LMFDB - Embedded newform 4003.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4003,2,Mod(1,4003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4003, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4003.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:	$31.9641159291$
Analytic rank:	$0$
Dimension:	$179$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.79615 q^{2} +2.84308 q^{3} +5.81846 q^{4} -1.26517 q^{5} -7.94968 q^{6} +1.49582 q^{7} -10.6770 q^{8} +5.08309 q^{9} +O(q^{10})$	\(q-2.79615 q^{2} +2.84308 q^{3} +5.81846 q^{4} -1.26517 q^{5} -7.94968 q^{6} +1.49582 q^{7} -10.6770 q^{8} +5.08309 q^{9} +3.53762 q^{10} +4.92555 q^{11} +16.5423 q^{12} -4.76131 q^{13} -4.18255 q^{14} -3.59699 q^{15} +18.2176 q^{16} +3.33808 q^{17} -14.2131 q^{18} -5.93158 q^{19} -7.36136 q^{20} +4.25274 q^{21} -13.7726 q^{22} +6.14295 q^{23} -30.3555 q^{24} -3.39934 q^{25} +13.3133 q^{26} +5.92239 q^{27} +8.70339 q^{28} -5.16727 q^{29} +10.0577 q^{30} -1.18225 q^{31} -29.5851 q^{32} +14.0037 q^{33} -9.33379 q^{34} -1.89248 q^{35} +29.5758 q^{36} +8.04154 q^{37} +16.5856 q^{38} -13.5368 q^{39} +13.5082 q^{40} +10.2738 q^{41} -11.8913 q^{42} +2.79504 q^{43} +28.6591 q^{44} -6.43099 q^{45} -17.1766 q^{46} -0.138774 q^{47} +51.7940 q^{48} -4.76251 q^{49} +9.50506 q^{50} +9.49043 q^{51} -27.7035 q^{52} +12.5426 q^{53} -16.5599 q^{54} -6.23168 q^{55} -15.9709 q^{56} -16.8640 q^{57} +14.4485 q^{58} -4.31429 q^{59} -20.9289 q^{60} +11.5511 q^{61} +3.30576 q^{62} +7.60340 q^{63} +46.2892 q^{64} +6.02388 q^{65} -39.1565 q^{66} -3.19332 q^{67} +19.4225 q^{68} +17.4649 q^{69} +5.29165 q^{70} +12.9549 q^{71} -54.2721 q^{72} -1.25682 q^{73} -22.4853 q^{74} -9.66458 q^{75} -34.5127 q^{76} +7.36775 q^{77} +37.8508 q^{78} -0.937548 q^{79} -23.0484 q^{80} +1.58855 q^{81} -28.7271 q^{82} -8.51842 q^{83} +24.7444 q^{84} -4.22326 q^{85} -7.81536 q^{86} -14.6909 q^{87} -52.5901 q^{88} -11.5679 q^{89} +17.9820 q^{90} -7.12207 q^{91} +35.7425 q^{92} -3.36124 q^{93} +0.388034 q^{94} +7.50448 q^{95} -84.1127 q^{96} +2.35504 q^{97} +13.3167 q^{98} +25.0370 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9}+O(q^{10}) $ 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9} + 9 q^{10} + 46 q^{11} + 33 q^{12} + 47 q^{13} + 22 q^{14} + 36 q^{15} + 222 q^{16} + 103 q^{17} + 43 q^{18} + 12 q^{19} + 102 q^{20} + 50 q^{21} + 39 q^{22} + 121 q^{23} - 3 q^{24} + 246 q^{25} + 52 q^{26} + 49 q^{27} + 41 q^{28} + 138 q^{29} + 28 q^{30} + 5 q^{31} + 137 q^{32} + 63 q^{33} + 2 q^{34} + 72 q^{35} + 279 q^{36} + 118 q^{37} + 123 q^{38} + q^{39} + 9 q^{40} + 50 q^{41} + 48 q^{42} + 48 q^{43} + 108 q^{44} + 158 q^{45} + 13 q^{46} + 85 q^{47} + 50 q^{48} + 230 q^{49} + 78 q^{50} + 15 q^{51} + 41 q^{52} + 399 q^{53} - 5 q^{54} + 24 q^{55} + 53 q^{56} + 45 q^{57} + 27 q^{58} + 48 q^{59} + 66 q^{60} + 46 q^{61} + 81 q^{62} + 78 q^{63} + 252 q^{64} + 153 q^{65} + 6 q^{66} + 70 q^{67} + 240 q^{68} + 120 q^{69} - 31 q^{70} + 86 q^{71} + 89 q^{72} + 45 q^{73} + 68 q^{74} + 17 q^{75} - 13 q^{76} + 362 q^{77} + 69 q^{78} + 31 q^{79} + 169 q^{80} + 303 q^{81} + 25 q^{82} + 106 q^{83} + 13 q^{84} + 115 q^{85} + 95 q^{86} + 32 q^{87} + 83 q^{88} + 105 q^{89} - 38 q^{90} + 3 q^{91} + 310 q^{92} + 298 q^{93} - 17 q^{94} + 102 q^{95} - 82 q^{96} + 34 q^{97} + 81 q^{98} + 58 q^{99}+O(q^{100}) \) 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9 + 9 * q^10 + 46 * q^11 + 33 * q^12 + 47 * q^13 + 22 * q^14 + 36 * q^15 + 222 * q^16 + 103 * q^17 + 43 * q^18 + 12 * q^19 + 102 * q^20 + 50 * q^21 + 39 * q^22 + 121 * q^23 - 3 * q^24 + 246 * q^25 + 52 * q^26 + 49 * q^27 + 41 * q^28 + 138 * q^29 + 28 * q^30 + 5 * q^31 + 137 * q^32 + 63 * q^33 + 2 * q^34 + 72 * q^35 + 279 * q^36 + 118 * q^37 + 123 * q^38 + q^39 + 9 * q^40 + 50 * q^41 + 48 * q^42 + 48 * q^43 + 108 * q^44 + 158 * q^45 + 13 * q^46 + 85 * q^47 + 50 * q^48 + 230 * q^49 + 78 * q^50 + 15 * q^51 + 41 * q^52 + 399 * q^53 - 5 * q^54 + 24 * q^55 + 53 * q^56 + 45 * q^57 + 27 * q^58 + 48 * q^59 + 66 * q^60 + 46 * q^61 + 81 * q^62 + 78 * q^63 + 252 * q^64 + 153 * q^65 + 6 * q^66 + 70 * q^67 + 240 * q^68 + 120 * q^69 - 31 * q^70 + 86 * q^71 + 89 * q^72 + 45 * q^73 + 68 * q^74 + 17 * q^75 - 13 * q^76 + 362 * q^77 + 69 * q^78 + 31 * q^79 + 169 * q^80 + 303 * q^81 + 25 * q^82 + 106 * q^83 + 13 * q^84 + 115 * q^85 + 95 * q^86 + 32 * q^87 + 83 * q^88 + 105 * q^89 - 38 * q^90 + 3 * q^91 + 310 * q^92 + 298 * q^93 - 17 * q^94 + 102 * q^95 - 82 * q^96 + 34 * q^97 + 81 * q^98 + 58 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.79615	−1.97718	−0.988589	−	0.150640i	$-0.951867\pi$
$2$	−2.79615	−1.97718	−0.988589	+	0.150640i	$0.951867\pi$
$3$	2.84308	1.64145	0.820726	−	0.571322i	$-0.193569\pi$
$3$	2.84308	1.64145	0.820726	+	0.571322i	$0.193569\pi$
$4$	5.81846	2.90923
$5$	−1.26517	−0.565803	−0.282901	−	0.959149i	$-0.591297\pi$
$5$	−1.26517	−0.565803	−0.282901	+	0.959149i	$0.591297\pi$
$6$	−7.94968	−3.24544
$7$	1.49582	0.565368	0.282684	−	0.959213i	$-0.408775\pi$
$7$	1.49582	0.565368	0.282684	+	0.959213i	$0.408775\pi$
$8$	−10.6770	−3.77489
$9$	5.08309	1.69436
$10$	3.53762	1.11869
$11$	4.92555	1.48511	0.742555	−	0.669785i	$-0.233614\pi$
$11$	4.92555	1.48511	0.742555	+	0.669785i	$0.233614\pi$
$12$	16.5423	4.77536
$13$	−4.76131	−1.32055	−0.660275	−	0.751024i	$-0.729560\pi$
$13$	−4.76131	−1.32055	−0.660275	+	0.751024i	$0.729560\pi$
$14$	−4.18255	−1.11783
$15$	−3.59699	−0.928738
$16$	18.2176	4.55439
$17$	3.33808	0.809604	0.404802	−	0.914404i	$-0.367340\pi$
$17$	3.33808	0.809604	0.404802	+	0.914404i	$0.367340\pi$
$18$	−14.2131	−3.35006
$19$	−5.93158	−1.36080	−0.680399	−	0.732842i	$-0.738194\pi$
$19$	−5.93158	−1.36080	−0.680399	+	0.732842i	$0.738194\pi$
$20$	−7.36136	−1.64605
$21$	4.25274	0.928024
$22$	−13.7726	−2.93633
$23$	6.14295	1.28089	0.640447	−	0.768002i	$-0.278749\pi$
$23$	6.14295	1.28089	0.640447	+	0.768002i	$0.278749\pi$
$24$	−30.3555	−6.19630
$25$	−3.39934	−0.679867
$26$	13.3133	2.61096
$27$	5.92239	1.13977
$28$	8.70339	1.64479
$29$	−5.16727	−0.959538	−0.479769	−	0.877395i	$-0.659279\pi$
$29$	−5.16727	−0.959538	−0.479769	+	0.877395i	$0.659279\pi$
$30$	10.0577	1.83628
$31$	−1.18225	−0.212339	−0.106170	−	0.994348i	$-0.533859\pi$
$31$	−1.18225	−0.212339	−0.106170	+	0.994348i	$0.533859\pi$
$32$	−29.5851	−5.22995
$33$	14.0037	2.43774
$34$	−9.33379	−1.60073
$35$	−1.89248	−0.319887
$36$	29.5758	4.92930
$37$	8.04154	1.32202	0.661010	−	0.750377i	$-0.270128\pi$
$37$	8.04154	1.32202	0.661010	+	0.750377i	$0.270128\pi$
$38$	16.5856	2.69054
$39$	−13.5368	−2.16762
$40$	13.5082	2.13584
$41$	10.2738	1.60450	0.802249	−	0.596989i	$-0.203637\pi$
$41$	10.2738	1.60450	0.802249	+	0.596989i	$0.203637\pi$
$42$	−11.8913	−1.83487
$43$	2.79504	0.426240	0.213120	−	0.977026i	$-0.431637\pi$
$43$	2.79504	0.426240	0.213120	+	0.977026i	$0.431637\pi$
$44$	28.6591	4.32053
$45$	−6.43099	−0.958676
$46$	−17.1766	−2.53255
$47$	−0.138774	−0.0202423	−0.0101212	−	0.999949i	$-0.503222\pi$
$47$	−0.138774	−0.0202423	−0.0101212	+	0.999949i	$0.503222\pi$
$48$	51.7940	7.47581
$49$	−4.76251	−0.680359
$50$	9.50506	1.34422
$51$	9.49043	1.32893
$52$	−27.7035	−3.84178
$53$	12.5426	1.72285	0.861427	−	0.507881i	$-0.169571\pi$
$53$	12.5426	1.72285	0.861427	+	0.507881i	$0.169571\pi$
$54$	−16.5599	−2.25352
$55$	−6.23168	−0.840279
$56$	−15.9709	−2.13420
$57$	−16.8640	−2.23368
$58$	14.4485	1.89718
$59$	−4.31429	−0.561673	−0.280836	−	0.959756i	$-0.590612\pi$
$59$	−4.31429	−0.561673	−0.280836	+	0.959756i	$0.590612\pi$
$60$	−20.9289	−2.70191
$61$	11.5511	1.47897	0.739483	−	0.673175i	$-0.235070\pi$
$61$	11.5511	1.47897	0.739483	+	0.673175i	$0.235070\pi$
$62$	3.30576	0.419832
$63$	7.60340	0.957939
$64$	46.2892	5.78615
$65$	6.02388	0.747170
$66$	−39.1565	−4.81984
$67$	−3.19332	−0.390126	−0.195063	−	0.980791i	$-0.562491\pi$
$67$	−3.19332	−0.390126	−0.195063	+	0.980791i	$0.562491\pi$
$68$	19.4225	2.35533
$69$	17.4649	2.10253
$70$	5.29165	0.632473
$71$	12.9549	1.53747	0.768733	−	0.639569i	$-0.220887\pi$
$71$	12.9549	1.53747	0.768733	+	0.639569i	$0.220887\pi$
$72$	−54.2721	−6.39603
$73$	−1.25682	−0.147100	−0.0735500	−	0.997292i	$-0.523433\pi$
$73$	−1.25682	−0.147100	−0.0735500	+	0.997292i	$0.523433\pi$
$74$	−22.4853	−2.61387
$75$	−9.66458	−1.11597
$76$	−34.5127	−3.95888
$77$	7.36775	0.839633
$78$	37.8508	4.28576
$79$	−0.937548	−0.105482	−0.0527412	−	0.998608i	$-0.516796\pi$
$79$	−0.937548	−0.105482	−0.0527412	+	0.998608i	$0.516796\pi$
$80$	−23.0484	−2.57689
$81$	1.58855	0.176505
$82$	−28.7271	−3.17238
$83$	−8.51842	−0.935018	−0.467509	−	0.883988i	$-0.654848\pi$
$83$	−8.51842	−0.935018	−0.467509	+	0.883988i	$0.654848\pi$
$84$	24.7444	2.69984
$85$	−4.22326	−0.458076
$86$	−7.81536	−0.842752
$87$	−14.6909	−1.57504
$88$	−52.5901	−5.60612
$89$	−11.5679	−1.22619	−0.613095	−	0.790009i	$-0.710076\pi$
$89$	−11.5679	−1.22619	−0.613095	+	0.790009i	$0.710076\pi$
$90$	17.9820	1.89547
$91$	−7.12207	−0.746596
$92$	35.7425	3.72642
$93$	−3.36124	−0.348544
$94$	0.388034	0.0400227
$95$	7.50448	0.769944
$96$	−84.1127	−8.58471
$97$	2.35504	0.239118	0.119559	−	0.992827i	$-0.461852\pi$
$97$	2.35504	0.239118	0.119559	+	0.992827i	$0.461852\pi$
$98$	13.3167	1.34519
$99$	25.0370	2.51632
$100$	−19.7789	−1.97789
$101$	16.0123	1.59328	0.796642	−	0.604452i	$-0.206608\pi$
$101$	16.0123	1.59328	0.796642	+	0.604452i	$0.206608\pi$
$102$	−26.5367	−2.62752
$103$	2.33407	0.229983	0.114991	−	0.993366i	$-0.463316\pi$
$103$	2.33407	0.229983	0.114991	+	0.993366i	$0.463316\pi$
$104$	50.8364	4.98492
$105$	−5.38045	−0.525079
$106$	−35.0709	−3.40639
$107$	2.92833	0.283093	0.141546	−	0.989932i	$-0.454793\pi$
$107$	2.92833	0.283093	0.141546	+	0.989932i	$0.454793\pi$
$108$	34.4592	3.31584
$109$	6.28176	0.601684	0.300842	−	0.953674i	$-0.402732\pi$
$109$	6.28176	0.601684	0.300842	+	0.953674i	$0.402732\pi$
$110$	17.4247	1.66138
$111$	22.8627	2.17003
$112$	27.2502	2.57491
$113$	17.6914	1.66427	0.832133	−	0.554576i	$-0.187119\pi$
$113$	17.6914	1.66427	0.832133	+	0.554576i	$0.187119\pi$
$114$	47.1542	4.41639
$115$	−7.77190	−0.724733
$116$	−30.0656	−2.79152
$117$	−24.2022	−2.23749
$118$	12.0634	1.11053
$119$	4.99318	0.457724
$120$	38.4050	3.50588
$121$	13.2611	1.20555
$122$	−32.2986	−2.92418
$123$	29.2092	2.63371
$124$	−6.87890	−0.617743
$125$	10.6266	0.950474
$126$	−21.2603	−1.89402
$127$	6.47246	0.574338	0.287169	−	0.957880i	$-0.407286\pi$
$127$	6.47246	0.574338	0.287169	+	0.957880i	$0.407286\pi$
$128$	−70.2615	−6.21029
$129$	7.94652	0.699652
$130$	−16.8437	−1.47729
$131$	−1.82549	−0.159494	−0.0797468	−	0.996815i	$-0.525411\pi$
$131$	−1.82549	−0.159494	−0.0797468	+	0.996815i	$0.525411\pi$
$132$	81.4802	7.09194
$133$	−8.87260	−0.769352
$134$	8.92899	0.771348
$135$	−7.49286	−0.644882
$136$	−35.6407	−3.05616
$137$	4.23492	0.361814	0.180907	−	0.983500i	$-0.442097\pi$
$137$	4.23492	0.361814	0.180907	+	0.983500i	$0.442097\pi$
$138$	−48.8345	−4.15707
$139$	−0.312326	−0.0264911	−0.0132456	−	0.999912i	$-0.504216\pi$
$139$	−0.312326	−0.0264911	−0.0132456	+	0.999912i	$0.504216\pi$
$140$	−11.0113	−0.930624
$141$	−0.394546	−0.0332268
$142$	−36.2239	−3.03984
$143$	−23.4521	−1.96116
$144$	92.6016	7.71680
$145$	6.53749	0.542909
$146$	3.51426	0.290843
$147$	−13.5402	−1.11678
$148$	46.7894	3.84606
$149$	6.28162	0.514610	0.257305	−	0.966330i	$-0.417165\pi$
$149$	6.28162	0.514610	0.257305	+	0.966330i	$0.417165\pi$
$150$	27.0236	2.20647
$151$	−18.5292	−1.50788	−0.753942	−	0.656941i	$-0.771850\pi$
$151$	−18.5292	−1.50788	−0.753942	+	0.656941i	$0.771850\pi$
$152$	63.3315	5.13686
$153$	16.9678	1.37176
$154$	−20.6014	−1.66010
$155$	1.49576	0.120142
$156$	−78.7632	−6.30610
$157$	19.5786	1.56254	0.781271	−	0.624192i	$-0.214572\pi$
$157$	19.5786	1.56254	0.781271	+	0.624192i	$0.214572\pi$
$158$	2.62153	0.208557
$159$	35.6595	2.82798
$160$	37.4303	2.95912
$161$	9.18876	0.724176
$162$	−4.44182	−0.348983
$163$	22.7576	1.78251	0.891256	−	0.453501i	$-0.149825\pi$
$163$	22.7576	1.78251	0.891256	+	0.453501i	$0.149825\pi$
$164$	59.7777	4.66786
$165$	−17.7172	−1.37928
$166$	23.8188	1.84870
$167$	−0.280168	−0.0216801	−0.0108400	−	0.999941i	$-0.503451\pi$
$167$	−0.280168	−0.0216801	−0.0108400	+	0.999941i	$0.503451\pi$
$168$	−45.4065	−3.50319
$169$	9.67005	0.743850
$170$	11.8089	0.905698
$171$	−30.1508	−2.30569
$172$	16.2628	1.24003
$173$	−21.2049	−1.61218	−0.806089	−	0.591795i	$-0.798420\pi$
$173$	−21.2049	−1.61218	−0.806089	+	0.591795i	$0.798420\pi$
$174$	41.0781	3.11412
$175$	−5.08480	−0.384375
$176$	89.7316	6.76377
$177$	−12.2659	−0.921959
$178$	32.3455	2.42440
$179$	0.918450	0.0686482	0.0343241	−	0.999411i	$-0.489072\pi$
$179$	0.918450	0.0686482	0.0343241	+	0.999411i	$0.489072\pi$
$180$	−37.4185	−2.78901
$181$	−21.9938	−1.63479	−0.817393	−	0.576080i	$-0.804582\pi$
$181$	−21.9938	−1.63479	−0.817393	+	0.576080i	$0.804582\pi$
$182$	19.9144	1.47615
$183$	32.8407	2.42765
$184$	−65.5882	−4.83523
$185$	−10.1739	−0.748003
$186$	9.39854	0.689134
$187$	16.4419	1.20235
$188$	−0.807453	−0.0588896
$189$	8.85885	0.644387
$190$	−20.9837	−1.52232
$191$	18.8042	1.36063	0.680314	−	0.732921i	$-0.261844\pi$
$191$	18.8042	1.36063	0.680314	+	0.732921i	$0.261844\pi$
$192$	131.604	9.49769
$193$	−3.81857	−0.274867	−0.137433	−	0.990511i	$-0.543885\pi$
$193$	−3.81857	−0.274867	−0.137433	+	0.990511i	$0.543885\pi$
$194$	−6.58504	−0.472778
$195$	17.1264	1.22644
$196$	−27.7105	−1.97932
$197$	−2.48933	−0.177357	−0.0886787	−	0.996060i	$-0.528264\pi$
$197$	−2.48933	−0.177357	−0.0886787	+	0.996060i	$0.528264\pi$
$198$	−70.0073	−4.97521
$199$	−9.16711	−0.649840	−0.324920	−	0.945742i	$-0.605337\pi$
$199$	−9.16711	−0.649840	−0.324920	+	0.945742i	$0.605337\pi$
$200$	36.2947	2.56642
$201$	−9.07885	−0.640372
$202$	−44.7728	−3.15020
$203$	−7.72932	−0.542492
$204$	55.2197	3.86615
$205$	−12.9981	−0.907830
$206$	−6.52642	−0.454717
$207$	31.2252	2.17030
$208$	−86.7394	−6.01430
$209$	−29.2163	−2.02094
$210$	15.0446	1.03817
$211$	20.2028	1.39082	0.695409	−	0.718614i	$-0.255223\pi$
$211$	20.2028	1.39082	0.695409	+	0.718614i	$0.255223\pi$
$212$	72.9784	5.01218
$213$	36.8319	2.52368
$214$	−8.18806	−0.559724
$215$	−3.53621	−0.241168
$216$	−63.2333	−4.30248
$217$	−1.76844	−0.120050
$218$	−17.5648	−1.18964
$219$	−3.57324	−0.241457
$220$	−36.2588	−2.44457
$221$	−15.8936	−1.06912
$222$	−63.9276	−4.29054
$223$	−10.2915	−0.689169	−0.344584	−	0.938755i	$-0.611980\pi$
$223$	−10.2915	−0.689169	−0.344584	+	0.938755i	$0.611980\pi$
$224$	−44.2540	−2.95685
$225$	−17.2791	−1.15194
$226$	−49.4678	−3.29055
$227$	−3.90405	−0.259121	−0.129561	−	0.991572i	$-0.541357\pi$
$227$	−3.90405	−0.259121	−0.129561	+	0.991572i	$0.541357\pi$
$228$	−98.1222	−6.49830
$229$	1.26841	0.0838189	0.0419095	−	0.999121i	$-0.486656\pi$
$229$	1.26841	0.0838189	0.0419095	+	0.999121i	$0.486656\pi$
$230$	21.7314	1.43293
$231$	20.9471	1.37822
$232$	55.1709	3.62215
$233$	26.5731	1.74086	0.870430	−	0.492292i	$-0.163841\pi$
$233$	26.5731	1.74086	0.870430	+	0.492292i	$0.163841\pi$
$234$	67.6729	4.42392
$235$	0.175574	0.0114532
$236$	−25.1025	−1.63404
$237$	−2.66552	−0.173144
$238$	−13.9617	−0.905002
$239$	−16.2010	−1.04796	−0.523978	−	0.851732i	$-0.675552\pi$
$239$	−16.2010	−1.04796	−0.523978	+	0.851732i	$0.675552\pi$
$240$	−65.5283	−4.22984
$241$	−14.7693	−0.951375	−0.475688	−	0.879614i	$-0.657801\pi$
$241$	−14.7693	−0.951375	−0.475688	+	0.879614i	$0.657801\pi$
$242$	−37.0800	−2.38359
$243$	−13.2508	−0.850040
$244$	67.2096	4.30266
$245$	6.02541	0.384949
$246$	−81.6734	−5.20731
$247$	28.2421	1.79700
$248$	12.6229	0.801556
$249$	−24.2185	−1.53479
$250$	−29.7136	−1.87925
$251$	−13.0063	−0.820947	−0.410474	−	0.911872i	$-0.634637\pi$
$251$	−13.0063	−0.820947	−0.410474	+	0.911872i	$0.634637\pi$
$252$	44.2401	2.78686
$253$	30.2574	1.90227
$254$	−18.0980	−1.13557
$255$	−12.0070	−0.751910
$256$	103.883	6.49270
$257$	−1.76279	−0.109960	−0.0549798	−	0.998487i	$-0.517509\pi$
$257$	−1.76279	−0.109960	−0.0549798	+	0.998487i	$0.517509\pi$
$258$	−22.2197	−1.38334
$259$	12.0287	0.747428
$260$	35.0497	2.17369
$261$	−26.2657	−1.62581
$262$	5.10434	0.315347
$263$	18.0872	1.11531	0.557653	−	0.830074i	$-0.311702\pi$
$263$	18.0872	1.11531	0.557653	+	0.830074i	$0.311702\pi$
$264$	−149.518	−9.20218
$265$	−15.8685	−0.974796
$266$	24.8091	1.52114
$267$	−32.8883	−2.01273
$268$	−18.5802	−1.13497
$269$	−11.0309	−0.672565	−0.336282	−	0.941761i	$-0.609170\pi$
$269$	−11.0309	−0.672565	−0.336282	+	0.941761i	$0.609170\pi$
$270$	20.9512	1.27505
$271$	−24.8325	−1.50847	−0.754233	−	0.656607i	$-0.771991\pi$
$271$	−24.8325	−1.50847	−0.754233	+	0.656607i	$0.771991\pi$
$272$	60.8118	3.68725
$273$	−20.2486	−1.22550
$274$	−11.8415	−0.715370
$275$	−16.7436	−1.00968
$276$	101.619	6.11673
$277$	0.558525	0.0335585	0.0167793	−	0.999859i	$-0.494659\pi$
$277$	0.558525	0.0335585	0.0167793	+	0.999859i	$0.494659\pi$
$278$	0.873310	0.0523777
$279$	−6.00951	−0.359780
$280$	20.2059	1.20754
$281$	−4.92880	−0.294028	−0.147014	−	0.989134i	$-0.546966\pi$
$281$	−4.92880	−0.294028	−0.147014	+	0.989134i	$0.546966\pi$
$282$	1.10321	0.0656953
$283$	−10.3237	−0.613683	−0.306841	−	0.951761i	$-0.599272\pi$
$283$	−10.3237	−0.613683	−0.306841	+	0.951761i	$0.599272\pi$
$284$	75.3777	4.47285
$285$	21.3358	1.26383
$286$	65.5755	3.87756
$287$	15.3678	0.907132
$288$	−150.384	−8.86144
$289$	−5.85719	−0.344541
$290$	−18.2798	−1.07343
$291$	6.69555	0.392500
$292$	−7.31277	−0.427948
$293$	−10.0064	−0.584581	−0.292290	−	0.956330i	$-0.594417\pi$
$293$	−10.0064	−0.584581	−0.292290	+	0.956330i	$0.594417\pi$
$294$	37.8604	2.20807
$295$	5.45833	0.317796
$296$	−85.8594	−4.99048
$297$	29.1711	1.69268
$298$	−17.5643	−1.01748
$299$	−29.2485	−1.69148
$300$	−56.2330	−3.24661
$301$	4.18089	0.240982
$302$	51.8104	2.98135
$303$	45.5242	2.61530
$304$	−108.059	−6.19761
$305$	−14.6141	−0.836804
$306$	−47.4445	−2.71222
$307$	−23.2725	−1.32823	−0.664116	−	0.747629i	$-0.731192\pi$
$307$	−23.2725	−1.32823	−0.664116	+	0.747629i	$0.731192\pi$
$308$	42.8690	2.44269
$309$	6.63595	0.377506
$310$	−4.18236	−0.237542
$311$	4.67899	0.265321	0.132661	−	0.991162i	$-0.457648\pi$
$311$	4.67899	0.265321	0.132661	+	0.991162i	$0.457648\pi$
$312$	144.532	8.18251
$313$	5.35732	0.302814	0.151407	−	0.988472i	$-0.451620\pi$
$313$	5.35732	0.302814	0.151407	+	0.988472i	$0.451620\pi$
$314$	−54.7447	−3.08942
$315$	−9.61963	−0.542005
$316$	−5.45509	−0.306873
$317$	15.2452	0.856253	0.428127	−	0.903719i	$-0.359174\pi$
$317$	15.2452	0.856253	0.428127	+	0.903719i	$0.359174\pi$
$318$	−99.7093	−5.59142
$319$	−25.4517	−1.42502
$320$	−58.5639	−3.27382
$321$	8.32548	0.464683
$322$	−25.6932	−1.43182
$323$	−19.8001	−1.10171
$324$	9.24291	0.513495
$325$	16.1853	0.897798
$326$	−63.6337	−3.52434
$327$	17.8595	0.987635
$328$	−109.693	−6.05680
$329$	−0.207582	−0.0114444
$330$	49.5398	2.72708
$331$	−7.71898	−0.424273	−0.212137	−	0.977240i	$-0.568042\pi$
$331$	−7.71898	−0.424273	−0.212137	+	0.977240i	$0.568042\pi$
$332$	−49.5641	−2.72018
$333$	40.8759	2.23998
$334$	0.783393	0.0428654
$335$	4.04010	0.220734
$336$	77.4746	4.22658
$337$	−26.9718	−1.46925	−0.734623	−	0.678476i	$-0.762641\pi$
$337$	−26.9718	−1.46925	−0.734623	+	0.678476i	$0.762641\pi$
$338$	−27.0389	−1.47072
$339$	50.2980	2.73181
$340$	−24.5728	−1.33265
$341$	−5.82326	−0.315347
$342$	84.3061	4.55875
$343$	−17.5946	−0.950021
$344$	−29.8426	−1.60901
$345$	−22.0961	−1.18961
$346$	59.2921	3.18756
$347$	28.9164	1.55231	0.776157	−	0.630539i	$-0.217166\pi$
$347$	28.9164	1.55231	0.776157	+	0.630539i	$0.217166\pi$
$348$	−85.4787	−4.58214
$349$	11.4444	0.612607	0.306303	−	0.951934i	$-0.400908\pi$
$349$	11.4444	0.612607	0.306303	+	0.951934i	$0.400908\pi$
$350$	14.2179	0.759978
$351$	−28.1983	−1.50512
$352$	−145.723	−7.76705
$353$	26.5199	1.41151	0.705755	−	0.708456i	$-0.250608\pi$
$353$	26.5199	1.41151	0.705755	+	0.708456i	$0.250608\pi$
$354$	34.2972	1.82288
$355$	−16.3902	−0.869903
$356$	−67.3071	−3.56727
$357$	14.1960	0.751332
$358$	−2.56813	−0.135730
$359$	33.8326	1.78562	0.892808	−	0.450437i	$-0.148732\pi$
$359$	33.8326	1.78562	0.892808	+	0.450437i	$0.148732\pi$
$360$	68.6637	3.61889
$361$	16.1837	0.851772
$362$	61.4980	3.23226
$363$	37.7023	1.97886
$364$	−41.4395	−2.17202
$365$	1.59010	0.0832296
$366$	−91.8275	−4.79990
$367$	−12.0348	−0.628213	−0.314107	−	0.949388i	$-0.601705\pi$
$367$	−12.0348	−0.628213	−0.314107	+	0.949388i	$0.601705\pi$
$368$	111.910	5.83369
$369$	52.2227	2.71860
$370$	28.4479	1.47893
$371$	18.7615	0.974046
$372$	−19.5572	−1.01400
$373$	13.9924	0.724498	0.362249	−	0.932081i	$-0.382009\pi$
$373$	13.9924	0.724498	0.362249	+	0.932081i	$0.382009\pi$
$374$	−45.9741	−2.37726
$375$	30.2123	1.56016
$376$	1.48169	0.0764125
$377$	24.6030	1.26712
$378$	−24.7707	−1.27407
$379$	11.0577	0.567996	0.283998	−	0.958825i	$-0.408339\pi$
$379$	11.0577	0.567996	0.283998	+	0.958825i	$0.408339\pi$
$380$	43.6645	2.23994
$381$	18.4017	0.942748
$382$	−52.5795	−2.69020
$383$	25.0874	1.28191	0.640953	−	0.767581i	$-0.278540\pi$
$383$	25.0874	1.28191	0.640953	+	0.767581i	$0.278540\pi$
$384$	−199.759	−10.1939
$385$	−9.32149	−0.475067
$386$	10.6773	0.543461
$387$	14.2075	0.722206
$388$	13.7027	0.695649
$389$	−23.2420	−1.17842	−0.589208	−	0.807981i	$-0.700560\pi$
$389$	−23.2420	−1.17842	−0.589208	+	0.807981i	$0.700560\pi$
$390$	−47.8879	−2.42490
$391$	20.5057	1.03702
$392$	50.8493	2.56828
$393$	−5.19001	−0.261801
$394$	6.96054	0.350667
$395$	1.18616	0.0596823
$396$	145.677	7.32055
$397$	−20.6708	−1.03744	−0.518719	−	0.854945i	$-0.673591\pi$
$397$	−20.6708	−1.03744	−0.518719	+	0.854945i	$0.673591\pi$
$398$	25.6326	1.28485
$399$	−25.2255	−1.26285
$400$	−61.9276	−3.09638
$401$	6.36074	0.317640	0.158820	−	0.987308i	$-0.449231\pi$
$401$	6.36074	0.317640	0.158820	+	0.987308i	$0.449231\pi$
$402$	25.3858	1.26613
$403$	5.62908	0.280404
$404$	93.1670	4.63523
$405$	−2.00979	−0.0998673
$406$	21.6123	1.07260
$407$	39.6090	1.96335
$408$	−101.329	−5.01655
$409$	−21.3726	−1.05681	−0.528403	−	0.848993i	$-0.677209\pi$
$409$	−21.3726	−1.05681	−0.528403	+	0.848993i	$0.677209\pi$
$410$	36.3448	1.79494
$411$	12.0402	0.593900
$412$	13.5807	0.669073
$413$	−6.45342	−0.317552
$414$	−87.3103	−4.29107
$415$	10.7773	0.529036
$416$	140.864	6.90641
$417$	−0.887967	−0.0434839
$418$	81.6933	3.99575
$419$	−33.2550	−1.62461	−0.812305	−	0.583232i	$-0.801788\pi$
$419$	−33.2550	−1.62461	−0.812305	+	0.583232i	$0.801788\pi$
$420$	−31.3060	−1.52757
$421$	7.90057	0.385050	0.192525	−	0.981292i	$-0.438332\pi$
$421$	7.90057	0.385050	0.192525	+	0.981292i	$0.438332\pi$
$422$	−56.4901	−2.74990
$423$	−0.705403	−0.0342979
$424$	−133.917	−6.50358
$425$	−11.3473	−0.550423
$426$	−102.987	−4.98976
$427$	17.2784	0.836160
$428$	17.0384	0.823582
$429$	−66.6761	−3.21915
$430$	9.88779	0.476831
$431$	−23.0392	−1.10976	−0.554879	−	0.831931i	$-0.687235\pi$
$431$	−23.0392	−1.10976	−0.554879	+	0.831931i	$0.687235\pi$
$432$	107.892	5.19094
$433$	19.2227	0.923782	0.461891	−	0.886937i	$-0.347171\pi$
$433$	19.2227	0.923782	0.461891	+	0.886937i	$0.347171\pi$
$434$	4.94483	0.237360
$435$	18.5866	0.891159
$436$	36.5502	1.75044
$437$	−36.4374	−1.74304
$438$	9.99133	0.477404
$439$	6.12377	0.292271	0.146136	−	0.989265i	$-0.453316\pi$
$439$	6.12377	0.292271	0.146136	+	0.989265i	$0.453316\pi$
$440$	66.5356	3.17196
$441$	−24.2083	−1.15278
$442$	44.4410	2.11384
$443$	12.1331	0.576460	0.288230	−	0.957561i	$-0.406933\pi$
$443$	12.1331	0.576460	0.288230	+	0.957561i	$0.406933\pi$
$444$	133.026	6.31312
$445$	14.6353	0.693782
$446$	28.7765	1.36261
$447$	17.8591	0.844708
$448$	69.2404	3.27130
$449$	−14.3561	−0.677507	−0.338754	−	0.940875i	$-0.610005\pi$
$449$	−14.3561	−0.677507	−0.338754	+	0.940875i	$0.610005\pi$
$450$	48.3151	2.27759
$451$	50.6042	2.38286
$452$	102.937	4.84173
$453$	−52.6799	−2.47512
$454$	10.9163	0.512328
$455$	9.01066	0.422426
$456$	180.056	8.43191
$457$	−15.0586	−0.704413	−0.352206	−	0.935922i	$-0.614568\pi$
$457$	−15.0586	−0.704413	−0.352206	+	0.935922i	$0.614568\pi$
$458$	−3.54667	−0.165725
$459$	19.7694	0.922759
$460$	−45.2205	−2.10842
$461$	22.6366	1.05429	0.527145	−	0.849776i	$-0.323263\pi$
$461$	22.6366	1.05429	0.527145	+	0.849776i	$0.323263\pi$
$462$	−58.5712	−2.72498
$463$	23.1363	1.07523	0.537617	−	0.843189i	$-0.319325\pi$
$463$	23.1363	1.07523	0.537617	+	0.843189i	$0.319325\pi$
$464$	−94.1351	−4.37011
$465$	4.25255	0.197207
$466$	−74.3023	−3.44199
$467$	−40.6633	−1.88167	−0.940835	−	0.338864i	$-0.889957\pi$
$467$	−40.6633	−1.88167	−0.940835	+	0.338864i	$0.889957\pi$
$468$	−140.819	−6.50938
$469$	−4.77663	−0.220564
$470$	−0.490931	−0.0226449
$471$	55.6635	2.56484
$472$	46.0637	2.12025
$473$	13.7671	0.633013
$474$	7.45320	0.342337
$475$	20.1634	0.925162
$476$	29.0526	1.33163
$477$	63.7550	2.91914
$478$	45.3004	2.07199
$479$	−2.67374	−0.122166	−0.0610831	−	0.998133i	$-0.519455\pi$
$479$	−2.67374	−0.122166	−0.0610831	+	0.998133i	$0.519455\pi$
$480$	106.417	4.85726
$481$	−38.2882	−1.74579
$482$	41.2972	1.88104
$483$	26.1244	1.18870
$484$	77.1590	3.50723
$485$	−2.97953	−0.135294
$486$	37.0513	1.68068
$487$	12.2058	0.553096	0.276548	−	0.961000i	$-0.410810\pi$
$487$	12.2058	0.553096	0.276548	+	0.961000i	$0.410810\pi$
$488$	−123.331	−5.58293
$489$	64.7016	2.92591
$490$	−16.8480	−0.761113
$491$	28.8155	1.30043	0.650214	−	0.759751i	$-0.274679\pi$
$491$	28.8155	1.30043	0.650214	+	0.759751i	$0.274679\pi$
$492$	169.953	7.66206
$493$	−17.2488	−0.776846
$494$	−78.9691	−3.55299
$495$	−31.6762	−1.42374
$496$	−21.5378	−0.967075
$497$	19.3783	0.869234
$498$	67.7187	3.03455
$499$	−19.8610	−0.889099	−0.444550	−	0.895754i	$-0.646636\pi$
$499$	−19.8610	−0.889099	−0.444550	+	0.895754i	$0.646636\pi$
$500$	61.8306	2.76515
$501$	−0.796540	−0.0355868
$502$	36.3675	1.62316
$503$	−25.3405	−1.12988	−0.564939	−	0.825132i	$-0.691100\pi$
$503$	−25.3405	−1.12988	−0.564939	+	0.825132i	$0.691100\pi$
$504$	−81.1815	−3.61611
$505$	−20.2583	−0.901485
$506$	−84.6043	−3.76112
$507$	27.4927	1.22099
$508$	37.6598	1.67088
$509$	5.25753	0.233036	0.116518	−	0.993189i	$-0.462827\pi$
$509$	5.25753	0.233036	0.116518	+	0.993189i	$0.462827\pi$
$510$	33.5735	1.48666
$511$	−1.87998	−0.0831656
$512$	−149.950	−6.62693
$513$	−35.1292	−1.55099
$514$	4.92901	0.217410
$515$	−2.95301	−0.130125
$516$	46.2365	2.03545
$517$	−0.683541	−0.0300621
$518$	−33.6341	−1.47780
$519$	−60.2871	−2.64631
$520$	−64.3169	−2.82048
$521$	−13.8674	−0.607544	−0.303772	−	0.952745i	$-0.598246\pi$
$521$	−13.8674	−0.607544	−0.303772	+	0.952745i	$0.598246\pi$
$522$	73.4429	3.21451
$523$	35.8802	1.56893	0.784466	−	0.620172i	$-0.212937\pi$
$523$	35.8802	1.56893	0.784466	+	0.620172i	$0.212937\pi$
$524$	−10.6215	−0.464004
$525$	−14.4565	−0.630933
$526$	−50.5746	−2.20516
$527$	−3.94646	−0.171911
$528$	255.114	11.1024
$529$	14.7358	0.640689
$530$	44.3708	1.92734
$531$	−21.9299	−0.951679
$532$	−51.6248	−2.23822
$533$	−48.9167	−2.11882
$534$	91.9607	3.97953
$535$	−3.70485	−0.160175
$536$	34.0950	1.47268
$537$	2.61123	0.112683
$538$	30.8440	1.32978
$539$	−23.4580	−1.01041
$540$	−43.5969	−1.87611
$541$	11.1441	0.479121	0.239560	−	0.970881i	$-0.422997\pi$
$541$	11.1441	0.479121	0.239560	+	0.970881i	$0.422997\pi$
$542$	69.4353	2.98250
$543$	−62.5301	−2.68342
$544$	−98.7575	−4.23419
$545$	−7.94752	−0.340434
$546$	56.6182	2.42303
$547$	20.2908	0.867570	0.433785	−	0.901016i	$-0.357178\pi$
$547$	20.2908	0.867570	0.433785	+	0.901016i	$0.357178\pi$
$548$	24.6407	1.05260
$549$	58.7153	2.50591
$550$	46.8177	1.99631
$551$	30.6501	1.30574
$552$	−186.472	−7.93680
$553$	−1.40241	−0.0596364
$554$	−1.56172	−0.0663512
$555$	−28.9253	−1.22781
$556$	−1.81726	−0.0770688
$557$	23.0940	0.978525	0.489262	−	0.872137i	$-0.337266\pi$
$557$	23.0940	0.978525	0.489262	+	0.872137i	$0.337266\pi$
$558$	16.8035	0.711348
$559$	−13.3081	−0.562871
$560$	−34.4763	−1.45689
$561$	46.7456	1.97360
$562$	13.7817	0.581345
$563$	−35.0952	−1.47909	−0.739543	−	0.673110i	$-0.764958\pi$
$563$	−35.0952	−1.47909	−0.739543	+	0.673110i	$0.764958\pi$
$564$	−2.29565	−0.0966644
$565$	−22.3827	−0.941647
$566$	28.8667	1.21336
$567$	2.37619	0.0997905
$568$	−138.320	−5.80376
$569$	−29.8372	−1.25084	−0.625421	−	0.780288i	$-0.715073\pi$
$569$	−29.8372	−1.25084	−0.625421	+	0.780288i	$0.715073\pi$
$570$	−59.6582	−2.49881
$571$	−29.3765	−1.22937	−0.614685	−	0.788773i	$-0.710717\pi$
$571$	−29.3765	−1.22937	−0.614685	+	0.788773i	$0.710717\pi$
$572$	−136.455	−5.70547
$573$	53.4619	2.23340
$574$	−42.9707	−1.79356
$575$	−20.8820	−0.870838
$576$	235.292	9.80385
$577$	9.87165	0.410962	0.205481	−	0.978661i	$-0.434124\pi$
$577$	9.87165	0.410962	0.205481	+	0.978661i	$0.434124\pi$
$578$	16.3776	0.681218
$579$	−10.8565	−0.451181
$580$	38.0381	1.57945
$581$	−12.7420	−0.528629
$582$	−18.7218	−0.776043
$583$	61.7791	2.55863
$584$	13.4191	0.555286
$585$	30.6199	1.26598
$586$	27.9794	1.15582
$587$	−5.02102	−0.207240	−0.103620	−	0.994617i	$-0.533043\pi$
$587$	−5.02102	−0.207240	−0.103620	+	0.994617i	$0.533043\pi$
$588$	−78.7831	−3.24896
$589$	7.01264	0.288951
$590$	−15.2623	−0.628339
$591$	−7.07736	−0.291124
$592$	146.497	6.02100
$593$	−39.0600	−1.60400	−0.802001	−	0.597323i	$-0.796231\pi$
$593$	−39.0600	−1.60400	−0.802001	+	0.597323i	$0.796231\pi$
$594$	−81.5667	−3.34672
$595$	−6.31724	−0.258982
$596$	36.5493	1.49712
$597$	−26.0628	−1.06668
$598$	81.7832	3.34436
$599$	44.9614	1.83707	0.918536	−	0.395338i	$-0.129373\pi$
$599$	44.9614	1.83707	0.918536	+	0.395338i	$0.129373\pi$
$600$	103.189	4.21266
$601$	19.5481	0.797385	0.398692	−	0.917085i	$-0.369464\pi$
$601$	19.5481	0.797385	0.398692	+	0.917085i	$0.369464\pi$
$602$	−11.6904	−0.476465
$603$	−16.2319	−0.661015
$604$	−107.811	−4.38678
$605$	−16.7776	−0.682105
$606$	−127.293	−5.17091
$607$	29.5348	1.19878	0.599390	−	0.800457i	$-0.295410\pi$
$607$	29.5348	1.19878	0.599390	+	0.800457i	$0.295410\pi$
$608$	175.486	7.11691
$609$	−21.9751	−0.890474
$610$	40.8634	1.65451
$611$	0.660748	0.0267310
$612$	98.7264	3.99078
$613$	19.9085	0.804099	0.402049	−	0.915618i	$-0.368298\pi$
$613$	19.9085	0.804099	0.402049	+	0.915618i	$0.368298\pi$
$614$	65.0735	2.62615
$615$	−36.9547	−1.49016
$616$	−78.6654	−3.16952
$617$	−28.0679	−1.12997	−0.564985	−	0.825101i	$-0.691118\pi$
$617$	−28.0679	−1.12997	−0.564985	+	0.825101i	$0.691118\pi$
$618$	−18.5551	−0.746396
$619$	22.8793	0.919598	0.459799	−	0.888023i	$-0.347921\pi$
$619$	22.8793	0.919598	0.459799	+	0.888023i	$0.347921\pi$
$620$	8.70300	0.349521
$621$	36.3810	1.45992
$622$	−13.0832	−0.524587
$623$	−17.3035	−0.693249
$624$	−246.607	−9.87218
$625$	3.55216	0.142086
$626$	−14.9799	−0.598716
$627$	−83.0643	−3.31727
$628$	113.917	4.54579
$629$	26.8433	1.07031
$630$	26.8979	1.07164
$631$	−17.5190	−0.697419	−0.348710	−	0.937231i	$-0.613380\pi$
$631$	−17.5190	−0.697419	−0.348710	+	0.937231i	$0.613380\pi$
$632$	10.0102	0.398184
$633$	57.4382	2.28296
$634$	−42.6278	−1.69296
$635$	−8.18879	−0.324962
$636$	207.483	8.22725
$637$	22.6758	0.898448
$638$	71.1667	2.81752
$639$	65.8511	2.60503
$640$	88.8930	3.51380
$641$	−28.6276	−1.13072	−0.565361	−	0.824844i	$-0.691263\pi$
$641$	−28.6276	−1.13072	−0.565361	+	0.824844i	$0.691263\pi$
$642$	−23.2793	−0.918761
$643$	12.0960	0.477020	0.238510	−	0.971140i	$-0.423341\pi$
$643$	12.0960	0.477020	0.238510	+	0.971140i	$0.423341\pi$
$644$	53.4645	2.10680
$645$	−10.0537	−0.395865
$646$	55.3641	2.17827
$647$	−45.1186	−1.77379	−0.886897	−	0.461967i	$-0.847144\pi$
$647$	−45.1186	−1.77379	−0.886897	+	0.461967i	$0.847144\pi$
$648$	−16.9609	−0.666288
$649$	−21.2503	−0.834146
$650$	−45.2565	−1.77511
$651$	−5.02782	−0.197056
$652$	132.414	5.18574
$653$	33.1597	1.29764	0.648819	−	0.760943i	$-0.275263\pi$
$653$	33.1597	1.29764	0.648819	+	0.760943i	$0.275263\pi$
$654$	−49.9380	−1.95273
$655$	2.30956	0.0902420
$656$	187.164	7.30751
$657$	−6.38854	−0.249241
$658$	0.580430	0.0226275
$659$	−5.63381	−0.219462	−0.109731	−	0.993961i	$-0.534999\pi$
$659$	−5.63381	−0.219462	−0.109731	+	0.993961i	$0.534999\pi$
$660$	−103.087	−4.01264
$661$	17.1942	0.668778	0.334389	−	0.942435i	$-0.391470\pi$
$661$	17.1942	0.668778	0.334389	+	0.942435i	$0.391470\pi$
$662$	21.5834	0.838864
$663$	−45.1869	−1.75491
$664$	90.9511	3.52959
$665$	11.2254	0.435301
$666$	−114.295	−4.42885
$667$	−31.7423	−1.22907
$668$	−1.63015	−0.0630723
$669$	−29.2595	−1.13124
$670$	−11.2967	−0.436431
$671$	56.8956	2.19643
$672$	−125.818	−4.85352
$673$	−41.4328	−1.59712	−0.798558	−	0.601918i	$-0.794403\pi$
$673$	−41.4328	−1.59712	−0.798558	+	0.601918i	$0.794403\pi$
$674$	75.4171	2.90496
$675$	−20.1322	−0.774889
$676$	56.2648	2.16403
$677$	−2.40437	−0.0924073	−0.0462037	−	0.998932i	$-0.514712\pi$
$677$	−2.40437	−0.0924073	−0.0462037	+	0.998932i	$0.514712\pi$
$678$	−140.641	−5.40128
$679$	3.52272	0.135190
$680$	45.0917	1.72919
$681$	−11.0995	−0.425335
$682$	16.2827	0.623497
$683$	−14.2227	−0.544217	−0.272108	−	0.962267i	$-0.587721\pi$
$683$	−14.2227	−0.544217	−0.272108	+	0.962267i	$0.587721\pi$
$684$	−175.431	−6.70778
$685$	−5.35791	−0.204715
$686$	49.1973	1.87836
$687$	3.60619	0.137585
$688$	50.9189	1.94126
$689$	−59.7190	−2.27511
$690$	61.7841	2.35208
$691$	37.0040	1.40770	0.703850	−	0.710349i	$-0.251463\pi$
$691$	37.0040	1.40770	0.703850	+	0.710349i	$0.251463\pi$
$692$	−123.380	−4.69020
$693$	37.4510	1.42264
$694$	−80.8547	−3.06920
$695$	0.395146	0.0149888
$696$	156.855	5.94558
$697$	34.2948	1.29901
$698$	−32.0004	−1.21123
$699$	75.5493	2.85754
$700$	−29.5857	−1.11824
$701$	−16.9223	−0.639146	−0.319573	−	0.947562i	$-0.603540\pi$
$701$	−16.9223	−0.639146	−0.319573	+	0.947562i	$0.603540\pi$
$702$	78.8468	2.97588
$703$	−47.6990	−1.79900
$704$	228.000	8.59307
$705$	0.499170	0.0187998
$706$	−74.1535	−2.79080
$707$	23.9516	0.900791
$708$	−71.3685	−2.68219
$709$	−44.2684	−1.66253	−0.831267	−	0.555874i	$-0.812384\pi$
$709$	−44.2684	−1.66253	−0.831267	+	0.555874i	$0.812384\pi$
$710$	45.8296	1.71995
$711$	−4.76564	−0.178726
$712$	123.510	4.62873
$713$	−7.26253	−0.271984
$714$	−39.6942	−1.48552
$715$	29.6709	1.10963
$716$	5.34397	0.199713
$717$	−46.0607	−1.72017
$718$	−94.6010	−3.53048
$719$	−45.5398	−1.69835	−0.849174	−	0.528113i	$-0.822900\pi$
$719$	−45.5398	−1.69835	−0.849174	+	0.528113i	$0.822900\pi$
$720$	−117.157	−4.36619
$721$	3.49136	0.130025
$722$	−45.2520	−1.68410
$723$	−41.9903	−1.56164
$724$	−127.970	−4.75597
$725$	17.5653	0.652358
$726$	−105.421	−3.91255
$727$	32.0878	1.19007	0.595035	−	0.803700i	$-0.297138\pi$
$727$	32.0878	1.19007	0.595035	+	0.803700i	$0.297138\pi$
$728$	76.0423	2.81832
$729$	−42.4387	−1.57180
$730$	−4.44616	−0.164560
$731$	9.33009	0.345086
$732$	191.082	7.06260
$733$	36.9407	1.36444	0.682218	−	0.731149i	$-0.261016\pi$
$733$	36.9407	1.36444	0.682218	+	0.731149i	$0.261016\pi$
$734$	33.6512	1.24209
$735$	17.1307	0.631876
$736$	−181.740	−6.69901
$737$	−15.7288	−0.579380
$738$	−146.023	−5.37516
$739$	29.5857	1.08833	0.544163	−	0.838979i	$-0.316847\pi$
$739$	29.5857	1.08833	0.544163	+	0.838979i	$0.316847\pi$
$740$	−59.1967	−2.17611
$741$	80.2945	2.94969
$742$	−52.4599	−1.92586
$743$	17.5388	0.643436	0.321718	−	0.946836i	$-0.395740\pi$
$743$	17.5388	0.643436	0.321718	+	0.946836i	$0.395740\pi$
$744$	35.8879	1.31572
$745$	−7.94734	−0.291168
$746$	−39.1248	−1.43246
$747$	−43.2999	−1.58426
$748$	95.6666	3.49792
$749$	4.38027	0.160051
$750$	−84.4782	−3.08471
$751$	−34.4354	−1.25657	−0.628283	−	0.777985i	$-0.716242\pi$
$751$	−34.4354	−1.25657	−0.628283	+	0.777985i	$0.716242\pi$
$752$	−2.52813	−0.0921915
$753$	−36.9778	−1.34755
$754$	−68.7936	−2.50531
$755$	23.4426	0.853165
$756$	51.5449	1.87467
$757$	34.6219	1.25836	0.629178	−	0.777261i	$-0.283392\pi$
$757$	34.6219	1.25836	0.629178	+	0.777261i	$0.283392\pi$
$758$	−30.9190	−1.12303
$759$	86.0242	3.12248
$760$	−80.1253	−2.90645
$761$	−32.8822	−1.19198	−0.595990	−	0.802992i	$-0.703240\pi$
$761$	−32.8822	−1.19198	−0.595990	+	0.802992i	$0.703240\pi$
$762$	−51.4540	−1.86398
$763$	9.39640	0.340173
$764$	109.412	3.95838
$765$	−21.4672	−0.776148
$766$	−70.1481	−2.53455
$767$	20.5417	0.741717
$768$	295.348	10.6575
$769$	−1.70785	−0.0615867	−0.0307934	−	0.999526i	$-0.509803\pi$
$769$	−1.70785	−0.0615867	−0.0307934	+	0.999526i	$0.509803\pi$
$770$	26.0643	0.939292
$771$	−5.01174	−0.180493
$772$	−22.2182	−0.799651
$773$	28.6116	1.02909	0.514544	−	0.857464i	$-0.327961\pi$
$773$	28.6116	1.02909	0.514544	+	0.857464i	$0.327961\pi$
$774$	−39.7262	−1.42793
$775$	4.01888	0.144362
$776$	−25.1447	−0.902643
$777$	34.1986	1.22687
$778$	64.9882	2.32994
$779$	−60.9399	−2.18340
$780$	99.6491	3.56801
$781$	63.8102	2.28331
$782$	−57.3370	−2.05037
$783$	−30.6026	−1.09365
$784$	−86.7614	−3.09862
$785$	−24.7703	−0.884091
$786$	14.5120	0.517627
$787$	−40.4917	−1.44337	−0.721687	−	0.692220i	$-0.756633\pi$
$787$	−40.4917	−1.44337	−0.721687	+	0.692220i	$0.756633\pi$
$788$	−14.4841	−0.515974
$789$	51.4234	1.83072
$790$	−3.31669	−0.118002
$791$	26.4632	0.940923
$792$	−267.320	−9.49881
$793$	−54.9983	−1.95305
$794$	57.7987	2.05120
$795$	−45.1155	−1.60008
$796$	−53.3385	−1.89053
$797$	11.5779	0.410110	0.205055	−	0.978750i	$-0.434263\pi$
$797$	11.5779	0.410110	0.205055	+	0.978750i	$0.434263\pi$
$798$	70.5343	2.49689
$799$	−0.463241	−0.0163883
$800$	100.570	3.55567
$801$	−58.8005	−2.07761
$802$	−17.7856	−0.628031
$803$	−6.19054	−0.218460
$804$	−52.8249	−1.86299
$805$	−11.6254	−0.409741
$806$	−15.7397	−0.554409
$807$	−31.3617	−1.10398
$808$	−170.963	−6.01447
$809$	10.9459	0.384839	0.192420	−	0.981313i	$-0.438367\pi$
$809$	10.9459	0.384839	0.192420	+	0.981313i	$0.438367\pi$
$810$	5.61968	0.197455
$811$	25.5099	0.895773	0.447886	−	0.894090i	$-0.352177\pi$
$811$	25.5099	0.895773	0.447886	+	0.894090i	$0.352177\pi$
$812$	−44.9727	−1.57823
$813$	−70.6007	−2.47607
$814$	−110.753	−3.88188
$815$	−28.7923	−1.00855
$816$	172.893	6.05245
$817$	−16.5790	−0.580027
$818$	59.7610	2.08949
$819$	−36.2021	−1.26501
$820$	−75.6292	−2.64109
$821$	19.5910	0.683730	0.341865	−	0.939749i	$-0.388941\pi$
$821$	19.5910	0.683730	0.341865	+	0.939749i	$0.388941\pi$
$822$	−33.6663	−1.17425
$823$	−6.71766	−0.234163	−0.117081	−	0.993122i	$-0.537354\pi$
$823$	−6.71766	−0.234163	−0.117081	+	0.993122i	$0.537354\pi$
$824$	−24.9209	−0.868159
$825$	−47.6034	−1.65734
$826$	18.0447	0.627856
$827$	20.5720	0.715357	0.357679	−	0.933845i	$-0.383568\pi$
$827$	20.5720	0.715357	0.357679	+	0.933845i	$0.383568\pi$
$828$	181.683	6.31390
$829$	43.3899	1.50699	0.753496	−	0.657452i	$-0.228366\pi$
$829$	43.3899	1.50699	0.753496	+	0.657452i	$0.228366\pi$
$830$	−30.1349	−1.04600
$831$	1.58793	0.0550847
$832$	−220.397	−7.64090
$833$	−15.8977	−0.550822
$834$	2.48289	0.0859754
$835$	0.354462	0.0122666
$836$	−169.994	−5.87937
$837$	−7.00177	−0.242017
$838$	92.9859	3.21214
$839$	18.6169	0.642728	0.321364	−	0.946956i	$-0.395859\pi$
$839$	18.6169	0.642728	0.321364	+	0.946956i	$0.395859\pi$
$840$	57.4471	1.98211
$841$	−2.29933	−0.0792872
$842$	−22.0912	−0.761312
$843$	−14.0130	−0.482632
$844$	117.549	4.04621
$845$	−12.2343	−0.420872
$846$	1.97241	0.0678130
$847$	19.8362	0.681580
$848$	228.495	7.84655
$849$	−29.3512	−1.00733
$850$	31.7287	1.08828
$851$	49.3988	1.69337
$852$	214.305	7.34196
$853$	−6.04742	−0.207060	−0.103530	−	0.994626i	$-0.533014\pi$
$853$	−6.04742	−0.207060	−0.103530	+	0.994626i	$0.533014\pi$
$854$	−48.3130	−1.65324
$855$	38.1460	1.30456
$856$	−31.2658	−1.06864
$857$	−22.6356	−0.773218	−0.386609	−	0.922244i	$-0.626354\pi$
$857$	−22.6356	−0.773218	−0.386609	+	0.922244i	$0.626354\pi$
$858$	186.436	6.36483
$859$	−39.8238	−1.35877	−0.679386	−	0.733781i	$-0.737754\pi$
$859$	−39.8238	−1.35877	−0.679386	+	0.733781i	$0.737754\pi$
$860$	−20.5753	−0.701613
$861$	43.6918	1.48901
$862$	64.4210	2.19419
$863$	−55.5345	−1.89042	−0.945208	−	0.326470i	$-0.894141\pi$
$863$	−55.5345	−1.89042	−0.945208	+	0.326470i	$0.894141\pi$
$864$	−175.214	−5.96092
$865$	26.8279	0.912175
$866$	−53.7495	−1.82648
$867$	−16.6525	−0.565547
$868$	−10.2896	−0.349252
$869$	−4.61794	−0.156653
$870$	−51.9709	−1.76198
$871$	15.2044	0.515180
$872$	−67.0703	−2.27129
$873$	11.9709	0.405153
$874$	101.885	3.44630
$875$	15.8955	0.537367
$876$	−20.7908	−0.702455
$877$	−30.2177	−1.02038	−0.510190	−	0.860062i	$-0.670425\pi$
$877$	−30.2177	−1.02038	−0.510190	+	0.860062i	$0.670425\pi$
$878$	−17.1230	−0.577872
$879$	−28.4490	−0.959561
$880$	−113.526	−3.82696
$881$	18.8691	0.635718	0.317859	−	0.948138i	$-0.397036\pi$
$881$	18.8691	0.635718	0.317859	+	0.948138i	$0.397036\pi$
$882$	67.6901	2.27924
$883$	54.4480	1.83232	0.916161	−	0.400811i	$-0.131272\pi$
$883$	54.4480	1.83232	0.916161	+	0.400811i	$0.131272\pi$
$884$	−92.4765	−3.11032
$885$	15.5185	0.521647
$886$	−33.9259	−1.13976
$887$	39.4443	1.32441	0.662205	−	0.749323i	$-0.269621\pi$
$887$	39.4443	1.32441	0.662205	+	0.749323i	$0.269621\pi$
$888$	−244.105	−8.19163
$889$	9.68165	0.324712
$890$	−40.9226	−1.37173
$891$	7.82448	0.262130
$892$	−59.8806	−2.00495
$893$	0.823152	0.0275457
$894$	−49.9368	−1.67014
$895$	−1.16200	−0.0388414
$896$	−105.099	−3.51110
$897$	−83.1557	−2.77649
$898$	40.1419	1.33955
$899$	6.10903	0.203747
$900$	−100.538	−3.35127
$901$	41.8681	1.39483
$902$	−141.497	−4.71133
$903$	11.8866	0.395561
$904$	−188.891	−6.28242
$905$	27.8260	0.924967
$906$	147.301	4.89375
$907$	−11.4866	−0.381406	−0.190703	−	0.981648i	$-0.561077\pi$
$907$	−11.4866	−0.381406	−0.190703	+	0.981648i	$0.561077\pi$
$908$	−22.7156	−0.753843
$909$	81.3920	2.69960
$910$	−25.1952	−0.835211
$911$	−21.5228	−0.713083	−0.356542	−	0.934279i	$-0.616044\pi$
$911$	−21.5228	−0.713083	−0.356542	+	0.934279i	$0.616044\pi$
$912$	−307.220	−10.1731
$913$	−41.9579	−1.38860
$914$	42.1062	1.39275
$915$	−41.5492	−1.37357
$916$	7.38019	0.243849
$917$	−2.73061	−0.0901726
$918$	−55.2784	−1.82446
$919$	8.02539	0.264733	0.132367	−	0.991201i	$-0.457742\pi$
$919$	8.02539	0.264733	0.132367	+	0.991201i	$0.457742\pi$
$920$	82.9805	2.73579
$921$	−66.1656	−2.18023
$922$	−63.2952	−2.08452
$923$	−61.6824	−2.03030
$924$	121.880	4.00955
$925$	−27.3359	−0.898798
$926$	−64.6925	−2.12593
$927$	11.8643	0.389675
$928$	152.874	5.01834
$929$	−15.5311	−0.509557	−0.254779	−	0.966999i	$-0.582003\pi$
$929$	−15.5311	−0.509557	−0.254779	+	0.966999i	$0.582003\pi$
$930$	−11.8908	−0.389914
$931$	28.2492	0.925832
$932$	154.614	5.06456
$933$	13.3027	0.435512
$934$	113.701	3.72040
$935$	−20.8019	−0.680294
$936$	258.406	8.44628
$937$	19.7309	0.644581	0.322291	−	0.946641i	$-0.395547\pi$
$937$	19.7309	0.644581	0.322291	+	0.946641i	$0.395547\pi$
$938$	13.3562	0.436095
$939$	15.2313	0.497054
$940$	1.02157	0.0333199
$941$	−9.79476	−0.319300	−0.159650	−	0.987174i	$-0.551037\pi$
$941$	−9.79476	−0.319300	−0.159650	+	0.987174i	$0.551037\pi$
$942$	−155.643	−5.07114
$943$	63.1115	2.05519
$944$	−78.5959	−2.55808
$945$	−11.2080	−0.364596
$946$	−38.4950	−1.25158
$947$	−23.2767	−0.756393	−0.378196	−	0.925725i	$-0.623456\pi$
$947$	−23.2767	−0.756393	−0.378196	+	0.925725i	$0.623456\pi$
$948$	−15.5092	−0.503717
$949$	5.98412	0.194253
$950$	−56.3800	−1.82921
$951$	43.3432	1.40550
$952$	−53.3122	−1.72786
$953$	7.49975	0.242941	0.121470	−	0.992595i	$-0.461239\pi$
$953$	7.49975	0.242941	0.121470	+	0.992595i	$0.461239\pi$
$954$	−178.269	−5.77166
$955$	−23.7906	−0.769847
$956$	−94.2649	−3.04874
$957$	−72.3610	−2.33910
$958$	7.47617	0.241544
$959$	6.33469	0.204558
$960$	−166.502	−5.37382
$961$	−29.6023	−0.954912
$962$	107.060	3.45174
$963$	14.8850	0.479662
$964$	−85.9347	−2.76777
$965$	4.83116	0.155520
$966$	−73.0477	−2.35027
$967$	1.68436	0.0541653	0.0270827	−	0.999633i	$-0.491378\pi$
$967$	1.68436	0.0541653	0.0270827	+	0.999633i	$0.491378\pi$
$968$	−141.588	−4.55082
$969$	−56.2933	−1.80840
$970$	8.33122	0.267499
$971$	9.20275	0.295330	0.147665	−	0.989037i	$-0.452824\pi$
$971$	9.20275	0.295330	0.147665	+	0.989037i	$0.452824\pi$
$972$	−77.0993	−2.47296
$973$	−0.467184	−0.0149772
$974$	−34.1291	−1.09357
$975$	46.0160	1.47369
$976$	210.433	6.73579
$977$	6.10257	0.195239	0.0976193	−	0.995224i	$-0.468877\pi$
$977$	6.10257	0.195239	0.0976193	+	0.995224i	$0.468877\pi$
$978$	−180.915	−5.78504
$979$	−56.9781	−1.82103
$980$	35.0586	1.11991
$981$	31.9308	1.01947
$982$	−80.5726	−2.57118
$983$	−28.6288	−0.913117	−0.456558	−	0.889693i	$-0.650918\pi$
$983$	−28.6288	−0.913117	−0.456558	+	0.889693i	$0.650918\pi$
$984$	−311.867	−9.94195
$985$	3.14944	0.100349
$986$	48.2302	1.53596
$987$	−0.590172	−0.0187854
$988$	164.325	5.22789
$989$	17.1698	0.545968
$990$	88.5714	2.81499
$991$	42.0015	1.33422	0.667110	−	0.744959i	$-0.267531\pi$
$991$	42.0015	1.33422	0.667110	+	0.744959i	$0.267531\pi$
$992$	34.9771	1.11052
$993$	−21.9457	−0.696424
$994$	−54.1846	−1.71863
$995$	11.5980	0.367681
$996$	−140.915	−4.46505
$997$	−23.9229	−0.757644	−0.378822	−	0.925469i	$-0.623671\pi$
$997$	−23.9229	−0.757644	−0.378822	+	0.925469i	$0.623671\pi$
$998$	55.5343	1.75791
$999$	47.6251	1.50679

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4003.2.a.c.1.1	✓	179

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4003.2.a.c.1.1	✓	179	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:	\( N \)	\(=\)	\( 4003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.79615 q^{2} +2.84308 q^{3} +5.81846 q^{4} -1.26517 q^{5} -7.94968 q^{6} +1.49582 q^{7} -10.6770 q^{8} +5.08309 q^{9} +O(q^{10})\)	\(q-2.79615 q^{2} +2.84308 q^{3} +5.81846 q^{4} -1.26517 q^{5} -7.94968 q^{6} +1.49582 q^{7} -10.6770 q^{8} +5.08309 q^{9} +3.53762 q^{10} +4.92555 q^{11} +16.5423 q^{12} -4.76131 q^{13} -4.18255 q^{14} -3.59699 q^{15} +18.2176 q^{16} +3.33808 q^{17} -14.2131 q^{18} -5.93158 q^{19} -7.36136 q^{20} +4.25274 q^{21} -13.7726 q^{22} +6.14295 q^{23} -30.3555 q^{24} -3.39934 q^{25} +13.3133 q^{26} +5.92239 q^{27} +8.70339 q^{28} -5.16727 q^{29} +10.0577 q^{30} -1.18225 q^{31} -29.5851 q^{32} +14.0037 q^{33} -9.33379 q^{34} -1.89248 q^{35} +29.5758 q^{36} +8.04154 q^{37} +16.5856 q^{38} -13.5368 q^{39} +13.5082 q^{40} +10.2738 q^{41} -11.8913 q^{42} +2.79504 q^{43} +28.6591 q^{44} -6.43099 q^{45} -17.1766 q^{46} -0.138774 q^{47} +51.7940 q^{48} -4.76251 q^{49} +9.50506 q^{50} +9.49043 q^{51} -27.7035 q^{52} +12.5426 q^{53} -16.5599 q^{54} -6.23168 q^{55} -15.9709 q^{56} -16.8640 q^{57} +14.4485 q^{58} -4.31429 q^{59} -20.9289 q^{60} +11.5511 q^{61} +3.30576 q^{62} +7.60340 q^{63} +46.2892 q^{64} +6.02388 q^{65} -39.1565 q^{66} -3.19332 q^{67} +19.4225 q^{68} +17.4649 q^{69} +5.29165 q^{70} +12.9549 q^{71} -54.2721 q^{72} -1.25682 q^{73} -22.4853 q^{74} -9.66458 q^{75} -34.5127 q^{76} +7.36775 q^{77} +37.8508 q^{78} -0.937548 q^{79} -23.0484 q^{80} +1.58855 q^{81} -28.7271 q^{82} -8.51842 q^{83} +24.7444 q^{84} -4.22326 q^{85} -7.81536 q^{86} -14.6909 q^{87} -52.5901 q^{88} -11.5679 q^{89} +17.9820 q^{90} -7.12207 q^{91} +35.7425 q^{92} -3.36124 q^{93} +0.388034 q^{94} +7.50448 q^{95} -84.1127 q^{96} +2.35504 q^{97} +13.3167 q^{98} +25.0370 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9}+O(q^{10}) \) 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9} + 9 q^{10} + 46 q^{11} + 33 q^{12} + 47 q^{13} + 22 q^{14} + 36 q^{15} + 222 q^{16} + 103 q^{17} + 43 q^{18} + 12 q^{19} + 102 q^{20} + 50 q^{21} + 39 q^{22} + 121 q^{23} - 3 q^{24} + 246 q^{25} + 52 q^{26} + 49 q^{27} + 41 q^{28} + 138 q^{29} + 28 q^{30} + 5 q^{31} + 137 q^{32} + 63 q^{33} + 2 q^{34} + 72 q^{35} + 279 q^{36} + 118 q^{37} + 123 q^{38} + q^{39} + 9 q^{40} + 50 q^{41} + 48 q^{42} + 48 q^{43} + 108 q^{44} + 158 q^{45} + 13 q^{46} + 85 q^{47} + 50 q^{48} + 230 q^{49} + 78 q^{50} + 15 q^{51} + 41 q^{52} + 399 q^{53} - 5 q^{54} + 24 q^{55} + 53 q^{56} + 45 q^{57} + 27 q^{58} + 48 q^{59} + 66 q^{60} + 46 q^{61} + 81 q^{62} + 78 q^{63} + 252 q^{64} + 153 q^{65} + 6 q^{66} + 70 q^{67} + 240 q^{68} + 120 q^{69} - 31 q^{70} + 86 q^{71} + 89 q^{72} + 45 q^{73} + 68 q^{74} + 17 q^{75} - 13 q^{76} + 362 q^{77} + 69 q^{78} + 31 q^{79} + 169 q^{80} + 303 q^{81} + 25 q^{82} + 106 q^{83} + 13 q^{84} + 115 q^{85} + 95 q^{86} + 32 q^{87} + 83 q^{88} + 105 q^{89} - 38 q^{90} + 3 q^{91} + 310 q^{92} + 298 q^{93} - 17 q^{94} + 102 q^{95} - 82 q^{96} + 34 q^{97} + 81 q^{98} + 58 q^{99}+O(q^{100}) \) 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9 + 9 * q^10 + 46 * q^11 + 33 * q^12 + 47 * q^13 + 22 * q^14 + 36 * q^15 + 222 * q^16 + 103 * q^17 + 43 * q^18 + 12 * q^19 + 102 * q^20 + 50 * q^21 + 39 * q^22 + 121 * q^23 - 3 * q^24 + 246 * q^25 + 52 * q^26 + 49 * q^27 + 41 * q^28 + 138 * q^29 + 28 * q^30 + 5 * q^31 + 137 * q^32 + 63 * q^33 + 2 * q^34 + 72 * q^35 + 279 * q^36 + 118 * q^37 + 123 * q^38 + q^39 + 9 * q^40 + 50 * q^41 + 48 * q^42 + 48 * q^43 + 108 * q^44 + 158 * q^45 + 13 * q^46 + 85 * q^47 + 50 * q^48 + 230 * q^49 + 78 * q^50 + 15 * q^51 + 41 * q^52 + 399 * q^53 - 5 * q^54 + 24 * q^55 + 53 * q^56 + 45 * q^57 + 27 * q^58 + 48 * q^59 + 66 * q^60 + 46 * q^61 + 81 * q^62 + 78 * q^63 + 252 * q^64 + 153 * q^65 + 6 * q^66 + 70 * q^67 + 240 * q^68 + 120 * q^69 - 31 * q^70 + 86 * q^71 + 89 * q^72 + 45 * q^73 + 68 * q^74 + 17 * q^75 - 13 * q^76 + 362 * q^77 + 69 * q^78 + 31 * q^79 + 169 * q^80 + 303 * q^81 + 25 * q^82 + 106 * q^83 + 13 * q^84 + 115 * q^85 + 95 * q^86 + 32 * q^87 + 83 * q^88 + 105 * q^89 - 38 * q^90 + 3 * q^91 + 310 * q^92 + 298 * q^93 - 17 * q^94 + 102 * q^95 - 82 * q^96 + 34 * q^97 + 81 * q^98 + 58 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more