LMFDB - Embedded newform 2303.4.a.n.1.10

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			1.10
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)

$f(q)$	$=$	$q-4.41806 q^{2} -1.05773 q^{3} +11.5193 q^{4} +10.7523 q^{5} +4.67309 q^{6} -15.5483 q^{8} -25.8812 q^{9} +O(q^{10})$	\(q-4.41806 q^{2} -1.05773 q^{3} +11.5193 q^{4} +10.7523 q^{5} +4.67309 q^{6} -15.5483 q^{8} -25.8812 q^{9} -47.5044 q^{10} -0.390434 q^{11} -12.1842 q^{12} -40.1358 q^{13} -11.3730 q^{15} -23.4607 q^{16} +76.4477 q^{17} +114.345 q^{18} +14.2734 q^{19} +123.859 q^{20} +1.72496 q^{22} +71.5317 q^{23} +16.4458 q^{24} -9.38781 q^{25} +177.323 q^{26} +55.9338 q^{27} +99.7591 q^{29} +50.2466 q^{30} -260.539 q^{31} +228.037 q^{32} +0.412972 q^{33} -337.751 q^{34} -298.133 q^{36} -346.095 q^{37} -63.0607 q^{38} +42.4527 q^{39} -167.180 q^{40} -92.0055 q^{41} -388.659 q^{43} -4.49751 q^{44} -278.283 q^{45} -316.032 q^{46} -47.0000 q^{47} +24.8150 q^{48} +41.4759 q^{50} -80.8607 q^{51} -462.335 q^{52} +440.505 q^{53} -247.119 q^{54} -4.19806 q^{55} -15.0973 q^{57} -440.742 q^{58} +219.593 q^{59} -131.008 q^{60} +223.776 q^{61} +1151.08 q^{62} -819.797 q^{64} -431.553 q^{65} -1.82453 q^{66} +394.340 q^{67} +880.621 q^{68} -75.6609 q^{69} +516.434 q^{71} +402.409 q^{72} -576.563 q^{73} +1529.07 q^{74} +9.92973 q^{75} +164.419 q^{76} -187.558 q^{78} +652.948 q^{79} -252.257 q^{80} +639.630 q^{81} +406.486 q^{82} -828.925 q^{83} +821.989 q^{85} +1717.12 q^{86} -105.518 q^{87} +6.07059 q^{88} +295.504 q^{89} +1229.47 q^{90} +823.993 q^{92} +275.578 q^{93} +207.649 q^{94} +153.472 q^{95} -241.201 q^{96} -756.018 q^{97} +10.1049 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.41806	−1.56202	−0.781010	−	0.624518i	$-0.785295\pi$
$2$	−4.41806	−1.56202	−0.781010	+	0.624518i	$0.785295\pi$
$3$	−1.05773	−0.203559	−0.101780	−	0.994807i	$-0.532454\pi$
$3$	−1.05773	−0.203559	−0.101780	+	0.994807i	$0.532454\pi$
$4$	11.5193	1.43991
$5$	10.7523	0.961716	0.480858	−	0.876799i	$-0.340325\pi$
$5$	10.7523	0.961716	0.480858	+	0.876799i	$0.340325\pi$
$6$	4.67309	0.317964
$7$	0	0
$7$	0	0
$8$	−15.5483	−0.687145
$9$	−25.8812	−0.958564
$10$	−47.5044	−1.50222
$11$	−0.390434	−0.0107018	−0.00535092	−	0.999986i	$-0.501703\pi$
$11$	−0.390434	−0.0107018	−0.00535092	+	0.999986i	$0.501703\pi$
$12$	−12.1842	−0.293107
$13$	−40.1358	−0.856283	−0.428141	−	0.903712i	$-0.640831\pi$
$13$	−40.1358	−0.856283	−0.428141	+	0.903712i	$0.640831\pi$
$14$	0	0
$15$	−11.3730	−0.195766
$16$	−23.4607	−0.366573
$17$	76.4477	1.09066	0.545332	−	0.838220i	$-0.316404\pi$
$17$	76.4477	1.09066	0.545332	+	0.838220i	$0.316404\pi$
$18$	114.345	1.49730
$19$	14.2734	0.172344	0.0861721	−	0.996280i	$-0.472536\pi$
$19$	14.2734	0.172344	0.0861721	+	0.996280i	$0.472536\pi$
$20$	123.859	1.38478
$21$	0	0
$22$	1.72496	0.0167165
$23$	71.5317	0.648496	0.324248	−	0.945972i	$-0.394889\pi$
$23$	71.5317	0.648496	0.324248	+	0.945972i	$0.394889\pi$
$24$	16.4458	0.139875
$25$	−9.38781	−0.0751025
$26$	177.323	1.33753
$27$	55.9338	0.398684
$28$	0	0
$29$	99.7591	0.638786	0.319393	−	0.947622i	$-0.396521\pi$
$29$	99.7591	0.638786	0.319393	+	0.947622i	$0.396521\pi$
$30$	50.2466	0.305791
$31$	−260.539	−1.50949	−0.754744	−	0.656020i	$-0.772239\pi$
$31$	−260.539	−1.50949	−0.754744	+	0.656020i	$0.772239\pi$
$32$	228.037	1.25974
$33$	0.412972	0.00217846
$34$	−337.751	−1.70364
$35$	0	0
$36$	−298.133	−1.38024
$37$	−346.095	−1.53777	−0.768887	−	0.639384i	$-0.779189\pi$
$37$	−346.095	−1.53777	−0.768887	+	0.639384i	$0.779189\pi$
$38$	−63.0607	−0.269205
$39$	42.4527	0.174304
$40$	−167.180	−0.660838
$41$	−92.0055	−0.350460	−0.175230	−	0.984528i	$-0.556067\pi$
$41$	−92.0055	−0.350460	−0.175230	+	0.984528i	$0.556067\pi$
$42$	0	0
$43$	−388.659	−1.37837	−0.689186	−	0.724585i	$-0.742032\pi$
$43$	−388.659	−1.37837	−0.689186	+	0.724585i	$0.742032\pi$
$44$	−4.49751	−0.0154097
$45$	−278.283	−0.921866
$46$	−316.032	−1.01296
$47$	−47.0000	−0.145865
$47$	−47.0000	−0.145865
$48$	24.8150	0.0746194
$49$	0	0
$50$	41.4759	0.117312
$51$	−80.8607	−0.222015
$52$	−462.335	−1.23297
$53$	440.505	1.14166	0.570831	−	0.821068i	$-0.306621\pi$
$53$	440.505	1.14166	0.570831	+	0.821068i	$0.306621\pi$
$54$	−247.119	−0.622752
$55$	−4.19806	−0.0102921
$56$	0	0
$57$	−15.0973	−0.0350823
$58$	−440.742	−0.997797
$59$	219.593	0.484552	0.242276	−	0.970207i	$-0.422106\pi$
$59$	219.593	0.484552	0.242276	+	0.970207i	$0.422106\pi$
$60$	−131.008	−0.281885
$61$	223.776	0.469699	0.234849	−	0.972032i	$-0.424540\pi$
$61$	223.776	0.469699	0.234849	+	0.972032i	$0.424540\pi$
$62$	1151.08	2.35785
$63$	0	0
$64$	−819.797	−1.60117
$65$	−431.553	−0.823501
$66$	−1.82453	−0.00340280
$67$	394.340	0.719050	0.359525	−	0.933135i	$-0.382939\pi$
$67$	394.340	0.719050	0.359525	+	0.933135i	$0.382939\pi$
$68$	880.621	1.57046
$69$	−75.6609	−0.132007
$70$	0	0
$71$	516.434	0.863232	0.431616	−	0.902057i	$-0.357944\pi$
$71$	516.434	0.863232	0.431616	+	0.902057i	$0.357944\pi$
$72$	402.409	0.658672
$73$	−576.563	−0.924405	−0.462202	−	0.886774i	$-0.652941\pi$
$73$	−576.563	−0.924405	−0.462202	+	0.886774i	$0.652941\pi$
$74$	1529.07	2.40204
$75$	9.92973	0.0152878
$76$	164.419	0.248160
$77$	0	0
$78$	−187.558	−0.272267
$79$	652.948	0.929904	0.464952	−	0.885336i	$-0.346072\pi$
$79$	652.948	0.929904	0.464952	+	0.885336i	$0.346072\pi$
$80$	−252.257	−0.352539
$81$	639.630	0.877408
$82$	406.486	0.547425
$83$	−828.925	−1.09622	−0.548110	−	0.836406i	$-0.684653\pi$
$83$	−828.925	−1.09622	−0.548110	+	0.836406i	$0.684653\pi$
$84$	0	0
$85$	821.989	1.04891
$86$	1717.12	2.15304
$87$	−105.518	−0.130031
$88$	6.07059	0.00735371
$89$	295.504	0.351948	0.175974	−	0.984395i	$-0.443692\pi$
$89$	295.504	0.351948	0.175974	+	0.984395i	$0.443692\pi$
$90$	1229.47	1.43997
$91$	0	0
$92$	823.993	0.933774
$93$	275.578	0.307270
$94$	207.649	0.227844
$95$	153.472	0.165746
$96$	−241.201	−0.256432
$97$	−756.018	−0.791361	−0.395680	−	0.918388i	$-0.629491\pi$
$97$	−756.018	−0.791361	−0.395680	+	0.918388i	$0.629491\pi$
$98$	0	0
$99$	10.1049	0.0102584
$100$	−108.141	−0.108141
$101$	1108.30	1.09189	0.545943	−	0.837823i	$-0.316172\pi$
$101$	1108.30	1.09189	0.545943	+	0.837823i	$0.316172\pi$
$102$	357.247	0.346792
$103$	1946.39	1.86198	0.930988	−	0.365049i	$-0.118948\pi$
$103$	1946.39	1.86198	0.930988	+	0.365049i	$0.118948\pi$
$104$	624.045	0.588390
$105$	0	0
$106$	−1946.18	−1.78330
$107$	689.817	0.623244	0.311622	−	0.950206i	$-0.399128\pi$
$107$	689.817	0.623244	0.311622	+	0.950206i	$0.399128\pi$
$108$	644.316	0.574068
$109$	161.406	0.141834	0.0709171	−	0.997482i	$-0.477407\pi$
$109$	161.406	0.141834	0.0709171	+	0.997482i	$0.477407\pi$
$110$	18.5473	0.0160765
$111$	366.073	0.313028
$112$	0	0
$113$	−1481.41	−1.23327	−0.616633	−	0.787251i	$-0.711504\pi$
$113$	−1481.41	−1.23327	−0.616633	+	0.787251i	$0.711504\pi$
$114$	66.7009	0.0547992
$115$	769.132	0.623669
$116$	1149.15	0.919794
$117$	1038.76	0.820801
$118$	−970.175	−0.756880
$119$	0	0
$120$	176.831	0.134520
$121$	−1330.85	−0.999885
$122$	−988.657	−0.733679
$123$	97.3166	0.0713393
$124$	−3001.21	−2.17352
$125$	−1444.98	−1.03394
$126$	0	0
$127$	−970.885	−0.678363	−0.339182	−	0.940721i	$-0.610150\pi$
$127$	−970.885	−0.678363	−0.339182	+	0.940721i	$0.610150\pi$
$128$	1797.62	1.24131
$129$	411.095	0.280580
$130$	1906.63	1.28632
$131$	−470.551	−0.313834	−0.156917	−	0.987612i	$-0.550155\pi$
$131$	−470.551	−0.313834	−0.156917	+	0.987612i	$0.550155\pi$
$132$	4.75713	0.00313678
$133$	0	0
$134$	−1742.22	−1.12317
$135$	601.418	0.383421
$136$	−1188.63	−0.749444
$137$	2045.62	1.27568	0.637842	−	0.770167i	$-0.279827\pi$
$137$	2045.62	1.27568	0.637842	+	0.770167i	$0.279827\pi$
$138$	334.275	0.206198
$139$	−1206.92	−0.736469	−0.368235	−	0.929733i	$-0.620038\pi$
$139$	−1206.92	−0.736469	−0.368235	+	0.929733i	$0.620038\pi$
$140$	0	0
$141$	49.7131	0.0296922
$142$	−2281.64	−1.34839
$143$	15.6704	0.00916380
$144$	607.191	0.351384
$145$	1072.64	0.614331
$146$	2547.29	1.44394
$147$	0	0
$148$	−3986.76	−2.21425
$149$	3210.89	1.76541	0.882707	−	0.469924i	$-0.155719\pi$
$149$	3210.89	1.76541	0.882707	+	0.469924i	$0.155719\pi$
$150$	−43.8701	−0.0238799
$151$	−2386.97	−1.28641	−0.643207	−	0.765692i	$-0.722397\pi$
$151$	−2386.97	−1.28641	−0.643207	+	0.765692i	$0.722397\pi$
$152$	−221.927	−0.118426
$153$	−1978.56	−1.04547
$154$	0	0
$155$	−2801.39	−1.45170
$156$	489.023	0.250982
$157$	−486.712	−0.247413	−0.123707	−	0.992319i	$-0.539478\pi$
$157$	−486.712	−0.247413	−0.123707	+	0.992319i	$0.539478\pi$
$158$	−2884.77	−1.45253
$159$	−465.933	−0.232396
$160$	2451.93	1.21151
$161$	0	0
$162$	−2825.93	−1.37053
$163$	2229.26	1.07122	0.535610	−	0.844466i	$-0.320082\pi$
$163$	2229.26	1.07122	0.535610	+	0.844466i	$0.320082\pi$
$164$	−1059.84	−0.504630
$165$	4.44040	0.00209506
$166$	3662.24	1.71232
$167$	680.871	0.315493	0.157747	−	0.987480i	$-0.449577\pi$
$167$	680.871	0.315493	0.157747	+	0.987480i	$0.449577\pi$
$168$	0	0
$169$	−586.116	−0.266780
$170$	−3631.60	−1.63842
$171$	−369.413	−0.165203
$172$	−4477.07	−1.98473
$173$	−1507.70	−0.662591	−0.331296	−	0.943527i	$-0.607486\pi$
$173$	−1507.70	−0.662591	−0.331296	+	0.943527i	$0.607486\pi$
$174$	466.184	0.203111
$175$	0	0
$176$	9.15984	0.00392301
$177$	−232.269	−0.0986351
$178$	−1305.56	−0.549751
$179$	−954.516	−0.398569	−0.199284	−	0.979942i	$-0.563862\pi$
$179$	−954.516	−0.398569	−0.199284	+	0.979942i	$0.563862\pi$
$180$	−3205.61	−1.32740
$181$	3798.51	1.55989	0.779947	−	0.625845i	$-0.215246\pi$
$181$	3798.51	1.55989	0.779947	+	0.625845i	$0.215246\pi$
$182$	0	0
$183$	−236.694	−0.0956115
$184$	−1112.20	−0.445611
$185$	−3721.32	−1.47890
$186$	−1217.52	−0.479963
$187$	−29.8478	−0.0116721
$188$	−541.405	−0.210032
$189$	0	0
$190$	−678.049	−0.258899
$191$	5196.21	1.96851	0.984254	−	0.176762i	$-0.0565623\pi$
$191$	5196.21	1.96851	0.984254	+	0.176762i	$0.0565623\pi$
$192$	867.120	0.325932
$193$	2004.03	0.747426	0.373713	−	0.927544i	$-0.378084\pi$
$193$	2004.03	0.747426	0.373713	+	0.927544i	$0.378084\pi$
$194$	3340.13	1.23612
$195$	456.464	0.167631
$196$	0	0
$197$	271.205	0.0980839	0.0490420	−	0.998797i	$-0.484383\pi$
$197$	271.205	0.0980839	0.0490420	+	0.998797i	$0.484383\pi$
$198$	−44.6441	−0.0160238
$199$	−701.004	−0.249713	−0.124856	−	0.992175i	$-0.539847\pi$
$199$	−701.004	−0.249713	−0.124856	+	0.992175i	$0.539847\pi$
$200$	145.965	0.0516063
$201$	−417.104	−0.146369
$202$	−4896.56	−1.70555
$203$	0	0
$204$	−931.455	−0.319681
$205$	−989.272	−0.337043
$206$	−8599.27	−2.90845
$207$	−1851.33	−0.621624
$208$	941.614	0.313890
$209$	−5.57281	−0.00184440
$210$	0	0
$211$	−567.512	−0.185162	−0.0925808	−	0.995705i	$-0.529512\pi$
$211$	−567.512	−0.185162	−0.0925808	+	0.995705i	$0.529512\pi$
$212$	5074.29	1.64389
$213$	−546.246	−0.175719
$214$	−3047.66	−0.973521
$215$	−4178.99	−1.32560
$216$	−869.677	−0.273954
$217$	0	0
$218$	−713.103	−0.221548
$219$	609.845	0.188171
$220$	−48.3586	−0.0148197
$221$	−3068.29	−0.933917
$222$	−1617.33	−0.488957
$223$	−4305.91	−1.29303	−0.646513	−	0.762903i	$-0.723773\pi$
$223$	−4305.91	−1.29303	−0.646513	+	0.762903i	$0.723773\pi$
$224$	0	0
$225$	242.968	0.0719905
$226$	6544.94	1.92639
$227$	1337.14	0.390964	0.195482	−	0.980707i	$-0.437373\pi$
$227$	1337.14	0.390964	0.195482	+	0.980707i	$0.437373\pi$
$228$	−173.910	−0.0505153
$229$	1338.92	0.386368	0.193184	−	0.981163i	$-0.438119\pi$
$229$	1338.92	0.386368	0.193184	+	0.981163i	$0.438119\pi$
$230$	−3398.07	−0.974183
$231$	0	0
$232$	−1551.09	−0.438939
$233$	−2458.48	−0.691247	−0.345624	−	0.938373i	$-0.612333\pi$
$233$	−2458.48	−0.691247	−0.345624	+	0.938373i	$0.612333\pi$
$234$	−4589.32	−1.28211
$235$	−505.359	−0.140281
$236$	2529.55	0.697710
$237$	−690.640	−0.189291
$238$	0	0
$239$	−1950.67	−0.527944	−0.263972	−	0.964530i	$-0.585033\pi$
$239$	−1950.67	−0.527944	−0.263972	+	0.964530i	$0.585033\pi$
$240$	266.818	0.0717627
$241$	−2095.77	−0.560168	−0.280084	−	0.959976i	$-0.590362\pi$
$241$	−2095.77	−0.560168	−0.280084	+	0.959976i	$0.590362\pi$
$242$	5879.77	1.56184
$243$	−2186.77	−0.577288
$244$	2577.74	0.676323
$245$	0	0
$246$	−429.951	−0.111434
$247$	−572.874	−0.147575
$248$	4050.94	1.03724
$249$	876.775	0.223146
$250$	6384.01	1.61504
$251$	−5459.55	−1.37292	−0.686462	−	0.727166i	$-0.740837\pi$
$251$	−5459.55	−1.37292	−0.686462	+	0.727166i	$0.740837\pi$
$252$	0	0
$253$	−27.9284	−0.00694009
$254$	4289.43	1.05962
$255$	−869.439	−0.213515
$256$	−1383.60	−0.337793
$257$	−5323.79	−1.29217	−0.646087	−	0.763264i	$-0.723596\pi$
$257$	−5323.79	−1.29217	−0.646087	+	0.763264i	$0.723596\pi$
$258$	−1816.24	−0.438272
$259$	0	0
$260$	−4971.17	−1.18577
$261$	−2581.89	−0.612317
$262$	2078.92	0.490214
$263$	−1303.48	−0.305611	−0.152806	−	0.988256i	$-0.548831\pi$
$263$	−1303.48	−0.305611	−0.152806	+	0.988256i	$0.548831\pi$
$264$	−6.42101	−0.00149692
$265$	4736.45	1.09795
$266$	0	0
$267$	−312.563	−0.0716424
$268$	4542.51	1.03537
$269$	−2185.06	−0.495261	−0.247630	−	0.968855i	$-0.579652\pi$
$269$	−2185.06	−0.495261	−0.247630	+	0.968855i	$0.579652\pi$
$270$	−2657.10	−0.598911
$271$	5272.48	1.18185	0.590924	−	0.806728i	$-0.298763\pi$
$271$	5272.48	1.18185	0.590924	+	0.806728i	$0.298763\pi$
$272$	−1793.51	−0.399808
$273$	0	0
$274$	−9037.66	−1.99264
$275$	3.66532	0.000803735 0
$276$	−871.558	−0.190078
$277$	3316.70	0.719426	0.359713	−	0.933063i	$-0.382875\pi$
$277$	3316.70	0.719426	0.359713	+	0.933063i	$0.382875\pi$
$278$	5332.23	1.15038
$279$	6743.06	1.44694
$280$	0	0
$281$	4182.32	0.887888	0.443944	−	0.896055i	$-0.353579\pi$
$281$	4182.32	0.887888	0.443944	+	0.896055i	$0.353579\pi$
$282$	−219.635	−0.0463798
$283$	7704.79	1.61838	0.809191	−	0.587546i	$-0.199906\pi$
$283$	7704.79	1.61838	0.809191	+	0.587546i	$0.199906\pi$
$284$	5948.94	1.24297
$285$	−162.331	−0.0337392
$286$	−69.2327	−0.0143140
$287$	0	0
$288$	−5901.88	−1.20754
$289$	931.249	0.189548
$290$	−4738.99	−0.959598
$291$	799.659	0.161089
$292$	−6641.58	−1.33106
$293$	6335.64	1.26325	0.631624	−	0.775275i	$-0.282389\pi$
$293$	6335.64	1.26325	0.631624	+	0.775275i	$0.282389\pi$
$294$	0	0
$295$	2361.13	0.466001
$296$	5381.20	1.05667
$297$	−21.8384	−0.00426665
$298$	−14185.9	−2.75761
$299$	−2870.99	−0.555296
$300$	114.383	0.0220130
$301$	0	0
$302$	10545.8	2.00940
$303$	−1172.28	−0.222263
$304$	−334.864	−0.0631768
$305$	2406.11	0.451717
$306$	8741.40	1.63305
$307$	−3952.64	−0.734817	−0.367409	−	0.930060i	$-0.619755\pi$
$307$	−3952.64	−0.734817	−0.367409	+	0.930060i	$0.619755\pi$
$308$	0	0
$309$	−2058.75	−0.379023
$310$	12376.7	2.26758
$311$	3902.19	0.711489	0.355744	−	0.934583i	$-0.384227\pi$
$311$	3902.19	0.711489	0.355744	+	0.934583i	$0.384227\pi$
$312$	−660.068	−0.119772
$313$	−4077.17	−0.736279	−0.368139	−	0.929771i	$-0.620005\pi$
$313$	−4077.17	−0.736279	−0.368139	+	0.929771i	$0.620005\pi$
$314$	2150.32	0.386465
$315$	0	0
$316$	7521.48	1.33898
$317$	5454.70	0.966456	0.483228	−	0.875494i	$-0.339464\pi$
$317$	5454.70	0.966456	0.483228	+	0.875494i	$0.339464\pi$
$318$	2058.52	0.363007
$319$	−38.9493	−0.00683619
$320$	−8814.71	−1.53987
$321$	−729.637	−0.126867
$322$	0	0
$323$	1091.17	0.187970
$324$	7368.07	1.26339
$325$	376.788	0.0643090
$326$	−9848.99	−1.67327
$327$	−170.724	−0.0288717
$328$	1430.53	0.240817
$329$	0	0
$330$	−19.6180	−0.00327252
$331$	−2412.44	−0.400604	−0.200302	−	0.979734i	$-0.564192\pi$
$331$	−2412.44	−0.400604	−0.200302	+	0.979734i	$0.564192\pi$
$332$	−9548.61	−1.57846
$333$	8957.36	1.47405
$334$	−3008.13	−0.492807
$335$	4240.07	0.691522
$336$	0	0
$337$	2433.92	0.393424	0.196712	−	0.980461i	$-0.436974\pi$
$337$	2433.92	0.393424	0.196712	+	0.980461i	$0.436974\pi$
$338$	2589.50	0.416716
$339$	1566.92	0.251043
$340$	9468.71	1.51033
$341$	101.723	0.0161543
$342$	1632.09	0.258050
$343$	0	0
$344$	6043.00	0.947141
$345$	−813.530	−0.126954
$346$	6661.11	1.03498
$347$	−4556.82	−0.704966	−0.352483	−	0.935818i	$-0.614663\pi$
$347$	−4556.82	−0.704966	−0.352483	+	0.935818i	$0.614663\pi$
$348$	−1215.49	−0.187233
$349$	−2222.72	−0.340915	−0.170458	−	0.985365i	$-0.554525\pi$
$349$	−2222.72	−0.340915	−0.170458	+	0.985365i	$0.554525\pi$
$350$	0	0
$351$	−2244.95	−0.341386
$352$	−89.0334	−0.0134815
$353$	7637.90	1.15163	0.575814	−	0.817581i	$-0.304685\pi$
$353$	7637.90	1.15163	0.575814	+	0.817581i	$0.304685\pi$
$354$	1026.18	0.154070
$355$	5552.86	0.830184
$356$	3403.99	0.506773
$357$	0	0
$358$	4217.11	0.622573
$359$	5700.44	0.838044	0.419022	−	0.907976i	$-0.362373\pi$
$359$	5700.44	0.838044	0.419022	+	0.907976i	$0.362373\pi$
$360$	4326.83	0.633456
$361$	−6655.27	−0.970297
$362$	−16782.0	−2.43659
$363$	1407.67	0.203536
$364$	0	0
$365$	−6199.38	−0.889015
$366$	1045.73	0.149347
$367$	10404.2	1.47982	0.739909	−	0.672707i	$-0.234869\pi$
$367$	10404.2	1.47982	0.739909	+	0.672707i	$0.234869\pi$
$368$	−1678.18	−0.237721
$369$	2381.22	0.335938
$370$	16441.0	2.31008
$371$	0	0
$372$	3174.46	0.442441
$373$	−8248.29	−1.14499	−0.572494	−	0.819909i	$-0.694024\pi$
$373$	−8248.29	−1.14499	−0.572494	+	0.819909i	$0.694024\pi$
$374$	131.869	0.0182321
$375$	1528.39	0.210469
$376$	730.771	0.100230
$377$	−4003.91	−0.546982
$378$	0	0
$379$	−8617.75	−1.16798	−0.583990	−	0.811761i	$-0.698509\pi$
$379$	−8617.75	−1.16798	−0.583990	+	0.811761i	$0.698509\pi$
$380$	1767.88	0.238659
$381$	1026.93	0.138087
$382$	−22957.2	−3.07485
$383$	11387.9	1.51931	0.759655	−	0.650326i	$-0.225368\pi$
$383$	11387.9	1.51931	0.759655	+	0.650326i	$0.225368\pi$
$384$	−1901.38	−0.252681
$385$	0	0
$386$	−8853.93	−1.16750
$387$	10059.0	1.32126
$388$	−8708.77	−1.13949
$389$	4164.27	0.542768	0.271384	−	0.962471i	$-0.412519\pi$
$389$	4164.27	0.542768	0.271384	+	0.962471i	$0.412519\pi$
$390$	−2016.69	−0.261843
$391$	5468.44	0.707291
$392$	0	0
$393$	497.713	0.0638837
$394$	−1198.20	−0.153209
$395$	7020.70	0.894303
$396$	116.401	0.0147711
$397$	3794.15	0.479655	0.239828	−	0.970816i	$-0.422909\pi$
$397$	3794.15	0.479655	0.239828	+	0.970816i	$0.422909\pi$
$398$	3097.08	0.390056
$399$	0	0
$400$	220.244	0.0275306
$401$	−4669.40	−0.581492	−0.290746	−	0.956800i	$-0.593904\pi$
$401$	−4669.40	−0.581492	−0.290746	+	0.956800i	$0.593904\pi$
$402$	1842.79	0.228632
$403$	10456.9	1.29255
$404$	12766.8	1.57221
$405$	6877.50	0.843817
$406$	0	0
$407$	135.127	0.0164570
$408$	1257.25	0.152556
$409$	−628.137	−0.0759398	−0.0379699	−	0.999279i	$-0.512089\pi$
$409$	−628.137	−0.0759398	−0.0379699	+	0.999279i	$0.512089\pi$
$410$	4370.66	0.526468
$411$	−2163.70	−0.259677
$412$	22421.0	2.68107
$413$	0	0
$414$	8179.28	0.970990
$415$	−8912.86	−1.05425
$416$	−9152.46	−1.07869
$417$	1276.59	0.149915
$418$	24.6210	0.00288099
$419$	7429.30	0.866217	0.433108	−	0.901342i	$-0.357417\pi$
$419$	7429.30	0.866217	0.433108	+	0.901342i	$0.357417\pi$
$420$	0	0
$421$	8528.06	0.987250	0.493625	−	0.869675i	$-0.335672\pi$
$421$	8528.06	0.987250	0.493625	+	0.869675i	$0.335672\pi$
$422$	2507.30	0.289226
$423$	1216.42	0.139821
$424$	−6849.11	−0.784487
$425$	−717.677	−0.0819116
$426$	2413.35	0.274477
$427$	0	0
$428$	7946.19	0.897415
$429$	−16.5750	−0.00186538
$430$	18463.0	2.07062
$431$	−8069.86	−0.901883	−0.450942	−	0.892553i	$-0.648912\pi$
$431$	−8069.86	−0.901883	−0.450942	+	0.892553i	$0.648912\pi$
$432$	−1312.25	−0.146147
$433$	−960.163	−0.106565	−0.0532823	−	0.998579i	$-0.516968\pi$
$433$	−960.163	−0.106565	−0.0532823	+	0.998579i	$0.516968\pi$
$434$	0	0
$435$	−1134.56	−0.125053
$436$	1859.28	0.204228
$437$	1021.00	0.111765
$438$	−2694.33	−0.293927
$439$	4790.91	0.520860	0.260430	−	0.965493i	$-0.416136\pi$
$439$	4790.91	0.520860	0.260430	+	0.965493i	$0.416136\pi$
$440$	65.2728	0.00707218
$441$	0	0
$442$	13555.9	1.45880
$443$	−18188.3	−1.95068	−0.975339	−	0.220710i	$-0.929162\pi$
$443$	−18188.3	−1.95068	−0.975339	+	0.220710i	$0.929162\pi$
$444$	4216.90	0.450732
$445$	3177.36	0.338474
$446$	19023.8	2.01973
$447$	−3396.24	−0.359366
$448$	0	0
$449$	1353.55	0.142268	0.0711338	−	0.997467i	$-0.477338\pi$
$449$	1353.55	0.142268	0.0711338	+	0.997467i	$0.477338\pi$
$450$	−1073.45	−0.112451
$451$	35.9221	0.00375056
$452$	−17064.7	−1.77579
$453$	2524.75	0.261862
$454$	−5907.56	−0.610694
$455$	0	0
$456$	234.738	0.0241066
$457$	9223.73	0.944131	0.472066	−	0.881563i	$-0.343509\pi$
$457$	9223.73	0.944131	0.472066	+	0.881563i	$0.343509\pi$
$458$	−5915.43	−0.603515
$459$	4276.01	0.434830
$460$	8859.83	0.898025
$461$	5926.61	0.598763	0.299381	−	0.954134i	$-0.403220\pi$
$461$	5926.61	0.598763	0.299381	+	0.954134i	$0.403220\pi$
$462$	0	0
$463$	−7740.07	−0.776915	−0.388458	−	0.921467i	$-0.626992\pi$
$463$	−7740.07	−0.776915	−0.388458	+	0.921467i	$0.626992\pi$
$464$	−2340.42	−0.234162
$465$	2963.10	0.295507
$466$	10861.7	1.07974
$467$	5179.87	0.513267	0.256634	−	0.966509i	$-0.417387\pi$
$467$	5179.87	0.513267	0.256634	+	0.966509i	$0.417387\pi$
$468$	11965.8	1.18188
$469$	0	0
$470$	2232.71	0.219121
$471$	514.808	0.0503633
$472$	−3414.30	−0.332957
$473$	151.746	0.0147511
$474$	3051.29	0.295676
$475$	−133.996	−0.0129435
$476$	0	0
$477$	−11400.8	−1.09435
$478$	8618.20	0.824659
$479$	−1965.80	−0.187515	−0.0937577	−	0.995595i	$-0.529888\pi$
$479$	−1965.80	−0.187515	−0.0937577	+	0.995595i	$0.529888\pi$
$480$	−2593.47	−0.246615
$481$	13890.8	1.31677
$482$	9259.24	0.874994
$483$	0	0
$484$	−15330.4	−1.43974
$485$	−8128.94	−0.761064
$486$	9661.26	0.901736
$487$	15672.0	1.45824	0.729122	−	0.684384i	$-0.239929\pi$
$487$	15672.0	1.45824	0.729122	+	0.684384i	$0.239929\pi$
$488$	−3479.34	−0.322751
$489$	−2357.94	−0.218057
$490$	0	0
$491$	9809.53	0.901625	0.450812	−	0.892619i	$-0.351134\pi$
$491$	9809.53	0.901625	0.450812	+	0.892619i	$0.351134\pi$
$492$	1121.02	0.102722
$493$	7626.36	0.696701
$494$	2530.99	0.230516
$495$	108.651	0.00986566
$496$	6112.41	0.553338
$497$	0	0
$498$	−3873.65	−0.348559
$499$	2241.03	0.201046	0.100523	−	0.994935i	$-0.467948\pi$
$499$	2241.03	0.201046	0.100523	+	0.994935i	$0.467948\pi$
$500$	−16645.1	−1.48878
$501$	−720.174	−0.0642216
$502$	24120.6	2.14453
$503$	10895.1	0.965781	0.482891	−	0.875681i	$-0.339587\pi$
$503$	10895.1	0.965781	0.482891	+	0.875681i	$0.339587\pi$
$504$	0	0
$505$	11916.8	1.05008
$506$	123.389	0.0108406
$507$	619.950	0.0543056
$508$	−11183.9	−0.976781
$509$	20981.9	1.82712	0.913560	−	0.406703i	$-0.133322\pi$
$509$	20981.9	1.82712	0.913560	+	0.406703i	$0.133322\pi$
$510$	3841.23	0.333515
$511$	0	0
$512$	−8268.10	−0.713676
$513$	798.365	0.0687109
$514$	23520.8	2.01840
$515$	20928.2	1.79069
$516$	4735.51	0.404010
$517$	18.3504	0.00156102
$518$	0	0
$519$	1594.73	0.134877
$520$	6709.92	0.565864
$521$	20234.7	1.70153	0.850767	−	0.525543i	$-0.176138\pi$
$521$	20234.7	1.70153	0.850767	+	0.525543i	$0.176138\pi$
$522$	11406.9	0.956452
$523$	−13570.3	−1.13458	−0.567291	−	0.823518i	$-0.692008\pi$
$523$	−13570.3	−1.13458	−0.567291	+	0.823518i	$0.692008\pi$
$524$	−5420.40	−0.451891
$525$	0	0
$526$	5758.84	0.477371
$527$	−19917.6	−1.64634
$528$	−9.68860	−0.000798564 0
$529$	−7050.21	−0.579453
$530$	−20925.9	−1.71503
$531$	−5683.33	−0.464474
$532$	0	0
$533$	3692.72	0.300093
$534$	1380.92	0.111907
$535$	7417.13	0.599384
$536$	−6131.33	−0.494092
$537$	1009.62	0.0811324
$538$	9653.71	0.773608
$539$	0	0
$540$	6927.89	0.552090
$541$	−22615.9	−1.79729	−0.898645	−	0.438676i	$-0.855448\pi$
$541$	−22615.9	−1.79729	−0.898645	+	0.438676i	$0.855448\pi$
$542$	−23294.2	−1.84607
$543$	−4017.78	−0.317531
$544$	17432.9	1.37395
$545$	1735.49	0.136404
$546$	0	0
$547$	3668.80	0.286776	0.143388	−	0.989667i	$-0.454200\pi$
$547$	3668.80	0.286776	0.143388	+	0.989667i	$0.454200\pi$
$548$	23564.0	1.83687
$549$	−5791.60	−0.450236
$550$	−16.1936	−0.00125545
$551$	1423.90	0.110091
$552$	1176.40	0.0907082
$553$	0	0
$554$	−14653.4	−1.12376
$555$	3936.13	0.301044
$556$	−13902.8	−1.06045
$557$	11515.7	0.876010	0.438005	−	0.898973i	$-0.355685\pi$
$557$	11515.7	0.876010	0.438005	+	0.898973i	$0.355685\pi$
$558$	−29791.2	−2.26015
$559$	15599.2	1.18028
$560$	0	0
$561$	31.5707	0.00237597
$562$	−18477.8	−1.38690
$563$	13583.4	1.01682	0.508412	−	0.861114i	$-0.330233\pi$
$563$	13583.4	1.01682	0.508412	+	0.861114i	$0.330233\pi$
$564$	572.658	0.0427540
$565$	−15928.5	−1.18605
$566$	−34040.2	−2.52795
$567$	0	0
$568$	−8029.68	−0.593166
$569$	−4354.61	−0.320834	−0.160417	−	0.987049i	$-0.551284\pi$
$569$	−4354.61	−0.320834	−0.160417	+	0.987049i	$0.551284\pi$
$570$	717.189	0.0527013
$571$	801.798	0.0587639	0.0293820	−	0.999568i	$-0.490646\pi$
$571$	801.798	0.0587639	0.0293820	+	0.999568i	$0.490646\pi$
$572$	180.511	0.0131950
$573$	−5496.17	−0.400708
$574$	0	0
$575$	−671.527	−0.0487036
$576$	21217.3	1.53482
$577$	21727.2	1.56761	0.783807	−	0.621005i	$-0.213275\pi$
$577$	21727.2	1.56761	0.783807	+	0.621005i	$0.213275\pi$
$578$	−4114.31	−0.296078
$579$	−2119.71	−0.152146
$580$	12356.0	0.884580
$581$	0	0
$582$	−3532.94	−0.251624
$583$	−171.988	−0.0122179
$584$	8964.58	0.635200
$585$	11169.1	0.789378
$586$	−27991.2	−1.97322
$587$	−2106.69	−0.148130	−0.0740651	−	0.997253i	$-0.523597\pi$
$587$	−2106.69	−0.148130	−0.0740651	+	0.997253i	$0.523597\pi$
$588$	0	0
$589$	−3718.77	−0.260152
$590$	−10431.6	−0.727904
$591$	−286.860	−0.0199659
$592$	8119.62	0.563707
$593$	17193.0	1.19061	0.595304	−	0.803501i	$-0.297032\pi$
$593$	17193.0	1.19061	0.595304	+	0.803501i	$0.297032\pi$
$594$	96.4836	0.00666459
$595$	0	0
$596$	36987.1	2.54203
$597$	741.469	0.0508314
$598$	12684.2	0.867383
$599$	−9147.18	−0.623946	−0.311973	−	0.950091i	$-0.600990\pi$
$599$	−9147.18	−0.623946	−0.311973	+	0.950091i	$0.600990\pi$
$600$	−154.391	−0.0105049
$601$	2129.56	0.144537	0.0722684	−	0.997385i	$-0.476976\pi$
$601$	2129.56	0.144537	0.0722684	+	0.997385i	$0.476976\pi$
$602$	0	0
$603$	−10206.0	−0.689255
$604$	−27496.1	−1.85232
$605$	−14309.7	−0.961606
$606$	5179.21	0.347180
$607$	3139.51	0.209932	0.104966	−	0.994476i	$-0.466527\pi$
$607$	3139.51	0.209932	0.104966	+	0.994476i	$0.466527\pi$
$608$	3254.87	0.217109
$609$	0	0
$610$	−10630.3	−0.705591
$611$	1886.38	0.124902
$612$	−22791.5	−1.50538
$613$	−17700.0	−1.16622	−0.583112	−	0.812392i	$-0.698165\pi$
$613$	−17700.0	−1.16622	−0.583112	+	0.812392i	$0.698165\pi$
$614$	17463.0	1.14780
$615$	1046.38	0.0686082
$616$	0	0
$617$	21878.2	1.42753	0.713764	−	0.700386i	$-0.246989\pi$
$617$	21878.2	1.42753	0.713764	+	0.700386i	$0.246989\pi$
$618$	9095.67	0.592041
$619$	10263.8	0.666458	0.333229	−	0.942846i	$-0.391862\pi$
$619$	10263.8	0.666458	0.333229	+	0.942846i	$0.391862\pi$
$620$	−32270.0	−2.09031
$621$	4001.04	0.258545
$622$	−17240.1	−1.11136
$623$	0	0
$624$	−995.969	−0.0638953
$625$	−14363.4	−0.919257
$626$	18013.2	1.15008
$627$	5.89451	0.000375445 0
$628$	−5606.57	−0.356252
$629$	−26458.2	−1.67720
$630$	0	0
$631$	−11571.2	−0.730021	−0.365010	−	0.931003i	$-0.618935\pi$
$631$	−11571.2	−0.730021	−0.365010	+	0.931003i	$0.618935\pi$
$632$	−10152.2	−0.638979
$633$	600.271	0.0376914
$634$	−24099.2	−1.50962
$635$	−10439.3	−0.652393
$636$	−5367.21	−0.334628
$637$	0	0
$638$	172.081	0.0106783
$639$	−13365.9	−0.827463
$640$	19328.5	1.19379
$641$	−10160.2	−0.626056	−0.313028	−	0.949744i	$-0.601343\pi$
$641$	−10160.2	−0.626056	−0.313028	+	0.949744i	$0.601343\pi$
$642$	3223.58	0.198169
$643$	24318.8	1.49151	0.745754	−	0.666222i	$-0.232090\pi$
$643$	24318.8	1.49151	0.745754	+	0.666222i	$0.232090\pi$
$644$	0	0
$645$	4420.22	0.269839
$646$	−4820.85	−0.293613
$647$	29365.6	1.78436	0.892181	−	0.451678i	$-0.149174\pi$
$647$	29365.6	1.78436	0.892181	+	0.451678i	$0.149174\pi$
$648$	−9945.18	−0.602906
$649$	−85.7365	−0.00518559
$650$	−1664.67	−0.100452
$651$	0	0
$652$	25679.4	1.54246
$653$	13213.0	0.791831	0.395915	−	0.918287i	$-0.370427\pi$
$653$	13213.0	0.791831	0.395915	+	0.918287i	$0.370427\pi$
$654$	754.267	0.0450981
$655$	−5059.51	−0.301819
$656$	2158.51	0.128469
$657$	14922.1	0.886101
$658$	0	0
$659$	16662.7	0.984956	0.492478	−	0.870325i	$-0.336091\pi$
$659$	16662.7	0.984956	0.492478	+	0.870325i	$0.336091\pi$
$660$	51.1501	0.00301669
$661$	−1994.87	−0.117385	−0.0586924	−	0.998276i	$-0.518693\pi$
$661$	−1994.87	−0.117385	−0.0586924	+	0.998276i	$0.518693\pi$
$662$	10658.3	0.625751
$663$	3245.41	0.190107
$664$	12888.4	0.753263
$665$	0	0
$666$	−39574.2	−2.30250
$667$	7135.95	0.414250
$668$	7843.13	0.454281
$669$	4554.46	0.263207
$670$	−18732.9	−1.08017
$671$	−87.3698	−0.00502664
$672$	0	0
$673$	14520.5	0.831686	0.415843	−	0.909436i	$-0.363487\pi$
$673$	14520.5	0.831686	0.415843	+	0.909436i	$0.363487\pi$
$674$	−10753.2	−0.614536
$675$	−525.096	−0.0299422
$676$	−6751.62	−0.384139
$677$	24494.7	1.39056	0.695278	−	0.718740i	$-0.255281\pi$
$677$	24494.7	1.39056	0.695278	+	0.718740i	$0.255281\pi$
$678$	−6922.75	−0.392134
$679$	0	0
$680$	−12780.6	−0.720753
$681$	−1414.32	−0.0795845
$682$	−449.419	−0.0252333
$683$	8710.45	0.487988	0.243994	−	0.969777i	$-0.421542\pi$
$683$	8710.45	0.487988	0.243994	+	0.969777i	$0.421542\pi$
$684$	−4255.36	−0.237877
$685$	21995.1	1.22685
$686$	0	0
$687$	−1416.21	−0.0786488
$688$	9118.21	0.505274
$689$	−17680.0	−0.977585
$690$	3594.22	0.198304
$691$	18416.7	1.01390	0.506948	−	0.861976i	$-0.330774\pi$
$691$	18416.7	1.01390	0.506948	+	0.861976i	$0.330774\pi$
$692$	−17367.6	−0.954070
$693$	0	0
$694$	20132.3	1.10117
$695$	−12977.1	−0.708274
$696$	1640.62	0.0893501
$697$	−7033.61	−0.382234
$698$	9820.11	0.532517
$699$	2600.40	0.140710
$700$	0	0
$701$	−17262.8	−0.930110	−0.465055	−	0.885282i	$-0.653966\pi$
$701$	−17262.8	−0.930110	−0.465055	+	0.885282i	$0.653966\pi$
$702$	9918.32	0.533252
$703$	−4939.95	−0.265027
$704$	320.076	0.0171354
$705$	534.531	0.0285554
$706$	−33744.7	−1.79887
$707$	0	0
$708$	−2675.57	−0.142025
$709$	−6956.55	−0.368489	−0.184245	−	0.982880i	$-0.558984\pi$
$709$	−6956.55	−0.368489	−0.184245	+	0.982880i	$0.558984\pi$
$710$	−24532.9	−1.29676
$711$	−16899.1	−0.891372
$712$	−4594.60	−0.241840
$713$	−18636.8	−0.978896
$714$	0	0
$715$	168.493	0.00881297
$716$	−10995.3	−0.573903
$717$	2063.28	0.107468
$718$	−25184.9	−1.30904
$719$	−16720.3	−0.867262	−0.433631	−	0.901091i	$-0.642768\pi$
$719$	−16720.3	−0.867262	−0.433631	+	0.901091i	$0.642768\pi$
$720$	6528.71	0.337931
$721$	0	0
$722$	29403.4	1.51562
$723$	2216.75	0.114027
$724$	43756.0	2.24610
$725$	−936.520	−0.0479745
$726$	−6219.18	−0.317927
$727$	16002.8	0.816384	0.408192	−	0.912896i	$-0.366159\pi$
$727$	16002.8	0.816384	0.408192	+	0.912896i	$0.366159\pi$
$728$	0	0
$729$	−14957.0	−0.759895
$730$	27389.2	1.38866
$731$	−29712.1	−1.50334
$732$	−2726.54	−0.137672
$733$	22424.9	1.12999	0.564996	−	0.825094i	$-0.308878\pi$
$733$	22424.9	1.12999	0.564996	+	0.825094i	$0.308878\pi$
$734$	−45966.3	−2.31151
$735$	0	0
$736$	16311.9	0.816936
$737$	−153.964	−0.00769515
$738$	−10520.4	−0.524742
$739$	28545.5	1.42093	0.710463	−	0.703734i	$-0.248485\pi$
$739$	28545.5	1.42093	0.710463	+	0.703734i	$0.248485\pi$
$740$	−42866.9	−2.12948
$741$	605.944	0.0300404
$742$	0	0
$743$	−6770.73	−0.334312	−0.167156	−	0.985930i	$-0.553458\pi$
$743$	−6770.73	−0.334312	−0.167156	+	0.985930i	$0.553458\pi$
$744$	−4284.78	−0.211139
$745$	34524.5	1.69783
$746$	36441.4	1.78849
$747$	21453.6	1.05080
$748$	−343.824	−0.0168068
$749$	0	0
$750$	−6752.53	−0.328757
$751$	16108.3	0.782691	0.391345	−	0.920244i	$-0.372010\pi$
$751$	16108.3	0.782691	0.391345	+	0.920244i	$0.372010\pi$
$752$	1102.65	0.0534702
$753$	5774.70	0.279471
$754$	17689.5	0.854397
$755$	−25665.4	−1.23716
$756$	0	0
$757$	27445.1	1.31771	0.658856	−	0.752269i	$-0.271041\pi$
$757$	27445.1	1.31771	0.658856	+	0.752269i	$0.271041\pi$
$758$	38073.8	1.82441
$759$	29.5406	0.00141272
$760$	−2386.23	−0.113892
$761$	−17362.6	−0.827062	−0.413531	−	0.910490i	$-0.635705\pi$
$761$	−17362.6	−0.827062	−0.413531	+	0.910490i	$0.635705\pi$
$762$	−4537.04	−0.215695
$763$	0	0
$764$	59856.6	2.83447
$765$	−21274.1	−1.00545
$766$	−50312.6	−2.37319
$767$	−8813.54	−0.414913
$768$	1463.47	0.0687608
$769$	996.605	0.0467341	0.0233670	−	0.999727i	$-0.492561\pi$
$769$	996.605	0.0467341	0.0233670	+	0.999727i	$0.492561\pi$
$770$	0	0
$771$	5631.10	0.263034
$772$	23085.0	1.07623
$773$	−1272.28	−0.0591990	−0.0295995	−	0.999562i	$-0.509423\pi$
$773$	−1272.28	−0.0591990	−0.0295995	+	0.999562i	$0.509423\pi$
$774$	−44441.2	−2.06383
$775$	2445.89	0.113366
$776$	11754.8	0.543780
$777$	0	0
$778$	−18398.0	−0.847815
$779$	−1313.23	−0.0603997
$780$	5258.13	0.241374
$781$	−201.633	−0.00923817
$782$	−24159.9	−1.10480
$783$	5579.91	0.254674
$784$	0	0
$785$	−5233.28	−0.237941
$786$	−2198.93	−0.0997877
$787$	−8186.59	−0.370801	−0.185400	−	0.982663i	$-0.559358\pi$
$787$	−8186.59	−0.370801	−0.185400	+	0.982663i	$0.559358\pi$
$788$	3124.08	0.141232
$789$	1378.72	0.0622101
$790$	−31017.9	−1.39692
$791$	0	0
$792$	−157.114	−0.00704900
$793$	−8981.44	−0.402195
$794$	−16762.8	−0.749231
$795$	−5009.86	−0.223499
$796$	−8075.05	−0.359563
$797$	22274.1	0.989951	0.494975	−	0.868907i	$-0.335177\pi$
$797$	22274.1	0.989951	0.494975	+	0.868907i	$0.335177\pi$
$798$	0	0
$799$	−3593.04	−0.159090
$800$	−2140.77	−0.0946096
$801$	−7648.02	−0.337365
$802$	20629.7	0.908303
$803$	225.109	0.00989283
$804$	−4804.73	−0.210758
$805$	0	0
$806$	−46199.4	−2.01899
$807$	2311.19	0.100815
$808$	−17232.3	−0.750283
$809$	30653.8	1.33217	0.666087	−	0.745874i	$-0.267968\pi$
$809$	30653.8	1.33217	0.666087	+	0.745874i	$0.267968\pi$
$810$	−30385.2	−1.31806
$811$	38633.7	1.67277	0.836383	−	0.548145i	$-0.184666\pi$
$811$	38633.7	1.67277	0.836383	+	0.548145i	$0.184666\pi$
$812$	0	0
$813$	−5576.84	−0.240576
$814$	−597.000	−0.0257062
$815$	23969.6	1.03021
$816$	1897.05	0.0813847
$817$	−5547.49	−0.237555
$818$	2775.15	0.118620
$819$	0	0
$820$	−11395.7	−0.485310
$821$	8012.27	0.340597	0.170298	−	0.985393i	$-0.445527\pi$
$821$	8012.27	0.340597	0.170298	+	0.985393i	$0.445527\pi$
$822$	9559.36	0.405621
$823$	−21154.7	−0.895998	−0.447999	−	0.894034i	$-0.647863\pi$
$823$	−21154.7	−0.895998	−0.447999	+	0.894034i	$0.647863\pi$
$824$	−30263.1	−1.27945
$825$	−3.87690	−0.000163608 0
$826$	0	0
$827$	13722.6	0.577002	0.288501	−	0.957480i	$-0.406843\pi$
$827$	13722.6	0.577002	0.288501	+	0.957480i	$0.406843\pi$
$828$	−21325.9	−0.895082
$829$	−3863.93	−0.161882	−0.0809408	−	0.996719i	$-0.525792\pi$
$829$	−3863.93	−0.161882	−0.0809408	+	0.996719i	$0.525792\pi$
$830$	39377.6	1.64676
$831$	−3508.15	−0.146446
$832$	32903.2	1.37105
$833$	0	0
$834$	−5640.03	−0.234171
$835$	7320.94	0.303415
$836$	−64.1947	−0.00265577
$837$	−14572.9	−0.601808
$838$	−32823.1	−1.35305
$839$	282.584	0.0116280	0.00581400	−	0.999983i	$-0.498149\pi$
$839$	282.584	0.0116280	0.00581400	+	0.999983i	$0.498149\pi$
$840$	0	0
$841$	−14437.1	−0.591952
$842$	−37677.5	−1.54210
$843$	−4423.75	−0.180738
$844$	−6537.32	−0.266616
$845$	−6302.10	−0.256567
$846$	−5374.21	−0.218403
$847$	0	0
$848$	−10334.6	−0.418502
$849$	−8149.55	−0.329437
$850$	3170.74	0.127948
$851$	−24756.8	−0.997240
$852$	−6292.35	−0.253019
$853$	−14734.1	−0.591424	−0.295712	−	0.955277i	$-0.595557\pi$
$853$	−14734.1	−0.591424	−0.295712	+	0.955277i	$0.595557\pi$
$854$	0	0
$855$	−3972.04	−0.158878
$856$	−10725.5	−0.428259
$857$	−16771.7	−0.668508	−0.334254	−	0.942483i	$-0.608484\pi$
$857$	−16771.7	−0.668508	−0.334254	+	0.942483i	$0.608484\pi$
$858$	73.2292	0.00291376
$859$	−9430.86	−0.374595	−0.187297	−	0.982303i	$-0.559973\pi$
$859$	−9430.86	−0.374595	−0.187297	+	0.982303i	$0.559973\pi$
$860$	−48138.8	−1.90874
$861$	0	0
$862$	35653.2	1.40876
$863$	9302.91	0.366946	0.183473	−	0.983025i	$-0.441266\pi$
$863$	9302.91	0.366946	0.183473	+	0.983025i	$0.441266\pi$
$864$	12755.0	0.502238
$865$	−16211.3	−0.637224
$866$	4242.06	0.166456
$867$	−985.006	−0.0385842
$868$	0	0
$869$	−254.933	−0.00995168
$870$	5012.55	0.195335
$871$	−15827.2	−0.615710
$872$	−2509.60	−0.0974606
$873$	19566.7	0.758570
$874$	−4510.84	−0.174578
$875$	0	0
$876$	7024.96	0.270949
$877$	−27238.6	−1.04878	−0.524391	−	0.851478i	$-0.675707\pi$
$877$	−27238.6	−1.04878	−0.524391	+	0.851478i	$0.675707\pi$
$878$	−21166.5	−0.813594
$879$	−6701.36	−0.257146
$880$	98.4895	0.00377282
$881$	−10957.8	−0.419046	−0.209523	−	0.977804i	$-0.567191\pi$
$881$	−10957.8	−0.419046	−0.209523	+	0.977804i	$0.567191\pi$
$882$	0	0
$883$	−1077.77	−0.0410755	−0.0205378	−	0.999789i	$-0.506538\pi$
$883$	−1077.77	−0.0410755	−0.0205378	+	0.999789i	$0.506538\pi$
$884$	−35344.4	−1.34475
$885$	−2497.43	−0.0948589
$886$	80356.9	3.04700
$887$	25537.0	0.966685	0.483342	−	0.875431i	$-0.339423\pi$
$887$	25537.0	0.966685	0.483342	+	0.875431i	$0.339423\pi$
$888$	−5691.83	−0.215096
$889$	0	0
$890$	−14037.8	−0.528704
$891$	−249.733	−0.00938987
$892$	−49600.9	−1.86184
$893$	−670.850	−0.0251390
$894$	15004.8	0.561338
$895$	−10263.2	−0.383310
$896$	0	0
$897$	3036.71	0.113036
$898$	−5980.08	−0.222225
$899$	−25991.1	−0.964240
$900$	2798.81	0.103660
$901$	33675.6	1.24517
$902$	−158.706	−0.00585846
$903$	0	0
$904$	23033.4	0.847432
$905$	40842.7	1.50018
$906$	−11154.5	−0.409033
$907$	−39974.5	−1.46343	−0.731715	−	0.681611i	$-0.761280\pi$
$907$	−39974.5	−1.46343	−0.731715	+	0.681611i	$0.761280\pi$
$908$	15402.8	0.562953
$909$	−28684.3	−1.04664
$910$	0	0
$911$	−12985.2	−0.472247	−0.236124	−	0.971723i	$-0.575877\pi$
$911$	−12985.2	−0.472247	−0.236124	+	0.971723i	$0.575877\pi$
$912$	354.194	0.0128602
$913$	323.640	0.0117316
$914$	−40751.0	−1.47475
$915$	−2545.01	−0.0919511
$916$	15423.4	0.556334
$917$	0	0
$918$	−18891.7	−0.679214
$919$	2675.61	0.0960396	0.0480198	−	0.998846i	$-0.484709\pi$
$919$	2675.61	0.0960396	0.0480198	+	0.998846i	$0.484709\pi$
$920$	−11958.7	−0.428551
$921$	4180.80	0.149579
$922$	−26184.1	−0.935280
$923$	−20727.5	−0.739170
$924$	0	0
$925$	3249.07	0.115491
$926$	34196.1	1.21356
$927$	−50375.0	−1.78482
$928$	22748.8	0.804705
$929$	12962.0	0.457771	0.228886	−	0.973453i	$-0.426492\pi$
$929$	12962.0	0.457771	0.228886	+	0.973453i	$0.426492\pi$
$930$	−13091.2	−0.461588
$931$	0	0
$932$	−28319.9	−0.995332
$933$	−4127.45	−0.144830
$934$	−22885.0	−0.801734
$935$	−320.932	−0.0112253
$936$	−16151.0	−0.564010
$937$	−3511.35	−0.122423	−0.0612117	−	0.998125i	$-0.519496\pi$
$937$	−3511.35	−0.122423	−0.0612117	+	0.998125i	$0.519496\pi$
$938$	0	0
$939$	4312.52	0.149876
$940$	−5821.36	−0.201991
$941$	−46921.0	−1.62549	−0.812743	−	0.582622i	$-0.802027\pi$
$941$	−46921.0	−1.62549	−0.812743	+	0.582622i	$0.802027\pi$
$942$	−2274.45	−0.0786685
$943$	−6581.32	−0.227272
$944$	−5151.80	−0.177624
$945$	0	0
$946$	−670.422	−0.0230415
$947$	−6133.60	−0.210470	−0.105235	−	0.994447i	$-0.533560\pi$
$947$	−6133.60	−0.210470	−0.105235	+	0.994447i	$0.533560\pi$
$948$	−7955.66	−0.272561
$949$	23140.8	0.791552
$950$	592.002	0.0202180
$951$	−5769.58	−0.196731
$952$	0	0
$953$	45658.8	1.55198	0.775988	−	0.630748i	$-0.217252\pi$
$953$	45658.8	1.55198	0.775988	+	0.630748i	$0.217252\pi$
$954$	50369.5	1.70940
$955$	55871.3	1.89314
$956$	−22470.3	−0.760191
$957$	41.1977	0.00139157
$958$	8685.04	0.292903
$959$	0	0
$960$	9323.55	0.313454
$961$	38089.4	1.27855
$962$	−61370.4	−2.05682
$963$	−17853.3	−0.597419
$964$	−24141.7	−0.806590
$965$	21548.0	0.718812
$966$	0	0
$967$	11383.9	0.378575	0.189288	−	0.981922i	$-0.439382\pi$
$967$	11383.9	0.378575	0.189288	+	0.981922i	$0.439382\pi$
$968$	20692.4	0.687066
$969$	−1154.16	−0.0382630
$970$	35914.2	1.18880
$971$	−31372.7	−1.03687	−0.518433	−	0.855118i	$-0.673484\pi$
$971$	−31372.7	−1.03687	−0.518433	+	0.855118i	$0.673484\pi$
$972$	−25189.9	−0.831242
$973$	0	0
$974$	−69239.7	−2.27781
$975$	−398.538	−0.0130907
$976$	−5249.94	−0.172179
$977$	45915.2	1.50354	0.751769	−	0.659426i	$-0.229201\pi$
$977$	45915.2	1.50354	0.751769	+	0.659426i	$0.229201\pi$
$978$	10417.5	0.340609
$979$	−115.375	−0.00376649
$980$	0	0
$981$	−4177.39	−0.135957
$982$	−43339.1	−1.40836
$983$	−20214.1	−0.655879	−0.327940	−	0.944699i	$-0.606354\pi$
$983$	−20214.1	−0.655879	−0.327940	+	0.944699i	$0.606354\pi$
$984$	−1513.11	−0.0490205
$985$	2916.08	0.0943289
$986$	−33693.7	−1.08826
$987$	0	0
$988$	−6599.09	−0.212495
$989$	−27801.5	−0.893868
$990$	−480.027	−0.0154104
$991$	32741.4	1.04951	0.524754	−	0.851254i	$-0.324157\pi$
$991$	32741.4	1.04951	0.524754	+	0.851254i	$0.324157\pi$
$992$	−59412.5	−1.90156
$993$	2551.70	0.0815466
$994$	0	0
$995$	−7537.41	−0.240153
$996$	10099.8	0.321310
$997$	46301.5	1.47080	0.735398	−	0.677636i	$-0.236995\pi$
$997$	46301.5	1.47080	0.735398	+	0.677636i	$0.236995\pi$
$998$	−9901.00	−0.314039
$999$	−19358.4	−0.613086

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2303.4.a.n.1.10	yes	68
7.6	odd	2		2303.4.a.m.1.10	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2303.4.a.m.1.10	✓	68	7.6	odd	2
2303.4.a.n.1.10	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)

\(f(q)\)	\(=\)	\(q-4.41806 q^{2} -1.05773 q^{3} +11.5193 q^{4} +10.7523 q^{5} +4.67309 q^{6} -15.5483 q^{8} -25.8812 q^{9} +O(q^{10})\)	\(q-4.41806 q^{2} -1.05773 q^{3} +11.5193 q^{4} +10.7523 q^{5} +4.67309 q^{6} -15.5483 q^{8} -25.8812 q^{9} -47.5044 q^{10} -0.390434 q^{11} -12.1842 q^{12} -40.1358 q^{13} -11.3730 q^{15} -23.4607 q^{16} +76.4477 q^{17} +114.345 q^{18} +14.2734 q^{19} +123.859 q^{20} +1.72496 q^{22} +71.5317 q^{23} +16.4458 q^{24} -9.38781 q^{25} +177.323 q^{26} +55.9338 q^{27} +99.7591 q^{29} +50.2466 q^{30} -260.539 q^{31} +228.037 q^{32} +0.412972 q^{33} -337.751 q^{34} -298.133 q^{36} -346.095 q^{37} -63.0607 q^{38} +42.4527 q^{39} -167.180 q^{40} -92.0055 q^{41} -388.659 q^{43} -4.49751 q^{44} -278.283 q^{45} -316.032 q^{46} -47.0000 q^{47} +24.8150 q^{48} +41.4759 q^{50} -80.8607 q^{51} -462.335 q^{52} +440.505 q^{53} -247.119 q^{54} -4.19806 q^{55} -15.0973 q^{57} -440.742 q^{58} +219.593 q^{59} -131.008 q^{60} +223.776 q^{61} +1151.08 q^{62} -819.797 q^{64} -431.553 q^{65} -1.82453 q^{66} +394.340 q^{67} +880.621 q^{68} -75.6609 q^{69} +516.434 q^{71} +402.409 q^{72} -576.563 q^{73} +1529.07 q^{74} +9.92973 q^{75} +164.419 q^{76} -187.558 q^{78} +652.948 q^{79} -252.257 q^{80} +639.630 q^{81} +406.486 q^{82} -828.925 q^{83} +821.989 q^{85} +1717.12 q^{86} -105.518 q^{87} +6.07059 q^{88} +295.504 q^{89} +1229.47 q^{90} +823.993 q^{92} +275.578 q^{93} +207.649 q^{94} +153.472 q^{95} -241.201 q^{96} -756.018 q^{97} +10.1049 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 2 q^{2} + 24 q^{3} + 254 q^{4} + 40 q^{5} + 48 q^{6} - 66 q^{8} + 576 q^{9}+O(q^{10}) \) 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

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Database

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