LMFDB - Embedded newform 435.4.a.h.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [435,4,Mod(1,435)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(435, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("435.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 435 = 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	435.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:	$25.6658308525$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 49x^{4} + 27x^{3} + 692x^{2} - 82x - 2588 $ x^6 - x^5 - 49x^4 + 27x^3 + 692x^2 - 82x - 2588
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$4.39070$ of defining polynomial
Character	$\chi$	$=$	435.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.39070 q^{2} +3.00000 q^{3} +11.2783 q^{4} -5.00000 q^{5} +13.1721 q^{6} +31.5336 q^{7} +14.3939 q^{8} +9.00000 q^{9} -21.9535 q^{10} -5.28853 q^{11} +33.8348 q^{12} -5.98731 q^{13} +138.455 q^{14} -15.0000 q^{15} -27.0267 q^{16} +84.6758 q^{17} +39.5163 q^{18} +57.3480 q^{19} -56.3914 q^{20} +94.6008 q^{21} -23.2204 q^{22} +31.0898 q^{23} +43.1818 q^{24} +25.0000 q^{25} -26.2885 q^{26} +27.0000 q^{27} +355.645 q^{28} +29.0000 q^{29} -65.8606 q^{30} -14.6873 q^{31} -233.818 q^{32} -15.8656 q^{33} +371.786 q^{34} -157.668 q^{35} +101.504 q^{36} -7.76174 q^{37} +251.798 q^{38} -17.9619 q^{39} -71.9697 q^{40} -399.867 q^{41} +415.364 q^{42} -17.9967 q^{43} -59.6455 q^{44} -45.0000 q^{45} +136.506 q^{46} -262.798 q^{47} -81.0800 q^{48} +651.368 q^{49} +109.768 q^{50} +254.027 q^{51} -67.5265 q^{52} -64.9925 q^{53} +118.549 q^{54} +26.4427 q^{55} +453.893 q^{56} +172.044 q^{57} +127.330 q^{58} +122.788 q^{59} -169.174 q^{60} +264.384 q^{61} -64.4877 q^{62} +283.802 q^{63} -810.411 q^{64} +29.9366 q^{65} -69.6611 q^{66} +622.712 q^{67} +954.997 q^{68} +93.2694 q^{69} -692.274 q^{70} +327.717 q^{71} +129.545 q^{72} -833.518 q^{73} -34.0795 q^{74} +75.0000 q^{75} +646.787 q^{76} -166.767 q^{77} -78.8655 q^{78} -666.457 q^{79} +135.133 q^{80} +81.0000 q^{81} -1755.70 q^{82} -1320.72 q^{83} +1066.93 q^{84} -423.379 q^{85} -79.0180 q^{86} +87.0000 q^{87} -76.1229 q^{88} -189.059 q^{89} -197.582 q^{90} -188.801 q^{91} +350.640 q^{92} -44.0620 q^{93} -1153.87 q^{94} -286.740 q^{95} -701.453 q^{96} -137.630 q^{97} +2859.97 q^{98} -47.5968 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} + 18 q^{3} + 51 q^{4} - 30 q^{5} + 3 q^{6} + 47 q^{7} + 51 q^{8} + 54 q^{9} - 5 q^{10} + 81 q^{11} + 153 q^{12} + 169 q^{13} - 30 q^{14} - 90 q^{15} + 131 q^{16} - q^{17} + 9 q^{18} + 116 q^{19}+ \cdots + 729 q^{99}+O(q^{100}) $ 6 * q + q^2 + 18 * q^3 + 51 * q^4 - 30 * q^5 + 3 * q^6 + 47 * q^7 + 51 * q^8 + 54 * q^9 - 5 * q^10 + 81 * q^11 + 153 * q^12 + 169 * q^13 - 30 * q^14 - 90 * q^15 + 131 * q^16 - q^17 + 9 * q^18 + 116 * q^19 - 255 * q^20 + 141 * q^21 + 90 * q^22 - 52 * q^23 + 153 * q^24 + 150 * q^25 + 294 * q^26 + 162 * q^27 + 344 * q^28 + 174 * q^29 - 15 * q^30 + 340 * q^31 + 499 * q^32 + 243 * q^33 + 920 * q^34 - 235 * q^35 + 459 * q^36 + 332 * q^37 - 378 * q^38 + 507 * q^39 - 255 * q^40 - 616 * q^41 - 90 * q^42 + 334 * q^43 - 52 * q^44 - 270 * q^45 - 158 * q^46 - 85 * q^47 + 393 * q^48 + 879 * q^49 + 25 * q^50 - 3 * q^51 + 2220 * q^52 - 850 * q^53 + 27 * q^54 - 405 * q^55 - 624 * q^56 + 348 * q^57 + 29 * q^58 - 758 * q^59 - 765 * q^60 - 36 * q^61 - 152 * q^62 + 423 * q^63 + 1795 * q^64 - 845 * q^65 + 270 * q^66 + 939 * q^67 - 186 * q^68 - 156 * q^69 + 150 * q^70 - 1388 * q^71 + 459 * q^72 + 1708 * q^73 - 814 * q^74 + 450 * q^75 + 566 * q^76 + 2585 * q^77 + 882 * q^78 + 1250 * q^79 - 655 * q^80 + 486 * q^81 + 1372 * q^82 - 748 * q^83 + 1032 * q^84 + 5 * q^85 - 800 * q^86 + 522 * q^87 + 536 * q^88 + 1099 * q^89 - 45 * q^90 + 539 * q^91 + 1698 * q^92 + 1020 * q^93 - 4542 * q^94 - 580 * q^95 + 1497 * q^96 - 22 * q^97 - 1433 * q^98 + 729 * q^99

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 $

$2$	4.39070	1.55235	0.776174	−	0.630519i	$-0.217158\pi$
$2$	4.39070	1.55235	0.776174	+	0.630519i	$0.217158\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	11.2783	1.40978
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	13.1721	0.896249
$7$	31.5336	1.70265	0.851327	−	0.524635i	$-0.175798\pi$
$7$	31.5336	1.70265	0.851327	+	0.524635i	$0.175798\pi$
$8$	14.3939	0.636128
$9$	9.00000	0.333333
$10$	−21.9535	−0.694231
$11$	−5.28853	−0.144959	−0.0724797	−	0.997370i	$-0.523091\pi$
$11$	−5.28853	−0.144959	−0.0724797	+	0.997370i	$0.523091\pi$
$12$	33.8348	0.813940
$13$	−5.98731	−0.127737	−0.0638685	−	0.997958i	$-0.520344\pi$
$13$	−5.98731	−0.127737	−0.0638685	+	0.997958i	$0.520344\pi$
$14$	138.455	2.64311
$15$	−15.0000	−0.258199
$16$	−27.0267	−0.422292
$17$	84.6758	1.20805	0.604026	−	0.796965i	$-0.293562\pi$
$17$	84.6758	1.20805	0.604026	+	0.796965i	$0.293562\pi$
$18$	39.5163	0.517449
$19$	57.3480	0.692449	0.346225	−	0.938152i	$-0.387464\pi$
$19$	57.3480	0.692449	0.346225	+	0.938152i	$0.387464\pi$
$20$	−56.3914	−0.630475
$21$	94.6008	0.983028
$22$	−23.2204	−0.225027
$23$	31.0898	0.281855	0.140928	−	0.990020i	$-0.454991\pi$
$23$	31.0898	0.281855	0.140928	+	0.990020i	$0.454991\pi$
$24$	43.1818	0.367269
$25$	25.0000	0.200000
$26$	−26.2885	−0.198292
$27$	27.0000	0.192450
$28$	355.645	2.40038
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	−65.8606	−0.400815
$31$	−14.6873	−0.0850942	−0.0425471	−	0.999094i	$-0.513547\pi$
$31$	−14.6873	−0.0850942	−0.0425471	+	0.999094i	$0.513547\pi$
$32$	−233.818	−1.29167
$33$	−15.8656	−0.0836923
$34$	371.786	1.87532
$35$	−157.668	−0.761450
$36$	101.504	0.469928
$37$	−7.76174	−0.0344871	−0.0172435	−	0.999851i	$-0.505489\pi$
$37$	−7.76174	−0.0344871	−0.0172435	+	0.999851i	$0.505489\pi$
$38$	251.798	1.07492
$39$	−17.9619	−0.0737490
$40$	−71.9697	−0.284485
$41$	−399.867	−1.52314	−0.761569	−	0.648084i	$-0.775571\pi$
$41$	−399.867	−1.52314	−0.761569	+	0.648084i	$0.775571\pi$
$42$	415.364	1.52600
$43$	−17.9967	−0.0638247	−0.0319124	−	0.999491i	$-0.510160\pi$
$43$	−17.9967	−0.0638247	−0.0319124	+	0.999491i	$0.510160\pi$
$44$	−59.6455	−0.204361
$45$	−45.0000	−0.149071
$46$	136.506	0.437538
$47$	−262.798	−0.815595	−0.407798	−	0.913072i	$-0.633703\pi$
$47$	−262.798	−0.815595	−0.407798	+	0.913072i	$0.633703\pi$
$48$	−81.0800	−0.243810
$49$	651.368	1.89903
$50$	109.768	0.310470
$51$	254.027	0.697469
$52$	−67.5265	−0.180082
$53$	−64.9925	−0.168442	−0.0842209	−	0.996447i	$-0.526840\pi$
$53$	−64.9925	−0.168442	−0.0842209	+	0.996447i	$0.526840\pi$
$54$	118.549	0.298750
$55$	26.4427	0.0648278
$56$	453.893	1.08311
$57$	172.044	0.399786
$58$	127.330	0.288264
$59$	122.788	0.270942	0.135471	−	0.990781i	$-0.456745\pi$
$59$	122.788	0.270942	0.135471	+	0.990781i	$0.456745\pi$
$60$	−169.174	−0.364005
$61$	264.384	0.554932	0.277466	−	0.960735i	$-0.410505\pi$
$61$	264.384	0.554932	0.277466	+	0.960735i	$0.410505\pi$
$62$	−64.4877	−0.132096
$63$	283.802	0.567552
$64$	−810.411	−1.58283
$65$	29.9366	0.0571257
$66$	−69.6611	−0.129920
$67$	622.712	1.13547	0.567734	−	0.823212i	$-0.307820\pi$
$67$	622.712	1.13547	0.567734	+	0.823212i	$0.307820\pi$
$68$	954.997	1.70309
$69$	93.2694	0.162729
$70$	−692.274	−1.18204
$71$	327.717	0.547786	0.273893	−	0.961760i	$-0.411689\pi$
$71$	327.717	0.547786	0.273893	+	0.961760i	$0.411689\pi$
$72$	129.545	0.212043
$73$	−833.518	−1.33638	−0.668191	−	0.743989i	$-0.732931\pi$
$73$	−833.518	−1.33638	−0.668191	+	0.743989i	$0.732931\pi$
$74$	−34.0795	−0.0535360
$75$	75.0000	0.115470
$76$	646.787	0.976204
$77$	−166.767	−0.246816
$78$	−78.8655	−0.114484
$79$	−666.457	−0.949143	−0.474571	−	0.880217i	$-0.657397\pi$
$79$	−666.457	−0.949143	−0.474571	+	0.880217i	$0.657397\pi$
$80$	135.133	0.188855
$81$	81.0000	0.111111
$82$	−1755.70	−2.36444
$83$	−1320.72	−1.74660	−0.873301	−	0.487182i	$-0.838025\pi$
$83$	−1320.72	−1.74660	−0.873301	+	0.487182i	$0.838025\pi$
$84$	1066.93	1.38586
$85$	−423.379	−0.540257
$86$	−79.0180	−0.0990782
$87$	87.0000	0.107211
$88$	−76.1229	−0.0922128
$89$	−189.059	−0.225172	−0.112586	−	0.993642i	$-0.535913\pi$
$89$	−189.059	−0.225172	−0.112586	+	0.993642i	$0.535913\pi$
$90$	−197.582	−0.231410
$91$	−188.801	−0.217492
$92$	350.640	0.397355
$93$	−44.0620	−0.0491292
$94$	−1153.87	−1.26609
$95$	−286.740	−0.309673
$96$	−701.453	−0.745747
$97$	−137.630	−0.144064	−0.0720321	−	0.997402i	$-0.522948\pi$
$97$	−137.630	−0.144064	−0.0720321	+	0.997402i	$0.522948\pi$
$98$	2859.97	2.94796
$99$	−47.5968	−0.0483198
$100$	281.957	0.281957
$101$	−1721.15	−1.69565	−0.847826	−	0.530275i	$-0.822089\pi$
$101$	−1721.15	−1.69565	−0.847826	+	0.530275i	$0.822089\pi$
$102$	1115.36	1.08272
$103$	797.585	0.762994	0.381497	−	0.924370i	$-0.375409\pi$
$103$	797.585	0.762994	0.381497	+	0.924370i	$0.375409\pi$
$104$	−86.1810	−0.0812571
$105$	−473.004	−0.439624
$106$	−285.363	−0.261480
$107$	−778.452	−0.703325	−0.351662	−	0.936127i	$-0.614384\pi$
$107$	−778.452	−0.703325	−0.351662	+	0.936127i	$0.614384\pi$
$108$	304.513	0.271313
$109$	721.205	0.633752	0.316876	−	0.948467i	$-0.397366\pi$
$109$	721.205	0.633752	0.316876	+	0.948467i	$0.397366\pi$
$110$	116.102	0.100635
$111$	−23.2852	−0.0199111
$112$	−852.249	−0.719017
$113$	−559.024	−0.465386	−0.232693	−	0.972550i	$-0.574754\pi$
$113$	−559.024	−0.465386	−0.232693	+	0.972550i	$0.574754\pi$
$114$	755.394	0.620607
$115$	−155.449	−0.126050
$116$	327.070	0.261790
$117$	−53.8858	−0.0425790
$118$	539.124	0.420597
$119$	2670.13	2.05690
$120$	−215.909	−0.164248
$121$	−1303.03	−0.978987
$122$	1160.83	0.861448
$123$	−1199.60	−0.879384
$124$	−165.648	−0.119965
$125$	−125.000	−0.0894427
$126$	1246.09	0.881038
$127$	−626.324	−0.437616	−0.218808	−	0.975768i	$-0.570217\pi$
$127$	−626.324	−0.437616	−0.218808	+	0.975768i	$0.570217\pi$
$128$	−1687.73	−1.16544
$129$	−53.9900	−0.0368492
$130$	131.443	0.0886790
$131$	1764.12	1.17658	0.588289	−	0.808651i	$-0.299802\pi$
$131$	1764.12	1.17658	0.588289	+	0.808651i	$0.299802\pi$
$132$	−178.937	−0.117988
$133$	1808.39	1.17900
$134$	2734.14	1.76264
$135$	−135.000	−0.0860663
$136$	1218.82	0.768476
$137$	−433.723	−0.270478	−0.135239	−	0.990813i	$-0.543180\pi$
$137$	−433.723	−0.270478	−0.135239	+	0.990813i	$0.543180\pi$
$138$	409.518	0.252613
$139$	−504.659	−0.307947	−0.153974	−	0.988075i	$-0.549207\pi$
$139$	−504.659	−0.307947	−0.153974	+	0.988075i	$0.549207\pi$
$140$	−1778.22	−1.07348
$141$	−788.393	−0.470884
$142$	1438.91	0.850355
$143$	31.6641	0.0185167
$144$	−243.240	−0.140764
$145$	−145.000	−0.0830455
$146$	−3659.73	−2.07453
$147$	1954.11	1.09641
$148$	−87.5391	−0.0486194
$149$	−354.655	−0.194997	−0.0974983	−	0.995236i	$-0.531084\pi$
$149$	−354.655	−0.194997	−0.0974983	+	0.995236i	$0.531084\pi$
$150$	329.303	0.179250
$151$	−325.611	−0.175483	−0.0877413	−	0.996143i	$-0.527965\pi$
$151$	−325.611	−0.175483	−0.0877413	+	0.996143i	$0.527965\pi$
$152$	825.464	0.440487
$153$	762.082	0.402684
$154$	−732.222	−0.383144
$155$	73.4366	0.0380553
$156$	−202.580	−0.103970
$157$	−2690.09	−1.36747	−0.683733	−	0.729732i	$-0.739645\pi$
$157$	−2690.09	−1.36747	−0.683733	+	0.729732i	$0.739645\pi$
$158$	−2926.22	−1.47340
$159$	−194.978	−0.0972499
$160$	1169.09	0.577653
$161$	980.374	0.479902
$162$	355.647	0.172483
$163$	1411.51	0.678270	0.339135	−	0.940738i	$-0.389866\pi$
$163$	1411.51	0.678270	0.339135	+	0.940738i	$0.389866\pi$
$164$	−4509.81	−2.14730
$165$	79.3280	0.0374283
$166$	−5798.89	−2.71133
$167$	−2538.25	−1.17614	−0.588072	−	0.808809i	$-0.700113\pi$
$167$	−2538.25	−1.17614	−0.588072	+	0.808809i	$0.700113\pi$
$168$	1361.68	0.625332
$169$	−2161.15	−0.983683
$170$	−1858.93	−0.838667
$171$	516.132	0.230816
$172$	−202.971	−0.0899791
$173$	−305.030	−0.134052	−0.0670260	−	0.997751i	$-0.521351\pi$
$173$	−305.030	−0.134052	−0.0670260	+	0.997751i	$0.521351\pi$
$174$	381.991	0.166429
$175$	788.340	0.340531
$176$	142.932	0.0612152
$177$	368.363	0.156429
$178$	−830.104	−0.349545
$179$	3093.43	1.29170	0.645849	−	0.763465i	$-0.276504\pi$
$179$	3093.43	1.29170	0.645849	+	0.763465i	$0.276504\pi$
$180$	−507.522	−0.210158
$181$	2800.38	1.15000	0.575001	−	0.818153i	$-0.305002\pi$
$181$	2800.38	1.15000	0.575001	+	0.818153i	$0.305002\pi$
$182$	−828.971	−0.337623
$183$	793.151	0.320390
$184$	447.505	0.179296
$185$	38.8087	0.0154231
$186$	−193.463	−0.0762656
$187$	−447.811	−0.175118
$188$	−2963.91	−1.14981
$189$	851.407	0.327676
$190$	−1258.99	−0.480720
$191$	4208.78	1.59443	0.797217	−	0.603693i	$-0.206305\pi$
$191$	4208.78	1.59443	0.797217	+	0.603693i	$0.206305\pi$
$192$	−2431.23	−0.913849
$193$	−247.563	−0.0923315	−0.0461658	−	0.998934i	$-0.514700\pi$
$193$	−247.563	−0.0923315	−0.0461658	+	0.998934i	$0.514700\pi$
$194$	−604.293	−0.223638
$195$	89.8097	0.0329816
$196$	7346.31	2.67723
$197$	−4574.07	−1.65426	−0.827129	−	0.562013i	$-0.810027\pi$
$197$	−4574.07	−1.65426	−0.827129	+	0.562013i	$0.810027\pi$
$198$	−208.983	−0.0750091
$199$	2601.05	0.926551	0.463276	−	0.886214i	$-0.346674\pi$
$199$	2601.05	0.926551	0.463276	+	0.886214i	$0.346674\pi$
$200$	359.849	0.127226
$201$	1868.13	0.655563
$202$	−7557.06	−2.63224
$203$	914.475	0.316175
$204$	2864.99	0.983281
$205$	1999.33	0.681168
$206$	3501.96	1.18443
$207$	279.808	0.0939518
$208$	161.817	0.0539423
$209$	−303.287	−0.100377
$210$	−2076.82	−0.682449
$211$	244.148	0.0796582	0.0398291	−	0.999207i	$-0.487319\pi$
$211$	244.148	0.0796582	0.0398291	+	0.999207i	$0.487319\pi$
$212$	−733.004	−0.237467
$213$	983.150	0.316265
$214$	−3417.95	−1.09181
$215$	89.9833	0.0285433
$216$	388.636	0.122423
$217$	−463.144	−0.144886
$218$	3166.60	0.983803
$219$	−2500.56	−0.771561
$220$	298.228	0.0913932
$221$	−506.980	−0.154313
$222$	−102.239	−0.0309090
$223$	4179.26	1.25500	0.627498	−	0.778618i	$-0.284079\pi$
$223$	4179.26	1.25500	0.627498	+	0.778618i	$0.284079\pi$
$224$	−7373.12	−2.19927
$225$	225.000	0.0666667
$226$	−2454.51	−0.722441
$227$	4034.64	1.17968	0.589842	−	0.807518i	$-0.299190\pi$
$227$	4034.64	1.17968	0.589842	+	0.807518i	$0.299190\pi$
$228$	1940.36	0.563612
$229$	4501.53	1.29899	0.649497	−	0.760364i	$-0.274980\pi$
$229$	4501.53	1.29899	0.649497	+	0.760364i	$0.274980\pi$
$230$	−682.531	−0.195673
$231$	−500.300	−0.142499
$232$	417.424	0.118126
$233$	−4710.72	−1.32450	−0.662252	−	0.749282i	$-0.730399\pi$
$233$	−4710.72	−1.32450	−0.662252	+	0.749282i	$0.730399\pi$
$234$	−236.597	−0.0660974
$235$	1313.99	0.364745
$236$	1384.83	0.381970
$237$	−1999.37	−0.547988
$238$	11723.8	3.19302
$239$	−496.634	−0.134412	−0.0672062	−	0.997739i	$-0.521409\pi$
$239$	−496.634	−0.134412	−0.0672062	+	0.997739i	$0.521409\pi$
$240$	405.400	0.109035
$241$	6414.62	1.71453	0.857266	−	0.514874i	$-0.172161\pi$
$241$	6414.62	1.71453	0.857266	+	0.514874i	$0.172161\pi$
$242$	−5721.22	−1.51973
$243$	243.000	0.0641500
$244$	2981.79	0.782335
$245$	−3256.84	−0.849274
$246$	−5267.09	−1.36511
$247$	−343.360	−0.0884514
$248$	−211.409	−0.0541309
$249$	−3962.16	−1.00840
$250$	−548.838	−0.138846
$251$	4741.55	1.19237	0.596183	−	0.802848i	$-0.296683\pi$
$251$	4741.55	1.19237	0.596183	+	0.802848i	$0.296683\pi$
$252$	3200.80	0.800126
$253$	−164.420	−0.0408576
$254$	−2750.00	−0.679333
$255$	−1270.14	−0.311918
$256$	−927.044	−0.226329
$257$	−6110.47	−1.48312	−0.741558	−	0.670889i	$-0.765913\pi$
$257$	−6110.47	−1.48312	−0.741558	+	0.670889i	$0.765913\pi$
$258$	−237.054	−0.0572028
$259$	−244.756	−0.0587196
$260$	337.633	0.0805350
$261$	261.000	0.0618984
$262$	7745.72	1.82646
$263$	−3905.40	−0.915654	−0.457827	−	0.889041i	$-0.651372\pi$
$263$	−3905.40	−0.915654	−0.457827	+	0.889041i	$0.651372\pi$
$264$	−228.369	−0.0532391
$265$	324.963	0.0753294
$266$	7940.10	1.83022
$267$	−567.178	−0.130003
$268$	7023.11	1.60076
$269$	−6684.63	−1.51513	−0.757563	−	0.652762i	$-0.773610\pi$
$269$	−6684.63	−1.51513	−0.757563	+	0.652762i	$0.773610\pi$
$270$	−592.745	−0.133605
$271$	−6784.76	−1.52083	−0.760415	−	0.649438i	$-0.775004\pi$
$271$	−6784.76	−1.52083	−0.760415	+	0.649438i	$0.775004\pi$
$272$	−2288.50	−0.510151
$273$	−566.404	−0.125569
$274$	−1904.35	−0.419875
$275$	−132.213	−0.0289919
$276$	1051.92	0.229413
$277$	3811.10	0.826666	0.413333	−	0.910580i	$-0.364364\pi$
$277$	3811.10	0.826666	0.413333	+	0.910580i	$0.364364\pi$
$278$	−2215.81	−0.478041
$279$	−132.186	−0.0283647
$280$	−2269.46	−0.484380
$281$	1848.27	0.392380	0.196190	−	0.980566i	$-0.437143\pi$
$281$	1848.27	0.392380	0.196190	+	0.980566i	$0.437143\pi$
$282$	−3461.60	−0.730976
$283$	1381.94	0.290275	0.145138	−	0.989411i	$-0.453638\pi$
$283$	1381.94	0.290275	0.145138	+	0.989411i	$0.453638\pi$
$284$	3696.08	0.772261
$285$	−860.220	−0.178790
$286$	139.028	0.0287443
$287$	−12609.2	−2.59338
$288$	−2104.36	−0.430557
$289$	2256.98	0.459390
$290$	−636.652	−0.128915
$291$	−412.890	−0.0831755
$292$	−9400.65	−1.88401
$293$	6221.44	1.24048	0.620239	−	0.784413i	$-0.287036\pi$
$293$	6221.44	1.24048	0.620239	+	0.784413i	$0.287036\pi$
$294$	8579.90	1.70201
$295$	−613.938	−0.121169
$296$	−111.722	−0.0219382
$297$	−142.790	−0.0278974
$298$	−1557.19	−0.302702
$299$	−186.144	−0.0360034
$300$	845.871	0.162788
$301$	−567.499	−0.108671
$302$	−1429.66	−0.272410
$303$	−5163.45	−0.978985
$304$	−1549.93	−0.292416
$305$	−1321.92	−0.248173
$306$	3346.08	0.625106
$307$	8135.50	1.51244	0.756218	−	0.654320i	$-0.227045\pi$
$307$	8135.50	1.51244	0.756218	+	0.654320i	$0.227045\pi$
$308$	−1880.84	−0.347957
$309$	2392.75	0.440515
$310$	322.438	0.0590751
$311$	3117.65	0.568444	0.284222	−	0.958759i	$-0.408265\pi$
$311$	3117.65	0.568444	0.284222	+	0.958759i	$0.408265\pi$
$312$	−258.543	−0.0469138
$313$	7536.36	1.36096	0.680480	−	0.732767i	$-0.261771\pi$
$313$	7536.36	1.36096	0.680480	+	0.732767i	$0.261771\pi$
$314$	−11811.4	−2.12278
$315$	−1419.01	−0.253817
$316$	−7516.49	−1.33809
$317$	3579.28	0.634172	0.317086	−	0.948397i	$-0.397296\pi$
$317$	3579.28	0.634172	0.317086	+	0.948397i	$0.397296\pi$
$318$	−856.089	−0.150966
$319$	−153.367	−0.0269183
$320$	4052.05	0.707865
$321$	−2335.35	−0.406065
$322$	4304.53	0.744976
$323$	4855.98	0.836515
$324$	913.540	0.156643
$325$	−149.683	−0.0255474
$326$	6197.52	1.05291
$327$	2163.62	0.365897
$328$	−5755.66	−0.968911
$329$	−8286.96	−1.38868
$330$	348.306	0.0581018
$331$	−6257.20	−1.03905	−0.519527	−	0.854454i	$-0.673892\pi$
$331$	−6257.20	−1.03905	−0.519527	+	0.854454i	$0.673892\pi$
$332$	−14895.5	−2.46233
$333$	−69.8557	−0.0114957
$334$	−11144.7	−1.82578
$335$	−3113.56	−0.507797
$336$	−2556.75	−0.415125
$337$	−4034.64	−0.652168	−0.326084	−	0.945341i	$-0.605729\pi$
$337$	−4034.64	−0.652168	−0.326084	+	0.945341i	$0.605729\pi$
$338$	−9488.98	−1.52702
$339$	−1677.07	−0.268691
$340$	−4774.98	−0.761647
$341$	77.6744	0.0123352
$342$	2266.18	0.358307
$343$	9723.97	1.53074
$344$	−259.043	−0.0406007
$345$	−466.347	−0.0727748
$346$	−1339.30	−0.208095
$347$	−10221.1	−1.58126	−0.790630	−	0.612294i	$-0.790247\pi$
$347$	−10221.1	−1.58126	−0.790630	+	0.612294i	$0.790247\pi$
$348$	981.210	0.151145
$349$	−2543.26	−0.390079	−0.195040	−	0.980795i	$-0.562484\pi$
$349$	−2543.26	−0.390079	−0.195040	+	0.980795i	$0.562484\pi$
$350$	3461.37	0.528623
$351$	−161.657	−0.0245830
$352$	1236.55	0.187240
$353$	11741.3	1.77034	0.885168	−	0.465272i	$-0.154044\pi$
$353$	11741.3	1.77034	0.885168	+	0.465272i	$0.154044\pi$
$354$	1617.37	0.242832
$355$	−1638.58	−0.244978
$356$	−2132.27	−0.317443
$357$	8010.40	1.18755
$358$	13582.3	2.00517
$359$	5475.18	0.804927	0.402463	−	0.915436i	$-0.368154\pi$
$359$	5475.18	0.804927	0.402463	+	0.915436i	$0.368154\pi$
$360$	−647.727	−0.0948284
$361$	−3570.21	−0.520514
$362$	12295.6	1.78520
$363$	−3909.09	−0.565218
$364$	−2129.36	−0.306617
$365$	4167.59	0.597649
$366$	3482.49	0.497357
$367$	11158.0	1.58704	0.793522	−	0.608542i	$-0.208245\pi$
$367$	11158.0	1.58704	0.793522	+	0.608542i	$0.208245\pi$
$368$	−840.254	−0.119025
$369$	−3598.80	−0.507713
$370$	170.398	0.0239420
$371$	−2049.45	−0.286798
$372$	−496.943	−0.0692616
$373$	5823.05	0.808327	0.404163	−	0.914687i	$-0.367563\pi$
$373$	5823.05	0.808327	0.404163	+	0.914687i	$0.367563\pi$
$374$	−1966.20	−0.271845
$375$	−375.000	−0.0516398
$376$	−3782.70	−0.518823
$377$	−173.632	−0.0237202
$378$	3738.28	0.508667
$379$	2272.79	0.308036	0.154018	−	0.988068i	$-0.450779\pi$
$379$	2272.79	0.308036	0.154018	+	0.988068i	$0.450779\pi$
$380$	−3233.93	−0.436572
$381$	−1878.97	−0.252658
$382$	18479.5	2.47512
$383$	8686.06	1.15884	0.579422	−	0.815028i	$-0.303278\pi$
$383$	8686.06	1.15884	0.579422	+	0.815028i	$0.303278\pi$
$384$	−5063.19	−0.672865
$385$	833.833	0.110379
$386$	−1086.98	−0.143331
$387$	−161.970	−0.0212749
$388$	−1552.23	−0.203099
$389$	5410.18	0.705159	0.352580	−	0.935782i	$-0.385305\pi$
$389$	5410.18	0.705159	0.352580	+	0.935782i	$0.385305\pi$
$390$	394.328	0.0511989
$391$	2632.55	0.340496
$392$	9375.76	1.20803
$393$	5292.35	0.679298
$394$	−20083.4	−2.56798
$395$	3332.28	0.424470
$396$	−536.810	−0.0681205
$397$	13470.8	1.70297	0.851486	−	0.524377i	$-0.175702\pi$
$397$	13470.8	1.70297	0.851486	+	0.524377i	$0.175702\pi$
$398$	11420.4	1.43833
$399$	5425.17	0.680697
$400$	−675.667	−0.0844584
$401$	1749.26	0.217840	0.108920	−	0.994050i	$-0.465261\pi$
$401$	1749.26	0.217840	0.108920	+	0.994050i	$0.465261\pi$
$402$	8202.43	1.01766
$403$	87.9376	0.0108697
$404$	−19411.6	−2.39050
$405$	−405.000	−0.0496904
$406$	4015.19	0.490814
$407$	41.0482	0.00499923
$408$	3656.45	0.443680
$409$	−4261.47	−0.515198	−0.257599	−	0.966252i	$-0.582931\pi$
$409$	−4261.47	−0.515198	−0.257599	+	0.966252i	$0.582931\pi$
$410$	8778.48	1.05741
$411$	−1301.17	−0.156160
$412$	8995.38	1.07566
$413$	3871.94	0.461321
$414$	1228.56	0.145846
$415$	6603.60	0.781104
$416$	1399.94	0.164994
$417$	−1513.98	−0.177793
$418$	−1331.64	−0.155820
$419$	−3355.37	−0.391218	−0.195609	−	0.980682i	$-0.562668\pi$
$419$	−3355.37	−0.391218	−0.195609	+	0.980682i	$0.562668\pi$
$420$	−5334.67	−0.619775
$421$	−7859.86	−0.909896	−0.454948	−	0.890518i	$-0.650342\pi$
$421$	−7859.86	−0.909896	−0.454948	+	0.890518i	$0.650342\pi$
$422$	1071.98	0.123657
$423$	−2365.18	−0.271865
$424$	−935.499	−0.107151
$425$	2116.89	0.241610
$426$	4316.72	0.490953
$427$	8336.98	0.944858
$428$	−8779.59	−0.991537
$429$	94.9923	0.0106906
$430$	395.090	0.0443091
$431$	−9083.57	−1.01517	−0.507587	−	0.861600i	$-0.669463\pi$
$431$	−9083.57	−1.01517	−0.507587	+	0.861600i	$0.669463\pi$
$432$	−729.720	−0.0812701
$433$	10303.2	1.14351	0.571756	−	0.820424i	$-0.306262\pi$
$433$	10303.2	1.14351	0.571756	+	0.820424i	$0.306262\pi$
$434$	−2033.53	−0.224914
$435$	−435.000	−0.0479463
$436$	8133.95	0.893453
$437$	1782.94	0.195171
$438$	−10979.2	−1.19773
$439$	10285.7	1.11824	0.559122	−	0.829086i	$-0.311139\pi$
$439$	10285.7	1.11824	0.559122	+	0.829086i	$0.311139\pi$
$440$	380.614	0.0412388
$441$	5862.32	0.633011
$442$	−2226.00	−0.239547
$443$	11628.0	1.24710	0.623549	−	0.781784i	$-0.285690\pi$
$443$	11628.0	1.24710	0.623549	+	0.781784i	$0.285690\pi$
$444$	−262.617	−0.0280704
$445$	945.297	0.100700
$446$	18349.9	1.94819
$447$	−1063.97	−0.112581
$448$	−25555.2	−2.69502
$449$	−13543.0	−1.42346	−0.711730	−	0.702453i	$-0.752088\pi$
$449$	−13543.0	−1.42346	−0.711730	+	0.702453i	$0.752088\pi$
$450$	987.908	0.103490
$451$	2114.71	0.220793
$452$	−6304.83	−0.656094
$453$	−976.834	−0.101315
$454$	17714.9	1.83128
$455$	944.007	0.0972654
$456$	2476.39	0.254315
$457$	16383.2	1.67696	0.838481	−	0.544930i	$-0.183444\pi$
$457$	16383.2	1.67696	0.838481	+	0.544930i	$0.183444\pi$
$458$	19764.9	2.01649
$459$	2286.25	0.232490
$460$	−1753.20	−0.177703
$461$	13577.7	1.37175	0.685877	−	0.727717i	$-0.259419\pi$
$461$	13577.7	1.37175	0.685877	+	0.727717i	$0.259419\pi$
$462$	−2196.67	−0.221208
$463$	−17986.2	−1.80538	−0.902688	−	0.430297i	$-0.858409\pi$
$463$	−17986.2	−1.80538	−0.902688	+	0.430297i	$0.858409\pi$
$464$	−783.774	−0.0784176
$465$	220.310	0.0219712
$466$	−20683.4	−2.05609
$467$	792.472	0.0785251	0.0392625	−	0.999229i	$-0.487499\pi$
$467$	792.472	0.0785251	0.0392625	+	0.999229i	$0.487499\pi$
$468$	−607.739	−0.0600272
$469$	19636.3	1.93331
$470$	5769.33	0.566212
$471$	−8070.26	−0.789507
$472$	1767.40	0.172354
$473$	95.1759	0.00925199
$474$	−8778.65	−0.850668
$475$	1433.70	0.138490
$476$	30114.5	2.89978
$477$	−584.933	−0.0561472
$478$	−2180.57	−0.208655
$479$	−6655.02	−0.634813	−0.317407	−	0.948290i	$-0.602812\pi$
$479$	−6655.02	−0.634813	−0.317407	+	0.948290i	$0.602812\pi$
$480$	3507.27	0.333508
$481$	46.4719	0.00440528
$482$	28164.7	2.66155
$483$	2941.12	0.277072
$484$	−14695.9	−1.38016
$485$	688.151	0.0644274
$486$	1066.94	0.0995832
$487$	−13972.7	−1.30013	−0.650064	−	0.759880i	$-0.725258\pi$
$487$	−13972.7	−1.30013	−0.650064	+	0.759880i	$0.725258\pi$
$488$	3805.53	0.353008
$489$	4234.53	0.391600
$490$	−14299.8	−1.31837
$491$	3638.63	0.334438	0.167219	−	0.985920i	$-0.446521\pi$
$491$	3638.63	0.334438	0.167219	+	0.985920i	$0.446521\pi$
$492$	−13529.4	−1.23974
$493$	2455.60	0.224330
$494$	−1507.59	−0.137307
$495$	237.984	0.0216093
$496$	396.950	0.0359346
$497$	10334.1	0.932691
$498$	−17396.7	−1.56539
$499$	11313.5	1.01496	0.507478	−	0.861665i	$-0.330578\pi$
$499$	11313.5	1.01496	0.507478	+	0.861665i	$0.330578\pi$
$500$	−1409.78	−0.126095
$501$	−7614.76	−0.679047
$502$	20818.7	1.85097
$503$	−4598.92	−0.407665	−0.203833	−	0.979006i	$-0.565340\pi$
$503$	−4598.92	−0.407665	−0.203833	+	0.979006i	$0.565340\pi$
$504$	4085.04	0.361036
$505$	8605.75	0.758318
$506$	−721.917	−0.0634252
$507$	−6483.46	−0.567930
$508$	−7063.86	−0.616945
$509$	6967.41	0.606729	0.303364	−	0.952875i	$-0.401890\pi$
$509$	6967.41	0.606729	0.303364	+	0.952875i	$0.401890\pi$
$510$	−5576.79	−0.484205
$511$	−26283.8	−2.27540
$512$	9431.48	0.814095
$513$	1548.40	0.133262
$514$	−26829.3	−2.30231
$515$	−3987.92	−0.341221
$516$	−608.914	−0.0519495
$517$	1389.81	0.118228
$518$	−1074.65	−0.0911533
$519$	−915.090	−0.0773949
$520$	430.905	0.0363393
$521$	−11038.5	−0.928228	−0.464114	−	0.885776i	$-0.653627\pi$
$521$	−11038.5	−0.928228	−0.464114	+	0.885776i	$0.653627\pi$
$522$	1145.97	0.0960879
$523$	−15368.6	−1.28493	−0.642467	−	0.766314i	$-0.722089\pi$
$523$	−15368.6	−1.28493	−0.642467	+	0.766314i	$0.722089\pi$
$524$	19896.2	1.65872
$525$	2365.02	0.196606
$526$	−17147.4	−1.42141
$527$	−1243.66	−0.102798
$528$	428.795	0.0353426
$529$	−11200.4	−0.920558
$530$	1426.81	0.116937
$531$	1105.09	0.0903141
$532$	20395.5	1.66214
$533$	2394.12	0.194561
$534$	−2490.31	−0.201810
$535$	3892.26	0.314536
$536$	8963.28	0.722303
$537$	9280.30	0.745762
$538$	−29350.2	−2.35200
$539$	−3444.78	−0.275283
$540$	−1522.57	−0.121335
$541$	−10945.5	−0.869839	−0.434920	−	0.900469i	$-0.643223\pi$
$541$	−10945.5	−0.869839	−0.434920	+	0.900469i	$0.643223\pi$
$542$	−29789.9	−2.36086
$543$	8401.13	0.663954
$544$	−19798.7	−1.56041
$545$	−3606.03	−0.283422
$546$	−2486.91	−0.194927
$547$	10140.1	0.792616	0.396308	−	0.918118i	$-0.370291\pi$
$547$	10140.1	0.792616	0.396308	+	0.918118i	$0.370291\pi$
$548$	−4891.64	−0.381315
$549$	2379.45	0.184977
$550$	−580.510	−0.0450055
$551$	1663.09	0.128585
$552$	1342.52	0.103517
$553$	−21015.8	−1.61606
$554$	16733.4	1.28327
$555$	116.426	0.00890453
$556$	−5691.69	−0.434139
$557$	18329.0	1.39430	0.697151	−	0.716925i	$-0.254451\pi$
$557$	18329.0	1.39430	0.697151	+	0.716925i	$0.254451\pi$
$558$	−580.389	−0.0440320
$559$	107.752	0.00815278
$560$	4261.24	0.321554
$561$	−1343.43	−0.101105
$562$	8115.21	0.609110
$563$	2868.99	0.214766	0.107383	−	0.994218i	$-0.465753\pi$
$563$	2868.99	0.214766	0.107383	+	0.994218i	$0.465753\pi$
$564$	−8891.72	−0.663845
$565$	2795.12	0.208127
$566$	6067.69	0.450608
$567$	2554.22	0.189184
$568$	4717.14	0.348462
$569$	18562.0	1.36759	0.683795	−	0.729674i	$-0.260328\pi$
$569$	18562.0	1.36759	0.683795	+	0.729674i	$0.260328\pi$
$570$	−3776.97	−0.277544
$571$	−10162.6	−0.744815	−0.372408	−	0.928069i	$-0.621468\pi$
$571$	−10162.6	−0.744815	−0.372408	+	0.928069i	$0.621468\pi$
$572$	357.116	0.0261045
$573$	12626.4	0.920547
$574$	−55363.4	−4.02583
$575$	777.245	0.0563711
$576$	−7293.70	−0.527611
$577$	2525.24	0.182196	0.0910981	−	0.995842i	$-0.470962\pi$
$577$	2525.24	0.182196	0.0910981	+	0.995842i	$0.470962\pi$
$578$	9909.74	0.713133
$579$	−742.689	−0.0533076
$580$	−1635.35	−0.117076
$581$	−41647.1	−2.97386
$582$	−1812.88	−0.129117
$583$	343.715	0.0244172
$584$	−11997.6	−0.850111
$585$	269.429	0.0190419
$586$	27316.5	1.92565
$587$	3327.35	0.233960	0.116980	−	0.993134i	$-0.462679\pi$
$587$	3327.35	0.233960	0.116980	+	0.993134i	$0.462679\pi$
$588$	22038.9	1.54570
$589$	−842.289	−0.0589234
$590$	−2695.62	−0.188097
$591$	−13722.2	−0.955086
$592$	209.774	0.0145636
$593$	−16731.4	−1.15864	−0.579321	−	0.815099i	$-0.696682\pi$
$593$	−16731.4	−1.15864	−0.579321	+	0.815099i	$0.696682\pi$
$594$	−626.950	−0.0433065
$595$	−13350.7	−0.919872
$596$	−3999.90	−0.274903
$597$	7803.16	0.534945
$598$	−817.305	−0.0558898
$599$	−12851.1	−0.876600	−0.438300	−	0.898829i	$-0.644419\pi$
$599$	−12851.1	−0.876600	−0.438300	+	0.898829i	$0.644419\pi$
$600$	1079.55	0.0734538
$601$	−8773.05	−0.595441	−0.297720	−	0.954653i	$-0.596226\pi$
$601$	−8773.05	−0.595441	−0.297720	+	0.954653i	$0.596226\pi$
$602$	−2491.72	−0.168696
$603$	5604.40	0.378489
$604$	−3672.33	−0.247393
$605$	6515.16	0.437816
$606$	−22671.2	−1.51973
$607$	−19083.1	−1.27605	−0.638023	−	0.770017i	$-0.720247\pi$
$607$	−19083.1	−1.27605	−0.638023	+	0.770017i	$0.720247\pi$
$608$	−13409.0	−0.894417
$609$	2743.42	0.182544
$610$	−5804.15	−0.385251
$611$	1573.45	0.104182
$612$	8594.97	0.567698
$613$	20976.8	1.38213	0.691063	−	0.722794i	$-0.257142\pi$
$613$	20976.8	1.38213	0.691063	+	0.722794i	$0.257142\pi$
$614$	35720.6	2.34783
$615$	5998.00	0.393273
$616$	−2400.43	−0.157007
$617$	−15290.1	−0.997658	−0.498829	−	0.866700i	$-0.666236\pi$
$617$	−15290.1	−0.997658	−0.498829	+	0.866700i	$0.666236\pi$
$618$	10505.9	0.683832
$619$	18786.8	1.21988	0.609938	−	0.792449i	$-0.291194\pi$
$619$	18786.8	1.21988	0.609938	+	0.792449i	$0.291194\pi$
$620$	828.239	0.0536498
$621$	839.425	0.0542431
$622$	13688.7	0.882422
$623$	−5961.73	−0.383389
$624$	485.451	0.0311436
$625$	625.000	0.0400000
$626$	33089.9	2.11268
$627$	−909.860	−0.0579527
$628$	−30339.5	−1.92783
$629$	−657.231	−0.0416622
$630$	−6230.46	−0.394012
$631$	14273.7	0.900516	0.450258	−	0.892898i	$-0.351332\pi$
$631$	14273.7	0.900516	0.450258	+	0.892898i	$0.351332\pi$
$632$	−9592.94	−0.603777
$633$	732.445	0.0459907
$634$	15715.6	0.984456
$635$	3131.62	0.195708
$636$	−2199.01	−0.137101
$637$	−3899.95	−0.242577
$638$	−673.391	−0.0417865
$639$	2949.45	0.182595
$640$	8438.66	0.521199
$641$	10936.9	0.673919	0.336959	−	0.941519i	$-0.390602\pi$
$641$	10936.9	0.673919	0.336959	+	0.941519i	$0.390602\pi$
$642$	−10253.9	−0.630354
$643$	5329.32	0.326855	0.163427	−	0.986555i	$-0.447745\pi$
$643$	5329.32	0.326855	0.163427	+	0.986555i	$0.447745\pi$
$644$	11056.9	0.676559
$645$	269.950	0.0164795
$646$	21321.2	1.29856
$647$	−15807.3	−0.960509	−0.480255	−	0.877129i	$-0.659456\pi$
$647$	−15807.3	−0.960509	−0.480255	+	0.877129i	$0.659456\pi$
$648$	1165.91	0.0706809
$649$	−649.367	−0.0392756
$650$	−657.213	−0.0396585
$651$	−1389.43	−0.0836500
$652$	15919.4	0.956215
$653$	−11047.2	−0.662037	−0.331019	−	0.943624i	$-0.607392\pi$
$653$	−11047.2	−0.662037	−0.331019	+	0.943624i	$0.607392\pi$
$654$	9499.79	0.567999
$655$	−8820.59	−0.526182
$656$	10807.1	0.643209
$657$	−7501.67	−0.445461
$658$	−36385.6	−2.15571
$659$	−20355.2	−1.20322	−0.601612	−	0.798789i	$-0.705475\pi$
$659$	−20355.2	−1.20322	−0.601612	+	0.798789i	$0.705475\pi$
$660$	894.683	0.0527659
$661$	−27873.5	−1.64017	−0.820086	−	0.572241i	$-0.806074\pi$
$661$	−27873.5	−1.64017	−0.820086	+	0.572241i	$0.806074\pi$
$662$	−27473.5	−1.61297
$663$	−1520.94	−0.0890926
$664$	−19010.4	−1.11106
$665$	−9041.95	−0.527266
$666$	−306.716	−0.0178453
$667$	901.605	0.0523392
$668$	−28627.1	−1.65811
$669$	12537.8	0.724572
$670$	−13670.7	−0.788277
$671$	−1398.20	−0.0804427
$672$	−22119.3	−1.26975
$673$	−9555.18	−0.547288	−0.273644	−	0.961831i	$-0.588229\pi$
$673$	−9555.18	−0.547288	−0.273644	+	0.961831i	$0.588229\pi$
$674$	−17714.9	−1.01239
$675$	675.000	0.0384900
$676$	−24374.1	−1.38678
$677$	17556.1	0.996658	0.498329	−	0.866988i	$-0.333947\pi$
$677$	17556.1	0.996658	0.498329	+	0.866988i	$0.333947\pi$
$678$	−7363.53	−0.417101
$679$	−4339.97	−0.245292
$680$	−6094.09	−0.343673
$681$	12103.9	0.681091
$682$	341.045	0.0191485
$683$	11046.7	0.618875	0.309437	−	0.950920i	$-0.399859\pi$
$683$	11046.7	0.618875	0.309437	+	0.950920i	$0.399859\pi$
$684$	5821.08	0.325401
$685$	2168.61	0.120961
$686$	42695.1	2.37625
$687$	13504.6	0.749974
$688$	486.390	0.0269527
$689$	389.130	0.0215162
$690$	−2047.59	−0.112972
$691$	−7999.45	−0.440396	−0.220198	−	0.975455i	$-0.570670\pi$
$691$	−7999.45	−0.440396	−0.220198	+	0.975455i	$0.570670\pi$
$692$	−3440.21	−0.188984
$693$	−1500.90	−0.0822719
$694$	−44877.8	−2.45467
$695$	2523.30	0.137718
$696$	1252.27	0.0682001
$697$	−33859.0	−1.84003
$698$	−11166.7	−0.605538
$699$	−14132.1	−0.764702
$700$	8891.12	0.480075
$701$	−25401.3	−1.36861	−0.684303	−	0.729198i	$-0.739893\pi$
$701$	−25401.3	−1.36861	−0.684303	+	0.729198i	$0.739893\pi$
$702$	−709.790	−0.0381614
$703$	−445.120	−0.0238806
$704$	4285.88	0.229447
$705$	3941.97	0.210586
$706$	51552.7	2.74818
$707$	−54274.1	−2.88711
$708$	4154.50	0.220531
$709$	−9479.34	−0.502122	−0.251061	−	0.967971i	$-0.580779\pi$
$709$	−9479.34	−0.502122	−0.251061	+	0.967971i	$0.580779\pi$
$710$	−7194.54	−0.380290
$711$	−5998.11	−0.316381
$712$	−2721.31	−0.143238
$713$	−456.626	−0.0239843
$714$	35171.3	1.84349
$715$	−158.320	−0.00828091
$716$	34888.6	1.82102
$717$	−1489.90	−0.0776030
$718$	24039.9	1.24953
$719$	−32420.3	−1.68161	−0.840803	−	0.541341i	$-0.817917\pi$
$719$	−32420.3	−1.68161	−0.840803	+	0.541341i	$0.817917\pi$
$720$	1216.20	0.0629516
$721$	25150.7	1.29912
$722$	−15675.7	−0.808019
$723$	19243.9	0.989885
$724$	31583.4	1.62126
$725$	725.000	0.0371391
$726$	−17163.7	−0.877416
$727$	−6808.51	−0.347337	−0.173668	−	0.984804i	$-0.555562\pi$
$727$	−6808.51	−0.347337	−0.173668	+	0.984804i	$0.555562\pi$
$728$	−2717.60	−0.138353
$729$	729.000	0.0370370
$730$	18298.7	0.927759
$731$	−1523.88	−0.0771036
$732$	8945.38	0.451681
$733$	20190.4	1.01740	0.508698	−	0.860945i	$-0.330127\pi$
$733$	20190.4	1.01740	0.508698	+	0.860945i	$0.330127\pi$
$734$	48991.6	2.46364
$735$	−9770.53	−0.490328
$736$	−7269.35	−0.364065
$737$	−3293.23	−0.164597
$738$	−15801.3	−0.788147
$739$	15130.0	0.753134	0.376567	−	0.926389i	$-0.377105\pi$
$739$	15130.0	0.753134	0.376567	+	0.926389i	$0.377105\pi$
$740$	437.695	0.0217432
$741$	−1030.08	−0.0510674
$742$	−8998.52	−0.445210
$743$	−13315.6	−0.657470	−0.328735	−	0.944422i	$-0.606622\pi$
$743$	−13315.6	−0.657470	−0.328735	+	0.944422i	$0.606622\pi$
$744$	−634.226	−0.0312525
$745$	1773.28	0.0872051
$746$	25567.3	1.25480
$747$	−11886.5	−0.582200
$748$	−5050.53	−0.246879
$749$	−24547.4	−1.19752
$750$	−1646.51	−0.0801629
$751$	−18846.4	−0.915734	−0.457867	−	0.889021i	$-0.651386\pi$
$751$	−18846.4	−0.915734	−0.457867	+	0.889021i	$0.651386\pi$
$752$	7102.55	0.344419
$753$	14224.7	0.688413
$754$	−762.367	−0.0368220
$755$	1628.06	0.0784782
$756$	9602.41	0.461953
$757$	699.522	0.0335859	0.0167930	−	0.999859i	$-0.494654\pi$
$757$	699.522	0.0335859	0.0167930	+	0.999859i	$0.494654\pi$
$758$	9979.16	0.478178
$759$	−493.259	−0.0235891
$760$	−4127.32	−0.196992
$761$	−37430.3	−1.78298	−0.891489	−	0.453041i	$-0.850339\pi$
$761$	−37430.3	−1.78298	−0.891489	+	0.453041i	$0.850339\pi$
$762$	−8250.01	−0.392213
$763$	22742.2	1.07906
$764$	47467.8	2.24781
$765$	−3810.41	−0.180086
$766$	38137.9	1.79893
$767$	−735.168	−0.0346093
$768$	−2781.13	−0.130671
$769$	30299.7	1.42085	0.710426	−	0.703772i	$-0.248502\pi$
$769$	30299.7	1.42085	0.710426	+	0.703772i	$0.248502\pi$
$770$	3661.11	0.171347
$771$	−18331.4	−0.856277
$772$	−2792.09	−0.130168
$773$	16926.9	0.787603	0.393802	−	0.919195i	$-0.371160\pi$
$773$	16926.9	0.787603	0.393802	+	0.919195i	$0.371160\pi$
$774$	−711.162	−0.0330261
$775$	−367.183	−0.0170188
$776$	−1981.04	−0.0916433
$777$	−734.267	−0.0339018
$778$	23754.5	1.09465
$779$	−22931.5	−1.05470
$780$	1012.90	0.0464969
$781$	−1733.14	−0.0794068
$782$	11558.8	0.528568
$783$	783.000	0.0357371
$784$	−17604.3	−0.801946
$785$	13450.4	0.611550
$786$	23237.2	1.05451
$787$	−20726.9	−0.938799	−0.469400	−	0.882986i	$-0.655530\pi$
$787$	−20726.9	−0.938799	−0.469400	+	0.882986i	$0.655530\pi$
$788$	−51587.6	−2.33215
$789$	−11716.2	−0.528653
$790$	14631.1	0.658924
$791$	−17628.1	−0.792391
$792$	−685.106	−0.0307376
$793$	−1582.95	−0.0708854
$794$	59146.3	2.64361
$795$	974.888	0.0434915
$796$	29335.4	1.30624
$797$	−25560.6	−1.13601	−0.568006	−	0.823025i	$-0.692285\pi$
$797$	−25560.6	−1.13601	−0.568006	+	0.823025i	$0.692285\pi$
$798$	23820.3	1.05668
$799$	−22252.6	−0.985282
$800$	−5845.44	−0.258334
$801$	−1701.54	−0.0750572
$802$	7680.49	0.338164
$803$	4408.09	0.193721
$804$	21069.3	0.924202
$805$	−4901.87	−0.214619
$806$	386.108	0.0168735
$807$	−20053.9	−0.874758
$808$	−24774.1	−1.07865
$809$	−45525.7	−1.97849	−0.989244	−	0.146273i	$-0.953272\pi$
$809$	−45525.7	−1.97849	−0.989244	+	0.146273i	$0.953272\pi$
$810$	−1778.23	−0.0771368
$811$	8515.77	0.368717	0.184358	−	0.982859i	$-0.440979\pi$
$811$	8515.77	0.368717	0.184358	+	0.982859i	$0.440979\pi$
$812$	10313.7	0.445739
$813$	−20354.3	−0.878051
$814$	180.231	0.00776054
$815$	−7057.55	−0.303332
$816$	−6865.51	−0.294536
$817$	−1032.07	−0.0441954
$818$	−18710.8	−0.799767
$819$	−1699.21	−0.0724973
$820$	22549.0	0.960300
$821$	18922.1	0.804369	0.402185	−	0.915559i	$-0.368251\pi$
$821$	18922.1	0.804369	0.402185	+	0.915559i	$0.368251\pi$
$822$	−5713.04	−0.242415
$823$	−13297.5	−0.563210	−0.281605	−	0.959530i	$-0.590867\pi$
$823$	−13297.5	−0.563210	−0.281605	+	0.959530i	$0.590867\pi$
$824$	11480.4	0.485362
$825$	−396.640	−0.0167385
$826$	17000.5	0.716131
$827$	−26020.8	−1.09411	−0.547056	−	0.837096i	$-0.684252\pi$
$827$	−26020.8	−1.09411	−0.547056	+	0.837096i	$0.684252\pi$
$828$	3155.76	0.132452
$829$	8756.88	0.366874	0.183437	−	0.983031i	$-0.441278\pi$
$829$	8756.88	0.366874	0.183437	+	0.983031i	$0.441278\pi$
$830$	28994.5	1.21255
$831$	11433.3	0.477276
$832$	4852.18	0.202186
$833$	55155.1	2.29413
$834$	−6647.43	−0.275997
$835$	12691.3	0.525987
$836$	−3420.55	−0.141510
$837$	−396.558	−0.0163764
$838$	−14732.4	−0.607307
$839$	−1131.02	−0.0465400	−0.0232700	−	0.999729i	$-0.507408\pi$
$839$	−1131.02	−0.0465400	−0.0232700	+	0.999729i	$0.507408\pi$
$840$	−6808.39	−0.279657
$841$	841.000	0.0344828
$842$	−34510.3	−1.41248
$843$	5544.82	0.226540
$844$	2753.57	0.112301
$845$	10805.8	0.439917
$846$	−10384.8	−0.422029
$847$	−41089.3	−1.66688
$848$	1756.53	0.0711316
$849$	4145.82	0.167590
$850$	9294.65	0.375063
$851$	−241.311	−0.00972037
$852$	11088.2	0.445865
$853$	−12199.3	−0.489679	−0.244839	−	0.969564i	$-0.578735\pi$
$853$	−12199.3	−0.489679	−0.244839	+	0.969564i	$0.578735\pi$
$854$	36605.2	1.46675
$855$	−2580.66	−0.103224
$856$	−11205.0	−0.447405
$857$	37800.4	1.50670	0.753348	−	0.657622i	$-0.228438\pi$
$857$	37800.4	1.50670	0.753348	+	0.657622i	$0.228438\pi$
$858$	417.083	0.0165955
$859$	30888.1	1.22688	0.613438	−	0.789743i	$-0.289786\pi$
$859$	30888.1	1.22688	0.613438	+	0.789743i	$0.289786\pi$
$860$	1014.86	0.0402399
$861$	−37827.7	−1.49729
$862$	−39883.3	−1.57590
$863$	38008.4	1.49921	0.749607	−	0.661883i	$-0.230242\pi$
$863$	38008.4	1.49921	0.749607	+	0.661883i	$0.230242\pi$
$864$	−6313.08	−0.248582
$865$	1525.15	0.0599499
$866$	45238.3	1.77513
$867$	6770.95	0.265229
$868$	−5223.47	−0.204258
$869$	3524.58	0.137587
$870$	−1909.96	−0.0744294
$871$	−3728.37	−0.145041
$872$	10381.0	0.403147
$873$	−1238.67	−0.0480214
$874$	7828.35	0.302973
$875$	−3941.70	−0.152290
$876$	−28202.0	−1.08773
$877$	45609.0	1.75611	0.878055	−	0.478561i	$-0.158841\pi$
$877$	45609.0	1.75611	0.878055	+	0.478561i	$0.158841\pi$
$878$	45161.4	1.73590
$879$	18664.3	0.716191
$880$	−714.658	−0.0273762
$881$	15306.9	0.585360	0.292680	−	0.956210i	$-0.405453\pi$
$881$	15306.9	0.585360	0.292680	+	0.956210i	$0.405453\pi$
$882$	25739.7	0.982654
$883$	−4293.37	−0.163628	−0.0818140	−	0.996648i	$-0.526071\pi$
$883$	−4293.37	−0.163628	−0.0818140	+	0.996648i	$0.526071\pi$
$884$	−5717.86	−0.217548
$885$	−1841.81	−0.0699570
$886$	51055.3	1.93593
$887$	15161.7	0.573935	0.286968	−	0.957940i	$-0.407353\pi$
$887$	15161.7	0.573935	0.286968	+	0.957940i	$0.407353\pi$
$888$	−335.166	−0.0126660
$889$	−19750.3	−0.745110
$890$	4150.52	0.156321
$891$	−428.371	−0.0161066
$892$	47134.9	1.76927
$893$	−15070.9	−0.564758
$894$	−4671.56	−0.174765
$895$	−15467.2	−0.577665
$896$	−53220.3	−1.98434
$897$	−558.433	−0.0207866
$898$	−59463.3	−2.20971
$899$	−425.932	−0.0158016
$900$	2537.61	0.0939856
$901$	−5503.29	−0.203486
$902$	9285.05	0.342748
$903$	−1702.50	−0.0627415
$904$	−8046.57	−0.296045
$905$	−14001.9	−0.514297
$906$	−4288.99	−0.157276
$907$	45095.6	1.65091	0.825454	−	0.564469i	$-0.190919\pi$
$907$	45095.6	1.65091	0.825454	+	0.564469i	$0.190919\pi$
$908$	45503.8	1.66310
$909$	−15490.3	−0.565217
$910$	4144.86	0.150990
$911$	10578.3	0.384714	0.192357	−	0.981325i	$-0.438387\pi$
$911$	10578.3	0.384714	0.192357	+	0.981325i	$0.438387\pi$
$912$	−4649.78	−0.168826
$913$	6984.67	0.253186
$914$	71933.6	2.60323
$915$	−3965.76	−0.143283
$916$	50769.5	1.83130
$917$	55629.0	2.00331
$918$	10038.2	0.360905
$919$	50326.0	1.80642	0.903210	−	0.429198i	$-0.141204\pi$
$919$	50326.0	1.80642	0.903210	+	0.429198i	$0.141204\pi$
$920$	−2237.53	−0.0801837
$921$	24406.5	0.873205
$922$	59615.9	2.12944
$923$	−1962.14	−0.0699726
$924$	−5642.52	−0.200893
$925$	−194.044	−0.00689742
$926$	−78972.0	−2.80257
$927$	7178.26	0.254331
$928$	−6780.71	−0.239858
$929$	8373.10	0.295708	0.147854	−	0.989009i	$-0.452763\pi$
$929$	8373.10	0.295708	0.147854	+	0.989009i	$0.452763\pi$
$930$	967.315	0.0341070
$931$	37354.7	1.31498
$932$	−53128.8	−1.86726
$933$	9352.96	0.328191
$934$	3479.51	0.121898
$935$	2239.05	0.0783154
$936$	−775.629	−0.0270857
$937$	53048.3	1.84953	0.924766	−	0.380537i	$-0.124261\pi$
$937$	53048.3	1.84953	0.924766	+	0.380537i	$0.124261\pi$
$938$	86217.4	3.00117
$939$	22609.1	0.785750
$940$	14819.5	0.514212
$941$	−1015.79	−0.0351899	−0.0175949	−	0.999845i	$-0.505601\pi$
$941$	−1015.79	−0.0351899	−0.0175949	+	0.999845i	$0.505601\pi$
$942$	−35434.1	−1.22559
$943$	−12431.8	−0.429305
$944$	−3318.54	−0.114417
$945$	−4257.04	−0.146541
$946$	417.889	0.0143623
$947$	−26038.4	−0.893490	−0.446745	−	0.894661i	$-0.647417\pi$
$947$	−26038.4	−0.893490	−0.446745	+	0.894661i	$0.647417\pi$
$948$	−22549.5	−0.772545
$949$	4990.53	0.170706
$950$	6294.95	0.214984
$951$	10737.9	0.366140
$952$	38433.7	1.30845
$953$	−22396.1	−0.761260	−0.380630	−	0.924727i	$-0.624293\pi$
$953$	−22396.1	−0.761260	−0.380630	+	0.924727i	$0.624293\pi$
$954$	−2568.27	−0.0871601
$955$	−21043.9	−0.713053
$956$	−5601.17	−0.189492
$957$	−460.102	−0.0155413
$958$	−29220.2	−0.985451
$959$	−13676.8	−0.460530
$960$	12156.2	0.408686
$961$	−29575.3	−0.992759
$962$	204.045	0.00683852
$963$	−7006.06	−0.234442
$964$	72345.9	2.41712
$965$	1237.82	0.0412919
$966$	12913.6	0.430112
$967$	−33614.9	−1.11787	−0.558936	−	0.829211i	$-0.688790\pi$
$967$	−33614.9	−1.11787	−0.558936	+	0.829211i	$0.688790\pi$
$968$	−18755.8	−0.622761
$969$	14568.0	0.482962
$970$	3021.47	0.100014
$971$	−30440.6	−1.00606	−0.503030	−	0.864269i	$-0.667781\pi$
$971$	−30440.6	−1.00606	−0.503030	+	0.864269i	$0.667781\pi$
$972$	2740.62	0.0904377
$973$	−15913.7	−0.524328
$974$	−61349.8	−2.01825
$975$	−449.048	−0.0147498
$976$	−7145.42	−0.234343
$977$	18698.6	0.612305	0.306153	−	0.951982i	$-0.400958\pi$
$977$	18698.6	0.612305	0.306153	+	0.951982i	$0.400958\pi$
$978$	18592.6	0.607899
$979$	999.847	0.0326407
$980$	−36731.6	−1.19729
$981$	6490.85	0.211251
$982$	15976.1	0.519164
$983$	−10438.4	−0.338692	−0.169346	−	0.985557i	$-0.554166\pi$
$983$	−10438.4	−0.338692	−0.169346	+	0.985557i	$0.554166\pi$
$984$	−17267.0	−0.559401
$985$	22870.3	0.739806
$986$	10781.8	0.348238
$987$	−24860.9	−0.801753
$988$	−3872.51	−0.124697
$989$	−559.513	−0.0179893
$990$	1044.92	0.0335451
$991$	20547.5	0.658641	0.329320	−	0.944218i	$-0.393180\pi$
$991$	20547.5	0.658641	0.329320	+	0.944218i	$0.393180\pi$
$992$	3434.16	0.109914
$993$	−18771.6	−0.599898
$994$	45373.9	1.44786
$995$	−13005.3	−0.414366
$996$	−44686.4	−1.42163
$997$	6486.05	0.206033	0.103017	−	0.994680i	$-0.467150\pi$
$997$	6486.05	0.206033	0.103017	+	0.994680i	$0.467150\pi$
$998$	49674.3	1.57556
$999$	−209.567	−0.00663704

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.4.a.h.1.5	✓	6
3.2	odd	2		1305.4.a.h.1.2		6
5.4	even	2		2175.4.a.k.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.4.a.h.1.5	✓	6	1.1	even	1	trivial
1305.4.a.h.1.2		6	3.2	odd	2
2175.4.a.k.1.2		6	5.4	even	2

Overview	Random
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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:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	435.a (trivial)

\(f(q)\)	\(=\)	\(q+4.39070 q^{2} +3.00000 q^{3} +11.2783 q^{4} -5.00000 q^{5} +13.1721 q^{6} +31.5336 q^{7} +14.3939 q^{8} +9.00000 q^{9} -21.9535 q^{10} -5.28853 q^{11} +33.8348 q^{12} -5.98731 q^{13} +138.455 q^{14} -15.0000 q^{15} -27.0267 q^{16} +84.6758 q^{17} +39.5163 q^{18} +57.3480 q^{19} -56.3914 q^{20} +94.6008 q^{21} -23.2204 q^{22} +31.0898 q^{23} +43.1818 q^{24} +25.0000 q^{25} -26.2885 q^{26} +27.0000 q^{27} +355.645 q^{28} +29.0000 q^{29} -65.8606 q^{30} -14.6873 q^{31} -233.818 q^{32} -15.8656 q^{33} +371.786 q^{34} -157.668 q^{35} +101.504 q^{36} -7.76174 q^{37} +251.798 q^{38} -17.9619 q^{39} -71.9697 q^{40} -399.867 q^{41} +415.364 q^{42} -17.9967 q^{43} -59.6455 q^{44} -45.0000 q^{45} +136.506 q^{46} -262.798 q^{47} -81.0800 q^{48} +651.368 q^{49} +109.768 q^{50} +254.027 q^{51} -67.5265 q^{52} -64.9925 q^{53} +118.549 q^{54} +26.4427 q^{55} +453.893 q^{56} +172.044 q^{57} +127.330 q^{58} +122.788 q^{59} -169.174 q^{60} +264.384 q^{61} -64.4877 q^{62} +283.802 q^{63} -810.411 q^{64} +29.9366 q^{65} -69.6611 q^{66} +622.712 q^{67} +954.997 q^{68} +93.2694 q^{69} -692.274 q^{70} +327.717 q^{71} +129.545 q^{72} -833.518 q^{73} -34.0795 q^{74} +75.0000 q^{75} +646.787 q^{76} -166.767 q^{77} -78.8655 q^{78} -666.457 q^{79} +135.133 q^{80} +81.0000 q^{81} -1755.70 q^{82} -1320.72 q^{83} +1066.93 q^{84} -423.379 q^{85} -79.0180 q^{86} +87.0000 q^{87} -76.1229 q^{88} -189.059 q^{89} -197.582 q^{90} -188.801 q^{91} +350.640 q^{92} -44.0620 q^{93} -1153.87 q^{94} -286.740 q^{95} -701.453 q^{96} -137.630 q^{97} +2859.97 q^{98} -47.5968 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} + 18 q^{3} + 51 q^{4} - 30 q^{5} + 3 q^{6} + 47 q^{7} + 51 q^{8} + 54 q^{9} - 5 q^{10} + 81 q^{11} + 153 q^{12} + 169 q^{13} - 30 q^{14} - 90 q^{15} + 131 q^{16} - q^{17} + 9 q^{18} + 116 q^{19}+ \cdots + 729 q^{99}+O(q^{100}) \) 6 * q + q^2 + 18 * q^3 + 51 * q^4 - 30 * q^5 + 3 * q^6 + 47 * q^7 + 51 * q^8 + 54 * q^9 - 5 * q^10 + 81 * q^11 + 153 * q^12 + 169 * q^13 - 30 * q^14 - 90 * q^15 + 131 * q^16 - q^17 + 9 * q^18 + 116 * q^19 - 255 * q^20 + 141 * q^21 + 90 * q^22 - 52 * q^23 + 153 * q^24 + 150 * q^25 + 294 * q^26 + 162 * q^27 + 344 * q^28 + 174 * q^29 - 15 * q^30 + 340 * q^31 + 499 * q^32 + 243 * q^33 + 920 * q^34 - 235 * q^35 + 459 * q^36 + 332 * q^37 - 378 * q^38 + 507 * q^39 - 255 * q^40 - 616 * q^41 - 90 * q^42 + 334 * q^43 - 52 * q^44 - 270 * q^45 - 158 * q^46 - 85 * q^47 + 393 * q^48 + 879 * q^49 + 25 * q^50 - 3 * q^51 + 2220 * q^52 - 850 * q^53 + 27 * q^54 - 405 * q^55 - 624 * q^56 + 348 * q^57 + 29 * q^58 - 758 * q^59 - 765 * q^60 - 36 * q^61 - 152 * q^62 + 423 * q^63 + 1795 * q^64 - 845 * q^65 + 270 * q^66 + 939 * q^67 - 186 * q^68 - 156 * q^69 + 150 * q^70 - 1388 * q^71 + 459 * q^72 + 1708 * q^73 - 814 * q^74 + 450 * q^75 + 566 * q^76 + 2585 * q^77 + 882 * q^78 + 1250 * q^79 - 655 * q^80 + 486 * q^81 + 1372 * q^82 - 748 * q^83 + 1032 * q^84 + 5 * q^85 - 800 * q^86 + 522 * q^87 + 536 * q^88 + 1099 * q^89 - 45 * q^90 + 539 * q^91 + 1698 * q^92 + 1020 * q^93 - 4542 * q^94 - 580 * q^95 + 1497 * q^96 - 22 * q^97 - 1433 * q^98 + 729 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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