LMFDB - Embedded Newform 4003.2.a.b.1.18

Newspace parameters

Level:	$ N $	=	$ 4003 $
Weight:	$ k $	=	$ 2 $
Character orbit:	$[\chi]$	=	4003.a (trivial)

Newform invariants

Self dual:	Yes
Analytic conductor:	$31.9641159291$
Analytic rank:	$1$
Dimension:	$152$
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	=	4003.1

$q$-expansion

$f(q)$	$=$	$q-2.37503 q^{2} -2.00580 q^{3} +3.64079 q^{4} +0.380635 q^{5} +4.76385 q^{6} +3.69515 q^{7} -3.89692 q^{8} +1.02324 q^{9} +O(q^{10})$	\(q-2.37503 q^{2} -2.00580 q^{3} +3.64079 q^{4} +0.380635 q^{5} +4.76385 q^{6} +3.69515 q^{7} -3.89692 q^{8} +1.02324 q^{9} -0.904022 q^{10} -5.88580 q^{11} -7.30269 q^{12} +3.92815 q^{13} -8.77610 q^{14} -0.763479 q^{15} +1.97375 q^{16} +7.17930 q^{17} -2.43023 q^{18} -2.89072 q^{19} +1.38581 q^{20} -7.41173 q^{21} +13.9790 q^{22} -2.31289 q^{23} +7.81645 q^{24} -4.85512 q^{25} -9.32949 q^{26} +3.96499 q^{27} +13.4532 q^{28} +2.31156 q^{29} +1.81329 q^{30} +7.04153 q^{31} +3.10613 q^{32} +11.8058 q^{33} -17.0511 q^{34} +1.40650 q^{35} +3.72540 q^{36} -1.79441 q^{37} +6.86556 q^{38} -7.87909 q^{39} -1.48331 q^{40} -10.3212 q^{41} +17.6031 q^{42} -0.380637 q^{43} -21.4289 q^{44} +0.389482 q^{45} +5.49320 q^{46} -0.614354 q^{47} -3.95895 q^{48} +6.65412 q^{49} +11.5311 q^{50} -14.4002 q^{51} +14.3016 q^{52} -13.7636 q^{53} -9.41698 q^{54} -2.24035 q^{55} -14.3997 q^{56} +5.79822 q^{57} -5.49004 q^{58} +3.52453 q^{59} -2.77966 q^{60} -10.4148 q^{61} -16.7239 q^{62} +3.78103 q^{63} -11.3246 q^{64} +1.49519 q^{65} -28.0391 q^{66} -4.27333 q^{67} +26.1383 q^{68} +4.63920 q^{69} -3.34049 q^{70} +3.16932 q^{71} -3.98749 q^{72} +15.9931 q^{73} +4.26179 q^{74} +9.73840 q^{75} -10.5245 q^{76} -21.7489 q^{77} +18.7131 q^{78} -0.687068 q^{79} +0.751278 q^{80} -11.0227 q^{81} +24.5133 q^{82} +1.33334 q^{83} -26.9845 q^{84} +2.73269 q^{85} +0.904025 q^{86} -4.63654 q^{87} +22.9365 q^{88} -15.9201 q^{89} -0.925032 q^{90} +14.5151 q^{91} -8.42074 q^{92} -14.1239 q^{93} +1.45911 q^{94} -1.10031 q^{95} -6.23027 q^{96} -6.95578 q^{97} -15.8038 q^{98} -6.02260 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} + O(q^{10}) $	\( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} - 15q^{10} - 40q^{11} - 53q^{12} - 59q^{13} - 36q^{14} - 40q^{15} + 118q^{16} - 93q^{17} - 59q^{18} - 16q^{19} - 108q^{20} - 62q^{21} - 37q^{22} - 107q^{23} - 31q^{24} + 101q^{25} - 64q^{26} - 63q^{27} - 53q^{28} - 124q^{29} - 68q^{30} - 15q^{31} - 129q^{32} - 49q^{33} - 76q^{35} + 45q^{36} - 98q^{37} - 125q^{38} - 47q^{39} - 7q^{40} - 56q^{41} - 84q^{42} - 62q^{43} - 114q^{44} - 142q^{45} - 3q^{46} - 111q^{47} - 92q^{48} + 117q^{49} - 64q^{50} - 21q^{51} - 85q^{52} - 347q^{53} + 3q^{54} - 16q^{55} - 73q^{56} - 115q^{57} - 29q^{58} - 50q^{59} - 54q^{60} - 62q^{61} - 55q^{62} - 70q^{63} + 64q^{64} - 147q^{65} + 34q^{66} - 86q^{67} - 174q^{68} - 104q^{69} - 7q^{70} - 86q^{71} - 139q^{72} - 27q^{73} - 52q^{74} - 49q^{75} - 11q^{76} - 346q^{77} - 59q^{78} - 17q^{79} - 149q^{80} - 8q^{81} - 31q^{82} - 106q^{83} - 51q^{84} - 69q^{85} - 85q^{86} - 32q^{87} - 113q^{88} - 59q^{89} + 10q^{90} - 9q^{91} - 314q^{92} - 230q^{93} + 7q^{94} - 74q^{95} - 54q^{96} - 60q^{97} - 77q^{98} - 96q^{99} + O(q^{100}) \)

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 $

$2$	−2.37503	−1.67940	−0.839701	−	0.543049i	$-0.817270\pi$
$2$	−2.37503	−1.67940	−0.839701	+	0.543049i	$0.817270\pi$
$3$	−2.00580	−1.15805	−0.579025	−	0.815310i	$-0.696567\pi$
$3$	−2.00580	−1.15805	−0.579025	+	0.815310i	$0.696567\pi$
$4$	3.64079	1.82039
$5$	0.380635	0.170225	0.0851127	−	0.996371i	$-0.472875\pi$
$5$	0.380635	0.170225	0.0851127	+	0.996371i	$0.472875\pi$
$6$	4.76385	1.94483
$7$	3.69515	1.39663	0.698317	−	0.715788i	$-0.253932\pi$
$7$	3.69515	1.39663	0.698317	+	0.715788i	$0.253932\pi$
$8$	−3.89692	−1.37777
$9$	1.02324	0.341080
$10$	−0.904022	−0.285877
$11$	−5.88580	−1.77464	−0.887318	−	0.461157i	$-0.847434\pi$
$11$	−5.88580	−1.77464	−0.887318	+	0.461157i	$0.847434\pi$
$12$	−7.30269	−2.10811
$13$	3.92815	1.08947	0.544737	−	0.838607i	$-0.316630\pi$
$13$	3.92815	1.08947	0.544737	+	0.838607i	$0.316630\pi$
$14$	−8.77610	−2.34551
$15$	−0.763479	−0.197129
$16$	1.97375	0.493437
$17$	7.17930	1.74124	0.870618	−	0.491960i	$-0.163719\pi$
$17$	7.17930	1.74124	0.870618	+	0.491960i	$0.163719\pi$
$18$	−2.43023	−0.572811
$19$	−2.89072	−0.663177	−0.331589	−	0.943424i	$-0.607585\pi$
$19$	−2.89072	−0.663177	−0.331589	+	0.943424i	$0.607585\pi$
$20$	1.38581	0.309877
$21$	−7.41173	−1.61737
$22$	13.9790	2.98033
$23$	−2.31289	−0.482271	−0.241136	−	0.970491i	$-0.577520\pi$
$23$	−2.31289	−0.482271	−0.241136	+	0.970491i	$0.577520\pi$
$24$	7.81645	1.59553
$25$	−4.85512	−0.971023
$26$	−9.32949	−1.82966
$27$	3.96499	0.763062
$28$	13.4532	2.54242
$29$	2.31156	0.429247	0.214623	−	0.976697i	$-0.431148\pi$
$29$	2.31156	0.429247	0.214623	+	0.976697i	$0.431148\pi$
$30$	1.81329	0.331060
$31$	7.04153	1.26470	0.632348	−	0.774684i	$-0.282091\pi$
$31$	7.04153	1.26470	0.632348	+	0.774684i	$0.282091\pi$
$32$	3.10613	0.549091
$33$	11.8058	2.05512
$34$	−17.0511	−2.92424
$35$	1.40650	0.237743
$36$	3.72540	0.620900
$37$	−1.79441	−0.295000	−0.147500	−	0.989062i	$-0.547123\pi$
$37$	−1.79441	−0.295000	−0.147500	+	0.989062i	$0.547123\pi$
$38$	6.86556	1.11374
$39$	−7.87909	−1.26166
$40$	−1.48331	−0.234531
$41$	−10.3212	−1.61191	−0.805954	−	0.591978i	$-0.798347\pi$
$41$	−10.3212	−1.61191	−0.805954	+	0.591978i	$0.798347\pi$
$42$	17.6031	2.71622
$43$	−0.380637	−0.0580465	−0.0290233	−	0.999579i	$-0.509240\pi$
$43$	−0.380637	−0.0580465	−0.0290233	+	0.999579i	$0.509240\pi$
$44$	−21.4289	−3.23054
$45$	0.389482	0.0580605
$46$	5.49320	0.809928
$47$	−0.614354	−0.0896128	−0.0448064	−	0.998996i	$-0.514267\pi$
$47$	−0.614354	−0.0896128	−0.0448064	+	0.998996i	$0.514267\pi$
$48$	−3.95895	−0.571425
$49$	6.65412	0.950588
$50$	11.5311	1.63074
$51$	−14.4002	−2.01644
$52$	14.3016	1.98327
$53$	−13.7636	−1.89057	−0.945285	−	0.326245i	$-0.894216\pi$
$53$	−13.7636	−1.89057	−0.945285	+	0.326245i	$0.894216\pi$
$54$	−9.41698	−1.28149
$55$	−2.24035	−0.302088
$56$	−14.3997	−1.92424
$57$	5.79822	0.767992
$58$	−5.49004	−0.720878
$59$	3.52453	0.458855	0.229428	−	0.973326i	$-0.426315\pi$
$59$	3.52453	0.458855	0.229428	+	0.973326i	$0.426315\pi$
$60$	−2.77966	−0.358853
$61$	−10.4148	−1.33348	−0.666738	−	0.745292i	$-0.732310\pi$
$61$	−10.4148	−1.33348	−0.666738	+	0.745292i	$0.732310\pi$
$62$	−16.7239	−2.12393
$63$	3.78103	0.476365
$64$	−11.3246	−1.41558
$65$	1.49519	0.185456
$66$	−28.0391	−3.45137
$67$	−4.27333	−0.522071	−0.261035	−	0.965329i	$-0.584064\pi$
$67$	−4.27333	−0.522071	−0.261035	+	0.965329i	$0.584064\pi$
$68$	26.1383	3.16973
$69$	4.63920	0.558494
$70$	−3.34049	−0.399265
$71$	3.16932	0.376130	0.188065	−	0.982157i	$-0.439779\pi$
$71$	3.16932	0.376130	0.188065	+	0.982157i	$0.439779\pi$
$72$	−3.98749	−0.469930
$73$	15.9931	1.87185	0.935923	−	0.352204i	$-0.114568\pi$
$73$	15.9931	1.87185	0.935923	+	0.352204i	$0.114568\pi$
$74$	4.26179	0.495424
$75$	9.73840	1.12449
$76$	−10.5245	−1.20724
$77$	−21.7489	−2.47852
$78$	18.7131	2.11884
$79$	−0.687068	−0.0773012	−0.0386506	−	0.999253i	$-0.512306\pi$
$79$	−0.687068	−0.0773012	−0.0386506	+	0.999253i	$0.512306\pi$
$80$	0.751278	0.0839954
$81$	−11.0227	−1.22474
$82$	24.5133	2.70704
$83$	1.33334	0.146353	0.0731765	−	0.997319i	$-0.476686\pi$
$83$	1.33334	0.146353	0.0731765	+	0.997319i	$0.476686\pi$
$84$	−26.9845	−2.94425
$85$	2.73269	0.296402
$86$	0.904025	0.0974835
$87$	−4.63654	−0.497089
$88$	22.9365	2.44504
$89$	−15.9201	−1.68753	−0.843764	−	0.536715i	$-0.819665\pi$
$89$	−15.9201	−1.68753	−0.843764	+	0.536715i	$0.819665\pi$
$90$	−0.925032	−0.0975070
$91$	14.5151	1.52160
$92$	−8.42074	−0.877923
$93$	−14.1239	−1.46458
$94$	1.45911	0.150496
$95$	−1.10031	−0.112890
$96$	−6.23027	−0.635874
$97$	−6.95578	−0.706253	−0.353126	−	0.935576i	$-0.614881\pi$
$97$	−6.95578	−0.706253	−0.353126	+	0.935576i	$0.614881\pi$
$98$	−15.8038	−1.59642
$99$	−6.02260	−0.605294
$100$	−17.6764	−1.76764
$101$	−4.82265	−0.479872	−0.239936	−	0.970789i	$-0.577126\pi$
$101$	−4.82265	−0.479872	−0.239936	+	0.970789i	$0.577126\pi$
$102$	34.2011	3.38641
$103$	−3.19513	−0.314825	−0.157413	−	0.987533i	$-0.550315\pi$
$103$	−3.19513	−0.314825	−0.157413	+	0.987533i	$0.550315\pi$
$104$	−15.3077	−1.50104
$105$	−2.82117	−0.275318
$106$	32.6889	3.17503
$107$	−12.9431	−1.25125	−0.625626	−	0.780123i	$-0.715156\pi$
$107$	−12.9431	−1.25125	−0.625626	+	0.780123i	$0.715156\pi$
$108$	14.4357	1.38907
$109$	−8.90516	−0.852960	−0.426480	−	0.904497i	$-0.640246\pi$
$109$	−8.90516	−0.852960	−0.426480	+	0.904497i	$0.640246\pi$
$110$	5.32090	0.507328
$111$	3.59924	0.341625
$112$	7.29329	0.689151
$113$	12.0402	1.13264	0.566322	−	0.824184i	$-0.308366\pi$
$113$	12.0402	1.13264	0.566322	+	0.824184i	$0.308366\pi$
$114$	−13.7710	−1.28977
$115$	−0.880368	−0.0820948
$116$	8.41591	0.781397
$117$	4.01945	0.371598
$118$	−8.37088	−0.770602
$119$	26.5286	2.43187
$120$	2.97522	0.271599
$121$	23.6427	2.14934
$122$	24.7355	2.23944
$123$	20.7024	1.86667
$124$	25.6367	2.30224
$125$	−3.75121	−0.335518
$126$	−8.98007	−0.800008
$127$	17.9513	1.59292	0.796460	−	0.604691i	$-0.206703\pi$
$127$	17.9513	1.59292	0.796460	+	0.604691i	$0.206703\pi$
$128$	20.6842	1.82824
$129$	0.763481	0.0672208
$130$	−3.55114	−0.311455
$131$	10.1338	0.885391	0.442695	−	0.896672i	$-0.354022\pi$
$131$	10.1338	0.885391	0.442695	+	0.896672i	$0.354022\pi$
$132$	42.9822	3.74112
$133$	−10.6816	−0.926216
$134$	10.1493	0.876767
$135$	1.50921	0.129892
$136$	−27.9772	−2.39902
$137$	−6.00931	−0.513410	−0.256705	−	0.966490i	$-0.582637\pi$
$137$	−6.00931	−0.513410	−0.256705	+	0.966490i	$0.582637\pi$
$138$	−11.0183	−0.937937
$139$	18.4916	1.56843	0.784217	−	0.620487i	$-0.213065\pi$
$139$	18.4916	1.56843	0.784217	+	0.620487i	$0.213065\pi$
$140$	5.12078	0.432785
$141$	1.23227	0.103776
$142$	−7.52725	−0.631673
$143$	−23.1203	−1.93342
$144$	2.01962	0.168302
$145$	0.879863	0.0730686
$146$	−37.9841	−3.14358
$147$	−13.3468	−1.10083
$148$	−6.53308	−0.537016
$149$	−14.7721	−1.21018	−0.605091	−	0.796156i	$-0.706863\pi$
$149$	−14.7721	−1.21018	−0.605091	+	0.796156i	$0.706863\pi$
$150$	−23.1290	−1.88848
$151$	18.8468	1.53373	0.766864	−	0.641810i	$-0.221816\pi$
$151$	18.8468	1.53373	0.766864	+	0.641810i	$0.221816\pi$
$152$	11.2649	0.913705
$153$	7.34615	0.593901
$154$	51.6544	4.16243
$155$	2.68026	0.215283
$156$	−28.6861	−2.29673
$157$	−4.58648	−0.366041	−0.183021	−	0.983109i	$-0.558588\pi$
$157$	−4.58648	−0.366041	−0.183021	+	0.983109i	$0.558588\pi$
$158$	1.63181	0.129820
$159$	27.6070	2.18938
$160$	1.18230	0.0934691
$161$	−8.54648	−0.673557
$162$	26.1793	2.05684
$163$	19.5549	1.53166	0.765831	−	0.643042i	$-0.222328\pi$
$163$	19.5549	1.53166	0.765831	+	0.643042i	$0.222328\pi$
$164$	−37.5774	−2.93431
$165$	4.49369	0.349833
$166$	−3.16673	−0.245786
$167$	−4.74414	−0.367112	−0.183556	−	0.983009i	$-0.558761\pi$
$167$	−4.74414	−0.367112	−0.183556	+	0.983009i	$0.558761\pi$
$168$	28.8829	2.22837
$169$	2.43038	0.186952
$170$	−6.49024	−0.497779
$171$	−2.95791	−0.226197
$172$	−1.38582	−0.105667
$173$	−3.22129	−0.244910	−0.122455	−	0.992474i	$-0.539077\pi$
$173$	−3.22129	−0.244910	−0.122455	+	0.992474i	$0.539077\pi$
$174$	11.0119	0.834813
$175$	−17.9404	−1.35616
$176$	−11.6171	−0.875671
$177$	−7.06951	−0.531377
$178$	37.8108	2.83404
$179$	−7.86653	−0.587972	−0.293986	−	0.955810i	$-0.594982\pi$
$179$	−7.86653	−0.587972	−0.293986	+	0.955810i	$0.594982\pi$
$180$	1.41802	0.105693
$181$	−11.0914	−0.824419	−0.412210	−	0.911089i	$-0.635243\pi$
$181$	−11.0914	−0.824419	−0.412210	+	0.911089i	$0.635243\pi$
$182$	−34.4739	−2.55537
$183$	20.8900	1.54423
$184$	9.01315	0.664459
$185$	−0.683018	−0.0502165
$186$	33.5448	2.45962
$187$	−42.2559	−3.09006
$188$	−2.23673	−0.163130
$189$	14.6512	1.06572
$190$	2.61328	0.189587
$191$	15.5546	1.12549	0.562745	−	0.826631i	$-0.309745\pi$
$191$	15.5546	1.12549	0.562745	+	0.826631i	$0.309745\pi$
$192$	22.7150	1.63931
$193$	2.87185	0.206720	0.103360	−	0.994644i	$-0.467041\pi$
$193$	2.87185	0.206720	0.103360	+	0.994644i	$0.467041\pi$
$194$	16.5202	1.18608
$195$	−2.99906	−0.214767
$196$	24.2262	1.73044
$197$	−19.2917	−1.37448	−0.687240	−	0.726431i	$-0.741178\pi$
$197$	−19.2917	−1.37448	−0.687240	+	0.726431i	$0.741178\pi$
$198$	14.3039	1.01653
$199$	6.06776	0.430132	0.215066	−	0.976600i	$-0.431003\pi$
$199$	6.06776	0.430132	0.215066	+	0.976600i	$0.431003\pi$
$200$	18.9200	1.33785
$201$	8.57146	0.604584
$202$	11.4540	0.805898
$203$	8.54157	0.599501
$204$	−52.4282	−3.67071
$205$	−3.92863	−0.274388
$206$	7.58853	0.528718
$207$	−2.36665	−0.164493
$208$	7.75318	0.537586
$209$	17.0142	1.17690
$210$	6.70037	0.462369
$211$	7.93815	0.546485	0.273242	−	0.961945i	$-0.411904\pi$
$211$	7.93815	0.546485	0.273242	+	0.961945i	$0.411904\pi$
$212$	−50.1102	−3.44158
$213$	−6.35704	−0.435577
$214$	30.7402	2.10136
$215$	−0.144884	−0.00988099
$216$	−15.4512	−1.05132
$217$	26.0195	1.76632
$218$	21.1501	1.43246
$219$	−32.0789	−2.16769
$220$	−8.15662	−0.549919
$221$	28.2014	1.89703
$222$	−8.54832	−0.573725
$223$	18.1382	1.21462	0.607311	−	0.794464i	$-0.292248\pi$
$223$	18.1382	1.21462	0.607311	+	0.794464i	$0.292248\pi$
$224$	11.4776	0.766879
$225$	−4.96796	−0.331197
$226$	−28.5958	−1.90216
$227$	13.3964	0.889148	0.444574	−	0.895742i	$-0.353355\pi$
$227$	13.3964	0.889148	0.444574	+	0.895742i	$0.353355\pi$
$228$	21.1101	1.39805
$229$	2.08349	0.137681	0.0688406	−	0.997628i	$-0.478070\pi$
$229$	2.08349	0.137681	0.0688406	+	0.997628i	$0.478070\pi$
$230$	2.09090	0.137870
$231$	43.6240	2.87025
$232$	−9.00798	−0.591403
$233$	−8.57263	−0.561611	−0.280806	−	0.959765i	$-0.590602\pi$
$233$	−8.57263	−0.561611	−0.280806	+	0.959765i	$0.590602\pi$
$234$	−9.54632	−0.624063
$235$	−0.233845	−0.0152544
$236$	12.8321	0.835296
$237$	1.37812	0.0895187
$238$	−63.0062	−4.08409
$239$	−12.5476	−0.811636	−0.405818	−	0.913954i	$-0.633013\pi$
$239$	−12.5476	−0.811636	−0.405818	+	0.913954i	$0.633013\pi$
$240$	−1.50691	−0.0972709
$241$	−16.1622	−1.04110	−0.520548	−	0.853832i	$-0.674272\pi$
$241$	−16.1622	−1.04110	−0.520548	+	0.853832i	$0.674272\pi$
$242$	−56.1522	−3.60960
$243$	10.2144	0.655254
$244$	−37.9180	−2.42745
$245$	2.53279	0.161814
$246$	−49.1688	−3.13489
$247$	−11.3552	−0.722514
$248$	−27.4403	−1.74246
$249$	−2.67442	−0.169484
$250$	8.90924	0.563470
$251$	12.4636	0.786695	0.393348	−	0.919390i	$-0.371317\pi$
$251$	12.4636	0.786695	0.393348	+	0.919390i	$0.371317\pi$
$252$	13.7659	0.867171
$253$	13.6132	0.855856
$254$	−42.6350	−2.67515
$255$	−5.48124	−0.343249
$256$	−26.4763	−1.65477
$257$	−10.7138	−0.668311	−0.334155	−	0.942518i	$-0.608451\pi$
$257$	−10.7138	−0.668311	−0.334155	+	0.942518i	$0.608451\pi$
$258$	−1.81329	−0.112891
$259$	−6.63063	−0.412007
$260$	5.44368	0.337603
$261$	2.36529	0.146408
$262$	−24.0680	−1.48693
$263$	−11.1142	−0.685333	−0.342666	−	0.939457i	$-0.611330\pi$
$263$	−11.1142	−0.685333	−0.342666	+	0.939457i	$0.611330\pi$
$264$	−46.0061	−2.83148
$265$	−5.23890	−0.321823
$266$	25.3693	1.55549
$267$	31.9326	1.95424
$268$	−15.5583	−0.950374
$269$	−6.00551	−0.366163	−0.183081	−	0.983098i	$-0.558607\pi$
$269$	−6.00551	−0.366163	−0.183081	+	0.983098i	$0.558607\pi$
$270$	−3.58443	−0.218142
$271$	−21.0775	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$271$	−21.0775	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$272$	14.1701	0.859190
$273$	−29.1144	−1.76208
$274$	14.2723	0.862221
$275$	28.5763	1.72321
$276$	16.8903	1.01668
$277$	−1.28704	−0.0773304	−0.0386652	−	0.999252i	$-0.512311\pi$
$277$	−1.28704	−0.0773304	−0.0386652	+	0.999252i	$0.512311\pi$
$278$	−43.9181	−2.63403
$279$	7.20519	0.431363
$280$	−5.48103	−0.327554
$281$	28.1334	1.67830	0.839150	−	0.543900i	$-0.183053\pi$
$281$	28.1334	1.67830	0.839150	+	0.543900i	$0.183053\pi$
$282$	−2.92669	−0.174282
$283$	−13.5533	−0.805660	−0.402830	−	0.915275i	$-0.631973\pi$
$283$	−13.5533	−0.805660	−0.402830	+	0.915275i	$0.631973\pi$
$284$	11.5388	0.684703
$285$	2.20701	0.130732
$286$	54.9116	3.24699
$287$	−38.1385	−2.25125
$288$	3.17832	0.187284
$289$	34.5423	2.03190
$290$	−2.08970	−0.122712
$291$	13.9519	0.817876
$292$	58.2273	3.40750
$293$	−32.1762	−1.87975	−0.939877	−	0.341514i	$-0.889060\pi$
$293$	−32.1762	−1.87975	−0.939877	+	0.341514i	$0.889060\pi$
$294$	31.6992	1.84873
$295$	1.34156	0.0781088
$296$	6.99269	0.406442
$297$	−23.3371	−1.35416
$298$	35.0844	2.03238
$299$	−9.08539	−0.525422
$300$	35.4554	2.04702
$301$	−1.40651	−0.0810698
$302$	−44.7617	−2.57575
$303$	9.67328	0.555716
$304$	−5.70555	−0.327236
$305$	−3.96423	−0.226991
$306$	−17.4474	−0.997399
$307$	−20.1560	−1.15037	−0.575183	−	0.818025i	$-0.695069\pi$
$307$	−20.1560	−1.15037	−0.575183	+	0.818025i	$0.695069\pi$
$308$	−79.1831	−4.51188
$309$	6.40879	0.364583
$310$	−6.36570	−0.361547
$311$	−15.0129	−0.851305	−0.425652	−	0.904887i	$-0.639955\pi$
$311$	−15.0129	−0.851305	−0.425652	+	0.904887i	$0.639955\pi$
$312$	30.7042	1.73828
$313$	−3.96499	−0.224115	−0.112057	−	0.993702i	$-0.535744\pi$
$313$	−3.96499	−0.224115	−0.112057	+	0.993702i	$0.535744\pi$
$314$	10.8931	0.614731
$315$	1.43919	0.0810893
$316$	−2.50147	−0.140719
$317$	−1.50386	−0.0844654	−0.0422327	−	0.999108i	$-0.513447\pi$
$317$	−1.50386	−0.0844654	−0.0422327	+	0.999108i	$0.513447\pi$
$318$	−65.5675	−3.67684
$319$	−13.6054	−0.761757
$320$	−4.31056	−0.240968
$321$	25.9612	1.44901
$322$	20.2982	1.13117
$323$	−20.7534	−1.15475
$324$	−40.1313	−2.22952
$325$	−19.0716	−1.05790
$326$	−46.4437	−2.57228
$327$	17.8620	0.987770
$328$	40.2211	2.22084
$329$	−2.27013	−0.125156
$330$	−10.6727	−0.587511
$331$	−5.91314	−0.325016	−0.162508	−	0.986707i	$-0.551958\pi$
$331$	−5.91314	−0.325016	−0.162508	+	0.986707i	$0.551958\pi$
$332$	4.85440	0.266420
$333$	−1.83612	−0.100619
$334$	11.2675	0.616529
$335$	−1.62658	−0.0888697
$336$	−14.6289	−0.798071
$337$	−27.3405	−1.48933	−0.744667	−	0.667436i	$-0.767392\pi$
$337$	−27.3405	−1.48933	−0.744667	+	0.667436i	$0.767392\pi$
$338$	−5.77223	−0.313968
$339$	−24.1502	−1.31166
$340$	9.94916	0.539569
$341$	−41.4451	−2.24438
$342$	7.02513	0.379875
$343$	−1.27809	−0.0690101
$344$	1.48331	0.0799747
$345$	1.76584	0.0950699
$346$	7.65066	0.411302
$347$	34.5288	1.85360	0.926802	−	0.375551i	$-0.122546\pi$
$347$	34.5288	1.85360	0.926802	+	0.375551i	$0.122546\pi$
$348$	−16.8806	−0.904897
$349$	−27.4704	−1.47045	−0.735227	−	0.677821i	$-0.762925\pi$
$349$	−27.4704	−1.47045	−0.735227	+	0.677821i	$0.762925\pi$
$350$	42.6090	2.27755
$351$	15.5751	0.831336
$352$	−18.2820	−0.974436
$353$	25.7140	1.36862	0.684310	−	0.729192i	$-0.260104\pi$
$353$	25.7140	1.36862	0.684310	+	0.729192i	$0.260104\pi$
$354$	16.7903	0.892396
$355$	1.20636	0.0640268
$356$	−57.9617	−3.07196
$357$	−53.2111	−2.81623
$358$	18.6833	0.987442
$359$	−16.4347	−0.867392	−0.433696	−	0.901059i	$-0.642791\pi$
$359$	−16.4347	−0.867392	−0.433696	+	0.901059i	$0.642791\pi$
$360$	−1.51778	−0.0799940
$361$	−10.6437	−0.560196
$362$	26.3425	1.38453
$363$	−47.4226	−2.48904
$364$	52.8464	2.76990
$365$	6.08753	0.318636
$366$	−49.6144	−2.59339
$367$	−34.7485	−1.81385	−0.906927	−	0.421287i	$-0.861579\pi$
$367$	−34.7485	−1.81385	−0.906927	+	0.421287i	$0.861579\pi$
$368$	−4.56506	−0.237970
$369$	−10.5611	−0.549790
$370$	1.62219	0.0843336
$371$	−50.8584	−2.64044
$372$	−51.4222	−2.66611
$373$	10.8726	0.562964	0.281482	−	0.959567i	$-0.409174\pi$
$373$	10.8726	0.562964	0.281482	+	0.959567i	$0.409174\pi$
$374$	100.359	5.18946
$375$	7.52418	0.388547
$376$	2.39409	0.123466
$377$	9.08017	0.467653
$378$	−34.7971	−1.78977
$379$	1.96246	0.100805	0.0504025	−	0.998729i	$-0.483950\pi$
$379$	1.96246	0.100805	0.0504025	+	0.998729i	$0.483950\pi$
$380$	−4.00600	−0.205503
$381$	−36.0068	−1.84468
$382$	−36.9426	−1.89015
$383$	5.22298	0.266882	0.133441	−	0.991057i	$-0.457397\pi$
$383$	5.22298	0.266882	0.133441	+	0.991057i	$0.457397\pi$
$384$	−41.4883	−2.11719
$385$	−8.27841	−0.421907
$386$	−6.82074	−0.347166
$387$	−0.389483	−0.0197985
$388$	−25.3245	−1.28566
$389$	31.9841	1.62166	0.810828	−	0.585284i	$-0.199017\pi$
$389$	31.9841	1.62166	0.810828	+	0.585284i	$0.199017\pi$
$390$	7.12287	0.360681
$391$	−16.6049	−0.839748
$392$	−25.9306	−1.30969
$393$	−20.3263	−1.02533
$394$	45.8185	2.30830
$395$	−0.261522	−0.0131586
$396$	−21.9270	−1.10187
$397$	−7.56001	−0.379426	−0.189713	−	0.981840i	$-0.560756\pi$
$397$	−7.56001	−0.379426	−0.189713	+	0.981840i	$0.560756\pi$
$398$	−14.4111	−0.722365
$399$	21.4253	1.07260
$400$	−9.58277	−0.479139
$401$	0.217122	0.0108425	0.00542127	−	0.999985i	$-0.498274\pi$
$401$	0.217122	0.0108425	0.00542127	+	0.999985i	$0.498274\pi$
$402$	−20.3575	−1.01534
$403$	27.6602	1.37785
$404$	−17.5582	−0.873555
$405$	−4.19563	−0.208483
$406$	−20.2865	−1.00680
$407$	10.5616	0.523518
$408$	56.1166	2.77819
$409$	28.2700	1.39786	0.698931	−	0.715190i	$-0.253660\pi$
$409$	28.2700	1.39786	0.698931	+	0.715190i	$0.253660\pi$
$410$	9.33063	0.460807
$411$	12.0535	0.594554
$412$	−11.6328	−0.573105
$413$	13.0237	0.640853
$414$	5.62086	0.276250
$415$	0.507516	0.0249130
$416$	12.2013	0.598220
$417$	−37.0904	−1.81632
$418$	−40.4094	−1.97649
$419$	−15.1265	−0.738977	−0.369488	−	0.929235i	$-0.620467\pi$
$419$	−15.1265	−0.738977	−0.369488	+	0.929235i	$0.620467\pi$
$420$	−10.2713	−0.501187
$421$	28.5594	1.39190	0.695951	−	0.718089i	$-0.254983\pi$
$421$	28.5594	1.39190	0.695951	+	0.718089i	$0.254983\pi$
$422$	−18.8534	−0.917768
$423$	−0.628633	−0.0305652
$424$	53.6355	2.60477
$425$	−34.8563	−1.69078
$426$	15.0982	0.731509
$427$	−38.4842	−1.86238
$428$	−47.1229	−2.27777
$429$	46.3748	2.23900
$430$	0.344104	0.0165942
$431$	3.70488	0.178458	0.0892288	−	0.996011i	$-0.471560\pi$
$431$	3.70488	0.178458	0.0892288	+	0.996011i	$0.471560\pi$
$432$	7.82588	0.376523
$433$	−2.36927	−0.113860	−0.0569298	−	0.998378i	$-0.518131\pi$
$433$	−2.36927	−0.113860	−0.0569298	+	0.998378i	$0.518131\pi$
$434$	−61.7972	−2.96636
$435$	−1.76483	−0.0846171
$436$	−32.4218	−1.55272
$437$	6.68593	0.319831
$438$	76.1885	3.64043
$439$	−31.7571	−1.51568	−0.757842	−	0.652439i	$-0.773746\pi$
$439$	−31.7571	−1.51568	−0.757842	+	0.652439i	$0.773746\pi$
$440$	8.73045	0.416208
$441$	6.80877	0.324227
$442$	−66.9792	−3.18588
$443$	7.81652	0.371374	0.185687	−	0.982609i	$-0.440549\pi$
$443$	7.81652	0.371374	0.185687	+	0.982609i	$0.440549\pi$
$444$	13.1041	0.621891
$445$	−6.05975	−0.287260
$446$	−43.0788	−2.03984
$447$	29.6300	1.40145
$448$	−41.8462	−1.97705
$449$	8.42855	0.397768	0.198884	−	0.980023i	$-0.436268\pi$
$449$	8.42855	0.397768	0.198884	+	0.980023i	$0.436268\pi$
$450$	11.7991	0.556213
$451$	60.7488	2.86055
$452$	43.8357	2.06186
$453$	−37.8029	−1.77613
$454$	−31.8168	−1.49324
$455$	5.52496	0.259014
$456$	−22.5952	−1.05812
$457$	5.75154	0.269045	0.134523	−	0.990911i	$-0.457050\pi$
$457$	5.75154	0.269045	0.134523	+	0.990911i	$0.457050\pi$
$458$	−4.94837	−0.231222
$459$	28.4658	1.32867
$460$	−3.20523	−0.149445
$461$	18.8788	0.879275	0.439638	−	0.898175i	$-0.355107\pi$
$461$	18.8788	0.879275	0.439638	+	0.898175i	$0.355107\pi$
$462$	−103.609	−4.82030
$463$	−26.3522	−1.22469	−0.612345	−	0.790591i	$-0.709774\pi$
$463$	−26.3522	−1.22469	−0.612345	+	0.790591i	$0.709774\pi$
$464$	4.56244	0.211806
$465$	−5.37606	−0.249309
$466$	20.3603	0.943172
$467$	−5.34430	−0.247305	−0.123652	−	0.992326i	$-0.539461\pi$
$467$	−5.34430	−0.247305	−0.123652	+	0.992326i	$0.539461\pi$
$468$	14.6339	0.676454
$469$	−15.7906	−0.729142
$470$	0.555390	0.0256182
$471$	9.19958	0.423894
$472$	−13.7348	−0.632196
$473$	2.24035	0.103011
$474$	−3.27309	−0.150338
$475$	14.0348	0.643960
$476$	96.5848	4.42696
$477$	−14.0834	−0.644836
$478$	29.8010	1.36306
$479$	−8.53830	−0.390125	−0.195062	−	0.980791i	$-0.562491\pi$
$479$	−8.53830	−0.390125	−0.195062	+	0.980791i	$0.562491\pi$
$480$	−2.37146	−0.108242
$481$	−7.04873	−0.321395
$482$	38.3857	1.74842
$483$	17.1425	0.780013
$484$	86.0780	3.91263
$485$	−2.64762	−0.120222
$486$	−24.2595	−1.10043
$487$	−18.1447	−0.822214	−0.411107	−	0.911587i	$-0.634858\pi$
$487$	−18.1447	−0.822214	−0.411107	+	0.911587i	$0.634858\pi$
$488$	40.5856	1.83722
$489$	−39.2233	−1.77374
$490$	−6.01547	−0.271751
$491$	−11.7271	−0.529237	−0.264619	−	0.964353i	$-0.585246\pi$
$491$	−11.7271	−0.529237	−0.264619	+	0.964353i	$0.585246\pi$
$492$	75.3729	3.39807
$493$	16.5954	0.747419
$494$	26.9690	1.21339
$495$	−2.29241	−0.103036
$496$	13.8982	0.624048
$497$	11.7111	0.525316
$498$	6.35183	0.284632
$499$	5.05800	0.226427	0.113214	−	0.993571i	$-0.463886\pi$
$499$	5.05800	0.226427	0.113214	+	0.993571i	$0.463886\pi$
$500$	−13.6573	−0.610775
$501$	9.51580	0.425135
$502$	−29.6015	−1.32118
$503$	6.50916	0.290229	0.145114	−	0.989415i	$-0.453645\pi$
$503$	6.50916	0.290229	0.145114	+	0.989415i	$0.453645\pi$
$504$	−14.7344	−0.656321
$505$	−1.83567	−0.0816863
$506$	−32.3319	−1.43733
$507$	−4.87486	−0.216500
$508$	65.3568	2.89974
$509$	−18.8379	−0.834973	−0.417487	−	0.908683i	$-0.637089\pi$
$509$	−18.8379	−0.834973	−0.417487	+	0.908683i	$0.637089\pi$
$510$	13.0181	0.576453
$511$	59.0967	2.61429
$512$	21.5138	0.950783
$513$	−11.4617	−0.506045
$514$	25.4457	1.12236
$515$	−1.21618	−0.0535912
$516$	2.77967	0.122368
$517$	3.61597	0.159030
$518$	15.7480	0.691926
$519$	6.46126	0.283618
$520$	−5.82665	−0.255516
$521$	−16.2888	−0.713625	−0.356813	−	0.934176i	$-0.616137\pi$
$521$	−16.2888	−0.713625	−0.356813	+	0.934176i	$0.616137\pi$
$522$	−5.61764	−0.245877
$523$	0.970548	0.0424391	0.0212196	−	0.999775i	$-0.493245\pi$
$523$	0.970548	0.0424391	0.0212196	+	0.999775i	$0.493245\pi$
$524$	36.8948	1.61176
$525$	35.9848	1.57051
$526$	26.3967	1.15095
$527$	50.5533	2.20213
$528$	23.3016	1.01407
$529$	−17.6505	−0.767414
$530$	12.4426	0.540470
$531$	3.60645	0.156506
$532$	−38.8896	−1.68608
$533$	−40.5434	−1.75613
$534$	−75.8409	−3.28196
$535$	−4.92658	−0.212995
$536$	16.6528	0.719293
$537$	15.7787	0.680901
$538$	14.2633	0.614935
$539$	−39.1648	−1.68695
$540$	5.49472	0.236455
$541$	−30.0294	−1.29106	−0.645532	−	0.763733i	$-0.723364\pi$
$541$	−30.0294	−1.29106	−0.645532	+	0.763733i	$0.723364\pi$
$542$	50.0598	2.15025
$543$	22.2472	0.954719
$544$	22.2998	0.956096
$545$	−3.38962	−0.145195
$546$	69.1477	2.95925
$547$	−36.1310	−1.54485	−0.772425	−	0.635105i	$-0.780957\pi$
$547$	−36.1310	−1.54485	−0.772425	+	0.635105i	$0.780957\pi$
$548$	−21.8786	−0.934607
$549$	−10.6568	−0.454823
$550$	−67.8696	−2.89397
$551$	−6.68209	−0.284666
$552$	−18.0786	−0.769476
$553$	−2.53882	−0.107962
$554$	3.05675	0.129869
$555$	1.37000	0.0581532
$556$	67.3238	2.85516
$557$	−5.65590	−0.239648	−0.119824	−	0.992795i	$-0.538233\pi$
$557$	−5.65590	−0.239648	−0.119824	+	0.992795i	$0.538233\pi$
$558$	−17.1126	−0.724432
$559$	−1.49520	−0.0632401
$560$	2.77608	0.117311
$561$	84.7570	3.57845
$562$	−66.8178	−2.81854
$563$	−23.4781	−0.989483	−0.494742	−	0.869040i	$-0.664737\pi$
$563$	−23.4781	−0.989483	−0.494742	+	0.869040i	$0.664737\pi$
$564$	4.48644	0.188913
$565$	4.58291	0.192805
$566$	32.1896	1.35303
$567$	−40.7305	−1.71052
$568$	−12.3506	−0.518220
$569$	−35.4718	−1.48705	−0.743527	−	0.668706i	$-0.766848\pi$
$569$	−35.4718	−1.48705	−0.743527	+	0.668706i	$0.766848\pi$
$570$	−5.24171	−0.219551
$571$	4.91958	0.205878	0.102939	−	0.994688i	$-0.467175\pi$
$571$	4.91958	0.205878	0.102939	+	0.994688i	$0.467175\pi$
$572$	−84.1762	−3.51958
$573$	−31.1994	−1.30337
$574$	90.5803	3.78075
$575$	11.2294	0.468297
$576$	−11.5878	−0.482827
$577$	−12.4617	−0.518786	−0.259393	−	0.965772i	$-0.583522\pi$
$577$	−12.4617	−0.518786	−0.259393	+	0.965772i	$0.583522\pi$
$578$	−82.0392	−3.41238
$579$	−5.76036	−0.239392
$580$	3.20339	0.133014
$581$	4.92689	0.204402
$582$	−33.1363	−1.37354
$583$	81.0096	3.35508
$584$	−62.3237	−2.57897
$585$	1.52994	0.0632554
$586$	76.4196	3.15686
$587$	14.9059	0.615233	0.307617	−	0.951510i	$-0.400469\pi$
$587$	14.9059	0.615233	0.307617	+	0.951510i	$0.400469\pi$
$588$	−48.5930	−2.00394
$589$	−20.3551	−0.838718
$590$	−3.18625	−0.131176
$591$	38.6954	1.59172
$592$	−3.54172	−0.145564
$593$	15.4188	0.633174	0.316587	−	0.948564i	$-0.397463\pi$
$593$	15.4188	0.633174	0.316587	+	0.948564i	$0.397463\pi$
$594$	55.4265	2.27418
$595$	10.0977	0.413966
$596$	−53.7822	−2.20301
$597$	−12.1707	−0.498114
$598$	21.5781	0.882394
$599$	18.7977	0.768055	0.384028	−	0.923322i	$-0.374537\pi$
$599$	18.7977	0.768055	0.384028	+	0.923322i	$0.374537\pi$
$600$	−37.9498	−1.54929
$601$	−39.1535	−1.59711	−0.798553	−	0.601925i	$-0.794401\pi$
$601$	−39.1535	−1.59711	−0.798553	+	0.601925i	$0.794401\pi$
$602$	3.34050	0.136149
$603$	−4.37265	−0.178068
$604$	68.6170	2.79199
$605$	8.99924	0.365871
$606$	−22.9744	−0.933270
$607$	−27.3324	−1.10939	−0.554694	−	0.832055i	$-0.687165\pi$
$607$	−27.3324	−1.10939	−0.554694	+	0.832055i	$0.687165\pi$
$608$	−8.97894	−0.364144
$609$	−17.1327	−0.694252
$610$	9.41519	0.381210
$611$	−2.41328	−0.0976308
$612$	26.7458	1.08113
$613$	46.8361	1.89169	0.945847	−	0.324613i	$-0.105234\pi$
$613$	46.8361	1.89169	0.945847	+	0.324613i	$0.105234\pi$
$614$	47.8713	1.93193
$615$	7.88006	0.317755
$616$	84.7538	3.41483
$617$	3.40628	0.137132	0.0685658	−	0.997647i	$-0.478158\pi$
$617$	3.40628	0.137132	0.0685658	+	0.997647i	$0.478158\pi$
$618$	−15.2211	−0.612282
$619$	19.2512	0.773771	0.386885	−	0.922128i	$-0.373551\pi$
$619$	19.2512	0.773771	0.386885	+	0.922128i	$0.373551\pi$
$620$	9.75824	0.391900
$621$	−9.17058	−0.368003
$622$	35.6562	1.42968
$623$	−58.8271	−2.35686
$624$	−15.5513	−0.622552
$625$	22.8477	0.913910
$626$	9.41699	0.376378
$627$	−34.1272	−1.36291
$628$	−16.6984	−0.666339
$629$	−12.8826	−0.513664
$630$	−3.41813	−0.136182
$631$	−22.0229	−0.876719	−0.438359	−	0.898800i	$-0.644440\pi$
$631$	−22.0229	−0.876719	−0.438359	+	0.898800i	$0.644440\pi$
$632$	2.67745	0.106503
$633$	−15.9224	−0.632857
$634$	3.57173	0.141851
$635$	6.83290	0.271155
$636$	100.511	3.98552
$637$	26.1384	1.03564
$638$	32.3133	1.27930
$639$	3.24298	0.128290
$640$	7.87313	0.311213
$641$	42.4663	1.67732	0.838659	−	0.544657i	$-0.183340\pi$
$641$	42.4663	1.67732	0.838659	+	0.544657i	$0.183340\pi$
$642$	−61.6587	−2.43348
$643$	−28.4350	−1.12137	−0.560684	−	0.828030i	$-0.689462\pi$
$643$	−28.4350	−1.12137	−0.560684	+	0.828030i	$0.689462\pi$
$644$	−31.1159	−1.22614
$645$	0.290608	0.0114427
$646$	49.2899	1.93929
$647$	−35.4993	−1.39562	−0.697811	−	0.716282i	$-0.745842\pi$
$647$	−35.4993	−1.39562	−0.697811	+	0.716282i	$0.745842\pi$
$648$	42.9546	1.68742
$649$	−20.7447	−0.814301
$650$	45.2958	1.77665
$651$	−52.1900	−2.04549
$652$	71.1954	2.78823
$653$	6.46573	0.253024	0.126512	−	0.991965i	$-0.459622\pi$
$653$	6.46573	0.253024	0.126512	+	0.991965i	$0.459622\pi$
$654$	−42.4228	−1.65886
$655$	3.85727	0.150716
$656$	−20.3715	−0.795375
$657$	16.3648	0.638450
$658$	5.39164	0.210188
$659$	−27.0816	−1.05495	−0.527475	−	0.849570i	$-0.676861\pi$
$659$	−27.0816	−1.05495	−0.527475	+	0.849570i	$0.676861\pi$
$660$	16.3606	0.636834
$661$	32.3165	1.25696	0.628482	−	0.777824i	$-0.283677\pi$
$661$	32.3165	1.25696	0.628482	+	0.777824i	$0.283677\pi$
$662$	14.0439	0.545832
$663$	−56.5664	−2.19686
$664$	−5.19592	−0.201641
$665$	−4.06581	−0.157665
$666$	4.36084	0.168979
$667$	−5.34640	−0.207013
$668$	−17.2724	−0.668289
$669$	−36.3816	−1.40659
$670$	3.86319	0.149248
$671$	61.2994	2.36644
$672$	−23.0218	−0.888084
$673$	−4.43995	−0.171148	−0.0855738	−	0.996332i	$-0.527272\pi$
$673$	−4.43995	−0.171148	−0.0855738	+	0.996332i	$0.527272\pi$
$674$	64.9347	2.50119
$675$	−19.2505	−0.740951
$676$	8.84849	0.340326
$677$	31.8338	1.22347	0.611735	−	0.791063i	$-0.290472\pi$
$677$	31.8338	1.22347	0.611735	+	0.791063i	$0.290472\pi$
$678$	57.3575	2.20280
$679$	−25.7026	−0.986377
$680$	−10.6491	−0.408374
$681$	−26.8705	−1.02968
$682$	98.4335	3.76921
$683$	−29.9231	−1.14497	−0.572487	−	0.819914i	$-0.694021\pi$
$683$	−29.9231	−1.14497	−0.572487	+	0.819914i	$0.694021\pi$
$684$	−10.7691	−0.411767
$685$	−2.28735	−0.0873953
$686$	3.03550	0.115896
$687$	−4.17908	−0.159442
$688$	−0.751280	−0.0286423
$689$	−54.0654	−2.05973
$690$	−4.19394	−0.159661
$691$	−44.5569	−1.69503	−0.847513	−	0.530775i	$-0.821901\pi$
$691$	−44.5569	−1.69503	−0.847513	+	0.530775i	$0.821901\pi$
$692$	−11.7280	−0.445832
$693$	−22.2544	−0.845374
$694$	−82.0071	−3.11295
$695$	7.03854	0.266987
$696$	18.0682	0.684874
$697$	−74.0993	−2.80671
$698$	65.2430	2.46948
$699$	17.1950	0.650374
$700$	−65.3171	−2.46875
$701$	−28.4049	−1.07284	−0.536420	−	0.843951i	$-0.680224\pi$
$701$	−28.4049	−1.07284	−0.536420	+	0.843951i	$0.680224\pi$
$702$	−36.9913	−1.39615
$703$	5.18715	0.195637
$704$	66.6546	2.51214
$705$	0.469047	0.0176653
$706$	−61.0717	−2.29846
$707$	−17.8204	−0.670206
$708$	−25.7386	−0.967315
$709$	−46.0109	−1.72798	−0.863989	−	0.503511i	$-0.832041\pi$
$709$	−46.0109	−1.72798	−0.863989	+	0.503511i	$0.832041\pi$
$710$	−2.86514	−0.107527
$711$	−0.703036	−0.0263659
$712$	62.0394	2.32502
$713$	−16.2863	−0.609927
$714$	126.378	4.72958
$715$	−8.80042	−0.329117
$716$	−28.6404	−1.07034
$717$	25.1680	0.939916
$718$	39.0330	1.45670
$719$	13.5356	0.504794	0.252397	−	0.967624i	$-0.418781\pi$
$719$	13.5356	0.504794	0.252397	+	0.967624i	$0.418781\pi$
$720$	0.768739	0.0286492
$721$	−11.8065	−0.439696
$722$	25.2792	0.940795
$723$	32.4181	1.20564
$724$	−40.3815	−1.50077
$725$	−11.2229	−0.416808
$726$	112.630	4.18010
$727$	46.0232	1.70691	0.853453	−	0.521169i	$-0.174504\pi$
$727$	46.0232	1.70691	0.853453	+	0.521169i	$0.174504\pi$
$728$	−56.5642	−2.09641
$729$	12.5801	0.465928
$730$	−14.4581	−0.535118
$731$	−2.73270	−0.101073
$732$	76.0560	2.81111
$733$	−26.8089	−0.990210	−0.495105	−	0.868833i	$-0.664870\pi$
$733$	−26.8089	−0.990210	−0.495105	+	0.868833i	$0.664870\pi$
$734$	82.5288	3.04619
$735$	−5.08028	−0.187389
$736$	−7.18413	−0.264811
$737$	25.1520	0.926486
$738$	25.0830	0.923319
$739$	−30.0325	−1.10476	−0.552381	−	0.833592i	$-0.686281\pi$
$739$	−30.0325	−1.10476	−0.552381	+	0.833592i	$0.686281\pi$
$740$	−2.48672	−0.0914137
$741$	22.7763	0.836707
$742$	120.790	4.43435
$743$	42.5036	1.55931	0.779653	−	0.626211i	$-0.215395\pi$
$743$	42.5036	1.55931	0.779653	+	0.626211i	$0.215395\pi$
$744$	55.0398	2.01786
$745$	−5.62280	−0.206004
$746$	−25.8229	−0.945443
$747$	1.36433	0.0499182
$748$	−153.845	−5.62512
$749$	−47.8265	−1.74754
$750$	−17.8702	−0.652526
$751$	1.51702	0.0553568	0.0276784	−	0.999617i	$-0.491189\pi$
$751$	1.51702	0.0553568	0.0276784	+	0.999617i	$0.491189\pi$
$752$	−1.21258	−0.0442183
$753$	−24.9995	−0.911033
$754$	−21.5657	−0.785377
$755$	7.17374	0.261079
$756$	53.3419	1.94003
$757$	−20.9129	−0.760093	−0.380046	−	0.924967i	$-0.624092\pi$
$757$	−20.9129	−0.760093	−0.380046	+	0.924967i	$0.624092\pi$
$758$	−4.66091	−0.169292
$759$	−27.3054	−0.991125
$760$	4.28782	0.155536
$761$	−11.5739	−0.419555	−0.209778	−	0.977749i	$-0.567274\pi$
$761$	−11.5739	−0.419555	−0.209778	+	0.977749i	$0.567274\pi$
$762$	85.5173	3.09796
$763$	−32.9059	−1.19127
$764$	56.6309	2.04883
$765$	2.79621	0.101097
$766$	−12.4048	−0.448202
$767$	13.8449	0.499910
$768$	53.1062	1.91631
$769$	18.2768	0.659078	0.329539	−	0.944142i	$-0.393107\pi$
$769$	18.2768	0.659078	0.329539	+	0.944142i	$0.393107\pi$
$770$	19.6615	0.708551
$771$	21.4898	0.773938
$772$	10.4558	0.376312
$773$	−6.03388	−0.217024	−0.108512	−	0.994095i	$-0.534609\pi$
$773$	−6.03388	−0.217024	−0.108512	+	0.994095i	$0.534609\pi$
$774$	0.925035	0.0332497
$775$	−34.1875	−1.22805
$776$	27.1061	0.973053
$777$	13.2997	0.477125
$778$	−75.9633	−2.72341
$779$	29.8359	1.06898
$780$	−10.9189	−0.390961
$781$	−18.6540	−0.667493
$782$	39.4373	1.41027
$783$	9.16532	0.327542
$784$	13.1335	0.469055
$785$	−1.74578	−0.0623095
$786$	48.2757	1.72194
$787$	47.1506	1.68074	0.840368	−	0.542016i	$-0.182339\pi$
$787$	47.1506	1.68074	0.840368	+	0.542016i	$0.182339\pi$
$788$	−70.2371	−2.50209
$789$	22.2929	0.793650
$790$	0.621125	0.0220986
$791$	44.4902	1.58189
$792$	23.4696	0.833955
$793$	−40.9109	−1.45279
$794$	17.9553	0.637209
$795$	10.5082	0.372687
$796$	22.0914	0.783009
$797$	−2.01393	−0.0713370	−0.0356685	−	0.999364i	$-0.511356\pi$
$797$	−2.01393	−0.0713370	−0.0356685	+	0.999364i	$0.511356\pi$
$798$	−50.8857	−1.80133
$799$	−4.41063	−0.156037
$800$	−15.0806	−0.533180
$801$	−16.2901	−0.575582
$802$	−0.515671	−0.0182090
$803$	−94.1320	−3.32185
$804$	31.2069	1.10058
$805$	−3.25309	−0.114656
$806$	−65.6939	−2.31397
$807$	12.0459	0.424035
$808$	18.7935	0.661153
$809$	−14.9044	−0.524011	−0.262005	−	0.965066i	$-0.584384\pi$
$809$	−14.9044	−0.524011	−0.262005	+	0.965066i	$0.584384\pi$
$810$	9.96476	0.350126
$811$	25.5094	0.895755	0.447877	−	0.894095i	$-0.352180\pi$
$811$	25.5094	0.895755	0.447877	+	0.894095i	$0.352180\pi$
$812$	31.0980	1.09133
$813$	42.2773	1.48273
$814$	−25.0841	−0.879197
$815$	7.44330	0.260728
$816$	−28.4224	−0.994985
$817$	1.10031	0.0384951
$818$	−67.1422	−2.34757
$819$	14.8525	0.518987
$820$	−14.3033	−0.499493
$821$	−33.6747	−1.17525	−0.587627	−	0.809132i	$-0.699938\pi$
$821$	−33.6747	−1.17525	−0.587627	+	0.809132i	$0.699938\pi$
$822$	−28.6274	−0.998496
$823$	−27.2548	−0.950044	−0.475022	−	0.879974i	$-0.657560\pi$
$823$	−27.2548	−0.950044	−0.475022	+	0.879974i	$0.657560\pi$
$824$	12.4511	0.433756
$825$	−57.3183	−1.99557
$826$	−30.9317	−1.07625
$827$	−35.5275	−1.23541	−0.617706	−	0.786409i	$-0.711938\pi$
$827$	−35.5275	−1.23541	−0.617706	+	0.786409i	$0.711938\pi$
$828$	−8.61645	−0.299442
$829$	−3.82252	−0.132762	−0.0663808	−	0.997794i	$-0.521145\pi$
$829$	−3.82252	−0.132762	−0.0663808	+	0.997794i	$0.521145\pi$
$830$	−1.20537	−0.0418389
$831$	2.58154	0.0895525
$832$	−44.4849	−1.54224
$833$	47.7719	1.65520
$834$	88.0909	3.05034
$835$	−1.80579	−0.0624918
$836$	61.9451	2.14242
$837$	27.9196	0.965042
$838$	35.9259	1.24104
$839$	−34.3715	−1.18664	−0.593318	−	0.804968i	$-0.702182\pi$
$839$	−34.3715	−1.18664	−0.593318	+	0.804968i	$0.702182\pi$
$840$	10.9939	0.379325
$841$	−23.6567	−0.815747
$842$	−67.8297	−2.33756
$843$	−56.4301	−1.94356
$844$	28.9011	0.994817
$845$	0.925088	0.0318240
$846$	1.49302	0.0513312
$847$	87.3632	3.00184
$848$	−27.1658	−0.932877
$849$	27.1852	0.932995
$850$	82.7850	2.83950
$851$	4.15029	0.142270
$852$	−23.1446	−0.792921
$853$	−3.79283	−0.129864	−0.0649320	−	0.997890i	$-0.520683\pi$
$853$	−3.79283	−0.129864	−0.0649320	+	0.997890i	$0.520683\pi$
$854$	91.4012	3.12768
$855$	−1.12588	−0.0385044
$856$	50.4380	1.72394
$857$	31.5703	1.07842	0.539211	−	0.842171i	$-0.318722\pi$
$857$	31.5703	1.07842	0.539211	+	0.842171i	$0.318722\pi$
$858$	−110.142	−3.76018
$859$	−25.6617	−0.875565	−0.437783	−	0.899081i	$-0.644236\pi$
$859$	−25.6617	−0.875565	−0.437783	+	0.899081i	$0.644236\pi$
$860$	−0.527491	−0.0179873
$861$	76.4983	2.60706
$862$	−8.79920	−0.299702
$863$	23.5739	0.802463	0.401232	−	0.915977i	$-0.368582\pi$
$863$	23.5739	0.802463	0.401232	+	0.915977i	$0.368582\pi$
$864$	12.3157	0.418990
$865$	−1.22614	−0.0416899
$866$	5.62708	0.191216
$867$	−69.2850	−2.35304
$868$	94.7314	3.21539
$869$	4.04395	0.137182
$870$	4.19153	0.142106
$871$	−16.7863	−0.568782
$872$	34.7027	1.17518
$873$	−7.11744	−0.240889
$874$	−15.8793	−0.537125
$875$	−13.8613	−0.468596
$876$	−116.792	−3.94605
$877$	22.1962	0.749512	0.374756	−	0.927124i	$-0.377727\pi$
$877$	22.1962	0.749512	0.374756	+	0.927124i	$0.377727\pi$
$878$	75.4242	2.54544
$879$	64.5391	2.17685
$880$	−4.42187	−0.149061
$881$	30.3799	1.02352	0.511762	−	0.859127i	$-0.328993\pi$
$881$	30.3799	1.02352	0.511762	+	0.859127i	$0.328993\pi$
$882$	−16.1711	−0.544508
$883$	−18.2820	−0.615239	−0.307620	−	0.951509i	$-0.599532\pi$
$883$	−18.2820	−0.615239	−0.307620	+	0.951509i	$0.599532\pi$
$884$	102.675	3.45334
$885$	−2.69091	−0.0904539
$886$	−18.5645	−0.623687
$887$	−47.2954	−1.58803	−0.794013	−	0.607901i	$-0.792012\pi$
$887$	−47.2954	−1.58803	−0.794013	+	0.607901i	$0.792012\pi$
$888$	−14.0259	−0.470680
$889$	66.3327	2.22473
$890$	14.3921	0.482425
$891$	64.8775	2.17348
$892$	66.0373	2.21109
$893$	1.77593	0.0594292
$894$	−70.3723	−2.35360
$895$	−2.99428	−0.100088
$896$	76.4311	2.55338
$897$	18.2235	0.608465
$898$	−20.0181	−0.668013
$899$	16.2769	0.542867
$900$	−18.0873	−0.602909
$901$	−98.8127	−3.29193
$902$	−144.281	−4.80402
$903$	2.82118	0.0938829
$904$	−46.9196	−1.56052
$905$	−4.22179	−0.140337
$906$	89.7831	2.98284
$907$	54.8948	1.82275	0.911376	−	0.411574i	$-0.135021\pi$
$907$	54.8948	1.82275	0.911376	+	0.411574i	$0.135021\pi$
$908$	48.7733	1.61860
$909$	−4.93474	−0.163675
$910$	−13.1220	−0.434989
$911$	3.34925	0.110966	0.0554829	−	0.998460i	$-0.482330\pi$
$911$	3.34925	0.110966	0.0554829	+	0.998460i	$0.482330\pi$
$912$	11.4442	0.378956
$913$	−7.84778	−0.259724
$914$	−13.6601	−0.451836
$915$	7.95147	0.262867
$916$	7.58556	0.250634
$917$	37.4457	1.23657
$918$	−67.6073	−2.23137
$919$	−4.45987	−0.147118	−0.0735588	−	0.997291i	$-0.523436\pi$
$919$	−4.45987	−0.147118	−0.0735588	+	0.997291i	$0.523436\pi$
$920$	3.43073	0.113108
$921$	40.4290	1.33218
$922$	−44.8379	−1.47666
$923$	12.4496	0.409783
$924$	158.826	5.22498
$925$	8.71209	0.286452
$926$	62.5873	2.05675
$927$	−3.26938	−0.107381
$928$	7.18001	0.235695
$929$	−41.8654	−1.37356	−0.686779	−	0.726866i	$-0.740976\pi$
$929$	−41.8654	−1.37356	−0.686779	+	0.726866i	$0.740976\pi$
$930$	12.7683	0.418690
$931$	−19.2352	−0.630408
$932$	−31.2111	−1.02235
$933$	30.1129	0.985854
$934$	12.6929	0.415324
$935$	−16.0841	−0.526007
$936$	−15.6635	−0.511976
$937$	−30.1671	−0.985516	−0.492758	−	0.870166i	$-0.664011\pi$
$937$	−30.1671	−0.985516	−0.492758	+	0.870166i	$0.664011\pi$
$938$	37.5032	1.22452
$939$	7.95299	0.259536
$940$	−0.851380	−0.0277689
$941$	−27.5051	−0.896641	−0.448321	−	0.893873i	$-0.647978\pi$
$941$	−27.5051	−0.896641	−0.448321	+	0.893873i	$0.647978\pi$
$942$	−21.8493	−0.711889
$943$	23.8719	0.777377
$944$	6.95654	0.226416
$945$	5.57677	0.181412
$946$	−5.32091	−0.172998
$947$	−41.3422	−1.34344	−0.671721	−	0.740804i	$-0.734445\pi$
$947$	−41.3422	−1.34344	−0.671721	+	0.740804i	$0.734445\pi$
$948$	5.01745	0.162959
$949$	62.8232	2.03933
$950$	−33.3331	−1.08147
$951$	3.01645	0.0978152
$952$	−103.380	−3.35056
$953$	−10.6417	−0.344720	−0.172360	−	0.985034i	$-0.555139\pi$
$953$	−10.6417	−0.344720	−0.172360	+	0.985034i	$0.555139\pi$
$954$	33.4486	1.08294
$955$	5.92062	0.191587
$956$	−45.6831	−1.47750
$957$	27.2898	0.882152
$958$	20.2787	0.655176
$959$	−22.2053	−0.717046
$960$	8.64613	0.279053
$961$	18.5832	0.599457
$962$	16.7410	0.539751
$963$	−13.2439	−0.426778
$964$	−58.8430	−1.89520
$965$	1.09313	0.0351890
$966$	−40.7141	−1.30995
$967$	−19.8862	−0.639497	−0.319749	−	0.947502i	$-0.603598\pi$
$967$	−19.8862	−0.639497	−0.319749	+	0.947502i	$0.603598\pi$
$968$	−92.1337	−2.96129
$969$	41.6271	1.33726
$970$	6.28818	0.201901
$971$	8.81261	0.282810	0.141405	−	0.989952i	$-0.454838\pi$
$971$	8.81261	0.282810	0.141405	+	0.989952i	$0.454838\pi$
$972$	37.1884	1.19282
$973$	68.3290	2.19053
$974$	43.0942	1.38083
$975$	38.2539	1.22511
$976$	−20.5561	−0.657986
$977$	22.4435	0.718031	0.359015	−	0.933332i	$-0.383113\pi$
$977$	22.4435	0.718031	0.359015	+	0.933332i	$0.383113\pi$
$978$	93.1568	2.97883
$979$	93.7026	2.99475
$980$	9.22135	0.294565
$981$	−9.11213	−0.290928
$982$	27.8523	0.888802
$983$	46.5258	1.48394	0.741971	−	0.670432i	$-0.233891\pi$
$983$	46.5258	1.48394	0.741971	+	0.670432i	$0.233891\pi$
$984$	−80.6755	−2.57184
$985$	−7.34312	−0.233971
$986$	−39.4146	−1.25522
$987$	4.55343	0.144937
$988$	−41.3418	−1.31526
$989$	0.880371	0.0279942
$990$	5.44456	0.173039
$991$	−6.35525	−0.201881	−0.100941	−	0.994892i	$-0.532185\pi$
$991$	−6.35525	−0.201881	−0.100941	+	0.994892i	$0.532185\pi$
$992$	21.8719	0.694433
$993$	11.8606	0.376385
$994$	−27.8143	−0.882216
$995$	2.30960	0.0732193
$996$	−9.73697	−0.308528
$997$	−26.0743	−0.825780	−0.412890	−	0.910781i	$-0.635481\pi$
$997$	−26.0743	−0.825780	−0.412890	+	0.910781i	$0.635481\pi$
$998$	−12.0129	−0.380262
$999$	−7.11483	−0.225103

Introduction	Features
Universe	News

Level:	\( N \)	=	\( 4003 \)
Weight:	\( k \)	=	\( 2 \)
Character orbit:	\([\chi]\)	=	4003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.37503 q^{2} -2.00580 q^{3} +3.64079 q^{4} +0.380635 q^{5} +4.76385 q^{6} +3.69515 q^{7} -3.89692 q^{8} +1.02324 q^{9} +O(q^{10})\)	\(q-2.37503 q^{2} -2.00580 q^{3} +3.64079 q^{4} +0.380635 q^{5} +4.76385 q^{6} +3.69515 q^{7} -3.89692 q^{8} +1.02324 q^{9} -0.904022 q^{10} -5.88580 q^{11} -7.30269 q^{12} +3.92815 q^{13} -8.77610 q^{14} -0.763479 q^{15} +1.97375 q^{16} +7.17930 q^{17} -2.43023 q^{18} -2.89072 q^{19} +1.38581 q^{20} -7.41173 q^{21} +13.9790 q^{22} -2.31289 q^{23} +7.81645 q^{24} -4.85512 q^{25} -9.32949 q^{26} +3.96499 q^{27} +13.4532 q^{28} +2.31156 q^{29} +1.81329 q^{30} +7.04153 q^{31} +3.10613 q^{32} +11.8058 q^{33} -17.0511 q^{34} +1.40650 q^{35} +3.72540 q^{36} -1.79441 q^{37} +6.86556 q^{38} -7.87909 q^{39} -1.48331 q^{40} -10.3212 q^{41} +17.6031 q^{42} -0.380637 q^{43} -21.4289 q^{44} +0.389482 q^{45} +5.49320 q^{46} -0.614354 q^{47} -3.95895 q^{48} +6.65412 q^{49} +11.5311 q^{50} -14.4002 q^{51} +14.3016 q^{52} -13.7636 q^{53} -9.41698 q^{54} -2.24035 q^{55} -14.3997 q^{56} +5.79822 q^{57} -5.49004 q^{58} +3.52453 q^{59} -2.77966 q^{60} -10.4148 q^{61} -16.7239 q^{62} +3.78103 q^{63} -11.3246 q^{64} +1.49519 q^{65} -28.0391 q^{66} -4.27333 q^{67} +26.1383 q^{68} +4.63920 q^{69} -3.34049 q^{70} +3.16932 q^{71} -3.98749 q^{72} +15.9931 q^{73} +4.26179 q^{74} +9.73840 q^{75} -10.5245 q^{76} -21.7489 q^{77} +18.7131 q^{78} -0.687068 q^{79} +0.751278 q^{80} -11.0227 q^{81} +24.5133 q^{82} +1.33334 q^{83} -26.9845 q^{84} +2.73269 q^{85} +0.904025 q^{86} -4.63654 q^{87} +22.9365 q^{88} -15.9201 q^{89} -0.925032 q^{90} +14.5151 q^{91} -8.42074 q^{92} -14.1239 q^{93} +1.45911 q^{94} -1.10031 q^{95} -6.23027 q^{96} -6.95578 q^{97} -15.8038 q^{98} -6.02260 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} + O(q^{10}) \)	\( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} - 15q^{10} - 40q^{11} - 53q^{12} - 59q^{13} - 36q^{14} - 40q^{15} + 118q^{16} - 93q^{17} - 59q^{18} - 16q^{19} - 108q^{20} - 62q^{21} - 37q^{22} - 107q^{23} - 31q^{24} + 101q^{25} - 64q^{26} - 63q^{27} - 53q^{28} - 124q^{29} - 68q^{30} - 15q^{31} - 129q^{32} - 49q^{33} - 76q^{35} + 45q^{36} - 98q^{37} - 125q^{38} - 47q^{39} - 7q^{40} - 56q^{41} - 84q^{42} - 62q^{43} - 114q^{44} - 142q^{45} - 3q^{46} - 111q^{47} - 92q^{48} + 117q^{49} - 64q^{50} - 21q^{51} - 85q^{52} - 347q^{53} + 3q^{54} - 16q^{55} - 73q^{56} - 115q^{57} - 29q^{58} - 50q^{59} - 54q^{60} - 62q^{61} - 55q^{62} - 70q^{63} + 64q^{64} - 147q^{65} + 34q^{66} - 86q^{67} - 174q^{68} - 104q^{69} - 7q^{70} - 86q^{71} - 139q^{72} - 27q^{73} - 52q^{74} - 49q^{75} - 11q^{76} - 346q^{77} - 59q^{78} - 17q^{79} - 149q^{80} - 8q^{81} - 31q^{82} - 106q^{83} - 51q^{84} - 69q^{85} - 85q^{86} - 32q^{87} - 113q^{88} - 59q^{89} + 10q^{90} - 9q^{91} - 314q^{92} - 230q^{93} + 7q^{94} - 74q^{95} - 54q^{96} - 60q^{97} - 77q^{98} - 96q^{99} + O(q^{100}) \)

Introduction and more

L-functions

Modular Forms

Varieties

Fields

Representations

Groups

Knowledge

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$-expansion

Coefficient data

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	4003.2.a.b.1.18

Level	4003
Weight	2
Character	4003.1
Self dual	Yes
Analytic conductor	31.964
Analytic rank	1
Dimension	152
CM	No

Self dual:	Yes
Analytic conductor:	\(31.9641159291\)
Analytic rank:	\(1\)
Dimension:	\(152\)
Fricke sign:	\(1\)
Sato-Tate group:	$\mathrm{SU}(2)$