LMFDB - Embedded newform 2303.4.a.n.1.19

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:	$68$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
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)

$f(q)$	$=$	$q-2.73998 q^{2} +0.0952364 q^{3} -0.492507 q^{4} +9.66207 q^{5} -0.260946 q^{6} +23.2693 q^{8} -26.9909 q^{9} +O(q^{10})$	\(q-2.73998 q^{2} +0.0952364 q^{3} -0.492507 q^{4} +9.66207 q^{5} -0.260946 q^{6} +23.2693 q^{8} -26.9909 q^{9} -26.4739 q^{10} -62.1560 q^{11} -0.0469046 q^{12} +5.74830 q^{13} +0.920182 q^{15} -59.8174 q^{16} -48.8214 q^{17} +73.9546 q^{18} -150.799 q^{19} -4.75864 q^{20} +170.306 q^{22} -166.427 q^{23} +2.21609 q^{24} -31.6443 q^{25} -15.7502 q^{26} -5.14190 q^{27} -116.264 q^{29} -2.52128 q^{30} -79.4609 q^{31} -22.2560 q^{32} -5.91951 q^{33} +133.770 q^{34} +13.2932 q^{36} -323.389 q^{37} +413.187 q^{38} +0.547448 q^{39} +224.830 q^{40} -428.126 q^{41} +205.165 q^{43} +30.6122 q^{44} -260.788 q^{45} +456.006 q^{46} -47.0000 q^{47} -5.69679 q^{48} +86.7048 q^{50} -4.64958 q^{51} -2.83108 q^{52} +509.225 q^{53} +14.0887 q^{54} -600.555 q^{55} -14.3616 q^{57} +318.560 q^{58} -433.890 q^{59} -0.453196 q^{60} -54.8451 q^{61} +217.721 q^{62} +539.520 q^{64} +55.5405 q^{65} +16.2193 q^{66} -499.032 q^{67} +24.0449 q^{68} -15.8499 q^{69} +560.862 q^{71} -628.060 q^{72} +795.818 q^{73} +886.080 q^{74} -3.01369 q^{75} +74.2697 q^{76} -1.50000 q^{78} +521.450 q^{79} -577.960 q^{80} +728.265 q^{81} +1173.06 q^{82} -73.5404 q^{83} -471.716 q^{85} -562.147 q^{86} -11.0725 q^{87} -1446.33 q^{88} -853.851 q^{89} +714.555 q^{90} +81.9663 q^{92} -7.56757 q^{93} +128.779 q^{94} -1457.04 q^{95} -2.11958 q^{96} -112.023 q^{97} +1677.65 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 2 q^{2} + 24 q^{3} + 254 q^{4} + 40 q^{5} + 48 q^{6} - 66 q^{8} + 576 q^{9}+O(q^{10}) $ 68 * q - 2 * q^2 + 24 * q^3 + 254 * q^4 + 40 * q^5 + 48 * q^6 - 66 * q^8 + 576 * q^9	\( 68 q - 2 q^{2} + 24 q^{3} + 254 q^{4} + 40 q^{5} + 48 q^{6} - 66 q^{8} + 576 q^{9} + 200 q^{10} - 20 q^{11} + 288 q^{12} + 520 q^{13} + 88 q^{15} + 1062 q^{16} + 784 q^{17} - 2 q^{18} + 532 q^{19} + 400 q^{20} - 4 q^{22} - 268 q^{23} + 576 q^{24} + 1864 q^{25} + 312 q^{26} + 864 q^{27} + 200 q^{29} + 792 q^{30} + 936 q^{31} + 30 q^{32} + 2112 q^{33} + 1088 q^{34} + 2130 q^{36} - 356 q^{37} + 1192 q^{38} - 488 q^{39} + 2400 q^{40} + 1476 q^{41} - 92 q^{43} + 192 q^{44} + 1848 q^{45} - 424 q^{46} - 3196 q^{47} + 2688 q^{48} - 1338 q^{50} - 148 q^{51} + 4980 q^{52} - 80 q^{53} + 4944 q^{54} + 2200 q^{55} + 2244 q^{57} - 356 q^{58} + 560 q^{59} - 736 q^{60} + 3944 q^{61} + 1488 q^{62} + 3778 q^{64} + 2004 q^{65} - 1000 q^{66} + 2768 q^{67} + 8192 q^{68} + 2208 q^{69} - 2448 q^{71} - 5234 q^{72} + 9532 q^{73} - 2000 q^{74} + 11136 q^{75} + 6384 q^{76} - 3460 q^{78} - 1520 q^{79} + 616 q^{80} + 6976 q^{81} + 4976 q^{82} + 3320 q^{83} + 3244 q^{85} - 2892 q^{86} + 2360 q^{87} - 2868 q^{88} + 8152 q^{89} + 5400 q^{90} - 4684 q^{92} + 2840 q^{93} + 94 q^{94} - 4256 q^{95} + 5376 q^{96} + 13968 q^{97} + 2380 q^{99}+O(q^{100}) \) 68 * q - 2 * q^2 + 24 * q^3 + 254 * q^4 + 40 * q^5 + 48 * q^6 - 66 * q^8 + 576 * q^9 + 200 * q^10 - 20 * q^11 + 288 * q^12 + 520 * q^13 + 88 * q^15 + 1062 * q^16 + 784 * q^17 - 2 * q^18 + 532 * q^19 + 400 * q^20 - 4 * q^22 - 268 * q^23 + 576 * q^24 + 1864 * q^25 + 312 * q^26 + 864 * q^27 + 200 * q^29 + 792 * q^30 + 936 * q^31 + 30 * q^32 + 2112 * q^33 + 1088 * q^34 + 2130 * q^36 - 356 * q^37 + 1192 * q^38 - 488 * q^39 + 2400 * q^40 + 1476 * q^41 - 92 * q^43 + 192 * q^44 + 1848 * q^45 - 424 * q^46 - 3196 * q^47 + 2688 * q^48 - 1338 * q^50 - 148 * q^51 + 4980 * q^52 - 80 * q^53 + 4944 * q^54 + 2200 * q^55 + 2244 * q^57 - 356 * q^58 + 560 * q^59 - 736 * q^60 + 3944 * q^61 + 1488 * q^62 + 3778 * q^64 + 2004 * q^65 - 1000 * q^66 + 2768 * q^67 + 8192 * q^68 + 2208 * q^69 - 2448 * q^71 - 5234 * q^72 + 9532 * q^73 - 2000 * q^74 + 11136 * q^75 + 6384 * q^76 - 3460 * q^78 - 1520 * q^79 + 616 * q^80 + 6976 * q^81 + 4976 * q^82 + 3320 * q^83 + 3244 * q^85 - 2892 * q^86 + 2360 * q^87 - 2868 * q^88 + 8152 * q^89 + 5400 * q^90 - 4684 * q^92 + 2840 * q^93 + 94 * q^94 - 4256 * q^95 + 5376 * q^96 + 13968 * q^97 + 2380 * 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 $

$2$	−2.73998	−0.968729	−0.484365	−	0.874866i	$-0.660949\pi$
$2$	−2.73998	−0.968729	−0.484365	+	0.874866i	$0.660949\pi$
$3$	0.0952364	0.0183283	0.00916413	−	0.999958i	$-0.497083\pi$
$3$	0.0952364	0.0183283	0.00916413	+	0.999958i	$0.497083\pi$
$4$	−0.492507	−0.0615634
$5$	9.66207	0.864202	0.432101	−	0.901825i	$-0.357772\pi$
$5$	9.66207	0.864202	0.432101	+	0.901825i	$0.357772\pi$
$6$	−0.260946	−0.0177551
$7$	0	0
$7$	0	0
$8$	23.2693	1.02837
$9$	−26.9909	−0.999664
$10$	−26.4739	−0.837178
$11$	−62.1560	−1.70370	−0.851851	−	0.523784i	$-0.824520\pi$
$11$	−62.1560	−1.70370	−0.851851	+	0.523784i	$0.824520\pi$
$12$	−0.0469046	−0.00112835
$13$	5.74830	0.122638	0.0613189	−	0.998118i	$-0.480469\pi$
$13$	5.74830	0.122638	0.0613189	+	0.998118i	$0.480469\pi$
$14$	0	0
$15$	0.920182	0.0158393
$16$	−59.8174	−0.934647
$17$	−48.8214	−0.696525	−0.348263	−	0.937397i	$-0.613228\pi$
$17$	−48.8214	−0.696525	−0.348263	+	0.937397i	$0.613228\pi$
$18$	73.9546	0.968404
$19$	−150.799	−1.82083	−0.910415	−	0.413697i	$-0.864237\pi$
$19$	−150.799	−1.82083	−0.910415	+	0.413697i	$0.864237\pi$
$20$	−4.75864	−0.0532032
$21$	0	0
$22$	170.306	1.65043
$23$	−166.427	−1.50880	−0.754400	−	0.656415i	$-0.772072\pi$
$23$	−166.427	−1.50880	−0.754400	+	0.656415i	$0.772072\pi$
$24$	2.21609	0.0188482
$25$	−31.6443	−0.253155
$26$	−15.7502	−0.118803
$27$	−5.14190	−0.0366504
$28$	0	0
$29$	−116.264	−0.744470	−0.372235	−	0.928138i	$-0.621408\pi$
$29$	−116.264	−0.744470	−0.372235	+	0.928138i	$0.621408\pi$
$30$	−2.52128	−0.0153440
$31$	−79.4609	−0.460374	−0.230187	−	0.973146i	$-0.573934\pi$
$31$	−79.4609	−0.460374	−0.230187	+	0.973146i	$0.573934\pi$
$32$	−22.2560	−0.122948
$33$	−5.91951	−0.0312259
$34$	133.770	0.674745
$35$	0	0
$36$	13.2932	0.0615427
$37$	−323.389	−1.43689	−0.718444	−	0.695585i	$-0.755145\pi$
$37$	−323.389	−1.43689	−0.718444	+	0.695585i	$0.755145\pi$
$38$	413.187	1.76389
$39$	0.547448	0.00224774
$40$	224.830	0.888718
$41$	−428.126	−1.63078	−0.815390	−	0.578912i	$-0.803477\pi$
$41$	−428.126	−1.63078	−0.815390	+	0.578912i	$0.803477\pi$
$42$	0	0
$43$	205.165	0.727612	0.363806	−	0.931475i	$-0.381477\pi$
$43$	205.165	0.727612	0.363806	+	0.931475i	$0.381477\pi$
$44$	30.6122	0.104886
$45$	−260.788	−0.863912
$46$	456.006	1.46162
$47$	−47.0000	−0.145865
$47$	−47.0000	−0.145865
$48$	−5.69679	−0.0171304
$49$	0	0
$50$	86.7048	0.245238
$51$	−4.64958	−0.0127661
$52$	−2.83108	−0.00755000
$53$	509.225	1.31976	0.659881	−	0.751370i	$-0.270607\pi$
$53$	509.225	1.31976	0.659881	+	0.751370i	$0.270607\pi$
$54$	14.0887	0.0355043
$55$	−600.555	−1.47234
$56$	0	0
$57$	−14.3616	−0.0333726
$58$	318.560	0.721190
$59$	−433.890	−0.957419	−0.478709	−	0.877973i	$-0.658895\pi$
$59$	−433.890	−0.957419	−0.478709	+	0.877973i	$0.658895\pi$
$60$	−0.453196	−0.000975122 0
$61$	−54.8451	−0.115118	−0.0575590	−	0.998342i	$-0.518332\pi$
$61$	−54.8451	−0.115118	−0.0575590	+	0.998342i	$0.518332\pi$
$62$	217.721	0.445978
$63$	0	0
$64$	539.520	1.05375
$65$	55.5405	0.105984
$66$	16.2193	0.0302494
$67$	−499.032	−0.909948	−0.454974	−	0.890505i	$-0.650351\pi$
$67$	−499.032	−0.909948	−0.454974	+	0.890505i	$0.650351\pi$
$68$	24.0449	0.0428804
$69$	−15.8499	−0.0276537
$70$	0	0
$71$	560.862	0.937494	0.468747	−	0.883333i	$-0.344706\pi$
$71$	560.862	0.937494	0.468747	+	0.883333i	$0.344706\pi$
$72$	−628.060	−1.02802
$73$	795.818	1.27594	0.637969	−	0.770062i	$-0.279775\pi$
$73$	795.818	1.27594	0.637969	+	0.770062i	$0.279775\pi$
$74$	886.080	1.39196
$75$	−3.01369	−0.00463988
$76$	74.2697	0.112096
$77$	0	0
$78$	−1.50000	−0.00217745
$79$	521.450	0.742630	0.371315	−	0.928507i	$-0.378907\pi$
$79$	521.450	0.742630	0.371315	+	0.928507i	$0.378907\pi$
$80$	−577.960	−0.807724
$81$	728.265	0.998992
$82$	1173.06	1.57978
$83$	−73.5404	−0.0972543	−0.0486272	−	0.998817i	$-0.515485\pi$
$83$	−73.5404	−0.0972543	−0.0486272	+	0.998817i	$0.515485\pi$
$84$	0	0
$85$	−471.716	−0.601939
$86$	−562.147	−0.704859
$87$	−11.0725	−0.0136448
$88$	−1446.33	−1.75203
$89$	−853.851	−1.01694	−0.508472	−	0.861079i	$-0.669789\pi$
$89$	−853.851	−1.01694	−0.508472	+	0.861079i	$0.669789\pi$
$90$	714.555	0.836897
$91$	0	0
$92$	81.9663	0.0928868
$93$	−7.56757	−0.00843786
$94$	128.779	0.141304
$95$	−1457.04	−1.57356
$96$	−2.11958	−0.00225342
$97$	−112.023	−0.117259	−0.0586297	−	0.998280i	$-0.518673\pi$
$97$	−112.023	−0.117259	−0.0586297	+	0.998280i	$0.518673\pi$
$98$	0	0
$99$	1677.65	1.70313
$100$	15.5850	0.0155850
$101$	518.533	0.510851	0.255426	−	0.966829i	$-0.417784\pi$
$101$	518.533	0.510851	0.255426	+	0.966829i	$0.417784\pi$
$102$	12.7398	0.0123669
$103$	1616.31	1.54621	0.773107	−	0.634276i	$-0.218702\pi$
$103$	1616.31	1.54621	0.773107	+	0.634276i	$0.218702\pi$
$104$	133.759	0.126117
$105$	0	0
$106$	−1395.27	−1.27849
$107$	−597.203	−0.539569	−0.269784	−	0.962921i	$-0.586952\pi$
$107$	−597.203	−0.539569	−0.269784	+	0.962921i	$0.586952\pi$
$108$	2.53242	0.00225632
$109$	−889.860	−0.781956	−0.390978	−	0.920400i	$-0.627863\pi$
$109$	−889.860	−0.781956	−0.390978	+	0.920400i	$0.627863\pi$
$110$	1645.51	1.42630
$111$	−30.7984	−0.0263357
$112$	0	0
$113$	2076.06	1.72831	0.864154	−	0.503227i	$-0.167854\pi$
$113$	2076.06	1.72831	0.864154	+	0.503227i	$0.167854\pi$
$114$	39.3505	0.0323291
$115$	−1608.03	−1.30391
$116$	57.2607	0.0458321
$117$	−155.152	−0.122597
$118$	1188.85	0.927479
$119$	0	0
$120$	21.4120	0.0162886
$121$	2532.36	1.90260
$122$	150.275	0.111518
$123$	−40.7732	−0.0298894
$124$	39.1350	0.0283422
$125$	−1513.51	−1.08298
$126$	0	0
$127$	−257.444	−0.179878	−0.0899389	−	0.995947i	$-0.528667\pi$
$127$	−257.444	−0.179878	−0.0899389	+	0.995947i	$0.528667\pi$
$128$	−1300.23	−0.897851
$129$	19.5392	0.0133359
$130$	−152.180	−0.102670
$131$	−940.658	−0.627371	−0.313686	−	0.949527i	$-0.601564\pi$
$131$	−940.658	−0.627371	−0.313686	+	0.949527i	$0.601564\pi$
$132$	2.91540	0.00192237
$133$	0	0
$134$	1367.34	0.881493
$135$	−49.6815	−0.0316733
$136$	−1136.04	−0.716284
$137$	299.667	0.186878	0.0934391	−	0.995625i	$-0.470214\pi$
$137$	299.667	0.186878	0.0934391	+	0.995625i	$0.470214\pi$
$138$	43.4284	0.0267889
$139$	917.087	0.559614	0.279807	−	0.960056i	$-0.409730\pi$
$139$	917.087	0.559614	0.279807	+	0.960056i	$0.409730\pi$
$140$	0	0
$141$	−4.47611	−0.00267345
$142$	−1536.75	−0.908178
$143$	−357.291	−0.208938
$144$	1614.53	0.934333
$145$	−1123.35	−0.643373
$146$	−2180.53	−1.23604
$147$	0	0
$148$	159.271	0.0884597
$149$	644.164	0.354174	0.177087	−	0.984195i	$-0.443333\pi$
$149$	644.164	0.354174	0.177087	+	0.984195i	$0.443333\pi$
$150$	8.25746	0.00449479
$151$	699.070	0.376752	0.188376	−	0.982097i	$-0.439678\pi$
$151$	699.070	0.376752	0.188376	+	0.982097i	$0.439678\pi$
$152$	−3509.00	−1.87248
$153$	1317.74	0.696291
$154$	0	0
$155$	−767.757	−0.397856
$156$	−0.269622	−0.000138378 0
$157$	−2661.94	−1.35316	−0.676579	−	0.736370i	$-0.736538\pi$
$157$	−2661.94	−1.35316	−0.676579	+	0.736370i	$0.736538\pi$
$158$	−1428.76	−0.719407
$159$	48.4967	0.0241889
$160$	−215.039	−0.106252
$161$	0	0
$162$	−1995.43	−0.967753
$163$	−822.517	−0.395242	−0.197621	−	0.980278i	$-0.563322\pi$
$163$	−822.517	−0.395242	−0.197621	+	0.980278i	$0.563322\pi$
$164$	210.855	0.100396
$165$	−57.1948	−0.0269855
$166$	201.499	0.0942131
$167$	−2469.65	−1.14435	−0.572177	−	0.820130i	$-0.693901\pi$
$167$	−2469.65	−1.14435	−0.572177	+	0.820130i	$0.693901\pi$
$168$	0	0
$169$	−2163.96	−0.984960
$170$	1292.49	0.583116
$171$	4070.22	1.82022
$172$	−101.045	−0.0447942
$173$	−2202.84	−0.968085	−0.484042	−	0.875045i	$-0.660832\pi$
$173$	−2202.84	−0.968085	−0.484042	+	0.875045i	$0.660832\pi$
$174$	30.3386	0.0132182
$175$	0	0
$176$	3718.01	1.59236
$177$	−41.3222	−0.0175478
$178$	2339.53	0.985143
$179$	134.818	0.0562949	0.0281474	−	0.999604i	$-0.491039\pi$
$179$	134.818	0.0562949	0.0281474	+	0.999604i	$0.491039\pi$
$180$	128.440	0.0531853
$181$	419.990	0.172473	0.0862364	−	0.996275i	$-0.472516\pi$
$181$	419.990	0.172473	0.0862364	+	0.996275i	$0.472516\pi$
$182$	0	0
$183$	−5.22325	−0.00210991
$184$	−3872.64	−1.55160
$185$	−3124.61	−1.24176
$186$	20.7350	0.00817400
$187$	3034.54	1.18667
$188$	23.1478	0.00897994
$189$	0	0
$190$	3992.25	1.52436
$191$	−1507.99	−0.571279	−0.285639	−	0.958337i	$-0.592206\pi$
$191$	−1507.99	−0.571279	−0.285639	+	0.958337i	$0.592206\pi$
$192$	51.3820	0.0193134
$193$	40.3011	0.0150307	0.00751537	−	0.999972i	$-0.497608\pi$
$193$	40.3011	0.0150307	0.00751537	+	0.999972i	$0.497608\pi$
$194$	306.940	0.113593
$195$	5.28948	0.00194250
$196$	0	0
$197$	1778.37	0.643165	0.321583	−	0.946882i	$-0.395785\pi$
$197$	1778.37	0.643165	0.321583	+	0.946882i	$0.395785\pi$
$198$	−4596.72	−1.64987
$199$	−4640.53	−1.65306	−0.826530	−	0.562893i	$-0.809688\pi$
$199$	−4640.53	−1.65306	−0.826530	+	0.562893i	$0.809688\pi$
$200$	−736.341	−0.260336
$201$	−47.5261	−0.0166778
$202$	−1420.77	−0.494876
$203$	0	0
$204$	2.28995	0.000785924 0
$205$	−4136.58	−1.40932
$206$	−4428.67	−1.49786
$207$	4492.01	1.50829
$208$	−343.848	−0.114623
$209$	9373.08	3.10215
$210$	0	0
$211$	1126.87	0.367663	0.183832	−	0.982958i	$-0.441150\pi$
$211$	1126.87	0.367663	0.183832	+	0.982958i	$0.441150\pi$
$212$	−250.797	−0.0812490
$213$	53.4145	0.0171826
$214$	1636.33	0.522696
$215$	1982.32	0.628804
$216$	−119.649	−0.0376900
$217$	0	0
$218$	2438.20	0.757504
$219$	75.7909	0.0233857
$220$	295.778	0.0906424
$221$	−280.640	−0.0854203
$222$	84.3871	0.0255121
$223$	−1280.09	−0.384400	−0.192200	−	0.981356i	$-0.561562\pi$
$223$	−1280.09	−0.384400	−0.192200	+	0.981356i	$0.561562\pi$
$224$	0	0
$225$	854.110	0.253069
$226$	−5688.35	−1.67426
$227$	−4413.42	−1.29044	−0.645218	−	0.763998i	$-0.723233\pi$
$227$	−4413.42	−1.29044	−0.645218	+	0.763998i	$0.723233\pi$
$228$	7.07319	0.00205453
$229$	−4174.55	−1.20464	−0.602318	−	0.798256i	$-0.705756\pi$
$229$	−4174.55	−1.20464	−0.602318	+	0.798256i	$0.705756\pi$
$230$	4405.97	1.26313
$231$	0	0
$232$	−2705.38	−0.765589
$233$	−6508.87	−1.83009	−0.915043	−	0.403356i	$-0.867844\pi$
$233$	−6508.87	−1.83009	−0.915043	+	0.403356i	$0.867844\pi$
$234$	425.113	0.118763
$235$	−454.118	−0.126057
$236$	213.694	0.0589419
$237$	49.6611	0.0136111
$238$	0	0
$239$	1892.88	0.512303	0.256151	−	0.966637i	$-0.417545\pi$
$239$	1892.88	0.512303	0.256151	+	0.966637i	$0.417545\pi$
$240$	−55.0429	−0.0148042
$241$	2442.35	0.652802	0.326401	−	0.945231i	$-0.394164\pi$
$241$	2442.35	0.652802	0.326401	+	0.945231i	$0.394164\pi$
$242$	−6938.62	−1.84311
$243$	208.189	0.0549602
$244$	27.0116	0.00708705
$245$	0	0
$246$	111.718	0.0289547
$247$	−866.840	−0.223303
$248$	−1849.00	−0.473434
$249$	−7.00373	−0.00178250
$250$	4146.99	1.04911
$251$	1203.08	0.302542	0.151271	−	0.988492i	$-0.451663\pi$
$251$	1203.08	0.302542	0.151271	+	0.988492i	$0.451663\pi$
$252$	0	0
$253$	10344.4	2.57054
$254$	705.392	0.174253
$255$	−44.9246	−0.0110325
$256$	−753.565	−0.183976
$257$	6213.39	1.50810	0.754048	−	0.656820i	$-0.228099\pi$
$257$	6213.39	1.50810	0.754048	+	0.656820i	$0.228099\pi$
$258$	−53.5369	−0.0129188
$259$	0	0
$260$	−27.3541	−0.00652472
$261$	3138.07	0.744220
$262$	2577.38	0.607753
$263$	−3508.84	−0.822679	−0.411340	−	0.911482i	$-0.634939\pi$
$263$	−3508.84	−0.822679	−0.411340	+	0.911482i	$0.634939\pi$
$264$	−137.743	−0.0321117
$265$	4920.17	1.14054
$266$	0	0
$267$	−81.3177	−0.0186388
$268$	245.777	0.0560194
$269$	4439.37	1.00622	0.503109	−	0.864223i	$-0.332189\pi$
$269$	4439.37	1.00622	0.503109	+	0.864223i	$0.332189\pi$
$270$	136.126	0.0306829
$271$	5929.88	1.32920	0.664602	−	0.747197i	$-0.268601\pi$
$271$	5929.88	1.32920	0.664602	+	0.747197i	$0.268601\pi$
$272$	2920.37	0.651005
$273$	0	0
$274$	−821.083	−0.181034
$275$	1966.88	0.431300
$276$	7.80618	0.00170245
$277$	−5653.66	−1.22634	−0.613168	−	0.789952i	$-0.710105\pi$
$277$	−5653.66	−1.22634	−0.613168	+	0.789952i	$0.710105\pi$
$278$	−2512.80	−0.542114
$279$	2144.72	0.460220
$280$	0	0
$281$	4271.88	0.906901	0.453451	−	0.891281i	$-0.350193\pi$
$281$	4271.88	0.906901	0.453451	+	0.891281i	$0.350193\pi$
$282$	12.2645	0.00258985
$283$	−6993.10	−1.46889	−0.734447	−	0.678667i	$-0.762558\pi$
$283$	−6993.10	−1.46889	−0.734447	+	0.678667i	$0.762558\pi$
$284$	−276.228	−0.0577153
$285$	−138.763	−0.0288407
$286$	978.971	0.202405
$287$	0	0
$288$	600.709	0.122907
$289$	−2529.47	−0.514852
$290$	3077.95	0.623254
$291$	−10.6686	−0.00214916
$292$	−391.946	−0.0785510
$293$	−1106.50	−0.220622	−0.110311	−	0.993897i	$-0.535185\pi$
$293$	−1106.50	−0.220622	−0.110311	+	0.993897i	$0.535185\pi$
$294$	0	0
$295$	−4192.28	−0.827403
$296$	−7525.04	−1.47765
$297$	319.600	0.0624413
$298$	−1765.00	−0.343099
$299$	−956.671	−0.185036
$300$	1.48426	0.000285647 0
$301$	0	0
$302$	−1915.44	−0.364970
$303$	49.3832	0.00936301
$304$	9020.43	1.70183
$305$	−529.918	−0.0994852
$306$	−3610.57	−0.674518
$307$	6225.65	1.15738	0.578692	−	0.815546i	$-0.303563\pi$
$307$	6225.65	1.15738	0.578692	+	0.815546i	$0.303563\pi$
$308$	0	0
$309$	153.932	0.0283394
$310$	2103.64	0.385415
$311$	4457.15	0.812675	0.406338	−	0.913723i	$-0.366806\pi$
$311$	4457.15	0.812675	0.406338	+	0.913723i	$0.366806\pi$
$312$	12.7387	0.00231150
$313$	999.351	0.180469	0.0902343	−	0.995921i	$-0.471238\pi$
$313$	999.351	0.180469	0.0902343	+	0.995921i	$0.471238\pi$
$314$	7293.66	1.31084
$315$	0	0
$316$	−256.818	−0.0457188
$317$	5678.16	1.00605	0.503024	−	0.864272i	$-0.332221\pi$
$317$	5678.16	1.00605	0.503024	+	0.864272i	$0.332221\pi$
$318$	−132.880	−0.0234325
$319$	7226.48	1.26836
$320$	5212.88	0.910653
$321$	−56.8755	−0.00988935
$322$	0	0
$323$	7362.24	1.26825
$324$	−358.676	−0.0615013
$325$	−181.901	−0.0310463
$326$	2253.68	0.382883
$327$	−84.7471	−0.0143319
$328$	−9962.18	−1.67704
$329$	0	0
$330$	156.713	0.0261416
$331$	−9082.49	−1.50821	−0.754107	−	0.656751i	$-0.771930\pi$
$331$	−9082.49	−1.50821	−0.754107	+	0.656751i	$0.771930\pi$
$332$	36.2192	0.00598730
$333$	8728.58	1.43641
$334$	6766.79	1.10857
$335$	−4821.69	−0.786379
$336$	0	0
$337$	−9049.37	−1.46276	−0.731381	−	0.681969i	$-0.761124\pi$
$337$	−9049.37	−1.46276	−0.731381	+	0.681969i	$0.761124\pi$
$338$	5929.20	0.954160
$339$	197.716	0.0316769
$340$	232.323	0.0370574
$341$	4938.97	0.784341
$342$	−11152.3	−1.76330
$343$	0	0
$344$	4774.04	0.748253
$345$	−153.143	−0.0238984
$346$	6035.73	0.937812
$347$	−5834.91	−0.902693	−0.451347	−	0.892349i	$-0.649056\pi$
$347$	−5834.91	−0.902693	−0.451347	+	0.892349i	$0.649056\pi$
$348$	5.45330	0.000840022 0
$349$	2825.05	0.433299	0.216650	−	0.976249i	$-0.430487\pi$
$349$	2825.05	0.433299	0.216650	+	0.976249i	$0.430487\pi$
$350$	0	0
$351$	−29.5572	−0.00449472
$352$	1383.34	0.209467
$353$	1889.78	0.284937	0.142469	−	0.989799i	$-0.454496\pi$
$353$	1889.78	0.284937	0.142469	+	0.989799i	$0.454496\pi$
$354$	113.222	0.0169991
$355$	5419.09	0.810184
$356$	420.527	0.0626065
$357$	0	0
$358$	−369.399	−0.0545345
$359$	578.144	0.0849953	0.0424976	−	0.999097i	$-0.486469\pi$
$359$	578.144	0.0849953	0.0424976	+	0.999097i	$0.486469\pi$
$360$	−6068.36	−0.888419
$361$	15881.5	2.31542
$362$	−1150.76	−0.167079
$363$	241.173	0.0348714
$364$	0	0
$365$	7689.25	1.10267
$366$	14.3116	0.00204393
$367$	−3450.55	−0.490782	−0.245391	−	0.969424i	$-0.578916\pi$
$367$	−3450.55	−0.490782	−0.245391	+	0.969424i	$0.578916\pi$
$368$	9955.22	1.41019
$369$	11555.5	1.63023
$370$	8561.37	1.20293
$371$	0	0
$372$	3.72708	0.000519463 0
$373$	2679.16	0.371908	0.185954	−	0.982558i	$-0.440463\pi$
$373$	2679.16	0.371908	0.185954	+	0.982558i	$0.440463\pi$
$374$	−8314.58	−1.14956
$375$	−144.141	−0.0198491
$376$	−1093.66	−0.150003
$377$	−668.319	−0.0913002
$378$	0	0
$379$	−4089.94	−0.554317	−0.277159	−	0.960824i	$-0.589393\pi$
$379$	−4089.94	−0.554317	−0.277159	+	0.960824i	$0.589393\pi$
$380$	717.600	0.0968739
$381$	−24.5181	−0.00329685
$382$	4131.86	0.553415
$383$	6367.73	0.849545	0.424773	−	0.905300i	$-0.360354\pi$
$383$	6367.73	0.849545	0.424773	+	0.905300i	$0.360354\pi$
$384$	−123.829	−0.0164560
$385$	0	0
$386$	−110.424	−0.0145607
$387$	−5537.59	−0.727368
$388$	55.1719	0.00721889
$389$	4677.42	0.609652	0.304826	−	0.952408i	$-0.401402\pi$
$389$	4677.42	0.609652	0.304826	+	0.952408i	$0.401402\pi$
$390$	−14.4931	−0.00188176
$391$	8125.19	1.05092
$392$	0	0
$393$	−89.5849	−0.0114986
$394$	−4872.70	−0.623053
$395$	5038.29	0.641782
$396$	−826.253	−0.104850
$397$	−9994.00	−1.26344	−0.631719	−	0.775198i	$-0.717650\pi$
$397$	−9994.00	−1.26344	−0.631719	+	0.775198i	$0.717650\pi$
$398$	12715.0	1.60137
$399$	0	0
$400$	1892.88	0.236610
$401$	494.956	0.0616382	0.0308191	−	0.999525i	$-0.490188\pi$
$401$	494.956	0.0616382	0.0308191	+	0.999525i	$0.490188\pi$
$402$	130.220	0.0161562
$403$	−456.765	−0.0564593
$404$	−255.381	−0.0314497
$405$	7036.55	0.863331
$406$	0	0
$407$	20100.6	2.44803
$408$	−108.192	−0.0131282
$409$	−2539.21	−0.306983	−0.153491	−	0.988150i	$-0.549052\pi$
$409$	−2539.21	−0.306983	−0.153491	+	0.988150i	$0.549052\pi$
$410$	11334.2	1.36525
$411$	28.5393	0.00342515
$412$	−796.045	−0.0951901
$413$	0	0
$414$	−12308.0	−1.46113
$415$	−710.553	−0.0840474
$416$	−127.934	−0.0150781
$417$	87.3401	0.0102567
$418$	−25682.1	−3.00514
$419$	−12843.4	−1.49747	−0.748734	−	0.662871i	$-0.769338\pi$
$419$	−12843.4	−1.49747	−0.748734	+	0.662871i	$0.769338\pi$
$420$	0	0
$421$	−8589.44	−0.994355	−0.497178	−	0.867649i	$-0.665630\pi$
$421$	−8589.44	−0.994355	−0.497178	+	0.867649i	$0.665630\pi$
$422$	−3087.60	−0.356166
$423$	1268.57	0.145816
$424$	11849.3	1.35720
$425$	1544.92	0.176329
$426$	−146.355	−0.0166453
$427$	0	0
$428$	294.127	0.0332177
$429$	−34.0271	−0.00382948
$430$	−5431.51	−0.609141
$431$	−3701.58	−0.413687	−0.206843	−	0.978374i	$-0.566319\pi$
$431$	−3701.58	−0.413687	−0.206843	+	0.978374i	$0.566319\pi$
$432$	307.575	0.0342551
$433$	6823.53	0.757317	0.378658	−	0.925537i	$-0.376386\pi$
$433$	6823.53	0.757317	0.378658	+	0.925537i	$0.376386\pi$
$434$	0	0
$435$	−106.984	−0.0117919
$436$	438.262	0.0481398
$437$	25097.1	2.74727
$438$	−207.666	−0.0226544
$439$	1926.62	0.209459	0.104729	−	0.994501i	$-0.466602\pi$
$439$	1926.62	0.209459	0.104729	+	0.994501i	$0.466602\pi$
$440$	−13974.5	−1.51411
$441$	0	0
$442$	768.948	0.0827492
$443$	−17646.1	−1.89253	−0.946266	−	0.323388i	$-0.895178\pi$
$443$	−17646.1	−1.89253	−0.946266	+	0.323388i	$0.895178\pi$
$444$	15.1684	0.00162131
$445$	−8249.97	−0.878845
$446$	3507.43	0.372380
$447$	61.3479	0.00649140
$448$	0	0
$449$	−15093.7	−1.58645	−0.793227	−	0.608926i	$-0.791601\pi$
$449$	−15093.7	−1.58645	−0.793227	+	0.608926i	$0.791601\pi$
$450$	−2340.24	−0.245156
$451$	26610.6	2.77836
$452$	−1022.47	−0.106400
$453$	66.5769	0.00690520
$454$	12092.7	1.25008
$455$	0	0
$456$	−334.184	−0.0343193
$457$	11880.9	1.21611	0.608056	−	0.793894i	$-0.291950\pi$
$457$	11880.9	1.21611	0.608056	+	0.793894i	$0.291950\pi$
$458$	11438.2	1.16697
$459$	251.035	0.0255279
$460$	791.965	0.0802729
$461$	16037.2	1.62024	0.810118	−	0.586267i	$-0.199403\pi$
$461$	16037.2	1.62024	0.810118	+	0.586267i	$0.199403\pi$
$462$	0	0
$463$	−13133.9	−1.31833	−0.659164	−	0.751999i	$-0.729090\pi$
$463$	−13133.9	−1.31833	−0.659164	+	0.751999i	$0.729090\pi$
$464$	6954.59	0.695817
$465$	−73.1185	−0.00729202
$466$	17834.2	1.77286
$467$	2326.38	0.230518	0.115259	−	0.993335i	$-0.463230\pi$
$467$	2326.38	0.230518	0.115259	+	0.993335i	$0.463230\pi$
$468$	76.4134	0.00754746
$469$	0	0
$470$	1244.27	0.122115
$471$	−253.513	−0.0248010
$472$	−10096.3	−0.984578
$473$	−12752.2	−1.23963
$474$	−136.070	−0.0131855
$475$	4771.94	0.460951
$476$	0	0
$477$	−13744.4	−1.31932
$478$	−5186.46	−0.496283
$479$	−2802.20	−0.267298	−0.133649	−	0.991029i	$-0.542670\pi$
$479$	−2802.20	−0.267298	−0.133649	+	0.991029i	$0.542670\pi$
$480$	−20.4795	−0.00194741
$481$	−1858.94	−0.176217
$482$	−6691.98	−0.632389
$483$	0	0
$484$	−1247.21	−0.117131
$485$	−1082.37	−0.101336
$486$	−570.433	−0.0532415
$487$	−15800.5	−1.47020	−0.735102	−	0.677957i	$-0.762866\pi$
$487$	−15800.5	−1.47020	−0.735102	+	0.677957i	$0.762866\pi$
$488$	−1276.21	−0.118384
$489$	−78.3335	−0.00724410
$490$	0	0
$491$	−16077.0	−1.47769	−0.738846	−	0.673875i	$-0.764629\pi$
$491$	−16077.0	−1.47769	−0.738846	+	0.673875i	$0.764629\pi$
$492$	20.0811	0.00184009
$493$	5676.16	0.518542
$494$	2375.13	0.216320
$495$	16209.6	1.47185
$496$	4753.14	0.430287
$497$	0	0
$498$	19.1901	0.00172676
$499$	7481.09	0.671141	0.335571	−	0.942015i	$-0.391071\pi$
$499$	7481.09	0.671141	0.335571	+	0.942015i	$0.391071\pi$
$500$	745.414	0.0666718
$501$	−235.201	−0.0209740
$502$	−3296.43	−0.293081
$503$	−21606.7	−1.91530	−0.957648	−	0.287941i	$-0.907029\pi$
$503$	−21606.7	−1.91530	−0.957648	+	0.287941i	$0.907029\pi$
$504$	0	0
$505$	5010.10	0.441479
$506$	−28343.5	−2.49016
$507$	−206.088	−0.0180526
$508$	126.793	0.0110739
$509$	9619.49	0.837675	0.418837	−	0.908061i	$-0.362438\pi$
$509$	9619.49	0.837675	0.418837	+	0.908061i	$0.362438\pi$
$510$	123.092	0.0106875
$511$	0	0
$512$	12466.6	1.07607
$513$	775.396	0.0667341
$514$	−17024.6	−1.46094
$515$	15616.9	1.33624
$516$	−9.62317	−0.000821001 0
$517$	2921.33	0.248511
$518$	0	0
$519$	−209.790	−0.0177433
$520$	1292.39	0.108990
$521$	1909.62	0.160580	0.0802900	−	0.996772i	$-0.474415\pi$
$521$	1909.62	0.160580	0.0802900	+	0.996772i	$0.474415\pi$
$522$	−8598.24	−0.720948
$523$	−8555.79	−0.715332	−0.357666	−	0.933850i	$-0.616427\pi$
$523$	−8555.79	−0.715332	−0.357666	+	0.933850i	$0.616427\pi$
$524$	463.280	0.0386231
$525$	0	0
$526$	9614.17	0.796954
$527$	3879.39	0.320662
$528$	354.090	0.0291852
$529$	15530.9	1.27648
$530$	−13481.2	−1.10488
$531$	11711.1	0.957097
$532$	0	0
$533$	−2460.99	−0.199995
$534$	222.809	0.0180560
$535$	−5770.22	−0.466296
$536$	−11612.1	−0.935761
$537$	12.8396	0.00103179
$538$	−12163.8	−0.974754
$539$	0	0
$540$	24.4685	0.00194992
$541$	23268.3	1.84914	0.924569	−	0.381015i	$-0.124426\pi$
$541$	23268.3	1.84914	0.924569	+	0.381015i	$0.124426\pi$
$542$	−16247.8	−1.28764
$543$	39.9983	0.00316113
$544$	1086.57	0.0856364
$545$	−8597.90	−0.675768
$546$	0	0
$547$	−1715.44	−0.134090	−0.0670448	−	0.997750i	$-0.521357\pi$
$547$	−1715.44	−0.134090	−0.0670448	+	0.997750i	$0.521357\pi$
$548$	−147.588	−0.0115049
$549$	1480.32	0.115079
$550$	−5389.22	−0.417813
$551$	17532.5	1.35555
$552$	−368.816	−0.0284381
$553$	0	0
$554$	15490.9	1.18799
$555$	−297.577	−0.0227593
$556$	−451.672	−0.0344517
$557$	−240.798	−0.0183177	−0.00915884	−	0.999958i	$-0.502915\pi$
$557$	−240.798	−0.0183177	−0.00915884	+	0.999958i	$0.502915\pi$
$558$	−5876.50	−0.445828
$559$	1179.35	0.0892328
$560$	0	0
$561$	288.999	0.0217496
$562$	−11704.9	−0.878542
$563$	−2878.72	−0.215495	−0.107747	−	0.994178i	$-0.534364\pi$
$563$	−2878.72	−0.215495	−0.107747	+	0.994178i	$0.534364\pi$
$564$	2.20452	0.000164587 0
$565$	20059.0	1.49361
$566$	19161.0	1.42296
$567$	0	0
$568$	13050.9	0.964088
$569$	17073.8	1.25794	0.628971	−	0.777428i	$-0.283476\pi$
$569$	17073.8	1.25794	0.628971	+	0.777428i	$0.283476\pi$
$570$	380.207	0.0279388
$571$	−9522.05	−0.697873	−0.348937	−	0.937146i	$-0.613457\pi$
$571$	−9522.05	−0.697873	−0.348937	+	0.937146i	$0.613457\pi$
$572$	175.968	0.0128629
$573$	−143.616	−0.0104705
$574$	0	0
$575$	5266.46	0.381959
$576$	−14562.1	−1.05340
$577$	25560.7	1.84420	0.922101	−	0.386948i	$-0.126471\pi$
$577$	25560.7	1.84420	0.922101	+	0.386948i	$0.126471\pi$
$578$	6930.70	0.498753
$579$	3.83813	0.000275487 0
$580$	553.257	0.0396082
$581$	0	0
$582$	29.2318	0.00208196
$583$	−31651.3	−2.24848
$584$	18518.1	1.31213
$585$	−1499.09	−0.105948
$586$	3031.78	0.213723
$587$	11227.5	0.789453	0.394727	−	0.918799i	$-0.370839\pi$
$587$	11227.5	0.789453	0.394727	+	0.918799i	$0.370839\pi$
$588$	0	0
$589$	11982.7	0.838263
$590$	11486.8	0.801530
$591$	169.366	0.0117881
$592$	19344.3	1.34298
$593$	−8757.49	−0.606453	−0.303227	−	0.952918i	$-0.598064\pi$
$593$	−8757.49	−0.606453	−0.303227	+	0.952918i	$0.598064\pi$
$594$	−875.698	−0.0604887
$595$	0	0
$596$	−317.255	−0.0218042
$597$	−441.948	−0.0302977
$598$	2621.26	0.179250
$599$	1669.01	0.113846	0.0569231	−	0.998379i	$-0.481871\pi$
$599$	1669.01	0.113846	0.0569231	+	0.998379i	$0.481871\pi$
$600$	−70.1265	−0.00477150
$601$	27909.9	1.89429	0.947145	−	0.320806i	$-0.103954\pi$
$601$	27909.9	1.89429	0.947145	+	0.320806i	$0.103954\pi$
$602$	0	0
$603$	13469.3	0.909642
$604$	−344.297	−0.0231941
$605$	24467.9	1.64423
$606$	−135.309	−0.00907022
$607$	2348.25	0.157022	0.0785110	−	0.996913i	$-0.474983\pi$
$607$	2348.25	0.157022	0.0785110	+	0.996913i	$0.474983\pi$
$608$	3356.19	0.223867
$609$	0	0
$610$	1451.96	0.0963743
$611$	−270.170	−0.0178886
$612$	−648.994	−0.0428660
$613$	−18308.8	−1.20634	−0.603169	−	0.797614i	$-0.706095\pi$
$613$	−18308.8	−1.20634	−0.603169	+	0.797614i	$0.706095\pi$
$614$	−17058.2	−1.12119
$615$	−393.953	−0.0258305
$616$	0	0
$617$	−7123.03	−0.464769	−0.232384	−	0.972624i	$-0.574653\pi$
$617$	−7123.03	−0.464769	−0.232384	+	0.972624i	$0.574653\pi$
$618$	−421.770	−0.0274532
$619$	−20503.9	−1.33138	−0.665688	−	0.746230i	$-0.731862\pi$
$619$	−20503.9	−1.33138	−0.665688	+	0.746230i	$0.731862\pi$
$620$	378.126	0.0244934
$621$	855.751	0.0552980
$622$	−12212.5	−0.787262
$623$	0	0
$624$	−32.7469	−0.00210084
$625$	−10668.1	−0.682758
$626$	−2738.20	−0.174825
$627$	892.659	0.0568570
$628$	1311.02	0.0833049
$629$	15788.3	1.00083
$630$	0	0
$631$	18537.2	1.16950	0.584750	−	0.811214i	$-0.301193\pi$
$631$	18537.2	1.16950	0.584750	+	0.811214i	$0.301193\pi$
$632$	12133.8	0.763697
$633$	107.319	0.00673863
$634$	−15558.1	−0.974589
$635$	−2487.44	−0.155451
$636$	−23.8850	−0.00148915
$637$	0	0
$638$	−19800.4	−1.22869
$639$	−15138.2	−0.937179
$640$	−12562.9	−0.775924
$641$	−11735.7	−0.723140	−0.361570	−	0.932345i	$-0.617759\pi$
$641$	−11735.7	−0.723140	−0.361570	+	0.932345i	$0.617759\pi$
$642$	155.838	0.00958011
$643$	24812.7	1.52180	0.760900	−	0.648869i	$-0.224758\pi$
$643$	24812.7	1.52180	0.760900	+	0.648869i	$0.224758\pi$
$644$	0	0
$645$	188.789	0.0115249
$646$	−20172.4	−1.22859
$647$	1433.72	0.0871180	0.0435590	−	0.999051i	$-0.486130\pi$
$647$	1433.72	0.0871180	0.0435590	+	0.999051i	$0.486130\pi$
$648$	16946.2	1.02733
$649$	26968.9	1.63116
$650$	498.405	0.0300755
$651$	0	0
$652$	405.095	0.0243324
$653$	17231.7	1.03266	0.516332	−	0.856389i	$-0.327297\pi$
$653$	17231.7	1.03266	0.516332	+	0.856389i	$0.327297\pi$
$654$	232.206	0.0138837
$655$	−9088.71	−0.542176
$656$	25609.3	1.52420
$657$	−21479.9	−1.27551
$658$	0	0
$659$	−27859.7	−1.64683	−0.823413	−	0.567443i	$-0.807933\pi$
$659$	−27859.7	−1.64683	−0.823413	+	0.567443i	$0.807933\pi$
$660$	28.1688	0.00166132
$661$	−9460.81	−0.556706	−0.278353	−	0.960479i	$-0.589789\pi$
$661$	−9460.81	−0.556706	−0.278353	+	0.960479i	$0.589789\pi$
$662$	24885.9	1.46105
$663$	−26.7272	−0.00156561
$664$	−1711.23	−0.100013
$665$	0	0
$666$	−23916.1	−1.39149
$667$	19349.4	1.12326
$668$	1216.32	0.0704503
$669$	−121.911	−0.00704539
$670$	13211.3	0.761788
$671$	3408.95	0.196127
$672$	0	0
$673$	−18909.2	−1.08306	−0.541529	−	0.840682i	$-0.682154\pi$
$673$	−18909.2	−1.08306	−0.541529	+	0.840682i	$0.682154\pi$
$674$	24795.1	1.41702
$675$	162.712	0.00927821
$676$	1065.76	0.0606374
$677$	−11779.3	−0.668706	−0.334353	−	0.942448i	$-0.608518\pi$
$677$	−11779.3	−0.668706	−0.334353	+	0.942448i	$0.608518\pi$
$678$	−541.738	−0.0306863
$679$	0	0
$680$	−10976.5	−0.619014
$681$	−420.318	−0.0236514
$682$	−13532.7	−0.759814
$683$	23932.6	1.34078	0.670391	−	0.742008i	$-0.266126\pi$
$683$	23932.6	1.34078	0.670391	+	0.742008i	$0.266126\pi$
$684$	−2004.61	−0.112059
$685$	2895.41	0.161501
$686$	0	0
$687$	−397.569	−0.0220789
$688$	−12272.4	−0.680060
$689$	2927.18	0.161853
$690$	419.608	0.0231510
$691$	31465.1	1.73225	0.866127	−	0.499823i	$-0.166602\pi$
$691$	31465.1	1.73225	0.866127	+	0.499823i	$0.166602\pi$
$692$	1084.91	0.0595986
$693$	0	0
$694$	15987.6	0.874466
$695$	8860.97	0.483620
$696$	−257.650	−0.0140319
$697$	20901.7	1.13588
$698$	−7740.58	−0.419750
$699$	−619.881	−0.0335423
$700$	0	0
$701$	16546.0	0.891489	0.445744	−	0.895160i	$-0.352939\pi$
$701$	16546.0	0.891489	0.445744	+	0.895160i	$0.352939\pi$
$702$	80.9862	0.00435417
$703$	48766.9	2.61633
$704$	−33534.4	−1.79528
$705$	−43.2485	−0.00231040
$706$	−5177.96	−0.276027
$707$	0	0
$708$	20.3514	0.00108030
$709$	22516.5	1.19270	0.596351	−	0.802724i	$-0.296617\pi$
$709$	22516.5	1.19270	0.596351	+	0.802724i	$0.296617\pi$
$710$	−14848.2	−0.784849
$711$	−14074.4	−0.742380
$712$	−19868.5	−1.04579
$713$	13224.4	0.694612
$714$	0	0
$715$	−3452.17	−0.180565
$716$	−66.3989	−0.00346570
$717$	180.271	0.00938962
$718$	−1584.10	−0.0823374
$719$	−30460.9	−1.57997	−0.789987	−	0.613123i	$-0.789913\pi$
$719$	−30460.9	−1.57997	−0.789987	+	0.613123i	$0.789913\pi$
$720$	15599.7	0.807452
$721$	0	0
$722$	−43514.9	−2.24301
$723$	232.600	0.0119647
$724$	−206.848	−0.0106180
$725$	3679.09	0.188466
$726$	−660.810	−0.0337809
$727$	21196.8	1.08136	0.540678	−	0.841229i	$-0.318168\pi$
$727$	21196.8	1.08136	0.540678	+	0.841229i	$0.318168\pi$
$728$	0	0
$729$	−19643.3	−0.997985
$730$	−21068.4	−1.06819
$731$	−10016.4	−0.506800
$732$	2.57249	0.000129893 0
$733$	−5794.01	−0.291960	−0.145980	−	0.989288i	$-0.546633\pi$
$733$	−5794.01	−0.291960	−0.145980	+	0.989288i	$0.546633\pi$
$734$	9454.43	0.475435
$735$	0	0
$736$	3703.99	0.185504
$737$	31017.8	1.55028
$738$	−31661.9	−1.57925
$739$	19620.6	0.976665	0.488333	−	0.872658i	$-0.337605\pi$
$739$	19620.6	0.976665	0.488333	+	0.872658i	$0.337605\pi$
$740$	1538.89	0.0764471
$741$	−82.5548	−0.00409275
$742$	0	0
$743$	8343.98	0.411993	0.205997	−	0.978553i	$-0.433956\pi$
$743$	8343.98	0.411993	0.205997	+	0.978553i	$0.433956\pi$
$744$	−176.092	−0.00867722
$745$	6223.96	0.306078
$746$	−7340.84	−0.360278
$747$	1984.92	0.0972216
$748$	−1494.53	−0.0730555
$749$	0	0
$750$	394.944	0.0192284
$751$	15510.6	0.753649	0.376824	−	0.926285i	$-0.377016\pi$
$751$	15510.6	0.753649	0.376824	+	0.926285i	$0.377016\pi$
$752$	2811.42	0.136332
$753$	114.577	0.00554506
$754$	1831.18	0.0884452
$755$	6754.46	0.325589
$756$	0	0
$757$	−28842.5	−1.38481	−0.692404	−	0.721510i	$-0.743448\pi$
$757$	−28842.5	−1.38481	−0.692404	+	0.721510i	$0.743448\pi$
$758$	11206.4	0.536984
$759$	985.165	0.0471136
$760$	−33904.2	−1.61820
$761$	−35092.3	−1.67161	−0.835804	−	0.549028i	$-0.814998\pi$
$761$	−35092.3	−1.67161	−0.835804	+	0.549028i	$0.814998\pi$
$762$	67.1790	0.00319375
$763$	0	0
$764$	742.695	0.0351698
$765$	12732.1	0.601737
$766$	−17447.5	−0.822980
$767$	−2494.13	−0.117416
$768$	−71.7668	−0.00337196
$769$	−37369.3	−1.75237	−0.876183	−	0.481978i	$-0.839918\pi$
$769$	−37369.3	−1.75237	−0.876183	+	0.481978i	$0.839918\pi$
$770$	0	0
$771$	591.741	0.0276408
$772$	−19.8485	−0.000925343 0
$773$	−33268.6	−1.54798	−0.773990	−	0.633197i	$-0.781742\pi$
$773$	−33268.6	−1.54798	−0.773990	+	0.633197i	$0.781742\pi$
$774$	15172.9	0.704622
$775$	2514.49	0.116546
$776$	−2606.69	−0.120586
$777$	0	0
$778$	−12816.0	−0.590588
$779$	64561.1	2.96937
$780$	−2.60511	−0.000119587 0
$781$	−34860.9	−1.59721
$782$	−22262.9	−1.01805
$783$	597.817	0.0272851
$784$	0	0
$785$	−25719.8	−1.16940
$786$	245.461	0.0111391
$787$	−3952.99	−0.179046	−0.0895229	−	0.995985i	$-0.528534\pi$
$787$	−3952.99	−0.179046	−0.0895229	+	0.995985i	$0.528534\pi$
$788$	−875.859	−0.0395954
$789$	−334.170	−0.0150783
$790$	−13804.8	−0.621713
$791$	0	0
$792$	39037.7	1.75144
$793$	−315.266	−0.0141178
$794$	27383.4	1.22393
$795$	468.579	0.0209041
$796$	2285.50	0.101768
$797$	−26875.4	−1.19445	−0.597225	−	0.802074i	$-0.703730\pi$
$797$	−26875.4	−1.19445	−0.597225	+	0.802074i	$0.703730\pi$
$798$	0	0
$799$	2294.61	0.101599
$800$	704.275	0.0311248
$801$	23046.2	1.01660
$802$	−1356.17	−0.0597107
$803$	−49464.8	−2.17382
$804$	23.4069	0.00102674
$805$	0	0
$806$	1251.53	0.0546938
$807$	422.789	0.0184422
$808$	12065.9	0.525343
$809$	−12516.3	−0.543942	−0.271971	−	0.962305i	$-0.587676\pi$
$809$	−12516.3	−0.543942	−0.271971	+	0.962305i	$0.587676\pi$
$810$	−19280.0	−0.836334
$811$	−28510.4	−1.23444	−0.617222	−	0.786789i	$-0.711742\pi$
$811$	−28510.4	−1.23444	−0.617222	+	0.786789i	$0.711742\pi$
$812$	0	0
$813$	564.741	0.0243620
$814$	−55075.2	−2.37148
$815$	−7947.22	−0.341569
$816$	278.126	0.0119318
$817$	−30938.7	−1.32486
$818$	6957.39	0.297383
$819$	0	0
$820$	2037.29	0.0867627
$821$	−25559.9	−1.08654	−0.543269	−	0.839559i	$-0.682814\pi$
$821$	−25559.9	−1.08654	−0.543269	+	0.839559i	$0.682814\pi$
$822$	−78.1970	−0.00331805
$823$	−13802.1	−0.584581	−0.292290	−	0.956330i	$-0.594417\pi$
$823$	−13802.1	−0.584581	−0.292290	+	0.956330i	$0.594417\pi$
$824$	37610.5	1.59008
$825$	187.319	0.00790498
$826$	0	0
$827$	4595.00	0.193209	0.0966045	−	0.995323i	$-0.469202\pi$
$827$	4595.00	0.193209	0.0966045	+	0.995323i	$0.469202\pi$
$828$	−2212.35	−0.0928556
$829$	33655.5	1.41002	0.705008	−	0.709199i	$-0.250943\pi$
$829$	33655.5	1.41002	0.705008	+	0.709199i	$0.250943\pi$
$830$	1946.90	0.0814192
$831$	−538.434	−0.0224766
$832$	3101.32	0.129230
$833$	0	0
$834$	−239.310	−0.00993601
$835$	−23861.9	−0.988954
$836$	−4616.31	−0.190979
$837$	408.580	0.0168729
$838$	35190.5	1.45064
$839$	−36805.2	−1.51449	−0.757244	−	0.653132i	$-0.773454\pi$
$839$	−36805.2	−1.51449	−0.757244	+	0.653132i	$0.773454\pi$
$840$	0	0
$841$	−10871.7	−0.445764
$842$	23534.9	0.963261
$843$	406.839	0.0166219
$844$	−554.992	−0.0226346
$845$	−20908.3	−0.851205
$846$	−3475.87	−0.141256
$847$	0	0
$848$	−30460.5	−1.23351
$849$	−665.998	−0.0269223
$850$	−4233.05	−0.170815
$851$	53820.6	2.16798
$852$	−26.3070	−0.00105782
$853$	−13469.1	−0.540647	−0.270323	−	0.962770i	$-0.587131\pi$
$853$	−13469.1	−0.540647	−0.270323	+	0.962770i	$0.587131\pi$
$854$	0	0
$855$	39326.7	1.57304
$856$	−13896.5	−0.554875
$857$	−34185.6	−1.36261	−0.681307	−	0.731998i	$-0.738588\pi$
$857$	−34185.6	−1.36261	−0.681307	+	0.731998i	$0.738588\pi$
$858$	93.2337	0.00370973
$859$	9084.15	0.360823	0.180412	−	0.983591i	$-0.442257\pi$
$859$	9084.15	0.360823	0.180412	+	0.983591i	$0.442257\pi$
$860$	−976.304	−0.0387113
$861$	0	0
$862$	10142.3	0.400750
$863$	−30343.8	−1.19689	−0.598444	−	0.801165i	$-0.704214\pi$
$863$	−30343.8	−1.19689	−0.598444	+	0.801165i	$0.704214\pi$
$864$	114.438	0.00450609
$865$	−21284.0	−0.836621
$866$	−18696.3	−0.733635
$867$	−240.898	−0.00943635
$868$	0	0
$869$	−32411.3	−1.26522
$870$	293.133	0.0114232
$871$	−2868.59	−0.111594
$872$	−20706.4	−0.804138
$873$	3023.59	0.117220
$874$	−68765.5	−2.66136
$875$	0	0
$876$	−37.3275	−0.00143970
$877$	29196.5	1.12417	0.562085	−	0.827080i	$-0.309999\pi$
$877$	29196.5	1.12417	0.562085	+	0.827080i	$0.309999\pi$
$878$	−5278.89	−0.202909
$879$	−105.379	−0.00404362
$880$	35923.7	1.37612
$881$	−22983.1	−0.878910	−0.439455	−	0.898265i	$-0.644828\pi$
$881$	−22983.1	−0.878910	−0.439455	+	0.898265i	$0.644828\pi$
$882$	0	0
$883$	13574.8	0.517360	0.258680	−	0.965963i	$-0.416713\pi$
$883$	13574.8	0.517360	0.258680	+	0.965963i	$0.416713\pi$
$884$	138.217	0.00525876
$885$	−399.258	−0.0151649
$886$	48350.0	1.83335
$887$	−14757.9	−0.558649	−0.279324	−	0.960197i	$-0.590110\pi$
$887$	−14757.9	−0.558649	−0.279324	+	0.960197i	$0.590110\pi$
$888$	−716.658	−0.0270827
$889$	0	0
$890$	22604.8	0.851363
$891$	−45266.0	−1.70199
$892$	630.454	0.0236650
$893$	7087.57	0.265595
$894$	−168.092	−0.00628841
$895$	1302.62	0.0486501
$896$	0	0
$897$	−91.1100	−0.00339139
$898$	41356.6	1.53684
$899$	9238.42	0.342735
$900$	−420.655	−0.0155798
$901$	−24861.1	−0.919248
$902$	−72912.4	−2.69148
$903$	0	0
$904$	48308.4	1.77734
$905$	4057.97	0.149051
$906$	−182.419	−0.00668927
$907$	−50799.7	−1.85973	−0.929866	−	0.367900i	$-0.880077\pi$
$907$	−50799.7	−1.85973	−0.929866	+	0.367900i	$0.880077\pi$
$908$	2173.64	0.0794436
$909$	−13995.7	−0.510679
$910$	0	0
$911$	7405.57	0.269328	0.134664	−	0.990891i	$-0.457005\pi$
$911$	7405.57	0.269328	0.134664	+	0.990891i	$0.457005\pi$
$912$	859.073	0.0311916
$913$	4570.97	0.165692
$914$	−32553.3	−1.17808
$915$	−50.4675	−0.00182339
$916$	2055.99	0.0741615
$917$	0	0
$918$	−687.831	−0.0247296
$919$	8188.46	0.293920	0.146960	−	0.989142i	$-0.453051\pi$
$919$	8188.46	0.293920	0.146960	+	0.989142i	$0.453051\pi$
$920$	−37417.7	−1.34090
$921$	592.909	0.0212128
$922$	−43941.7	−1.56957
$923$	3224.00	0.114972
$924$	0	0
$925$	10233.4	0.363755
$926$	35986.7	1.27710
$927$	−43625.8	−1.54569
$928$	2587.56	0.0915311
$929$	−10824.1	−0.382267	−0.191133	−	0.981564i	$-0.561216\pi$
$929$	−10824.1	−0.382267	−0.191133	+	0.981564i	$0.561216\pi$
$930$	200.343	0.00706399
$931$	0	0
$932$	3205.66	0.112666
$933$	424.483	0.0148949
$934$	−6374.23	−0.223309
$935$	29320.0	1.02552
$936$	−3610.28	−0.126074
$937$	−48255.9	−1.68245	−0.841223	−	0.540689i	$-0.818164\pi$
$937$	−48255.9	−1.68245	−0.841223	+	0.540689i	$0.818164\pi$
$938$	0	0
$939$	95.1746	0.00330768
$940$	223.656	0.00776048
$941$	−11590.4	−0.401527	−0.200764	−	0.979640i	$-0.564342\pi$
$941$	−11590.4	−0.401527	−0.200764	+	0.979640i	$0.564342\pi$
$942$	694.622	0.0240255
$943$	71251.6	2.46052
$944$	25954.2	0.894848
$945$	0	0
$946$	34940.8	1.20087
$947$	−41836.4	−1.43559	−0.717793	−	0.696257i	$-0.754847\pi$
$947$	−41836.4	−1.43559	−0.717793	+	0.696257i	$0.754847\pi$
$948$	−24.4584	−0.000837946 0
$949$	4574.60	0.156478
$950$	−13075.0	−0.446537
$951$	540.768	0.0184391
$952$	0	0
$953$	−10455.3	−0.355384	−0.177692	−	0.984086i	$-0.556863\pi$
$953$	−10455.3	−0.355384	−0.177692	+	0.984086i	$0.556863\pi$
$954$	37659.5	1.27806
$955$	−14570.3	−0.493701
$956$	−932.258	−0.0315391
$957$	688.225	0.0232468
$958$	7677.98	0.258940
$959$	0	0
$960$	496.456	0.0166907
$961$	−23477.0	−0.788056
$962$	5093.46	0.170706
$963$	16119.1	0.539387
$964$	−1202.87	−0.0401887
$965$	389.392	0.0129896
$966$	0	0
$967$	20967.3	0.697272	0.348636	−	0.937258i	$-0.386645\pi$
$967$	20967.3	0.697272	0.348636	+	0.937258i	$0.386645\pi$
$968$	58926.3	1.95657
$969$	701.153	0.0232449
$970$	2965.67	0.0981671
$971$	−24366.4	−0.805310	−0.402655	−	0.915352i	$-0.631912\pi$
$971$	−24366.4	−0.805310	−0.402655	+	0.915352i	$0.631912\pi$
$972$	−102.534	−0.00338353
$973$	0	0
$974$	43293.1	1.42423
$975$	−17.3236	−0.000569025 0
$976$	3280.69	0.107595
$977$	−28465.2	−0.932122	−0.466061	−	0.884753i	$-0.654327\pi$
$977$	−28465.2	−0.932122	−0.466061	+	0.884753i	$0.654327\pi$
$978$	214.632	0.00701757
$979$	53071.9	1.73257
$980$	0	0
$981$	24018.2	0.781693
$982$	44050.8	1.43148
$983$	47503.8	1.54134	0.770669	−	0.637235i	$-0.219922\pi$
$983$	47503.8	1.54134	0.770669	+	0.637235i	$0.219922\pi$
$984$	−948.763	−0.0307373
$985$	17182.7	0.555825
$986$	−15552.6	−0.502327
$987$	0	0
$988$	426.925	0.0137473
$989$	−34144.9	−1.09782
$990$	−44413.9	−1.42582
$991$	−56212.1	−1.80185	−0.900926	−	0.433973i	$-0.857111\pi$
$991$	−56212.1	−1.80185	−0.900926	+	0.433973i	$0.857111\pi$
$992$	1768.48	0.0566021
$993$	−864.984	−0.0276429
$994$	0	0
$995$	−44837.2	−1.42858
$996$	3.44938	0.000109737 0
$997$	−9314.94	−0.295895	−0.147947	−	0.988995i	$-0.547267\pi$
$997$	−9314.94	−0.295895	−0.147947	+	0.988995i	$0.547267\pi$
$998$	−20498.0	−0.650154
$999$	1662.84	0.0526625

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2303.4.a.n.1.19	yes	68
7.6	odd	2		2303.4.a.m.1.19	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2303.4.a.m.1.19	✓	68	7.6	odd	2
2303.4.a.n.1.19	yes	68	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)

\(f(q)\)	\(=\)	\(q-2.73998 q^{2} +0.0952364 q^{3} -0.492507 q^{4} +9.66207 q^{5} -0.260946 q^{6} +23.2693 q^{8} -26.9909 q^{9} +O(q^{10})\)	\(q-2.73998 q^{2} +0.0952364 q^{3} -0.492507 q^{4} +9.66207 q^{5} -0.260946 q^{6} +23.2693 q^{8} -26.9909 q^{9} -26.4739 q^{10} -62.1560 q^{11} -0.0469046 q^{12} +5.74830 q^{13} +0.920182 q^{15} -59.8174 q^{16} -48.8214 q^{17} +73.9546 q^{18} -150.799 q^{19} -4.75864 q^{20} +170.306 q^{22} -166.427 q^{23} +2.21609 q^{24} -31.6443 q^{25} -15.7502 q^{26} -5.14190 q^{27} -116.264 q^{29} -2.52128 q^{30} -79.4609 q^{31} -22.2560 q^{32} -5.91951 q^{33} +133.770 q^{34} +13.2932 q^{36} -323.389 q^{37} +413.187 q^{38} +0.547448 q^{39} +224.830 q^{40} -428.126 q^{41} +205.165 q^{43} +30.6122 q^{44} -260.788 q^{45} +456.006 q^{46} -47.0000 q^{47} -5.69679 q^{48} +86.7048 q^{50} -4.64958 q^{51} -2.83108 q^{52} +509.225 q^{53} +14.0887 q^{54} -600.555 q^{55} -14.3616 q^{57} +318.560 q^{58} -433.890 q^{59} -0.453196 q^{60} -54.8451 q^{61} +217.721 q^{62} +539.520 q^{64} +55.5405 q^{65} +16.2193 q^{66} -499.032 q^{67} +24.0449 q^{68} -15.8499 q^{69} +560.862 q^{71} -628.060 q^{72} +795.818 q^{73} +886.080 q^{74} -3.01369 q^{75} +74.2697 q^{76} -1.50000 q^{78} +521.450 q^{79} -577.960 q^{80} +728.265 q^{81} +1173.06 q^{82} -73.5404 q^{83} -471.716 q^{85} -562.147 q^{86} -11.0725 q^{87} -1446.33 q^{88} -853.851 q^{89} +714.555 q^{90} +81.9663 q^{92} -7.56757 q^{93} +128.779 q^{94} -1457.04 q^{95} -2.11958 q^{96} -112.023 q^{97} +1677.65 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 2 q^{2} + 24 q^{3} + 254 q^{4} + 40 q^{5} + 48 q^{6} - 66 q^{8} + 576 q^{9}+O(q^{10}) \) 68 * q - 2 * q^2 + 24 * q^3 + 254 * q^4 + 40 * q^5 + 48 * q^6 - 66 * q^8 + 576 * q^9	\( 68 q - 2 q^{2} + 24 q^{3} + 254 q^{4} + 40 q^{5} + 48 q^{6} - 66 q^{8} + 576 q^{9} + 200 q^{10} - 20 q^{11} + 288 q^{12} + 520 q^{13} + 88 q^{15} + 1062 q^{16} + 784 q^{17} - 2 q^{18} + 532 q^{19} + 400 q^{20} - 4 q^{22} - 268 q^{23} + 576 q^{24} + 1864 q^{25} + 312 q^{26} + 864 q^{27} + 200 q^{29} + 792 q^{30} + 936 q^{31} + 30 q^{32} + 2112 q^{33} + 1088 q^{34} + 2130 q^{36} - 356 q^{37} + 1192 q^{38} - 488 q^{39} + 2400 q^{40} + 1476 q^{41} - 92 q^{43} + 192 q^{44} + 1848 q^{45} - 424 q^{46} - 3196 q^{47} + 2688 q^{48} - 1338 q^{50} - 148 q^{51} + 4980 q^{52} - 80 q^{53} + 4944 q^{54} + 2200 q^{55} + 2244 q^{57} - 356 q^{58} + 560 q^{59} - 736 q^{60} + 3944 q^{61} + 1488 q^{62} + 3778 q^{64} + 2004 q^{65} - 1000 q^{66} + 2768 q^{67} + 8192 q^{68} + 2208 q^{69} - 2448 q^{71} - 5234 q^{72} + 9532 q^{73} - 2000 q^{74} + 11136 q^{75} + 6384 q^{76} - 3460 q^{78} - 1520 q^{79} + 616 q^{80} + 6976 q^{81} + 4976 q^{82} + 3320 q^{83} + 3244 q^{85} - 2892 q^{86} + 2360 q^{87} - 2868 q^{88} + 8152 q^{89} + 5400 q^{90} - 4684 q^{92} + 2840 q^{93} + 94 q^{94} - 4256 q^{95} + 5376 q^{96} + 13968 q^{97} + 2380 q^{99}+O(q^{100}) \) 68 * q - 2 * q^2 + 24 * q^3 + 254 * q^4 + 40 * q^5 + 48 * q^6 - 66 * q^8 + 576 * q^9 + 200 * q^10 - 20 * q^11 + 288 * q^12 + 520 * q^13 + 88 * q^15 + 1062 * q^16 + 784 * q^17 - 2 * q^18 + 532 * q^19 + 400 * q^20 - 4 * q^22 - 268 * q^23 + 576 * q^24 + 1864 * q^25 + 312 * q^26 + 864 * q^27 + 200 * q^29 + 792 * q^30 + 936 * q^31 + 30 * q^32 + 2112 * q^33 + 1088 * q^34 + 2130 * q^36 - 356 * q^37 + 1192 * q^38 - 488 * q^39 + 2400 * q^40 + 1476 * q^41 - 92 * q^43 + 192 * q^44 + 1848 * q^45 - 424 * q^46 - 3196 * q^47 + 2688 * q^48 - 1338 * q^50 - 148 * q^51 + 4980 * q^52 - 80 * q^53 + 4944 * q^54 + 2200 * q^55 + 2244 * q^57 - 356 * q^58 + 560 * q^59 - 736 * q^60 + 3944 * q^61 + 1488 * q^62 + 3778 * q^64 + 2004 * q^65 - 1000 * q^66 + 2768 * q^67 + 8192 * q^68 + 2208 * q^69 - 2448 * q^71 - 5234 * q^72 + 9532 * q^73 - 2000 * q^74 + 11136 * q^75 + 6384 * q^76 - 3460 * q^78 - 1520 * q^79 + 616 * q^80 + 6976 * q^81 + 4976 * q^82 + 3320 * q^83 + 3244 * q^85 - 2892 * q^86 + 2360 * q^87 - 2868 * q^88 + 8152 * q^89 + 5400 * q^90 - 4684 * q^92 + 2840 * q^93 + 94 * q^94 - 4256 * q^95 + 5376 * q^96 + 13968 * q^97 + 2380 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

Properties

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