LMFDB - Embedded newform 4001.2.a.a.1.97

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [4001,2,Mod(1,4001)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4001, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("4001.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$4001$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	4001.a (trivial)

Newform invariants

comment:select newform

sage:traces = [149] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$31.9481458487$
Analytic rank:	$1$
Dimension:	$149$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.97
Character	$\chi$	$=$	4001.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+0.949299 q^{2} -2.99427 q^{3} -1.09883 q^{4} -0.667150 q^{5} -2.84246 q^{6} -3.07808 q^{7} -2.94172 q^{8} +5.96565 q^{9} -0.633324 q^{10} +0.288414 q^{11} +3.29020 q^{12} -5.99437 q^{13} -2.92202 q^{14} +1.99763 q^{15} -0.594904 q^{16} +2.27154 q^{17} +5.66318 q^{18} +6.30951 q^{19} +0.733085 q^{20} +9.21660 q^{21} +0.273791 q^{22} +6.81467 q^{23} +8.80829 q^{24} -4.55491 q^{25} -5.69045 q^{26} -8.87995 q^{27} +3.38229 q^{28} +3.07356 q^{29} +1.89634 q^{30} -5.87852 q^{31} +5.31869 q^{32} -0.863589 q^{33} +2.15637 q^{34} +2.05354 q^{35} -6.55525 q^{36} +8.77473 q^{37} +5.98961 q^{38} +17.9488 q^{39} +1.96257 q^{40} -2.99493 q^{41} +8.74931 q^{42} +3.17439 q^{43} -0.316918 q^{44} -3.97998 q^{45} +6.46915 q^{46} +2.56978 q^{47} +1.78130 q^{48} +2.47458 q^{49} -4.32397 q^{50} -6.80162 q^{51} +6.58681 q^{52} +10.2849 q^{53} -8.42973 q^{54} -0.192415 q^{55} +9.05484 q^{56} -18.8924 q^{57} +2.91772 q^{58} -12.9026 q^{59} -2.19505 q^{60} -11.7728 q^{61} -5.58047 q^{62} -18.3627 q^{63} +6.23884 q^{64} +3.99914 q^{65} -0.819804 q^{66} +7.70025 q^{67} -2.49605 q^{68} -20.4049 q^{69} +1.94942 q^{70} -3.96848 q^{71} -17.5493 q^{72} +10.9683 q^{73} +8.32984 q^{74} +13.6386 q^{75} -6.93310 q^{76} -0.887761 q^{77} +17.0387 q^{78} +2.13603 q^{79} +0.396890 q^{80} +8.69202 q^{81} -2.84309 q^{82} -6.40009 q^{83} -10.1275 q^{84} -1.51546 q^{85} +3.01344 q^{86} -9.20306 q^{87} -0.848432 q^{88} +1.99471 q^{89} -3.77819 q^{90} +18.4512 q^{91} -7.48817 q^{92} +17.6019 q^{93} +2.43949 q^{94} -4.20939 q^{95} -15.9256 q^{96} +17.5603 q^{97} +2.34911 q^{98} +1.72058 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9} - 48 q^{10} - 31 q^{11} - 61 q^{12} - 54 q^{13} - 44 q^{14} - 65 q^{15} + 58 q^{16} - 26 q^{17} - 23 q^{18}+ \cdots - 131 q^{99}+O(q^{100})$ 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9 - 48 * q^10 - 31 * q^11 - 61 * q^12 - 54 * q^13 - 44 * q^14 - 65 * q^15 + 58 * q^16 - 26 * q^17 - 23 * q^18 - 86 * q^19 - 52 * q^20 - 30 * q^21 - 56 * q^22 - 63 * q^23 - 90 * q^24 + 92 * q^25 - 38 * q^26 - 103 * q^27 - 77 * q^28 - 51 * q^29 - 22 * q^30 - 256 * q^31 - 21 * q^32 - 36 * q^33 - 124 * q^34 - 50 * q^35 + 45 * q^36 - 42 * q^37 - 14 * q^38 - 119 * q^39 - 131 * q^40 - 55 * q^41 - 5 * q^42 - 55 * q^43 - 54 * q^44 - 68 * q^45 - 59 * q^46 - 82 * q^47 - 89 * q^48 + 30 * q^49 + 13 * q^50 - 83 * q^51 - 126 * q^52 - 23 * q^53 - 83 * q^54 - 244 * q^55 - 94 * q^56 - 14 * q^57 - 60 * q^58 - 93 * q^59 - 70 * q^60 - 139 * q^61 - 10 * q^62 - 120 * q^63 - 45 * q^64 - 37 * q^65 - 28 * q^66 - 110 * q^67 - 27 * q^68 - 79 * q^69 - 78 * q^70 - 123 * q^71 - 74 * q^73 - 25 * q^74 - 146 * q^75 - 192 * q^76 - q^77 + 26 * q^78 - 273 * q^79 - 51 * q^80 + 41 * q^81 - 120 * q^82 - 27 * q^83 - 14 * q^84 - 71 * q^85 + 3 * q^86 - 98 * q^87 - 143 * q^88 - 70 * q^89 - 24 * q^90 - 256 * q^91 - 47 * q^92 + 16 * q^93 - 151 * q^94 - 83 * q^95 - 137 * q^96 - 108 * q^97 + 17 * q^98 - 131 * q^99

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.949299	0.671256	0.335628	−	0.941995i	$-0.391052\pi$
$2$	0.949299	0.671256	0.335628	+	0.941995i	$0.391052\pi$
$3$	−2.99427	−1.72874	−0.864371	−	0.502854i	$-0.832283\pi$
$3$	−2.99427	−1.72874	−0.864371	+	0.502854i	$0.832283\pi$
$4$	−1.09883	−0.549416
$5$	−0.667150	−0.298358	−0.149179	−	0.988810i	$-0.547663\pi$
$5$	−0.667150	−0.298358	−0.149179	+	0.988810i	$0.547663\pi$
$6$	−2.84246	−1.16043
$7$	−3.07808	−1.16340	−0.581702	−	0.813402i	$-0.697613\pi$
$7$	−3.07808	−1.16340	−0.581702	+	0.813402i	$0.697613\pi$
$8$	−2.94172	−1.04005
$9$	5.96565	1.98855
$10$	−0.633324	−0.200275
$11$	0.288414	0.0869601	0.0434800	−	0.999054i	$-0.486156\pi$
$11$	0.288414	0.0869601	0.0434800	+	0.999054i	$0.486156\pi$
$12$	3.29020	0.949799
$13$	−5.99437	−1.66254	−0.831270	−	0.555869i	$-0.812386\pi$
$13$	−5.99437	−1.66254	−0.831270	+	0.555869i	$0.812386\pi$
$14$	−2.92202	−0.780942
$15$	1.99763	0.515785
$16$	−0.594904	−0.148726
$17$	2.27154	0.550931	0.275465	−	0.961311i	$-0.411168\pi$
$17$	2.27154	0.550931	0.275465	+	0.961311i	$0.411168\pi$
$18$	5.66318	1.33482
$19$	6.30951	1.44750	0.723751	−	0.690061i	$-0.242416\pi$
$19$	6.30951	1.44750	0.723751	+	0.690061i	$0.242416\pi$
$20$	0.733085	0.163923
$21$	9.21660	2.01123
$22$	0.273791	0.0583724
$23$	6.81467	1.42096	0.710478	−	0.703719i	$-0.248479\pi$
$23$	6.81467	1.42096	0.710478	+	0.703719i	$0.248479\pi$
$24$	8.80829	1.79799
$25$	−4.55491	−0.910982
$26$	−5.69045	−1.11599
$27$	−8.87995	−1.70895
$28$	3.38229	0.639193
$29$	3.07356	0.570745	0.285373	−	0.958417i	$-0.407883\pi$
$29$	3.07356	0.570745	0.285373	+	0.958417i	$0.407883\pi$
$30$	1.89634	0.346223
$31$	−5.87852	−1.05581	−0.527906	−	0.849303i	$-0.677023\pi$
$31$	−5.87852	−1.05581	−0.527906	+	0.849303i	$0.677023\pi$
$32$	5.31869	0.940221
$33$	−0.863589	−0.150332
$34$	2.15637	0.369815
$35$	2.05354	0.347112
$36$	−6.55525	−1.09254
$37$	8.77473	1.44256	0.721279	−	0.692645i	$-0.243555\pi$
$37$	8.77473	1.44256	0.721279	+	0.692645i	$0.243555\pi$
$38$	5.98961	0.971644
$39$	17.9488	2.87410
$40$	1.96257	0.310309
$41$	−2.99493	−0.467730	−0.233865	−	0.972269i	$-0.575137\pi$
$41$	−2.99493	−0.467730	−0.233865	+	0.972269i	$0.575137\pi$
$42$	8.74931	1.35005
$43$	3.17439	0.484090	0.242045	−	0.970265i	$-0.422182\pi$
$43$	3.17439	0.484090	0.242045	+	0.970265i	$0.422182\pi$
$44$	−0.316918	−0.0477773
$45$	−3.97998	−0.593300
$46$	6.46915	0.953825
$47$	2.56978	0.374841	0.187420	−	0.982280i	$-0.439987\pi$
$47$	2.56978	0.374841	0.187420	+	0.982280i	$0.439987\pi$
$48$	1.78130	0.257109
$49$	2.47458	0.353511
$50$	−4.32397	−0.611502
$51$	−6.80162	−0.952417
$52$	6.58681	0.913426
$53$	10.2849	1.41274	0.706372	−	0.707840i	$-0.250330\pi$
$53$	10.2849	1.41274	0.706372	+	0.707840i	$0.250330\pi$
$54$	−8.42973	−1.14714
$55$	−0.192415	−0.0259453
$56$	9.05484	1.21000
$57$	−18.8924	−2.50236
$58$	2.91772	0.383116
$59$	−12.9026	−1.67978	−0.839888	−	0.542760i	$-0.817379\pi$
$59$	−12.9026	−1.67978	−0.839888	+	0.542760i	$0.817379\pi$
$60$	−2.19505	−0.283380
$61$	−11.7728	−1.50735	−0.753675	−	0.657247i	$-0.771721\pi$
$61$	−11.7728	−1.50735	−0.753675	+	0.657247i	$0.771721\pi$
$62$	−5.58047	−0.708720
$63$	−18.3627	−2.31349
$64$	6.23884	0.779854
$65$	3.99914	0.496033
$66$	−0.819804	−0.100911
$67$	7.70025	0.940736	0.470368	−	0.882470i	$-0.344121\pi$
$67$	7.70025	0.940736	0.470368	+	0.882470i	$0.344121\pi$
$68$	−2.49605	−0.302690
$69$	−20.4049	−2.45647
$70$	1.94942	0.233001
$71$	−3.96848	−0.470972	−0.235486	−	0.971878i	$-0.575668\pi$
$71$	−3.96848	−0.470972	−0.235486	+	0.971878i	$0.575668\pi$
$72$	−17.5493	−2.06820
$73$	10.9683	1.28374	0.641872	−	0.766812i	$-0.278158\pi$
$73$	10.9683	1.28374	0.641872	+	0.766812i	$0.278158\pi$
$74$	8.32984	0.968324
$75$	13.6386	1.57485
$76$	−6.93310	−0.795281
$77$	−0.887761	−0.101170
$78$	17.0387	1.92926
$79$	2.13603	0.240322	0.120161	−	0.992754i	$-0.461659\pi$
$79$	2.13603	0.240322	0.120161	+	0.992754i	$0.461659\pi$
$80$	0.396890	0.0443736
$81$	8.69202	0.965780
$82$	−2.84309	−0.313967
$83$	−6.40009	−0.702501	−0.351251	−	0.936281i	$-0.614244\pi$
$83$	−6.40009	−0.702501	−0.351251	+	0.936281i	$0.614244\pi$
$84$	−10.1275	−1.10500
$85$	−1.51546	−0.164375
$86$	3.01344	0.324948
$87$	−9.20306	−0.986671
$88$	−0.848432	−0.0904432
$89$	1.99471	0.211439	0.105719	−	0.994396i	$-0.466285\pi$
$89$	1.99471	0.211439	0.105719	+	0.994396i	$0.466285\pi$
$90$	−3.77819	−0.398256
$91$	18.4512	1.93421
$92$	−7.48817	−0.780696
$93$	17.6019	1.82523
$94$	2.43949	0.251614
$95$	−4.20939	−0.431874
$96$	−15.9256	−1.62540
$97$	17.5603	1.78298	0.891489	−	0.453042i	$-0.149661\pi$
$97$	17.5603	1.78298	0.891489	+	0.453042i	$0.149661\pi$
$98$	2.34911	0.237296
$99$	1.72058	0.172924
$100$	5.00508	0.500508
$101$	3.56099	0.354332	0.177166	−	0.984181i	$-0.443307\pi$
$101$	3.56099	0.354332	0.177166	+	0.984181i	$0.443307\pi$
$102$	−6.45677	−0.639315
$103$	−9.61458	−0.947353	−0.473676	−	0.880699i	$-0.657073\pi$
$103$	−9.61458	−0.947353	−0.473676	+	0.880699i	$0.657073\pi$
$104$	17.6338	1.72913
$105$	−6.14885	−0.600066
$106$	9.76348	0.948313
$107$	−16.2010	−1.56621	−0.783103	−	0.621893i	$-0.786364\pi$
$107$	−16.2010	−1.56621	−0.783103	+	0.621893i	$0.786364\pi$
$108$	9.75758	0.938923
$109$	9.32186	0.892873	0.446436	−	0.894815i	$-0.352693\pi$
$109$	9.32186	0.892873	0.446436	+	0.894815i	$0.352693\pi$
$110$	−0.182660	−0.0174159
$111$	−26.2739	−2.49381
$112$	1.83116	0.173029
$113$	4.16028	0.391366	0.195683	−	0.980667i	$-0.437308\pi$
$113$	4.16028	0.391366	0.195683	+	0.980667i	$0.437308\pi$
$114$	−17.9345	−1.67972
$115$	−4.54640	−0.423954
$116$	−3.37732	−0.313576
$117$	−35.7603	−3.30604
$118$	−12.2484	−1.12756
$119$	−6.99200	−0.640955
$120$	−5.87645	−0.536444
$121$	−10.9168	−0.992438
$122$	−11.1759	−1.01182
$123$	8.96764	0.808585
$124$	6.45950	0.580080
$125$	6.37455	0.570157
$126$	−17.4317	−1.55294
$127$	−4.09047	−0.362971	−0.181485	−	0.983394i	$-0.558090\pi$
$127$	−4.09047	−0.362971	−0.181485	+	0.983394i	$0.558090\pi$
$128$	−4.71487	−0.416739
$129$	−9.50498	−0.836867
$130$	3.79638	0.332965
$131$	−2.16750	−0.189375	−0.0946876	−	0.995507i	$-0.530185\pi$
$131$	−2.16750	−0.189375	−0.0946876	+	0.995507i	$0.530185\pi$
$132$	0.948939	0.0825946
$133$	−19.4212	−1.68403
$134$	7.30984	0.631474
$135$	5.92426	0.509879
$136$	−6.68224	−0.572998
$137$	8.69615	0.742962	0.371481	−	0.928441i	$-0.378850\pi$
$137$	8.69615	0.742962	0.371481	+	0.928441i	$0.378850\pi$
$138$	−19.3704	−1.64892
$139$	10.4601	0.887217	0.443609	−	0.896221i	$-0.353698\pi$
$139$	10.4601	0.887217	0.443609	+	0.896221i	$0.353698\pi$
$140$	−2.25649	−0.190709
$141$	−7.69461	−0.648003
$142$	−3.76727	−0.316142
$143$	−1.72886	−0.144575
$144$	−3.54899	−0.295749
$145$	−2.05052	−0.170287
$146$	10.4122	0.861720
$147$	−7.40954	−0.611129
$148$	−9.64196	−0.792564
$149$	−14.0052	−1.14735	−0.573673	−	0.819084i	$-0.694482\pi$
$149$	−14.0052	−1.14735	−0.573673	+	0.819084i	$0.694482\pi$
$150$	12.9471	1.05713
$151$	−13.0105	−1.05878	−0.529388	−	0.848380i	$-0.677578\pi$
$151$	−13.0105	−1.05878	−0.529388	+	0.848380i	$0.677578\pi$
$152$	−18.5608	−1.50548
$153$	13.5512	1.09555
$154$	−0.842750	−0.0679108
$155$	3.92185	0.315011
$156$	−19.7227	−1.57908
$157$	1.11543	0.0890212	0.0445106	−	0.999009i	$-0.485827\pi$
$157$	1.11543	0.0890212	0.0445106	+	0.999009i	$0.485827\pi$
$158$	2.02773	0.161318
$159$	−30.7959	−2.44227
$160$	−3.54836	−0.280523
$161$	−20.9761	−1.65315
$162$	8.25132	0.648285
$163$	11.3558	0.889458	0.444729	−	0.895665i	$-0.353300\pi$
$163$	11.3558	0.889458	0.444729	+	0.895665i	$0.353300\pi$
$164$	3.29093	0.256979
$165$	0.576143	0.0448527
$166$	−6.07560	−0.471558
$167$	−18.6053	−1.43972	−0.719862	−	0.694117i	$-0.755795\pi$
$167$	−18.6053	−1.43972	−0.719862	+	0.694117i	$0.755795\pi$
$168$	−27.1126	−2.09178
$169$	22.9325	1.76404
$170$	−1.43862	−0.110337
$171$	37.6403	2.87843
$172$	−3.48812	−0.265967
$173$	−15.4904	−1.17771	−0.588857	−	0.808237i	$-0.700422\pi$
$173$	−15.4904	−1.17771	−0.588857	+	0.808237i	$0.700422\pi$
$174$	−8.73645	−0.662308
$175$	14.0204	1.05984
$176$	−0.171579	−0.0129332
$177$	38.6339	2.90390
$178$	1.89357	0.141929
$179$	−3.31672	−0.247903	−0.123952	−	0.992288i	$-0.539557\pi$
$179$	−3.31672	−0.247903	−0.123952	+	0.992288i	$0.539557\pi$
$180$	4.37333	0.325969
$181$	10.6529	0.791824	0.395912	−	0.918288i	$-0.370429\pi$
$181$	10.6529	0.791824	0.395912	+	0.918288i	$0.370429\pi$
$182$	17.5157	1.29835
$183$	35.2509	2.60582
$184$	−20.0468	−1.47787
$185$	−5.85406	−0.430399
$186$	16.7094	1.22519
$187$	0.655145	0.0479090
$188$	−2.82376	−0.205944
$189$	27.3332	1.98820
$190$	−3.99597	−0.289898
$191$	20.7835	1.50384	0.751920	−	0.659255i	$-0.229128\pi$
$191$	20.7835	1.50384	0.751920	+	0.659255i	$0.229128\pi$
$192$	−18.6808	−1.34817
$193$	−7.72335	−0.555939	−0.277970	−	0.960590i	$-0.589661\pi$
$193$	−7.72335	−0.555939	−0.277970	+	0.960590i	$0.589661\pi$
$194$	16.6700	1.19683
$195$	−11.9745	−0.857513
$196$	−2.71914	−0.194224
$197$	−12.2341	−0.871646	−0.435823	−	0.900032i	$-0.643543\pi$
$197$	−12.2341	−0.871646	−0.435823	+	0.900032i	$0.643543\pi$
$198$	1.63334	0.116076
$199$	−18.0823	−1.28182	−0.640911	−	0.767615i	$-0.721443\pi$
$199$	−18.0823	−1.28182	−0.640911	+	0.767615i	$0.721443\pi$
$200$	13.3993	0.947471
$201$	−23.0566	−1.62629
$202$	3.38045	0.237847
$203$	−9.46065	−0.664008
$204$	7.47383	0.523273
$205$	1.99807	0.139551
$206$	−9.12711	−0.635916
$207$	40.6539	2.82564
$208$	3.56608	0.247263
$209$	1.81975	0.125875
$210$	−5.83710	−0.402798
$211$	−8.07902	−0.556183	−0.278091	−	0.960555i	$-0.589702\pi$
$211$	−8.07902	−0.556183	−0.278091	+	0.960555i	$0.589702\pi$
$212$	−11.3014	−0.776185
$213$	11.8827	0.814189
$214$	−15.3795	−1.05132
$215$	−2.11779	−0.144432
$216$	26.1223	1.77740
$217$	18.0945	1.22834
$218$	8.84923	0.599346
$219$	−32.8421	−2.21926
$220$	0.211432	0.0142547
$221$	−13.6165	−0.915944
$222$	−24.9418	−1.67398
$223$	3.98485	0.266846	0.133423	−	0.991059i	$-0.457403\pi$
$223$	3.98485	0.266846	0.133423	+	0.991059i	$0.457403\pi$
$224$	−16.3714	−1.09386
$225$	−27.1730	−1.81153
$226$	3.94935	0.262707
$227$	4.13251	0.274285	0.137142	−	0.990551i	$-0.456208\pi$
$227$	4.13251	0.274285	0.137142	+	0.990551i	$0.456208\pi$
$228$	20.7596	1.37484
$229$	9.69108	0.640405	0.320202	−	0.947349i	$-0.396249\pi$
$229$	9.69108	0.640405	0.320202	+	0.947349i	$0.396249\pi$
$230$	−4.31589	−0.284582
$231$	2.65820	0.174896
$232$	−9.04153	−0.593606
$233$	6.89362	0.451616	0.225808	−	0.974172i	$-0.427498\pi$
$233$	6.89362	0.451616	0.225808	+	0.974172i	$0.427498\pi$
$234$	−33.9472	−2.21920
$235$	−1.71443	−0.111837
$236$	14.1778	0.922895
$237$	−6.39585	−0.415455
$238$	−6.63749	−0.430245
$239$	4.00494	0.259058	0.129529	−	0.991576i	$-0.458653\pi$
$239$	4.00494	0.259058	0.129529	+	0.991576i	$0.458653\pi$
$240$	−1.18840	−0.0767106
$241$	0.924588	0.0595579	0.0297790	−	0.999557i	$-0.490520\pi$
$241$	0.924588	0.0595579	0.0297790	+	0.999557i	$0.490520\pi$
$242$	−10.3633	−0.666179
$243$	0.613604	0.0393627
$244$	12.9363	0.828162
$245$	−1.65091	−0.105473
$246$	8.51297	0.542767
$247$	−37.8216	−2.40653
$248$	17.2929	1.09810
$249$	19.1636	1.21444
$250$	6.05136	0.382721
$251$	−2.09681	−0.132349	−0.0661747	−	0.997808i	$-0.521079\pi$
$251$	−2.09681	−0.132349	−0.0661747	+	0.997808i	$0.521079\pi$
$252$	20.1776	1.27107
$253$	1.96544	0.123566
$254$	−3.88308	−0.243646
$255$	4.53770	0.284162
$256$	−16.9535	−1.05959
$257$	−15.1769	−0.946709	−0.473354	−	0.880872i	$-0.656957\pi$
$257$	−15.1769	−0.946709	−0.473354	+	0.880872i	$0.656957\pi$
$258$	−9.02306	−0.561751
$259$	−27.0093	−1.67828
$260$	−4.39439	−0.272528
$261$	18.3358	1.13495
$262$	−2.05760	−0.127119
$263$	6.31579	0.389448	0.194724	−	0.980858i	$-0.437619\pi$
$263$	6.31579	0.389448	0.194724	+	0.980858i	$0.437619\pi$
$264$	2.54043	0.156353
$265$	−6.86159	−0.421504
$266$	−18.4365	−1.13041
$267$	−5.97270	−0.365523
$268$	−8.46128	−0.516855
$269$	−20.2336	−1.23366	−0.616831	−	0.787095i	$-0.711584\pi$
$269$	−20.2336	−1.23366	−0.616831	+	0.787095i	$0.711584\pi$
$270$	5.62389	0.342259
$271$	−15.0503	−0.914239	−0.457119	−	0.889405i	$-0.651119\pi$
$271$	−15.0503	−0.914239	−0.457119	+	0.889405i	$0.651119\pi$
$272$	−1.35135	−0.0819377
$273$	−55.2478	−3.34375
$274$	8.25524	0.498717
$275$	−1.31370	−0.0792191
$276$	22.4216	1.34962
$277$	−5.06323	−0.304220	−0.152110	−	0.988364i	$-0.548607\pi$
$277$	−5.06323	−0.304220	−0.152110	+	0.988364i	$0.548607\pi$
$278$	9.92979	0.595549
$279$	−35.0692	−2.09954
$280$	−6.04093	−0.361015
$281$	25.2268	1.50491	0.752453	−	0.658646i	$-0.228871\pi$
$281$	25.2268	1.50491	0.752453	+	0.658646i	$0.228871\pi$
$282$	−7.30449	−0.434976
$283$	32.4361	1.92812	0.964062	−	0.265676i	$-0.0855951\pi$
$283$	32.4361	1.92812	0.964062	+	0.265676i	$0.0855951\pi$
$284$	4.36069	0.258759
$285$	12.6040	0.746599
$286$	−1.64121	−0.0970465
$287$	9.21865	0.544160
$288$	31.7295	1.86968
$289$	−11.8401	−0.696476
$290$	−1.94656	−0.114306
$291$	−52.5803	−3.08231
$292$	−12.0523	−0.705309
$293$	3.66746	0.214255	0.107128	−	0.994245i	$-0.465835\pi$
$293$	3.66746	0.214255	0.107128	+	0.994245i	$0.465835\pi$
$294$	−7.03387	−0.410224
$295$	8.60796	0.501175
$296$	−25.8128	−1.50034
$297$	−2.56110	−0.148610
$298$	−13.2951	−0.770163
$299$	−40.8497	−2.36240
$300$	−14.9866	−0.865250
$301$	−9.77103	−0.563193
$302$	−12.3508	−0.710709
$303$	−10.6626	−0.612549
$304$	−3.75356	−0.215281
$305$	7.85420	0.449730
$306$	12.8642	0.735396
$307$	−18.8090	−1.07349	−0.536744	−	0.843745i	$-0.680346\pi$
$307$	−18.8090	−1.07349	−0.536744	+	0.843745i	$0.680346\pi$
$308$	0.975500	0.0555843
$309$	28.7886	1.63773
$310$	3.72301	0.211453
$311$	−20.9685	−1.18901	−0.594506	−	0.804091i	$-0.702652\pi$
$311$	−20.9685	−1.18901	−0.594506	+	0.804091i	$0.702652\pi$
$312$	−52.8002	−2.98922
$313$	−3.97427	−0.224639	−0.112320	−	0.993672i	$-0.535828\pi$
$313$	−3.97427	−0.224639	−0.112320	+	0.993672i	$0.535828\pi$
$314$	1.05888	0.0597560
$315$	12.2507	0.690248
$316$	−2.34714	−0.132037
$317$	14.4399	0.811023	0.405512	−	0.914090i	$-0.367093\pi$
$317$	14.4399	0.811023	0.405512	+	0.914090i	$0.367093\pi$
$318$	−29.2345	−1.63939
$319$	0.886456	0.0496320
$320$	−4.16224	−0.232676
$321$	48.5100	2.70757
$322$	−19.9126	−1.10968
$323$	14.3323	0.797473
$324$	−9.55107	−0.530615
$325$	27.3038	1.51454
$326$	10.7801	0.597053
$327$	−27.9122	−1.54355
$328$	8.81025	0.486465
$329$	−7.90999	−0.436092
$330$	0.546932	0.0301076
$331$	−17.3964	−0.956194	−0.478097	−	0.878307i	$-0.658673\pi$
$331$	−17.3964	−0.956194	−0.478097	+	0.878307i	$0.658673\pi$
$332$	7.03263	0.385966
$333$	52.3470	2.86860
$334$	−17.6620	−0.966423
$335$	−5.13722	−0.280676
$336$	−5.48299	−0.299122
$337$	−6.87024	−0.374246	−0.187123	−	0.982337i	$-0.559916\pi$
$337$	−6.87024	−0.374246	−0.187123	+	0.982337i	$0.559916\pi$
$338$	21.7698	1.18412
$339$	−12.4570	−0.676571
$340$	1.66524	0.0903101
$341$	−1.69545	−0.0918136
$342$	35.7319	1.93216
$343$	13.9296	0.752129
$344$	−9.33816	−0.503480
$345$	13.6131	0.732907
$346$	−14.7050	−0.790547
$347$	20.8859	1.12122	0.560608	−	0.828082i	$-0.310568\pi$
$347$	20.8859	1.12122	0.560608	+	0.828082i	$0.310568\pi$
$348$	10.1126	0.542093
$349$	18.3965	0.984742	0.492371	−	0.870385i	$-0.336130\pi$
$349$	18.3965	0.984742	0.492371	+	0.870385i	$0.336130\pi$
$350$	13.3095	0.711424
$351$	53.2298	2.84119
$352$	1.53399	0.0817617
$353$	14.9429	0.795332	0.397666	−	0.917530i	$-0.369820\pi$
$353$	14.9429	0.795332	0.397666	+	0.917530i	$0.369820\pi$
$354$	36.6751	1.94926
$355$	2.64757	0.140518
$356$	−2.19185	−0.116168
$357$	20.9359	1.10805
$358$	−3.14856	−0.166406
$359$	−24.4973	−1.29292	−0.646459	−	0.762949i	$-0.723751\pi$
$359$	−24.4973	−1.29292	−0.646459	+	0.762949i	$0.723751\pi$
$360$	11.7080	0.617064
$361$	20.8100	1.09526
$362$	10.1128	0.531516
$363$	32.6879	1.71567
$364$	−20.2747	−1.06268
$365$	−7.31750	−0.383016
$366$	33.4636	1.74917
$367$	21.2000	1.10663	0.553315	−	0.832972i	$-0.313363\pi$
$367$	21.2000	1.10663	0.553315	+	0.832972i	$0.313363\pi$
$368$	−4.05407	−0.211333
$369$	−17.8667	−0.930105
$370$	−5.55725	−0.288908
$371$	−31.6579	−1.64359
$372$	−19.3415	−1.00281
$373$	−12.8273	−0.664173	−0.332086	−	0.943249i	$-0.607753\pi$
$373$	−12.8273	−0.664173	−0.332086	+	0.943249i	$0.607753\pi$
$374$	0.621928	0.0321592
$375$	−19.0871	−0.985655
$376$	−7.55957	−0.389855
$377$	−18.4240	−0.948887
$378$	25.9474	1.33459
$379$	−33.3475	−1.71295	−0.856474	−	0.516190i	$-0.827350\pi$
$379$	−33.3475	−1.71295	−0.856474	+	0.516190i	$0.827350\pi$
$380$	4.62541	0.237279
$381$	12.2480	0.627482
$382$	19.7297	1.00946
$383$	−21.6700	−1.10729	−0.553643	−	0.832754i	$-0.686763\pi$
$383$	−21.6700	−1.10729	−0.553643	+	0.832754i	$0.686763\pi$
$384$	14.1176	0.720435
$385$	0.592269	0.0301848
$386$	−7.33177	−0.373177
$387$	18.9373	0.962637
$388$	−19.2958	−0.979597
$389$	5.95864	0.302115	0.151057	−	0.988525i	$-0.451732\pi$
$389$	5.95864	0.302115	0.151057	+	0.988525i	$0.451732\pi$
$390$	−11.3674	−0.575610
$391$	15.4798	0.782848
$392$	−7.27950	−0.367670
$393$	6.49008	0.327381
$394$	−11.6138	−0.585097
$395$	−1.42505	−0.0717021
$396$	−1.89062	−0.0950075
$397$	6.50375	0.326414	0.163207	−	0.986592i	$-0.447816\pi$
$397$	6.50375	0.326414	0.163207	+	0.986592i	$0.447816\pi$
$398$	−17.1655	−0.860431
$399$	58.1523	2.91125
$400$	2.70974	0.135487
$401$	8.78076	0.438490	0.219245	−	0.975670i	$-0.429641\pi$
$401$	8.78076	0.438490	0.219245	+	0.975670i	$0.429641\pi$
$402$	−21.8876	−1.09166
$403$	35.2380	1.75533
$404$	−3.91293	−0.194676
$405$	−5.79888	−0.288149
$406$	−8.98098	−0.445719
$407$	2.53076	0.125445
$408$	20.0084	0.990565
$409$	24.5031	1.21160	0.605801	−	0.795616i	$-0.292853\pi$
$409$	24.5031	1.21160	0.605801	+	0.795616i	$0.292853\pi$
$410$	1.89676	0.0936745
$411$	−26.0386	−1.28439
$412$	10.5648	0.520491
$413$	39.7152	1.95426
$414$	38.5927	1.89673
$415$	4.26982	0.209597
$416$	−31.8822	−1.56316
$417$	−31.3205	−1.53377
$418$	1.72749	0.0844942
$419$	−13.8345	−0.675858	−0.337929	−	0.941172i	$-0.609726\pi$
$419$	−13.8345	−0.675858	−0.337929	+	0.941172i	$0.609726\pi$
$420$	6.75655	0.329686
$421$	−24.4425	−1.19126	−0.595628	−	0.803260i	$-0.703097\pi$
$421$	−24.4425	−1.19126	−0.595628	+	0.803260i	$0.703097\pi$
$422$	−7.66941	−0.373341
$423$	15.3304	0.745390
$424$	−30.2554	−1.46933
$425$	−10.3467	−0.501888
$426$	11.2802	0.546529
$427$	36.2376	1.75366
$428$	17.8021	0.860498
$429$	5.17668	0.249932
$430$	−2.01042	−0.0969510
$431$	−14.3605	−0.691719	−0.345859	−	0.938286i	$-0.612413\pi$
$431$	−14.3605	−0.691719	−0.345859	+	0.938286i	$0.612413\pi$
$432$	5.28272	0.254165
$433$	30.7162	1.47613	0.738064	−	0.674730i	$-0.235740\pi$
$433$	30.7162	1.47613	0.738064	+	0.674730i	$0.235740\pi$
$434$	17.1771	0.824528
$435$	6.13981	0.294382
$436$	−10.2432	−0.490558
$437$	42.9972	2.05684
$438$	−31.1769	−1.48969
$439$	38.3939	1.83244	0.916220	−	0.400677i	$-0.131225\pi$
$439$	38.3939	1.83244	0.916220	+	0.400677i	$0.131225\pi$
$440$	0.566031	0.0269845
$441$	14.7624	0.702974
$442$	−12.9261	−0.614833
$443$	−8.05318	−0.382618	−0.191309	−	0.981530i	$-0.561273\pi$
$443$	−8.05318	−0.382618	−0.191309	+	0.981530i	$0.561273\pi$
$444$	28.8706	1.37014
$445$	−1.33077	−0.0630845
$446$	3.78282	0.179122
$447$	41.9352	1.98347
$448$	−19.2036	−0.907286
$449$	4.42158	0.208667	0.104334	−	0.994542i	$-0.466729\pi$
$449$	4.42158	0.208667	0.104334	+	0.994542i	$0.466729\pi$
$450$	−25.7953	−1.21600
$451$	−0.863781	−0.0406739
$452$	−4.57145	−0.215023
$453$	38.9568	1.83035
$454$	3.92299	0.184115
$455$	−12.3097	−0.577087
$456$	55.5761	2.60259
$457$	−5.79600	−0.271125	−0.135563	−	0.990769i	$-0.543284\pi$
$457$	−5.79600	−0.271125	−0.135563	+	0.990769i	$0.543284\pi$
$458$	9.19973	0.429875
$459$	−20.1712	−0.941511
$460$	4.99573	0.232927
$461$	35.6802	1.66179	0.830897	−	0.556427i	$-0.187828\pi$
$461$	35.6802	1.66179	0.830897	+	0.556427i	$0.187828\pi$
$462$	2.52342	0.117400
$463$	−14.6522	−0.680948	−0.340474	−	0.940254i	$-0.610587\pi$
$463$	−14.6522	−0.680948	−0.340474	+	0.940254i	$0.610587\pi$
$464$	−1.82847	−0.0848846
$465$	−11.7431	−0.544572
$466$	6.54410	0.303150
$467$	3.11058	0.143940	0.0719702	−	0.997407i	$-0.477071\pi$
$467$	3.11058	0.143940	0.0719702	+	0.997407i	$0.477071\pi$
$468$	39.2946	1.81639
$469$	−23.7020	−1.09446
$470$	−1.62750	−0.0750712
$471$	−3.33990	−0.153895
$472$	37.9558	1.74706
$473$	0.915538	0.0420965
$474$	−6.07157	−0.278877
$475$	−28.7393	−1.31865
$476$	7.68303	0.352151
$477$	61.3563	2.80931
$478$	3.80189	0.173894
$479$	−10.6551	−0.486842	−0.243421	−	0.969921i	$-0.578270\pi$
$479$	−10.6551	−0.486842	−0.243421	+	0.969921i	$0.578270\pi$
$480$	10.6248	0.484952
$481$	−52.5990	−2.39831
$482$	0.877710	0.0399786
$483$	62.8081	2.85787
$484$	11.9957	0.545261
$485$	−11.7153	−0.531966
$486$	0.582494	0.0264224
$487$	22.4545	1.01751	0.508755	−	0.860912i	$-0.330106\pi$
$487$	22.4545	1.01751	0.508755	+	0.860912i	$0.330106\pi$
$488$	34.6322	1.56773
$489$	−34.0024	−1.53764
$490$	−1.56721	−0.0707993
$491$	29.7991	1.34481	0.672407	−	0.740182i	$-0.265261\pi$
$491$	29.7991	1.34481	0.672407	+	0.740182i	$0.265261\pi$
$492$	−9.85393	−0.444250
$493$	6.98172	0.314441
$494$	−35.9040	−1.61540
$495$	−1.14788	−0.0515934
$496$	3.49715	0.157027
$497$	12.2153	0.547931
$498$	18.1920	0.815202
$499$	−38.2751	−1.71343	−0.856715	−	0.515789i	$-0.827499\pi$
$499$	−38.2751	−1.71343	−0.856715	+	0.515789i	$0.827499\pi$
$500$	−7.00456	−0.313254
$501$	55.7094	2.48891
$502$	−1.99050	−0.0888403
$503$	−38.3471	−1.70981	−0.854907	−	0.518781i	$-0.826386\pi$
$503$	−38.3471	−1.70981	−0.854907	+	0.518781i	$0.826386\pi$
$504$	54.0180	2.40615
$505$	−2.37571	−0.105718
$506$	1.86579	0.0829447
$507$	−68.6662	−3.04957
$508$	4.49474	0.199422
$509$	−12.6993	−0.562889	−0.281444	−	0.959578i	$-0.590813\pi$
$509$	−12.6993	−0.562889	−0.281444	+	0.959578i	$0.590813\pi$
$510$	4.30763	0.190745
$511$	−33.7613	−1.49351
$512$	−6.66419	−0.294518
$513$	−56.0282	−2.47370
$514$	−14.4074	−0.635484
$515$	6.41436	0.282651
$516$	10.4444	0.459788
$517$	0.741161	0.0325962
$518$	−25.6399	−1.12655
$519$	46.3825	2.03596
$520$	−11.7644	−0.515901
$521$	−25.7730	−1.12913	−0.564567	−	0.825387i	$-0.690957\pi$
$521$	−25.7730	−1.12913	−0.564567	+	0.825387i	$0.690957\pi$
$522$	17.4061	0.761845
$523$	−9.46474	−0.413864	−0.206932	−	0.978355i	$-0.566348\pi$
$523$	−9.46474	−0.413864	−0.206932	+	0.978355i	$0.566348\pi$
$524$	2.38172	0.104046
$525$	−41.9808	−1.83219
$526$	5.99557	0.261419
$527$	−13.3533	−0.581679
$528$	0.513753	0.0223582
$529$	23.4397	1.01912
$530$	−6.51370	−0.282937
$531$	−76.9724	−3.34032
$532$	21.3406	0.925233
$533$	17.9528	0.777620
$534$	−5.66987	−0.245359
$535$	10.8085	0.467290
$536$	−22.6520	−0.978416
$537$	9.93115	0.428561
$538$	−19.2077	−0.828103
$539$	0.713702	0.0307413
$540$	−6.50976	−0.280136
$541$	3.26360	0.140313	0.0701565	−	0.997536i	$-0.477650\pi$
$541$	3.26360	0.140313	0.0701565	+	0.997536i	$0.477650\pi$
$542$	−14.2872	−0.613688
$543$	−31.8977	−1.36886
$544$	12.0816	0.517996
$545$	−6.21908	−0.266396
$546$	−52.4466	−2.24451
$547$	32.6353	1.39538	0.697692	−	0.716398i	$-0.254210\pi$
$547$	32.6353	1.39538	0.697692	+	0.716398i	$0.254210\pi$
$548$	−9.55561	−0.408195
$549$	−70.2323	−2.99744
$550$	−1.24709	−0.0531763
$551$	19.3926	0.826155
$552$	60.0256	2.55486
$553$	−6.57487	−0.279592
$554$	−4.80651	−0.204209
$555$	17.5286	0.744049
$556$	−11.4939	−0.487451
$557$	32.9759	1.39723	0.698617	−	0.715496i	$-0.253799\pi$
$557$	32.9759	1.39723	0.698617	+	0.715496i	$0.253799\pi$
$558$	−33.2911	−1.40933
$559$	−19.0285	−0.804819
$560$	−1.22166	−0.0516245
$561$	−1.96168	−0.0828222
$562$	23.9478	1.01018
$563$	9.65745	0.407013	0.203506	−	0.979074i	$-0.434766\pi$
$563$	9.65745	0.407013	0.203506	+	0.979074i	$0.434766\pi$
$564$	8.45509	0.356023
$565$	−2.77553	−0.116767
$566$	30.7915	1.29426
$567$	−26.7547	−1.12359
$568$	11.6741	0.489836
$569$	4.99900	0.209569	0.104784	−	0.994495i	$-0.466585\pi$
$569$	4.99900	0.209569	0.104784	+	0.994495i	$0.466585\pi$
$570$	11.9650	0.501159
$571$	−21.0497	−0.880901	−0.440450	−	0.897777i	$-0.645181\pi$
$571$	−21.0497	−0.880901	−0.440450	+	0.897777i	$0.645181\pi$
$572$	1.89973	0.0794316
$573$	−62.2313	−2.59975
$574$	8.75125	0.365270
$575$	−31.0402	−1.29447
$576$	37.2187	1.55078
$577$	−16.8749	−0.702511	−0.351255	−	0.936280i	$-0.614245\pi$
$577$	−16.8749	−0.702511	−0.351255	+	0.936280i	$0.614245\pi$
$578$	−11.2398	−0.467513
$579$	23.1258	0.961075
$580$	2.25318	0.0935582
$581$	19.7000	0.817294
$582$	−49.9144	−2.06902
$583$	2.96632	0.122852
$584$	−32.2657	−1.33516
$585$	23.8575	0.986386
$586$	3.48151	0.143820
$587$	−18.4303	−0.760701	−0.380350	−	0.924842i	$-0.624197\pi$
$587$	−18.4303	−0.760701	−0.380350	+	0.924842i	$0.624197\pi$
$588$	8.14185	0.335764
$589$	−37.0906	−1.52829
$590$	8.17153	0.336416
$591$	36.6323	1.50685
$592$	−5.22012	−0.214546
$593$	12.7872	0.525107	0.262553	−	0.964917i	$-0.415435\pi$
$593$	12.7872	0.525107	0.262553	+	0.964917i	$0.415435\pi$
$594$	−2.43125	−0.0997554
$595$	4.66471	0.191234
$596$	15.3893	0.630371
$597$	54.1434	2.21594
$598$	−38.7785	−1.58577
$599$	−25.0885	−1.02509	−0.512544	−	0.858661i	$-0.671297\pi$
$599$	−25.0885	−1.02509	−0.512544	+	0.858661i	$0.671297\pi$
$600$	−40.1210	−1.63793
$601$	−42.7400	−1.74340	−0.871701	−	0.490038i	$-0.836983\pi$
$601$	−42.7400	−1.74340	−0.871701	+	0.490038i	$0.836983\pi$
$602$	−9.27562	−0.378046
$603$	45.9370	1.87070
$604$	14.2963	0.581708
$605$	7.28315	0.296102
$606$	−10.1220	−0.411177
$607$	−6.18185	−0.250914	−0.125457	−	0.992099i	$-0.540040\pi$
$607$	−6.18185	−0.250914	−0.125457	+	0.992099i	$0.540040\pi$
$608$	33.5584	1.36097
$609$	28.3277	1.14790
$610$	7.45599	0.301884
$611$	−15.4042	−0.623188
$612$	−14.8905	−0.601914
$613$	15.2898	0.617548	0.308774	−	0.951135i	$-0.400081\pi$
$613$	15.2898	0.617548	0.308774	+	0.951135i	$0.400081\pi$
$614$	−17.8554	−0.720584
$615$	−5.98276	−0.241248
$616$	2.61154	0.105222
$617$	−9.88094	−0.397792	−0.198896	−	0.980021i	$-0.563736\pi$
$617$	−9.88094	−0.397792	−0.198896	+	0.980021i	$0.563736\pi$
$618$	27.3290	1.09933
$619$	1.38431	0.0556403	0.0278201	−	0.999613i	$-0.491143\pi$
$619$	1.38431	0.0556403	0.0278201	+	0.999613i	$0.491143\pi$
$620$	−4.30945	−0.173072
$621$	−60.5139	−2.42834
$622$	−19.9053	−0.798131
$623$	−6.13987	−0.245989
$624$	−10.6778	−0.427454
$625$	18.5218	0.740871
$626$	−3.77277	−0.150790
$627$	−5.44883	−0.217605
$628$	−1.22567	−0.0489097
$629$	19.9322	0.794749
$630$	11.6296	0.463333
$631$	−7.16337	−0.285169	−0.142585	−	0.989783i	$-0.545541\pi$
$631$	−7.16337	−0.285169	−0.142585	+	0.989783i	$0.545541\pi$
$632$	−6.28360	−0.249948
$633$	24.1908	0.961497
$634$	13.7077	0.544404
$635$	2.72896	0.108295
$636$	33.8395	1.34182
$637$	−14.8335	−0.587726
$638$	0.841512	0.0333158
$639$	−23.6745	−0.936551
$640$	3.14552	0.124338
$641$	7.86465	0.310635	0.155318	−	0.987865i	$-0.450360\pi$
$641$	7.86465	0.310635	0.155318	+	0.987865i	$0.450360\pi$
$642$	46.0505	1.81747
$643$	−6.74667	−0.266063	−0.133031	−	0.991112i	$-0.542471\pi$
$643$	−6.74667	−0.266063	−0.133031	+	0.991112i	$0.542471\pi$
$644$	23.0492	0.908266
$645$	6.34124	0.249686
$646$	13.6057	0.535308
$647$	−37.2971	−1.46630	−0.733151	−	0.680066i	$-0.761951\pi$
$647$	−37.2971	−1.46630	−0.733151	+	0.680066i	$0.761951\pi$
$648$	−25.5695	−1.00446
$649$	−3.72129	−0.146073
$650$	25.9195	1.01665
$651$	−54.1799	−2.12348
$652$	−12.4782	−0.488682
$653$	1.44423	0.0565169	0.0282585	−	0.999601i	$-0.491004\pi$
$653$	1.44423	0.0565169	0.0282585	+	0.999601i	$0.491004\pi$
$654$	−26.4970	−1.03611
$655$	1.44605	0.0565017
$656$	1.78170	0.0695637
$657$	65.4331	2.55279
$658$	−7.50894	−0.292729
$659$	29.4506	1.14723	0.573616	−	0.819124i	$-0.305540\pi$
$659$	29.4506	1.14723	0.573616	+	0.819124i	$0.305540\pi$
$660$	−0.633084	−0.0246428
$661$	36.3427	1.41357	0.706783	−	0.707431i	$-0.250146\pi$
$661$	36.3427	1.41357	0.706783	+	0.707431i	$0.250146\pi$
$662$	−16.5144	−0.641851
$663$	40.7714	1.58343
$664$	18.8273	0.730640
$665$	12.9568	0.502445
$666$	49.6929	1.92556
$667$	20.9453	0.811004
$668$	20.4441	0.791008
$669$	−11.9317	−0.461307
$670$	−4.87676	−0.188406
$671$	−3.39543	−0.131079
$672$	49.0203	1.89100
$673$	−35.3331	−1.36199	−0.680995	−	0.732288i	$-0.738453\pi$
$673$	−35.3331	−1.36199	−0.680995	+	0.732288i	$0.738453\pi$
$674$	−6.52191	−0.251215
$675$	40.4474	1.55682
$676$	−25.1990	−0.969192
$677$	51.4884	1.97886	0.989430	−	0.145011i	$-0.0463216\pi$
$677$	51.4884	1.97886	0.989430	+	0.145011i	$0.0463216\pi$
$678$	−11.8254	−0.454152
$679$	−54.0520	−2.07433
$680$	4.45805	0.170959
$681$	−12.3739	−0.474167
$682$	−1.60948	−0.0616304
$683$	−24.5921	−0.940990	−0.470495	−	0.882403i	$-0.655925\pi$
$683$	−24.5921	−0.940990	−0.470495	+	0.882403i	$0.655925\pi$
$684$	−41.3604	−1.58146
$685$	−5.80163	−0.221669
$686$	13.2234	0.504871
$687$	−29.0177	−1.10709
$688$	−1.88846	−0.0719968
$689$	−61.6518	−2.34875
$690$	12.9229	0.491968
$691$	30.1151	1.14563	0.572816	−	0.819684i	$-0.305851\pi$
$691$	30.1151	1.14563	0.572816	+	0.819684i	$0.305851\pi$
$692$	17.0214	0.647055
$693$	−5.29607	−0.201181
$694$	19.8270	0.752622
$695$	−6.97847	−0.264709
$696$	27.0728	1.02619
$697$	−6.80313	−0.257687
$698$	17.4638	0.661014
$699$	−20.6414	−0.780728
$700$	−15.4060	−0.582294
$701$	40.9292	1.54588	0.772938	−	0.634481i	$-0.218786\pi$
$701$	40.9292	1.54588	0.772938	+	0.634481i	$0.218786\pi$
$702$	50.5309	1.90717
$703$	55.3643	2.08810
$704$	1.79937	0.0678162
$705$	5.13346	0.193337
$706$	14.1853	0.533871
$707$	−10.9610	−0.412232
$708$	−42.4521	−1.59545
$709$	2.94106	0.110454	0.0552269	−	0.998474i	$-0.482412\pi$
$709$	2.94106	0.110454	0.0552269	+	0.998474i	$0.482412\pi$
$710$	2.51333	0.0943237
$711$	12.7428	0.477893
$712$	−5.86787	−0.219908
$713$	−40.0601	−1.50026
$714$	19.8744	0.743782
$715$	1.15341	0.0431351
$716$	3.64452	0.136202
$717$	−11.9919	−0.447845
$718$	−23.2552	−0.867878
$719$	26.2380	0.978511	0.489256	−	0.872140i	$-0.337268\pi$
$719$	26.2380	0.978511	0.489256	+	0.872140i	$0.337268\pi$
$720$	2.36771	0.0882392
$721$	29.5944	1.10215
$722$	19.7549	0.735200
$723$	−2.76846	−0.102960
$724$	−11.7058	−0.435041
$725$	−13.9998	−0.519939
$726$	31.0306	1.15165
$727$	−11.1260	−0.412641	−0.206321	−	0.978484i	$-0.566149\pi$
$727$	−11.1260	−0.412641	−0.206321	+	0.978484i	$0.566149\pi$
$728$	−54.2781	−2.01168
$729$	−27.9134	−1.03383
$730$	−6.94650	−0.257101
$731$	7.21077	0.266700
$732$	−38.7348	−1.43168
$733$	−1.05286	−0.0388883	−0.0194442	−	0.999811i	$-0.506190\pi$
$733$	−1.05286	−0.0388883	−0.0194442	+	0.999811i	$0.506190\pi$
$734$	20.1251	0.742832
$735$	4.94327	0.182335
$736$	36.2451	1.33601
$737$	2.22086	0.0818064
$738$	−16.9609	−0.624338
$739$	33.5776	1.23517	0.617586	−	0.786503i	$-0.288111\pi$
$739$	33.5776	1.23517	0.617586	+	0.786503i	$0.288111\pi$
$740$	6.43263	0.236468
$741$	113.248	4.16027
$742$	−30.0528	−1.10327
$743$	−10.2980	−0.377796	−0.188898	−	0.981997i	$-0.560491\pi$
$743$	−10.2980	−0.377796	−0.188898	+	0.981997i	$0.560491\pi$
$744$	−51.7797	−1.89834
$745$	9.34353	0.342320
$746$	−12.1769	−0.445829
$747$	−38.1807	−1.39696
$748$	−0.719895	−0.0263220
$749$	49.8678	1.82213
$750$	−18.1194	−0.661627
$751$	−32.3794	−1.18154	−0.590770	−	0.806840i	$-0.701176\pi$
$751$	−32.3794	−1.18154	−0.590770	+	0.806840i	$0.701176\pi$
$752$	−1.52877	−0.0557486
$753$	6.27841	0.228798
$754$	−17.4899	−0.636945
$755$	8.67992	0.315894
$756$	−30.0346	−1.09235
$757$	7.52549	0.273518	0.136759	−	0.990604i	$-0.456331\pi$
$757$	7.52549	0.273518	0.136759	+	0.990604i	$0.456331\pi$
$758$	−31.6568	−1.14983
$759$	−5.88507	−0.213615
$760$	12.3828	0.449173
$761$	−48.3848	−1.75395	−0.876974	−	0.480539i	$-0.840441\pi$
$761$	−48.3848	−1.75395	−0.876974	+	0.480539i	$0.840441\pi$
$762$	11.6270	0.421201
$763$	−28.6934	−1.03877
$764$	−22.8375	−0.826233
$765$	−9.04070	−0.326867
$766$	−20.5713	−0.743272
$767$	77.3430	2.79269
$768$	50.7633	1.83176
$769$	−3.19139	−0.115085	−0.0575423	−	0.998343i	$-0.518326\pi$
$769$	−3.19139	−0.115085	−0.0575423	+	0.998343i	$0.518326\pi$
$770$	0.562241	0.0202617
$771$	45.4437	1.63662
$772$	8.48667	0.305442
$773$	34.1671	1.22890	0.614452	−	0.788954i	$-0.289377\pi$
$773$	34.1671	1.22890	0.614452	+	0.788954i	$0.289377\pi$
$774$	17.9772	0.646175
$775$	26.7761	0.961827
$776$	−51.6574	−1.85439
$777$	80.8732	2.90131
$778$	5.65653	0.202796
$779$	−18.8966	−0.677040
$780$	13.1580	0.471131
$781$	−1.14456	−0.0409557
$782$	14.6950	0.525491
$783$	−27.2930	−0.975373
$784$	−1.47213	−0.0525762
$785$	−0.744160	−0.0265602
$786$	6.16102	0.219756
$787$	53.2293	1.89742	0.948710	−	0.316148i	$-0.102390\pi$
$787$	53.2293	1.89742	0.948710	+	0.316148i	$0.102390\pi$
$788$	13.4433	0.478896
$789$	−18.9112	−0.673255
$790$	−1.35280	−0.0481305
$791$	−12.8057	−0.455317
$792$	−5.06145	−0.179851
$793$	70.5705	2.50603
$794$	6.17400	0.219107
$795$	20.5455	0.728672
$796$	19.8695	0.704254
$797$	−48.3377	−1.71221	−0.856105	−	0.516802i	$-0.827122\pi$
$797$	−48.3377	−1.71221	−0.856105	+	0.516802i	$0.827122\pi$
$798$	55.2039	1.95420
$799$	5.83737	0.206511
$800$	−24.2262	−0.856525
$801$	11.8997	0.420456
$802$	8.33556	0.294339
$803$	3.16341	0.111634
$804$	25.3354	0.893509
$805$	13.9942	0.493230
$806$	33.4514	1.17828
$807$	60.5848	2.13268
$808$	−10.4754	−0.368524
$809$	−16.7382	−0.588483	−0.294241	−	0.955731i	$-0.595067\pi$
$809$	−16.7382	−0.588483	−0.294241	+	0.955731i	$0.595067\pi$
$810$	−5.50487	−0.193421
$811$	−6.25111	−0.219506	−0.109753	−	0.993959i	$-0.535006\pi$
$811$	−6.25111	−0.219506	−0.109753	+	0.993959i	$0.535006\pi$
$812$	10.3957	0.364816
$813$	45.0646	1.58048
$814$	2.40244	0.0842056
$815$	−7.57604	−0.265377
$816$	4.04631	0.141649
$817$	20.0289	0.700721
$818$	23.2608	0.813294
$819$	110.073	3.84627
$820$	−2.19554	−0.0766717
$821$	−34.6421	−1.20902	−0.604509	−	0.796598i	$-0.706631\pi$
$821$	−34.6421	−1.20902	−0.604509	+	0.796598i	$0.706631\pi$
$822$	−24.7184	−0.862154
$823$	−3.25767	−0.113555	−0.0567775	−	0.998387i	$-0.518083\pi$
$823$	−3.25767	−0.113555	−0.0567775	+	0.998387i	$0.518083\pi$
$824$	28.2834	0.985298
$825$	3.93357	0.136949
$826$	37.7016	1.31181
$827$	−38.9434	−1.35420	−0.677098	−	0.735893i	$-0.736763\pi$
$827$	−38.9434	−1.35420	−0.677098	+	0.735893i	$0.736763\pi$
$828$	−44.6718	−1.55245
$829$	−21.0658	−0.731646	−0.365823	−	0.930684i	$-0.619212\pi$
$829$	−21.0658	−0.731646	−0.365823	+	0.930684i	$0.619212\pi$
$830$	4.05333	0.140693
$831$	15.1607	0.525918
$832$	−37.3979	−1.29654
$833$	5.62111	0.194760
$834$	−29.7325	−1.02955
$835$	12.4125	0.429554
$836$	−1.99960	−0.0691577
$837$	52.2009	1.80433
$838$	−13.1330	−0.453673
$839$	−48.1056	−1.66079	−0.830395	−	0.557175i	$-0.811885\pi$
$839$	−48.1056	−1.66079	−0.830395	+	0.557175i	$0.811885\pi$
$840$	18.0882	0.624101
$841$	−19.5533	−0.674250
$842$	−23.2033	−0.799637
$843$	−75.5359	−2.60159
$844$	8.87749	0.305576
$845$	−15.2994	−0.526316
$846$	14.5531	0.500347
$847$	33.6028	1.15461
$848$	−6.11855	−0.210112
$849$	−97.1224	−3.33323
$850$	−9.82209	−0.336895
$851$	59.7969	2.04981
$852$	−13.0571	−0.447328
$853$	−47.0803	−1.61200	−0.805999	−	0.591917i	$-0.798371\pi$
$853$	−47.0803	−1.61200	−0.805999	+	0.591917i	$0.798371\pi$
$854$	34.4003	1.17715
$855$	−25.1117	−0.858803
$856$	47.6586	1.62894
$857$	12.8105	0.437599	0.218799	−	0.975770i	$-0.429786\pi$
$857$	12.8105	0.437599	0.218799	+	0.975770i	$0.429786\pi$
$858$	4.91421	0.167768
$859$	8.98755	0.306651	0.153326	−	0.988176i	$-0.451002\pi$
$859$	8.98755	0.306651	0.153326	+	0.988176i	$0.451002\pi$
$860$	2.32710	0.0793534
$861$	−27.6031	−0.940712
$862$	−13.6324	−0.464320
$863$	−23.3426	−0.794591	−0.397296	−	0.917691i	$-0.630051\pi$
$863$	−23.3426	−0.794591	−0.397296	+	0.917691i	$0.630051\pi$
$864$	−47.2297	−1.60679
$865$	10.3344	0.351381
$866$	29.1589	0.990859
$867$	35.4524	1.20403
$868$	−19.8829	−0.674868
$869$	0.616061	0.0208984
$870$	5.82852	0.197605
$871$	−46.1582	−1.56401
$872$	−27.4223	−0.928636
$873$	104.759	3.54554
$874$	40.8172	1.38066
$875$	−19.6214	−0.663324
$876$	36.0879	1.21930
$877$	−16.5374	−0.558427	−0.279214	−	0.960229i	$-0.590074\pi$
$877$	−16.5374	−0.558427	−0.279214	+	0.960229i	$0.590074\pi$
$878$	36.4472	1.23003
$879$	−10.9814	−0.370392
$880$	0.114469	0.00385874
$881$	−44.3221	−1.49325	−0.746626	−	0.665245i	$-0.768327\pi$
$881$	−44.3221	−1.49325	−0.746626	+	0.665245i	$0.768327\pi$
$882$	14.0140	0.471875
$883$	−24.0672	−0.809925	−0.404963	−	0.914333i	$-0.632715\pi$
$883$	−24.0672	−0.809925	−0.404963	+	0.914333i	$0.632715\pi$
$884$	14.9622	0.503234
$885$	−25.7746	−0.866402
$886$	−7.64487	−0.256834
$887$	−48.9903	−1.64493	−0.822466	−	0.568814i	$-0.807403\pi$
$887$	−48.9903	−1.64493	−0.822466	+	0.568814i	$0.807403\pi$
$888$	77.2904	2.59370
$889$	12.5908	0.422282
$890$	−1.26330	−0.0423458
$891$	2.50690	0.0839843
$892$	−4.37869	−0.146609
$893$	16.2141	0.542583
$894$	39.8090	1.33141
$895$	2.21275	0.0739640
$896$	14.5127	0.484836
$897$	122.315	4.08398
$898$	4.19740	0.140069
$899$	−18.0679	−0.602600
$900$	29.8586	0.995286
$901$	23.3627	0.778324
$902$	−0.819986	−0.0273026
$903$	29.2571	0.973615
$904$	−12.2384	−0.407042
$905$	−7.10708	−0.236247
$906$	36.9816	1.22863
$907$	−32.5622	−1.08121	−0.540605	−	0.841277i	$-0.681805\pi$
$907$	−32.5622	−1.08121	−0.540605	+	0.841277i	$0.681805\pi$
$908$	−4.54094	−0.150696
$909$	21.2436	0.704607
$910$	−11.6856	−0.387373
$911$	25.4066	0.841757	0.420879	−	0.907117i	$-0.361722\pi$
$911$	25.4066	0.841757	0.420879	+	0.907117i	$0.361722\pi$
$912$	11.2392	0.372166
$913$	−1.84588	−0.0610896
$914$	−5.50213	−0.181994
$915$	−23.5176	−0.777468
$916$	−10.6489	−0.351849
$917$	6.67173	0.220320
$918$	−19.1485	−0.631995
$919$	−15.3234	−0.505473	−0.252737	−	0.967535i	$-0.581331\pi$
$919$	−15.3234	−0.505473	−0.252737	+	0.967535i	$0.581331\pi$
$920$	13.3742	0.440935
$921$	56.3193	1.85578
$922$	33.8712	1.11549
$923$	23.7885	0.783010
$924$	−2.92091	−0.0960909
$925$	−39.9681	−1.31414
$926$	−13.9094	−0.457090
$927$	−57.3572	−1.88386
$928$	16.3473	0.536626
$929$	1.95001	0.0639779	0.0319889	−	0.999488i	$-0.489816\pi$
$929$	1.95001	0.0639779	0.0319889	+	0.999488i	$0.489816\pi$
$930$	−11.1477	−0.365547
$931$	15.6134	0.511707
$932$	−7.57493	−0.248125
$933$	62.7852	2.05549
$934$	2.95287	0.0966208
$935$	−0.437080	−0.0142940
$936$	105.197	3.43846
$937$	−32.9330	−1.07587	−0.537937	−	0.842985i	$-0.680796\pi$
$937$	−32.9330	−1.07587	−0.537937	+	0.842985i	$0.680796\pi$
$938$	−22.5003	−0.734660
$939$	11.9000	0.388343
$940$	1.88387	0.0614450
$941$	10.7913	0.351788	0.175894	−	0.984409i	$-0.443718\pi$
$941$	10.7913	0.351788	0.175894	+	0.984409i	$0.443718\pi$
$942$	−3.17057	−0.103303
$943$	−20.4095	−0.664624
$944$	7.67581	0.249826
$945$	−18.2353	−0.593195
$946$	0.869119	0.0282575
$947$	−21.4727	−0.697768	−0.348884	−	0.937166i	$-0.613439\pi$
$947$	−21.4727	−0.697768	−0.348884	+	0.937166i	$0.613439\pi$
$948$	7.02797	0.228258
$949$	−65.7482	−2.13428
$950$	−27.2822	−0.885150
$951$	−43.2368	−1.40205
$952$	20.5685	0.666628
$953$	24.1400	0.781971	0.390985	−	0.920397i	$-0.372134\pi$
$953$	24.1400	0.781971	0.390985	+	0.920397i	$0.372134\pi$
$954$	58.2455	1.88577
$955$	−13.8657	−0.448683
$956$	−4.40076	−0.142331
$957$	−2.65429	−0.0858010
$958$	−10.1148	−0.326795
$959$	−26.7674	−0.864366
$960$	12.4629	0.402237
$961$	3.55695	0.114740
$962$	−49.9322	−1.60988
$963$	−96.6492	−3.11448
$964$	−1.01597	−0.0327221
$965$	5.15263	0.165869
$966$	59.6236	1.91836
$967$	−15.8818	−0.510723	−0.255361	−	0.966846i	$-0.582194\pi$
$967$	−15.8818	−0.510723	−0.255361	+	0.966846i	$0.582194\pi$
$968$	32.1142	1.03219
$969$	−42.9149	−1.37863
$970$	−11.1214	−0.357085
$971$	47.3609	1.51989	0.759943	−	0.649990i	$-0.225227\pi$
$971$	47.3609	1.51989	0.759943	+	0.649990i	$0.225227\pi$
$972$	−0.674248	−0.0216265
$973$	−32.1971	−1.03219
$974$	21.3160	0.683009
$975$	−81.7551	−2.61826
$976$	7.00367	0.224182
$977$	−22.5071	−0.720067	−0.360034	−	0.932939i	$-0.617235\pi$
$977$	−22.5071	−0.720067	−0.360034	+	0.932939i	$0.617235\pi$
$978$	−32.2785	−1.03215
$979$	0.575302	0.0183867
$980$	1.81407	0.0579485
$981$	55.6110	1.77552
$982$	28.2882	0.902714
$983$	−40.4311	−1.28955	−0.644777	−	0.764371i	$-0.723050\pi$
$983$	−40.4311	−1.28955	−0.644777	+	0.764371i	$0.723050\pi$
$984$	−26.3803	−0.840972
$985$	8.16199	0.260063
$986$	6.62774	0.211070
$987$	23.6846	0.753890
$988$	41.5596	1.32219
$989$	21.6324	0.687871
$990$	−1.08968	−0.0346324
$991$	0.865820	0.0275037	0.0137518	−	0.999905i	$-0.495623\pi$
$991$	0.865820	0.0275037	0.0137518	+	0.999905i	$0.495623\pi$
$992$	−31.2660	−0.992697
$993$	52.0896	1.65301
$994$	11.5960	0.367802
$995$	12.0636	0.382443
$996$	−21.0576	−0.667235
$997$	−56.6100	−1.79286	−0.896429	−	0.443188i	$-0.853848\pi$
$997$	−56.6100	−1.79286	−0.896429	+	0.443188i	$0.853848\pi$
$998$	−36.3345	−1.15015
$999$	−77.9192	−2.46525

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4001.2.a.a.1.97	✓	149

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4001.2.a.a.1.97	✓	149	1.1	even	1	trivial

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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Twists

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	4001.2.a.a.1.97

Level	$4001$
Weight	$2$
Character	4001.1
Self dual	yes
Analytic conductor	$31.948$
Analytic rank	$1$
Dimension	$149$
CM	no
Inner twists	$1$