−5346.74	−0.699586
$389$	−9213.87	−1.20093	−0.600465	−	0.799651i	$-0.705018\pi$
$389$	−9213.87	−1.20093	−0.600465	+	0.799651i	$0.705018\pi$
$390$	270.064	0.0350647
$391$	7946.64	1.02782
$392$	0	0
$393$	−1092.33	−0.140205
$394$	−3568.10	−0.456239
$395$	−250.857	−0.0319544
$396$	−7772.47	−0.986316
$397$	5068.27	0.640729	0.320365	−	0.947294i	$-0.396195\pi$
$397$	5068.27	0.640729	0.320365	+	0.947294i	$0.396195\pi$
$398$	14708.4	1.85243
$399$	0	0
$400$	9226.72	1.15334
$401$	7063.64	0.879655	0.439827	−	0.898082i	$-0.355040\pi$
$401$	7063.64	0.879655	0.439827	+	0.898082i	$0.355040\pi$
$402$	3301.54	0.409616
$403$	1479.55	0.182882
$404$	5995.94	0.738389
$405$	−978.482	−0.120052
$406$	0	0
$407$	11050.1	1.34578
$408$	707.304	0.0858254
$409$	10632.4	1.28542	0.642711	−	0.766109i	$-0.277810\pi$
$409$	10632.4	1.28542	0.642711	+	0.766109i	$0.277810\pi$
$410$	2521.77	0.303759
$411$	−1929.88	−0.231616
$412$	1682.97	0.201248
$413$	0	0
$414$	6394.93	0.759163
$415$	−162.447	−0.0192149
$416$	13178.7	1.55322
$417$	−2660.09	−0.312387
$418$	25077.5	2.93440
$419$	5140.73	0.599382	0.299691	−	0.954036i	$-0.403116\pi$
$419$	5140.73	0.599382	0.299691	+	0.954036i	$0.403116\pi$
$420$	0	0
$421$	−16436.9	−1.90282	−0.951410	−	0.307927i	$-0.900365\pi$
$421$	−16436.9	−1.90282	−0.951410	+	0.307927i	$0.900365\pi$
$422$	−5156.13	−0.594779
$423$	−1234.73	−0.141926
$424$	670.286	0.0767735
$425$	−15123.2	−1.72607
$426$	263.720	0.0299936
$427$	0	0
$428$	700.790	0.0791447
$429$	2336.43	0.262946
$430$	1161.80	0.130295
$431$	−11008.1	−1.23026	−0.615128	−	0.788428i	$-0.710896\pi$
$431$	−11008.1	−1.23026	−0.615128	+	0.788428i	$0.710896\pi$
$432$	3415.97	0.380442
$433$	16438.2	1.82441	0.912204	−	0.409736i	$-0.134379\pi$
$433$	16438.2	1.82441	0.912204	+	0.409736i	$0.134379\pi$
$434$	0	0
$435$	−271.558	−0.0299315
$436$	11942.5	1.31179
$437$	−9021.10	−0.987501
$438$	711.705	0.0776406
$439$	−1336.03	−0.145251	−0.0726255	−	0.997359i	$-0.523138\pi$
$439$	−1336.03	−0.145251	−0.0726255	+	0.997359i	$0.523138\pi$
$440$	−467.518	−0.0506547
$441$	0	0
$442$	−26672.5	−2.87032
$443$	1429.11	0.153271	0.0766357	−	0.997059i	$-0.475582\pi$
$443$	1429.11	0.153271	0.0766357	+	0.997059i	$0.475582\pi$
$444$	1231.98	0.131682
$445$	−682.450	−0.0726994
$446$	−11490.3	−1.21992
$447$	1525.62	0.161430
$448$	0	0
$449$	7325.73	0.769984	0.384992	−	0.922920i	$-0.374204\pi$
$449$	7325.73	0.769984	0.384992	+	0.922920i	$0.374204\pi$
$450$	−12170.1	−1.27490
$451$	21816.8	2.27785
$452$	7559.53	0.786660
$453$	−803.490	−0.0833361
$454$	15350.5	1.58686
$455$	0	0
$456$	−802.938	−0.0824583
$457$	−2416.72	−0.247373	−0.123686	−	0.992321i	$-0.539472\pi$
$457$	−2416.72	−0.247373	−0.123686	+	0.992321i	$0.539472\pi$
$458$	11118.7	1.13437
$459$	−5598.98	−0.569364
$460$	−585.615	−0.0593574
$461$	7086.46	0.715942	0.357971	−	0.933733i	$-0.383469\pi$
$461$	7086.46	0.715942	0.357971	+	0.933733i	$0.383469\pi$
$462$	0	0
$463$	208.064	0.0208845	0.0104423	−	0.999945i	$-0.496676\pi$
$463$	208.064	0.0208845	0.0104423	+	0.999945i	$0.496676\pi$
$464$	−16363.1	−1.63715
$465$	−32.0802	−0.00319932
$466$	−1820.45	−0.180967
$467$	16314.0	1.61654	0.808270	−	0.588812i	$-0.200404\pi$
$467$	16314.0	1.61654	0.808270	+	0.588812i	$0.200404\pi$
$468$	−9384.57	−0.926927
$469$	0	0
$470$	258.612	0.0253806
$471$	2343.59	0.229272
$472$	470.349	0.0458677
$473$	10051.2	0.977068
$474$	−553.413	−0.0536268
$475$	17168.0	1.65836
$476$	0	0
$477$	−2616.66	−0.251171
$478$	−3604.81	−0.344938
$479$	16003.2	1.52653	0.763263	−	0.646088i	$-0.223596\pi$
$479$	16003.2	1.52653	0.763263	+	0.646088i	$0.223596\pi$
$480$	−285.745	−0.0271717
$481$	13342.0	1.26475
$482$	−23780.2	−2.24721
$483$	0	0
$484$	5811.56	0.545789
$485$	1255.50	0.117545
$486$	−6789.37	−0.633687
$487$	−728.171	−0.0677548	−0.0338774	−	0.999426i	$-0.510786\pi$
$487$	−728.171	−0.0677548	−0.0338774	+	0.999426i	$0.510786\pi$
$488$	−1554.00	−0.144152
$489$	−1657.82	−0.153311
$490$	0	0
$491$	1038.45	0.0954470	0.0477235	−	0.998861i	$-0.484803\pi$
$491$	1038.45	0.0954470	0.0477235	+	0.998861i	$0.484803\pi$
$492$	2432.35	0.222884
$493$	26820.1	2.45013
$494$	30278.9	2.75771
$495$	1825.10	0.165721
$496$	−1933.03	−0.174991
$497$	0	0
$498$	−358.372	−0.0322470
$499$	12881.3	1.15561	0.577803	−	0.816177i	$-0.303910\pi$
$499$	12881.3	1.15561	0.577803	+	0.816177i	$0.303910\pi$
$500$	2248.27	0.201092
$501$	−962.704	−0.0858492
$502$	1306.13	0.116127
$503$	17516.2	1.55270	0.776349	−	0.630304i	$-0.217070\pi$
$503$	17516.2	1.55270	0.776349	+	0.630304i	$0.217070\pi$
$504$	0	0
$505$	−1407.94	−0.124064
$506$	−11587.8	−1.01806
$507$	944.942	0.0827739
$508$	−7170.92	−0.626296
$509$	9936.14	0.865249	0.432624	−	0.901574i	$-0.357588\pi$
$509$	9936.14	0.865249	0.432624	+	0.901574i	$0.357588\pi$
$510$	578.323	0.0502129
$511$	0	0
$512$	−13175.2	−1.13724
$513$	6356.01	0.547027
$514$	26800.4	2.29984
$515$	−395.188	−0.0338137
$516$	1120.60	0.0956043
$517$	2237.35	0.190326
$518$	0	0
$519$	646.633	0.0546899
$520$	−564.487	−0.0476046
$521$	−16932.6	−1.42386	−0.711928	−	0.702252i	$-0.752178\pi$
$521$	−16932.6	−1.42386	−0.711928	+	0.702252i	$0.752178\pi$
$522$	21583.0	1.80970
$523$	5492.37	0.459206	0.229603	−	0.973284i	$-0.426257\pi$
$523$	5492.37	0.459206	0.229603	+	0.973284i	$0.426257\pi$
$524$	−7950.22	−0.662799
$525$	0	0
$526$	26212.3	2.17284
$527$	3168.35	0.261889
$528$	−3052.54	−0.251600
$529$	−7998.55	−0.657397
$530$	548.056	0.0449170
$531$	−1836.15	−0.150060
$532$	0	0
$533$	26341.8	2.14070
$534$	−1505.55	−0.122006
$535$	−164.556	−0.0132979
$536$	−6900.87	−0.556105
$537$	−2426.26	−0.194974
$538$	−27251.8	−2.18385
$539$	0	0
$540$	412.608	0.0328811
$541$	−4841.65	−0.384767	−0.192383	−	0.981320i	$-0.561622\pi$
$541$	−4841.65	−0.384767	−0.192383	+	0.981320i	$0.561622\pi$
$542$	−17112.1	−1.35614
$543$	−2292.88	−0.181209
$544$	28221.3	2.22422
$545$	−2804.28	−0.220408
$546$	0	0
$547$	−22807.5	−1.78278	−0.891389	−	0.453239i	$-0.850268\pi$
$547$	−22807.5	−1.78278	−0.891389	+	0.453239i	$0.850268\pi$
$548$	−14046.1	−1.09493
$549$	6066.50	0.471607
$550$	22052.5	1.70968
$551$	−30446.4	−2.35401
$552$	371.020	0.0286081
$553$	0	0
$554$	3073.17	0.235680
$555$	−289.287	−0.0221253
$556$	−19360.8	−1.47676
$557$	19236.6	1.46334	0.731669	−	0.681660i	$-0.238742\pi$
$557$	19236.6	1.46334	0.731669	+	0.681660i	$0.238742\pi$
$558$	2549.68	0.193435
$559$	12135.9	0.918236
$560$	0	0
$561$	5003.30	0.376541
$562$	−10648.1	−0.799223
$563$	−1341.06	−0.100389	−0.0501945	−	0.998739i	$-0.515984\pi$
$563$	−1341.06	−0.100389	−0.0501945	+	0.998739i	$0.515984\pi$
$564$	249.442	0.0186231
$565$	−1775.09	−0.132175
$566$	26957.5	2.00196
$567$	0	0
$568$	−551.227	−0.0407201
$569$	−14516.2	−1.06951	−0.534755	−	0.845007i	$-0.679596\pi$
$569$	−14516.2	−1.06951	−0.534755	+	0.845007i	$0.679596\pi$
$570$	−656.518	−0.0482430
$571$	−1891.36	−0.138618	−0.0693089	−	0.997595i	$-0.522079\pi$
$571$	−1891.36	−0.138618	−0.0693089	+	0.997595i	$0.522079\pi$
$572$	17005.0	1.24304
$573$	2617.25	0.190815
$574$	0	0
$575$	−7932.93	−0.575350
$576$	6928.50	0.501194
$577$	−11592.7	−0.836410	−0.418205	−	0.908353i	$-0.637341\pi$
$577$	−11592.7	−0.836410	−0.418205	+	0.908353i	$0.637341\pi$
$578$	−38593.9	−2.77733
$579$	684.182	0.0491082
$580$	−1976.46	−0.141497
$581$	0	0
$582$	2769.74	0.197267
$583$	4741.44	0.336828
$584$	−1487.61	−0.105407
$585$	2203.64	0.155743
$586$	−4941.86	−0.348373
$587$	5670.80	0.398738	0.199369	−	0.979925i	$-0.436111\pi$
$587$	5670.80	0.398738	0.199369	+	0.979925i	$0.436111\pi$
$588$	0	0
$589$	−3596.74	−0.251615
$590$	384.578	0.0268353
$591$	808.138	0.0562476
$592$	−17431.4	−1.21018
$593$	−19983.1	−1.38383	−0.691913	−	0.721981i	$-0.743232\pi$
$593$	−19983.1	−1.38383	−0.691913	+	0.721981i	$0.743232\pi$
$594$	8164.40	0.563955
$595$	0	0
$596$	11103.8	0.763136
$597$	−3331.31	−0.228377
$598$	−13991.2	−0.956760
$599$	2553.76	0.174197	0.0870983	−	0.996200i	$-0.472241\pi$
$599$	2553.76	0.174197	0.0870983	+	0.996200i	$0.472241\pi$
$600$	−706.083	−0.0480429
$601$	−10266.4	−0.696797	−0.348399	−	0.937346i	$-0.613274\pi$
$601$	−10266.4	−0.696797	−0.348399	+	0.937346i	$0.613274\pi$
$602$	0	0
$603$	26939.6	1.81935
$604$	−5847.98	−0.393959
$605$	−1364.65	−0.0917037
$606$	−3106.04	−0.208208
$607$	21075.7	1.40929	0.704643	−	0.709562i	$-0.251107\pi$
$607$	21075.7	1.40929	0.704643	+	0.709562i	$0.251107\pi$
$608$	−32037.0	−2.13696
$609$	0	0
$610$	−1270.62	−0.0843376
$611$	2701.41	0.178866
$612$	−20096.4	−1.32737
$613$	−27946.6	−1.84136	−0.920680	−	0.390318i	$-0.872365\pi$
$613$	−27946.6	−1.84136	−0.920680	+	0.390318i	$0.872365\pi$
$614$	1408.91	0.0926043
$615$	−571.154	−0.0374490
$616$	0	0
$617$	7593.47	0.495465	0.247732	−	0.968829i	$-0.420315\pi$
$617$	7593.47	0.495465	0.247732	+	0.968829i	$0.420315\pi$
$618$	−871.821	−0.0567472
$619$	16428.0	1.06671	0.533357	−	0.845890i	$-0.320930\pi$
$619$	16428.0	1.06671	0.533357	+	0.845890i	$0.320930\pi$
$620$	−233.487	−0.0151243
$621$	−2936.97	−0.189785
$622$	−24203.2	−1.56023
$623$	0	0
$624$	−3685.67	−0.236450
$625$	14830.8	0.949174
$626$	−20543.2	−1.31161
$627$	−5679.79	−0.361769
$628$	17057.2	1.08385
$629$	28571.1	1.81113
$630$	0	0
$631$	−18211.6	−1.14896	−0.574479	−	0.818519i	$-0.694795\pi$
$631$	−18211.6	−1.14896	−0.574479	+	0.818519i	$0.694795\pi$
$632$	1156.74	0.0728050
$633$	1167.81	0.0733275
$634$	−13588.7	−0.851226
$635$	1683.84	0.105230
$636$	528.623	0.0329580
$637$	0	0
$638$	−39108.9	−2.42686
$639$	2151.88	0.133219
$640$	1225.82	0.0757104
$641$	572.471	0.0352749	0.0176375	−	0.999844i	$-0.494386\pi$
$641$	572.471	0.0352749	0.0176375	+	0.999844i	$0.494386\pi$
$642$	−363.026	−0.0223169
$643$	12136.5	0.744351	0.372175	−	0.928162i	$-0.378612\pi$
$643$	12136.5	0.744351	0.372175	+	0.928162i	$0.378612\pi$
$644$	0	0
$645$	−263.135	−0.0160635
$646$	64840.1	3.94907
$647$	2449.57	0.148845	0.0744223	−	0.997227i	$-0.476289\pi$
$647$	2449.57	0.148845	0.0744223	+	0.997227i	$0.476289\pi$
$648$	4511.94	0.273527
$649$	3327.14	0.201235
$650$	26626.5	1.60673
$651$	0	0
$652$	−12066.0	−0.724756
$653$	14730.5	0.882767	0.441384	−	0.897318i	$-0.354488\pi$
$653$	14730.5	0.882767	0.441384	+	0.897318i	$0.354488\pi$
$654$	−6186.50	−0.369895
$655$	1866.83	0.111364
$656$	−34415.6	−2.04833
$657$	5807.31	0.344847
$658$	0	0
$659$	13618.2	0.804993	0.402496	−	0.915422i	$-0.368143\pi$
$659$	13618.2	0.804993	0.402496	+	0.915422i	$0.368143\pi$
$660$	−368.710	−0.0217455
$661$	6646.79	0.391120	0.195560	−	0.980692i	$-0.437348\pi$
$661$	6646.79	0.391120	0.195560	+	0.980692i	$0.437348\pi$
$662$	11472.1	0.673527
$663$	6041.05	0.353868
$664$	749.068	0.0437793
$665$	0	0
$666$	22992.1	1.33773
$667$	14068.6	0.816699
$668$	−7006.77	−0.405839
$669$	2602.44	0.150398
$670$	−5642.46	−0.325354
$671$	−10992.6	−0.632438
$672$	0	0
$673$	20428.3	1.17007	0.585033	−	0.811010i	$-0.301082\pi$
$673$	20428.3	1.17007	0.585033	+	0.811010i	$0.301082\pi$
$674$	20623.1	1.17859
$675$	5589.32	0.318716
$676$	6877.50	0.391301
$677$	9953.33	0.565048	0.282524	−	0.959260i	$-0.408828\pi$
$677$	9953.33	0.565048	0.282524	+	0.959260i	$0.408828\pi$
$678$	−3916.02	−0.221820
$679$	0	0
$680$	−1208.81	−0.0681702
$681$	−3476.72	−0.195636
$682$	−4620.08	−0.259402
$683$	20879.8	1.16976	0.584878	−	0.811121i	$-0.301142\pi$
$683$	20879.8	1.16976	0.584878	+	0.811121i	$0.301142\pi$
$684$	22813.6	1.27529
$685$	3298.25	0.183970
$686$	0	0
$687$	−2518.27	−0.139852
$688$	−15855.5	−0.878614
$689$	5724.88	0.316546
$690$	303.362	0.0167374
$691$	18180.0	1.00087	0.500435	−	0.865774i	$-0.333173\pi$
$691$	18180.0	1.00087	0.500435	+	0.865774i	$0.333173\pi$
$692$	4706.34	0.258538
$693$	0	0
$694$	−19508.8	−1.06707
$695$	4546.21	0.248126
$696$	1252.20	0.0681960
$697$	56409.2	3.06550
$698$	−23456.2	−1.27196
$699$	412.313	0.0223106
$700$	0	0
$701$	−7945.43	−0.428095	−0.214048	−	0.976823i	$-0.568665\pi$
$701$	−7945.43	−0.428095	−0.214048	+	0.976823i	$0.568665\pi$
$702$	9857.80	0.529998
$703$	−32434.1	−1.74008
$704$	−12554.6	−0.672115
$705$	−58.5729	−0.00312906
$706$	16538.3	0.881627
$707$	0	0
$708$	370.942	0.0196905
$709$	−33173.0	−1.75718	−0.878588	−	0.477580i	$-0.841514\pi$
$709$	−33173.0	−1.75718	−0.878588	+	0.477580i	$0.841514\pi$
$710$	−450.708	−0.0238236
$711$	−4515.69	−0.238188
$712$	3146.89	0.165639
$713$	1661.98	0.0872952
$714$	0	0
$715$	−3993.05	−0.208855
$716$	−17658.9	−0.921709
$717$	816.453	0.0425258
$718$	−3416.65	−0.177588
$719$	35590.8	1.84605	0.923026	−	0.384737i	$-0.125708\pi$
$719$	35590.8	1.84605	0.923026	+	0.384737i	$0.125708\pi$
$720$	−2879.06	−0.149022
$721$	0	0
$722$	−47746.6	−2.46114
$723$	5385.96	0.277049
$724$	−16688.1	−0.856640
$725$	−26773.8	−1.37152
$726$	−3010.53	−0.153900
$727$	28030.8	1.42999	0.714995	−	0.699129i	$-0.246429\pi$
$727$	28030.8	1.42999	0.714995	+	0.699129i	$0.246429\pi$
$728$	0	0
$729$	−16564.9	−0.841583
$730$	−1216.33	−0.0616692
$731$	25988.2	1.31492
$732$	−1225.57	−0.0618829
$733$	39144.0	1.97246	0.986232	−	0.165370i	$-0.0528817\pi$
$733$	39144.0	1.97246	0.986232	+	0.165370i	$0.0528817\pi$
$734$	−14490.5	−0.728685
$735$	0	0
$736$	14803.6	0.741397
$737$	−48815.1	−2.43979
$738$	45394.4	2.26422
$739$	25858.1	1.28715	0.643576	−	0.765383i	$-0.277450\pi$
$739$	25858.1	1.28715	0.643576	+	0.765383i	$0.277450\pi$
$740$	−2105.50	−0.104594
$741$	−6857.85	−0.339986
$742$	0	0
$743$	13383.7	0.660834	0.330417	−	0.943835i	$-0.392811\pi$
$743$	13383.7	0.660834	0.330417	+	0.943835i	$0.392811\pi$
$744$	147.927	0.00728933
$745$	−2607.34	−0.128222
$746$	−8861.35	−0.434902
$747$	−2924.21	−0.143228
$748$	36415.1	1.78004
$749$	0	0
$750$	−1164.66	−0.0567031
$751$	23995.4	1.16592	0.582959	−	0.812502i	$-0.301895\pi$
$751$	23995.4	1.16592	0.582959	+	0.812502i	$0.301895\pi$
$752$	−3529.38	−0.171148
$753$	−295.825	−0.0143167
$754$	−47220.5	−2.28073
$755$	1373.20	0.0661930
$756$	0	0
$757$	3048.53	0.146368	0.0731841	−	0.997318i	$-0.476684\pi$
$757$	3048.53	0.146368	0.0731841	+	0.997318i	$0.476684\pi$
$758$	8312.34	0.398308
$759$	2624.51	0.125512
$760$	1372.25	0.0654958
$761$	1421.02	0.0676897	0.0338448	−	0.999427i	$-0.489225\pi$
$761$	1421.02	0.0676897	0.0338448	+	0.999427i	$0.489225\pi$
$762$	3714.71	0.176601
$763$	0	0
$764$	19048.9	0.902049
$765$	4718.95	0.223025
$766$	−38428.4	−1.81263
$767$	4017.23	0.189118
$768$	4505.95	0.211712
$769$	−27189.5	−1.27500	−0.637502	−	0.770449i	$-0.720032\pi$
$769$	−27189.5	−1.27500	−0.637502	+	0.770449i	$0.720032\pi$
$770$	0	0
$771$	−6070.02	−0.283536
$772$	4979.63	0.232151
$773$	−3606.47	−0.167808	−0.0839041	−	0.996474i	$-0.526739\pi$
$773$	−3606.47	−0.167808	−0.0839041	+	0.996474i	$0.526739\pi$
$774$	20913.6	0.971218
$775$	−3162.89	−0.146599
$776$	−5789.30	−0.267814
$777$	0	0
$778$	34739.0	1.60084
$779$	−64036.3	−2.94523
$780$	−445.185	−0.0204361
$781$	−3899.25	−0.178651
$782$	−29961.2	−1.37009
$783$	−9912.34	−0.452411
$784$	0	0
$785$	−4005.29	−0.182108
$786$	4118.40	0.186894
$787$	−4579.62	−0.207428	−0.103714	−	0.994607i	$-0.533073\pi$
$787$	−4579.62	−0.207428	−0.103714	+	0.994607i	$0.533073\pi$
$788$	5881.81	0.265902
$789$	−5936.82	−0.267879
$790$	945.804	0.0425952
$791$	0	0
$792$	−8415.81	−0.377579
$793$	−13272.6	−0.594357
$794$	−19108.9	−0.854092
$795$	−124.129	−0.00553761
$796$	−24246.0	−1.07962
$797$	29504.6	1.31130	0.655650	−	0.755065i	$-0.272395\pi$
$797$	29504.6	1.31130	0.655650	+	0.755065i	$0.272395\pi$
$798$	0	0
$799$	5784.88	0.256138
$800$	−28172.6	−1.24506
$801$	−12284.8	−0.541901
$802$	−26632.0	−1.17258
$803$	−10523.0	−0.462450
$804$	−5442.40	−0.238730
$805$	0	0
$806$	−5578.34	−0.243782
$807$	6172.26	0.269237
$808$	6492.23	0.282668
$809$	−20448.7	−0.888674	−0.444337	−	0.895860i	$-0.646561\pi$
$809$	−20448.7	−0.888674	−0.444337	+	0.895860i	$0.646561\pi$
$810$	3689.16	0.160030
$811$	−16494.0	−0.714157	−0.357078	−	0.934074i	$-0.616227\pi$
$811$	−16494.0	−0.714157	−0.357078	+	0.934074i	$0.616227\pi$
$812$	0	0
$813$	3875.72	0.167192
$814$	−41662.2	−1.79393
$815$	2833.28	0.121774
$816$	−7892.62	−0.338599
$817$	−29502.0	−1.26334
$818$	−40087.2	−1.71347
$819$	0	0
$820$	−4156.99	−0.177034
$821$	12594.6	0.535390	0.267695	−	0.963504i	$-0.413738\pi$
$821$	12594.6	0.535390	0.267695	+	0.963504i	$0.413738\pi$
$822$	7276.23	0.308744
$823$	−15604.7	−0.660931	−0.330466	−	0.943818i	$-0.607206\pi$
$823$	−15604.7	−0.660931	−0.330466	+	0.943818i	$0.607206\pi$
$824$	1822.28	0.0770413
$825$	−4994.67	−0.210778
$826$	0	0
$827$	−10506.2	−0.441762	−0.220881	−	0.975301i	$-0.570893\pi$
$827$	−10506.2	−0.441762	−0.220881	+	0.975301i	$0.570893\pi$
$828$	−10541.7	−0.442450
$829$	−8912.95	−0.373413	−0.186707	−	0.982416i	$-0.559781\pi$
$829$	−8912.95	−0.373413	−0.186707	+	0.982416i	$0.559781\pi$
$830$	612.472	0.0256135
$831$	−696.042	−0.0290559
$832$	−15158.6	−0.631646
$833$	0	0
$834$	10029.3	0.416412
$835$	1645.30	0.0681891
$836$	−41338.8	−1.71021
$837$	−1170.98	−0.0483573
$838$	−19382.1	−0.798977
$839$	11528.9	0.474402	0.237201	−	0.971461i	$-0.423770\pi$
$839$	11528.9	0.474402	0.237201	+	0.971461i	$0.423770\pi$
$840$	0	0
$841$	23092.7	0.946851
$842$	61972.1	2.53646
$843$	2411.69	0.0985325
$844$	8499.59	0.346644
$845$	−1614.94	−0.0657465
$846$	4655.29	0.189187
$847$	0	0
$848$	−7479.54	−0.302887
$849$	−6105.60	−0.246812
$850$	57018.8	2.30086
$851$	14987.1	0.603703
$852$	−434.727	−0.0174807
$853$	9943.85	0.399145	0.199573	−	0.979883i	$-0.436045\pi$
$853$	9943.85	0.399145	0.199573	+	0.979883i	$0.436045\pi$
$854$	0	0
$855$	−5356.99	−0.214275
$856$	758.796	0.0302980
$857$	25672.4	1.02328	0.511640	−	0.859200i	$-0.329038\pi$
$857$	25672.4	1.02328	0.511640	+	0.859200i	$0.329038\pi$
$858$	−8809.02	−0.350507
$859$	−15889.3	−0.631124	−0.315562	−	0.948905i	$-0.602193\pi$
$859$	−15889.3	−0.631124	−0.315562	+	0.948905i	$0.602193\pi$
$860$	−1915.16	−0.0759376
$861$	0	0
$862$	41503.6	1.63993
$863$	−2949.54	−0.116342	−0.0581712	−	0.998307i	$-0.518527\pi$
$863$	−2949.54	−0.116342	−0.0581712	+	0.998307i	$0.518527\pi$
$864$	−10430.2	−0.410697
$865$	−1105.12	−0.0434396
$866$	−61976.8	−2.43194
$867$	8741.12	0.342404
$868$	0	0
$869$	8182.52	0.319417
$870$	1023.85	0.0398987
$871$	−58940.0	−2.29289
$872$	12931.0	0.502178
$873$	22600.2	0.876177
$874$	34012.2	1.31634
$875$	0	0
$876$	−1173.21	−0.0452499
$877$	−28886.2	−1.11222	−0.556110	−	0.831109i	$-0.687706\pi$
$877$	−28886.2	−1.11222	−0.556110	+	0.831109i	$0.687706\pi$
$878$	5037.22	0.193620
$879$	1119.28	0.0429493
$880$	5216.91	0.199843
$881$	13913.4	0.532072	0.266036	−	0.963963i	$-0.414286\pi$
$881$	13913.4	0.532072	0.266036	+	0.963963i	$0.414286\pi$
$882$	0	0
$883$	−14238.8	−0.542667	−0.271333	−	0.962485i	$-0.587465\pi$
$883$	−14238.8	−0.542667	−0.271333	+	0.962485i	$0.587465\pi$
$884$	43968.1	1.67286
$885$	−87.1030	−0.00330840
$886$	−5388.17	−0.204311
$887$	−30153.5	−1.14144	−0.570719	−	0.821146i	$-0.693335\pi$
$887$	−30153.5	−1.14144	−0.570719	+	0.821146i	$0.693335\pi$
$888$	1333.95	0.0504104
$889$	0	0
$890$	2573.04	0.0969083
$891$	31916.4	1.20004
$892$	18941.1	0.710982
$893$	−6567.05	−0.246089
$894$	−5752.03	−0.215186
$895$	4146.58	0.154866
$896$	0	0
$897$	3168.86	0.117954
$898$	−27620.2	−1.02639
$899$	5609.20	0.208095
$900$	20061.7	0.743027
$901$	12259.4	0.453297
$902$	−82255.6	−3.03638
$903$	0	0
$904$	8185.25	0.301148
$905$	3918.62	0.143933
$906$	3029.39	0.111087
$907$	−47390.8	−1.73493	−0.867467	−	0.497494i	$-0.834253\pi$
$907$	−47390.8	−1.73493	−0.867467	+	0.497494i	$0.834253\pi$
$908$	−25304.3	−0.924839
$909$	−25344.4	−0.924774
$910$	0	0
$911$	48531.7	1.76501	0.882506	−	0.470301i	$-0.155855\pi$
$911$	48531.7	1.76501	0.882506	+	0.470301i	$0.155855\pi$
$912$	8959.77	0.325315
$913$	5298.73	0.192073
$914$	9111.74	0.329748
$915$	287.782	0.0103976
$916$	−18328.5	−0.661127
$917$	0	0
$918$	21109.8	0.758962
$919$	44296.0	1.58998	0.794989	−	0.606624i	$-0.207476\pi$
$919$	44296.0	1.58998	0.794989	+	0.606624i	$0.207476\pi$
$920$	−634.087	−0.0227231
$921$	−319.104	−0.0114168
$922$	−26718.0	−0.954351
$923$	−4708.00	−0.167894
$924$	0	0
$925$	−28521.8	−1.01383
$926$	−784.461	−0.0278391
$927$	−7113.80	−0.252047
$928$	49962.4	1.76734
$929$	−54821.4	−1.93609	−0.968047	−	0.250771i	$-0.919316\pi$
$929$	−54821.4	−1.93609	−0.968047	+	0.250771i	$0.919316\pi$
$930$	120.952	0.00426469
$931$	0	0
$932$	3000.90	0.105470
$933$	5481.77	0.192353
$934$	−61508.8	−2.15485
$935$	−8550.84	−0.299083
$936$	−10161.4	−0.354844
$937$	−16158.4	−0.563364	−0.281682	−	0.959508i	$-0.590892\pi$
$937$	−16158.4	−0.563364	−0.281682	+	0.959508i	$0.590892\pi$
$938$	0	0
$939$	4652.82	0.161703
$940$	−426.307	−0.0147921
$941$	−1277.74	−0.0442649	−0.0221324	−	0.999755i	$-0.507046\pi$
$941$	−1277.74	−0.0442649	−0.0221324	+	0.999755i	$0.507046\pi$
$942$	−8836.03	−0.305619
$943$	29589.7	1.02182
$944$	−5248.50	−0.180958
$945$	0	0
$946$	−37895.8	−1.30243
$947$	−25067.5	−0.860173	−0.430087	−	0.902788i	$-0.641517\pi$
$947$	−25067.5	−0.860173	−0.430087	+	0.902788i	$0.641517\pi$
$948$	912.269	0.0312543
$949$	−12705.6	−0.434605
$950$	−64728.2	−2.21059
$951$	3077.71	0.104944
$952$	0	0
$953$	−5706.17	−0.193957	−0.0969784	−	0.995286i	$-0.530918\pi$
$953$	−5706.17	−0.193957	−0.0969784	+	0.995286i	$0.530918\pi$
$954$	9865.57	0.334811
$955$	−4472.98	−0.151562
$956$	5942.33	0.201034
$957$	8857.75	0.299196
$958$	−60336.9	−2.03486
$959$	0	0
$960$	328.674	0.0110499
$961$	−29128.4	−0.977757
$962$	−50303.4	−1.68591
$963$	−2962.18	−0.0991226
$964$	39200.2	1.30970
$965$	−1169.29	−0.0390061
$966$	0	0
$967$	41576.4	1.38263	0.691316	−	0.722552i	$-0.257031\pi$
$967$	41576.4	1.38263	0.691316	+	0.722552i	$0.257031\pi$
$968$	6292.60	0.208938
$969$	−14685.6	−0.486863
$970$	−4733.59	−0.156687
$971$	−37704.1	−1.24612	−0.623060	−	0.782174i	$-0.714111\pi$
$971$	−37704.1	−1.24612	−0.623060	+	0.782174i	$0.714111\pi$
$972$	11191.9	0.369321
$973$	0	0
$974$	2745.42	0.0903171
$975$	−6030.62	−0.198087
$976$	17340.7	0.568711
$977$	32831.2	1.07509	0.537546	−	0.843235i	$-0.319352\pi$
$977$	32831.2	1.07509	0.537546	+	0.843235i	$0.319352\pi$
$978$	6250.48	0.204364
$979$	22260.4	0.726705
$980$	0	0
$981$	−50480.0	−1.64292
$982$	−3915.25	−0.127231
$983$	22919.0	0.743643	0.371822	−	0.928304i	$-0.378733\pi$
$983$	22919.0	0.743643	0.371822	+	0.928304i	$0.378733\pi$
$984$	2633.68	0.0853239
$985$	−1381.14	−0.0446769
$986$	−101119.	−3.26603
$987$	0	0
$988$	−49913.0	−1.60723
$989$	13632.2	0.438301
$990$	−6881.15	−0.220906
$991$	11425.7	0.366245	0.183122	−	0.983090i	$-0.441380\pi$
$991$	11425.7	0.366245	0.183122	+	0.983090i	$0.441380\pi$
$992$	5902.25	0.188908
$993$	−2598.31	−0.0830360
$994$	0	0
$995$	5693.34	0.181398
$996$	590.755	0.0187940
$997$	43127.7	1.36998	0.684989	−	0.728553i	$-0.259807\pi$
$997$	43127.7	1.36998	0.684989	+	0.728553i	$0.259807\pi$
$998$	−48566.3	−1.54042
$999$	−10559.5	−0.334422

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2303.4.a.h.1.8	yes	35
7.6	odd	2		2303.4.a.g.1.8	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2303.4.a.g.1.8	✓	35	7.6	odd	2
2303.4.a.h.1.8	yes	35	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:	\( N \)	\(=\)	\( 2303 = 7^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2303.a (trivial)

\(f(q)\)	\(=\)	\(q-3.77029 q^{2} +0.853932 q^{3} +6.21511 q^{4} -1.45940 q^{5} -3.21958 q^{6} +6.72955 q^{8} -26.2708 q^{9} +O(q^{10})\)	\(q-3.77029 q^{2} +0.853932 q^{3} +6.21511 q^{4} -1.45940 q^{5} -3.21958 q^{6} +6.72955 q^{8} -26.2708 q^{9} +5.50238 q^{10} +47.6033 q^{11} +5.30729 q^{12} +57.4768 q^{13} -1.24623 q^{15} -75.0933 q^{16} +123.083 q^{17} +99.0486 q^{18} -139.724 q^{19} -9.07036 q^{20} -179.478 q^{22} +64.5635 q^{23} +5.74658 q^{24} -122.870 q^{25} -216.704 q^{26} -45.4897 q^{27} +217.903 q^{29} +4.69866 q^{30} +25.7417 q^{31} +229.287 q^{32} +40.6500 q^{33} -464.057 q^{34} -163.276 q^{36} +232.129 q^{37} +526.802 q^{38} +49.0813 q^{39} -9.82114 q^{40} +458.304 q^{41} +211.144 q^{43} +295.860 q^{44} +38.3397 q^{45} -243.423 q^{46} +47.0000 q^{47} -64.1246 q^{48} +463.256 q^{50} +105.104 q^{51} +357.224 q^{52} +99.6033 q^{53} +171.509 q^{54} -69.4724 q^{55} -119.315 q^{57} -821.558 q^{58} +69.8931 q^{59} -7.74548 q^{60} -230.922 q^{61} -97.0538 q^{62} -263.734 q^{64} -83.8818 q^{65} -153.262 q^{66} -1025.46 q^{67} +764.972 q^{68} +55.1329 q^{69} -81.9115 q^{71} -176.791 q^{72} -221.056 q^{73} -875.196 q^{74} -104.923 q^{75} -868.403 q^{76} -185.051 q^{78} +171.890 q^{79} +109.591 q^{80} +670.466 q^{81} -1727.94 q^{82} +111.310 q^{83} -179.627 q^{85} -796.077 q^{86} +186.074 q^{87} +320.349 q^{88} +467.622 q^{89} -144.552 q^{90} +401.270 q^{92} +21.9817 q^{93} -177.204 q^{94} +203.914 q^{95} +195.796 q^{96} -860.280 q^{97} -1250.58 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9}+O(q^{10}) \) 35 * q + 5 * q^2 + 12 * q^3 + 139 * q^4 + 20 * q^5 + 24 * q^6 + 39 * q^8 + 303 * q^9	\( 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9} + 100 q^{10} + 40 q^{11} + 144 q^{12} + 328 q^{13} + 20 q^{15} + 643 q^{16} + 152 q^{17} + 51 q^{18} + 266 q^{19} + 1064 q^{20} - 168 q^{22} - 134 q^{23} + 288 q^{24} + 1137 q^{25} + 156 q^{26} + 672 q^{27} + 248 q^{29} - 216 q^{30} + 276 q^{31} + 347 q^{32} + 1056 q^{33} + 908 q^{34} + 909 q^{36} - 418 q^{37} + 164 q^{38} - 548 q^{39} + 1200 q^{40} + 918 q^{41} + 608 q^{43} + 1288 q^{44} + 876 q^{45} - 972 q^{46} + 1645 q^{47} + 1252 q^{48} - 367 q^{50} - 464 q^{51} + 3798 q^{52} - 218 q^{53} - 744 q^{54} + 1004 q^{55} - 436 q^{57} - 1270 q^{58} + 3760 q^{59} - 424 q^{60} + 956 q^{61} + 84 q^{62} + 2189 q^{64} - 596 q^{65} + 5500 q^{66} - 476 q^{67} + 256 q^{68} + 444 q^{69} + 852 q^{71} - 883 q^{72} + 6250 q^{73} + 1366 q^{74} - 2568 q^{75} + 1742 q^{76} - 1460 q^{78} + 632 q^{79} + 10124 q^{80} + 1267 q^{81} + 792 q^{82} + 796 q^{83} - 1228 q^{85} - 2864 q^{86} + 8360 q^{87} - 50 q^{88} + 908 q^{89} - 1858 q^{90} + 1696 q^{92} + 644 q^{93} + 235 q^{94} + 1320 q^{95} + 2688 q^{96} + 6184 q^{97} - 1812 q^{99}+O(q^{100}) \) 35 * q + 5 * q^2 + 12 * q^3 + 139 * q^4 + 20 * q^5 + 24 * q^6 + 39 * q^8 + 303 * q^9 + 100 * q^10 + 40 * q^11 + 144 * q^12 + 328 * q^13 + 20 * q^15 + 643 * q^16 + 152 * q^17 + 51 * q^18 + 266 * q^19 + 1064 * q^20 - 168 * q^22 - 134 * q^23 + 288 * q^24 + 1137 * q^25 + 156 * q^26 + 672 * q^27 + 248 * q^29 - 216 * q^30 + 276 * q^31 + 347 * q^32 + 1056 * q^33 + 908 * q^34 + 909 * q^36 - 418 * q^37 + 164 * q^38 - 548 * q^39 + 1200 * q^40 + 918 * q^41 + 608 * q^43 + 1288 * q^44 + 876 * q^45 - 972 * q^46 + 1645 * q^47 + 1252 * q^48 - 367 * q^50 - 464 * q^51 + 3798 * q^52 - 218 * q^53 - 744 * q^54 + 1004 * q^55 - 436 * q^57 - 1270 * q^58 + 3760 * q^59 - 424 * q^60 + 956 * q^61 + 84 * q^62 + 2189 * q^64 - 596 * q^65 + 5500 * q^66 - 476 * q^67 + 256 * q^68 + 444 * q^69 + 852 * q^71 - 883 * q^72 + 6250 * q^73 + 1366 * q^74 - 2568 * q^75 + 1742 * q^76 - 1460 * q^78 + 632 * q^79 + 10124 * q^80 + 1267 * q^81 + 792 * q^82 + 796 * q^83 - 1228 * q^85 - 2864 * q^86 + 8360 * q^87 - 50 * q^88 + 908 * q^89 - 1858 * q^90 + 1696 * q^92 + 644 * q^93 + 235 * q^94 + 1320 * q^95 + 2688 * q^96 + 6184 * q^97 - 1812 * q^99

Introduction

L-functions

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Database

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