LMFDB - Embedded newform 4001.2.a.b.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4001,2,Mod(1,4001)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$31.9481458487$
Analytic rank:	$0$
Dimension:	$184$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
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)

$f(q)$	$=$	$q-2.38954 q^{2} +1.02374 q^{3} +3.70989 q^{4} -0.691971 q^{5} -2.44626 q^{6} +1.59189 q^{7} -4.08584 q^{8} -1.95196 q^{9} +1.65349 q^{10} -3.76337 q^{11} +3.79795 q^{12} -6.60109 q^{13} -3.80387 q^{14} -0.708397 q^{15} +2.34348 q^{16} -3.52471 q^{17} +4.66428 q^{18} +8.47101 q^{19} -2.56713 q^{20} +1.62968 q^{21} +8.99271 q^{22} -5.10188 q^{23} -4.18283 q^{24} -4.52118 q^{25} +15.7736 q^{26} -5.06951 q^{27} +5.90572 q^{28} -2.57168 q^{29} +1.69274 q^{30} +3.37313 q^{31} +2.57184 q^{32} -3.85271 q^{33} +8.42243 q^{34} -1.10154 q^{35} -7.24155 q^{36} -1.47696 q^{37} -20.2418 q^{38} -6.75779 q^{39} +2.82728 q^{40} -0.0916968 q^{41} -3.89417 q^{42} -0.702722 q^{43} -13.9617 q^{44} +1.35070 q^{45} +12.1911 q^{46} -10.1367 q^{47} +2.39911 q^{48} -4.46590 q^{49} +10.8035 q^{50} -3.60838 q^{51} -24.4893 q^{52} +3.48172 q^{53} +12.1138 q^{54} +2.60414 q^{55} -6.50419 q^{56} +8.67210 q^{57} +6.14512 q^{58} +11.3479 q^{59} -2.62807 q^{60} +10.2702 q^{61} -8.06021 q^{62} -3.10730 q^{63} -10.8325 q^{64} +4.56776 q^{65} +9.20618 q^{66} +3.97791 q^{67} -13.0763 q^{68} -5.22299 q^{69} +2.63217 q^{70} +1.20708 q^{71} +7.97539 q^{72} +10.3051 q^{73} +3.52925 q^{74} -4.62850 q^{75} +31.4265 q^{76} -5.99086 q^{77} +16.1480 q^{78} +10.0280 q^{79} -1.62162 q^{80} +0.666026 q^{81} +0.219113 q^{82} +11.1174 q^{83} +6.04591 q^{84} +2.43900 q^{85} +1.67918 q^{86} -2.63273 q^{87} +15.3765 q^{88} +9.14236 q^{89} -3.22755 q^{90} -10.5082 q^{91} -18.9274 q^{92} +3.45320 q^{93} +24.2220 q^{94} -5.86169 q^{95} +2.63289 q^{96} +4.87256 q^{97} +10.6714 q^{98} +7.34595 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9} + 46 q^{10} + 25 q^{11} + 61 q^{12} + 52 q^{13} + 28 q^{14} + 59 q^{15} + 279 q^{16} + 16 q^{17} - 2 q^{18}+ \cdots + 53 q^{99}+O(q^{100})$ 184 * q + 3 * q^2 + 28 * q^3 + 217 * q^4 + 15 * q^5 + 31 * q^6 + 49 * q^7 + 6 * q^8 + 210 * q^9 + 46 * q^10 + 25 * q^11 + 61 * q^12 + 52 * q^13 + 28 * q^14 + 59 * q^15 + 279 * q^16 + 16 * q^17 - 2 * q^18 + 86 * q^19 + 26 * q^20 + 22 * q^21 + 54 * q^22 + 55 * q^23 + 72 * q^24 + 241 * q^25 + 32 * q^26 + 97 * q^27 + 75 * q^28 + 27 * q^29 - 10 * q^30 + 276 * q^31 + 20 * q^33 + 122 * q^34 + 30 * q^35 + 278 * q^36 + 42 * q^37 + 14 * q^38 + 113 * q^39 + 115 * q^40 + 39 * q^41 + 15 * q^42 + 65 * q^43 + 32 * q^44 + 54 * q^45 + 65 * q^46 + 82 * q^47 + 117 * q^48 + 297 * q^49 + 4 * q^50 + 45 * q^51 + 136 * q^52 + 21 * q^53 + 93 * q^54 + 252 * q^55 + 74 * q^56 + 14 * q^57 + 54 * q^58 + 95 * q^59 + 58 * q^60 + 131 * q^61 + 14 * q^62 + 88 * q^63 + 368 * q^64 - 9 * q^65 + 52 * q^66 + 90 * q^67 + 27 * q^68 + 101 * q^69 + 18 * q^70 + 117 * q^71 - 15 * q^72 + 72 * q^73 + 7 * q^74 + 150 * q^75 + 148 * q^76 + 7 * q^77 + 22 * q^78 + 287 * q^79 + 43 * q^80 + 244 * q^81 + 86 * q^82 + 25 * q^83 + 14 * q^84 + 41 * q^85 + 25 * q^86 + 82 * q^87 + 115 * q^88 + 48 * q^89 + 78 * q^90 + 272 * q^91 + 69 * q^92 + 44 * q^93 + 161 * q^94 + 37 * q^95 + 129 * q^96 + 106 * q^97 - 46 * q^98 + 53 * 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

)

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

$2$	−2.38954	−1.68966	−0.844829	−	0.535037i	$-0.820298\pi$
$2$	−2.38954	−1.68966	−0.844829	+	0.535037i	$0.820298\pi$
$3$	1.02374	0.591056	0.295528	−	0.955334i	$-0.404505\pi$
$3$	1.02374	0.591056	0.295528	+	0.955334i	$0.404505\pi$
$4$	3.70989	1.85494
$5$	−0.691971	−0.309459	−0.154729	−	0.987957i	$-0.549451\pi$
$5$	−0.691971	−0.309459	−0.154729	+	0.987957i	$0.549451\pi$
$6$	−2.44626	−0.998682
$7$	1.59189	0.601677	0.300838	−	0.953675i	$-0.402734\pi$
$7$	1.59189	0.601677	0.300838	+	0.953675i	$0.402734\pi$
$8$	−4.08584	−1.44456
$9$	−1.95196	−0.650653
$10$	1.65349	0.522879
$11$	−3.76337	−1.13470	−0.567349	−	0.823477i	$-0.692031\pi$
$11$	−3.76337	−1.13470	−0.567349	+	0.823477i	$0.692031\pi$
$12$	3.79795	1.09637
$13$	−6.60109	−1.83081	−0.915407	−	0.402530i	$-0.868131\pi$
$13$	−6.60109	−1.83081	−0.915407	+	0.402530i	$0.868131\pi$
$14$	−3.80387	−1.01663
$15$	−0.708397	−0.182907
$16$	2.34348	0.585870
$17$	−3.52471	−0.854868	−0.427434	−	0.904046i	$-0.640582\pi$
$17$	−3.52471	−0.854868	−0.427434	+	0.904046i	$0.640582\pi$
$18$	4.66428	1.09938
$19$	8.47101	1.94338	0.971692	−	0.236252i	$-0.0759189\pi$
$19$	8.47101	1.94338	0.971692	+	0.236252i	$0.0759189\pi$
$20$	−2.56713	−0.574028
$21$	1.62968	0.355624
$22$	8.99271	1.91725
$23$	−5.10188	−1.06382	−0.531908	−	0.846802i	$-0.678525\pi$
$23$	−5.10188	−1.06382	−0.531908	+	0.846802i	$0.678525\pi$
$24$	−4.18283	−0.853816
$25$	−4.52118	−0.904235
$26$	15.7736	3.09345
$27$	−5.06951	−0.975628
$28$	5.90572	1.11608
$29$	−2.57168	−0.477549	−0.238775	−	0.971075i	$-0.576746\pi$
$29$	−2.57168	−0.477549	−0.238775	+	0.971075i	$0.576746\pi$
$30$	1.69274	0.309051
$31$	3.37313	0.605832	0.302916	−	0.953017i	$-0.402040\pi$
$31$	3.37313	0.605832	0.302916	+	0.953017i	$0.402040\pi$
$32$	2.57184	0.454641
$33$	−3.85271	−0.670670
$34$	8.42243	1.44443
$35$	−1.10154	−0.186194
$36$	−7.24155	−1.20692
$37$	−1.47696	−0.242811	−0.121405	−	0.992603i	$-0.538740\pi$
$37$	−1.47696	−0.242811	−0.121405	+	0.992603i	$0.538740\pi$
$38$	−20.2418	−3.28365
$39$	−6.75779	−1.08211
$40$	2.82728	0.447032
$41$	−0.0916968	−0.0143206	−0.00716032	−	0.999974i	$-0.502279\pi$
$41$	−0.0916968	−0.0143206	−0.00716032	+	0.999974i	$0.502279\pi$
$42$	−3.89417	−0.600884
$43$	−0.702722	−0.107164	−0.0535820	−	0.998563i	$-0.517064\pi$
$43$	−0.702722	−0.107164	−0.0535820	+	0.998563i	$0.517064\pi$
$44$	−13.9617	−2.10480
$45$	1.35070	0.201350
$46$	12.1911	1.79748
$47$	−10.1367	−1.47859	−0.739295	−	0.673382i	$-0.764841\pi$
$47$	−10.1367	−1.47859	−0.739295	+	0.673382i	$0.764841\pi$
$48$	2.39911	0.346282
$49$	−4.46590	−0.637985
$50$	10.8035	1.52785
$51$	−3.60838	−0.505275
$52$	−24.4893	−3.39606
$53$	3.48172	0.478250	0.239125	−	0.970989i	$-0.423139\pi$
$53$	3.48172	0.478250	0.239125	+	0.970989i	$0.423139\pi$
$54$	12.1138	1.64848
$55$	2.60414	0.351143
$56$	−6.50419	−0.869159
$57$	8.67210	1.14865
$58$	6.14512	0.806894
$59$	11.3479	1.47737	0.738684	−	0.674052i	$-0.235448\pi$
$59$	11.3479	1.47737	0.738684	+	0.674052i	$0.235448\pi$
$60$	−2.62807	−0.339283
$61$	10.2702	1.31497	0.657483	−	0.753470i	$-0.271621\pi$
$61$	10.2702	1.31497	0.657483	+	0.753470i	$0.271621\pi$
$62$	−8.06021	−1.02365
$63$	−3.10730	−0.391483
$64$	−10.8325	−1.35406
$65$	4.56776	0.566561
$66$	9.20618	1.13320
$67$	3.97791	0.485979	0.242989	−	0.970029i	$-0.421872\pi$
$67$	3.97791	0.485979	0.242989	+	0.970029i	$0.421872\pi$
$68$	−13.0763	−1.58573
$69$	−5.22299	−0.628774
$70$	2.63217	0.314604
$71$	1.20708	0.143254	0.0716268	−	0.997431i	$-0.477181\pi$
$71$	1.20708	0.143254	0.0716268	+	0.997431i	$0.477181\pi$
$72$	7.97539	0.939908
$73$	10.3051	1.20612	0.603058	−	0.797697i	$-0.293949\pi$
$73$	10.3051	1.20612	0.603058	+	0.797697i	$0.293949\pi$
$74$	3.52925	0.410267
$75$	−4.62850	−0.534453
$76$	31.4265	3.60487
$77$	−5.99086	−0.682722
$78$	16.1480	1.82840
$79$	10.0280	1.12824	0.564118	−	0.825694i	$-0.309216\pi$
$79$	10.0280	1.12824	0.564118	+	0.825694i	$0.309216\pi$
$80$	−1.62162	−0.181303
$81$	0.666026	0.0740029
$82$	0.219113	0.0241970
$83$	11.1174	1.22030	0.610149	−	0.792287i	$-0.291110\pi$
$83$	11.1174	1.22030	0.610149	+	0.792287i	$0.291110\pi$
$84$	6.04591	0.659663
$85$	2.43900	0.264546
$86$	1.67918	0.181071
$87$	−2.63273	−0.282258
$88$	15.3765	1.63914
$89$	9.14236	0.969089	0.484544	−	0.874767i	$-0.338985\pi$
$89$	9.14236	0.969089	0.484544	+	0.874767i	$0.338985\pi$
$90$	−3.22755	−0.340213
$91$	−10.5082	−1.10156
$92$	−18.9274	−1.97332
$93$	3.45320	0.358080
$94$	24.2220	2.49831
$95$	−5.86169	−0.601397
$96$	2.63289	0.268718
$97$	4.87256	0.494734	0.247367	−	0.968922i	$-0.420435\pi$
$97$	4.87256	0.494734	0.247367	+	0.968922i	$0.420435\pi$
$98$	10.6714	1.07798
$99$	7.34595	0.738296
$100$	−16.7730	−1.67730
$101$	17.7420	1.76539	0.882697	−	0.469943i	$-0.155726\pi$
$101$	17.7420	1.76539	0.882697	+	0.469943i	$0.155726\pi$
$102$	8.62236	0.853741
$103$	0.798122	0.0786413	0.0393206	−	0.999227i	$-0.487481\pi$
$103$	0.798122	0.0786413	0.0393206	+	0.999227i	$0.487481\pi$
$104$	26.9710	2.64472
$105$	−1.12769	−0.110051
$106$	−8.31969	−0.808079
$107$	−16.3708	−1.58263	−0.791314	−	0.611411i	$-0.790602\pi$
$107$	−16.3708	−1.58263	−0.791314	+	0.611411i	$0.790602\pi$
$108$	−18.8073	−1.80973
$109$	3.36915	0.322706	0.161353	−	0.986897i	$-0.448414\pi$
$109$	3.36915	0.322706	0.161353	+	0.986897i	$0.448414\pi$
$110$	−6.22269	−0.593311
$111$	−1.51202	−0.143515
$112$	3.73056	0.352505
$113$	−18.1954	−1.71168	−0.855840	−	0.517240i	$-0.826959\pi$
$113$	−18.1954	−1.71168	−0.855840	+	0.517240i	$0.826959\pi$
$114$	−20.7223	−1.94082
$115$	3.53035	0.329207
$116$	−9.54064	−0.885826
$117$	12.8851	1.19122
$118$	−27.1162	−2.49625
$119$	−5.61094	−0.514354
$120$	2.89439	0.264221
$121$	3.16296	0.287542
$122$	−24.5410	−2.22184
$123$	−0.0938736	−0.00846430
$124$	12.5139	1.12378
$125$	6.58838	0.589282
$126$	7.42501	0.661472
$127$	17.0117	1.50955	0.754773	−	0.655986i	$-0.227747\pi$
$127$	17.0117	1.50955	0.754773	+	0.655986i	$0.227747\pi$
$128$	20.7409	1.83325
$129$	−0.719403	−0.0633399
$130$	−10.9148	−0.957295
$131$	−11.4909	−1.00397	−0.501984	−	0.864877i	$-0.667396\pi$
$131$	−11.4909	−1.00397	−0.501984	+	0.864877i	$0.667396\pi$
$132$	−14.2931	−1.24405
$133$	13.4849	1.16929
$134$	−9.50536	−0.821138
$135$	3.50795	0.301917
$136$	14.4014	1.23491
$137$	16.2002	1.38408	0.692039	−	0.721861i	$-0.256713\pi$
$137$	16.2002	1.38408	0.692039	+	0.721861i	$0.256713\pi$
$138$	12.4805	1.06241
$139$	9.43988	0.800680	0.400340	−	0.916367i	$-0.368892\pi$
$139$	9.43988	0.800680	0.400340	+	0.916367i	$0.368892\pi$
$140$	−4.08659	−0.345380
$141$	−10.3773	−0.873929
$142$	−2.88435	−0.242050
$143$	24.8424	2.07742
$144$	−4.57438	−0.381198
$145$	1.77953	0.147782
$146$	−24.6243	−2.03792
$147$	−4.57191	−0.377085
$148$	−5.47935	−0.450400
$149$	−1.26291	−0.103462	−0.0517310	−	0.998661i	$-0.516474\pi$
$149$	−1.26291	−0.103462	−0.0517310	+	0.998661i	$0.516474\pi$
$150$	11.0600	0.903043
$151$	−1.91704	−0.156006	−0.0780032	−	0.996953i	$-0.524854\pi$
$151$	−1.91704	−0.156006	−0.0780032	+	0.996953i	$0.524854\pi$
$152$	−34.6112	−2.80734
$153$	6.88010	0.556223
$154$	14.3154	1.15357
$155$	−2.33411	−0.187480
$156$	−25.0706	−2.00726
$157$	−18.3959	−1.46815	−0.734077	−	0.679066i	$-0.762385\pi$
$157$	−18.3959	−1.46815	−0.734077	+	0.679066i	$0.762385\pi$
$158$	−23.9622	−1.90633
$159$	3.56437	0.282673
$160$	−1.77964	−0.140693
$161$	−8.12162	−0.640073
$162$	−1.59149	−0.125040
$163$	0.977568	0.0765690	0.0382845	−	0.999267i	$-0.487811\pi$
$163$	0.977568	0.0765690	0.0382845	+	0.999267i	$0.487811\pi$
$164$	−0.340185	−0.0265640
$165$	2.66596	0.207545
$166$	−26.5655	−2.06189
$167$	−0.0268537	−0.00207800	−0.00103900	−	0.999999i	$-0.500331\pi$
$167$	−0.0268537	−0.00207800	−0.00103900	+	0.999999i	$0.500331\pi$
$168$	−6.65859	−0.513721
$169$	30.5744	2.35188
$170$	−5.82808	−0.446993
$171$	−16.5351	−1.26447
$172$	−2.60702	−0.198783
$173$	−0.0535446	−0.00407092	−0.00203546	−	0.999998i	$-0.500648\pi$
$173$	−0.0535446	−0.00407092	−0.00203546	+	0.999998i	$0.500648\pi$
$174$	6.29100	0.476919
$175$	−7.19720	−0.544057
$176$	−8.81939	−0.664786
$177$	11.6173	0.873206
$178$	−21.8460	−1.63743
$179$	2.77153	0.207154	0.103577	−	0.994621i	$-0.466971\pi$
$179$	2.77153	0.207154	0.103577	+	0.994621i	$0.466971\pi$
$180$	5.01094	0.373493
$181$	−0.157125	−0.0116790	−0.00583952	−	0.999983i	$-0.501859\pi$
$181$	−0.157125	−0.0116790	−0.00583952	+	0.999983i	$0.501859\pi$
$182$	25.1097	1.86126
$183$	10.5140	0.777218
$184$	20.8454	1.53675
$185$	1.02201	0.0751399
$186$	−8.25155	−0.605033
$187$	13.2648	0.970018
$188$	−37.6060	−2.74270
$189$	−8.07009	−0.587013
$190$	14.0067	1.01616
$191$	0.875373	0.0633398	0.0316699	−	0.999498i	$-0.489917\pi$
$191$	0.875373	0.0633398	0.0316699	+	0.999498i	$0.489917\pi$
$192$	−11.0896	−0.800323
$193$	13.6082	0.979542	0.489771	−	0.871851i	$-0.337080\pi$
$193$	13.6082	0.979542	0.489771	+	0.871851i	$0.337080\pi$
$194$	−11.6432	−0.835930
$195$	4.67619	0.334869
$196$	−16.5680	−1.18343
$197$	18.8162	1.34060	0.670299	−	0.742092i	$-0.266166\pi$
$197$	18.8162	1.34060	0.670299	+	0.742092i	$0.266166\pi$
$198$	−17.5534	−1.24747
$199$	−14.2695	−1.01154	−0.505770	−	0.862668i	$-0.668792\pi$
$199$	−14.2695	−1.01154	−0.505770	+	0.862668i	$0.668792\pi$
$200$	18.4728	1.30622
$201$	4.07234	0.287241
$202$	−42.3951	−2.98291
$203$	−4.09383	−0.287330
$204$	−13.3867	−0.937256
$205$	0.0634515	0.00443165
$206$	−1.90714	−0.132877
$207$	9.95866	0.692175
$208$	−15.4695	−1.07262
$209$	−31.8796	−2.20516
$210$	2.69465	0.185949
$211$	−17.2295	−1.18612	−0.593062	−	0.805157i	$-0.702081\pi$
$211$	−17.2295	−1.18612	−0.593062	+	0.805157i	$0.702081\pi$
$212$	12.9168	0.887127
$213$	1.23573	0.0846709
$214$	39.1187	2.67410
$215$	0.486263	0.0331629
$216$	20.7132	1.40935
$217$	5.36964	0.364515
$218$	−8.05072	−0.545263
$219$	10.5497	0.712882
$220$	9.66107	0.651349
$221$	23.2670	1.56510
$222$	3.61303	0.242491
$223$	−0.986263	−0.0660451	−0.0330225	−	0.999455i	$-0.510513\pi$
$223$	−0.986263	−0.0660451	−0.0330225	+	0.999455i	$0.510513\pi$
$224$	4.09407	0.273547
$225$	8.82515	0.588344
$226$	43.4786	2.89215
$227$	−14.6920	−0.975140	−0.487570	−	0.873084i	$-0.662117\pi$
$227$	−14.6920	−0.975140	−0.487570	+	0.873084i	$0.662117\pi$
$228$	32.1725	2.13068
$229$	26.9013	1.77769	0.888844	−	0.458210i	$-0.151509\pi$
$229$	26.9013	1.77769	0.888844	+	0.458210i	$0.151509\pi$
$230$	−8.43591	−0.556247
$231$	−6.13307	−0.403527
$232$	10.5075	0.689849
$233$	0.300260	0.0196707	0.00983534	−	0.999952i	$-0.496869\pi$
$233$	0.300260	0.0196707	0.00983534	+	0.999952i	$0.496869\pi$
$234$	−30.7893	−2.01276
$235$	7.01430	0.457562
$236$	42.0993	2.74043
$237$	10.2660	0.666850
$238$	13.4076	0.869083
$239$	−22.7322	−1.47042	−0.735211	−	0.677838i	$-0.762917\pi$
$239$	−22.7322	−1.47042	−0.735211	+	0.677838i	$0.762917\pi$
$240$	−1.66012	−0.107160
$241$	−27.3276	−1.76032	−0.880162	−	0.474673i	$-0.842566\pi$
$241$	−27.3276	−1.76032	−0.880162	+	0.474673i	$0.842566\pi$
$242$	−7.55800	−0.485847
$243$	15.8904	1.01937
$244$	38.1013	2.43919
$245$	3.09027	0.197430
$246$	0.224314	0.0143018
$247$	−55.9180	−3.55797
$248$	−13.7820	−0.875161
$249$	11.3813	0.721264
$250$	−15.7432	−0.995685
$251$	−16.9066	−1.06714	−0.533569	−	0.845757i	$-0.679149\pi$
$251$	−16.9066	−1.06714	−0.533569	+	0.845757i	$0.679149\pi$
$252$	−11.5277	−0.726179
$253$	19.2003	1.20711
$254$	−40.6501	−2.55062
$255$	2.49690	0.156362
$256$	−27.8962	−1.74351
$257$	−9.92468	−0.619084	−0.309542	−	0.950886i	$-0.600176\pi$
$257$	−9.92468	−0.619084	−0.309542	+	0.950886i	$0.600176\pi$
$258$	1.71904	0.107023
$259$	−2.35115	−0.146094
$260$	16.9459	1.05094
$261$	5.01982	0.310719
$262$	27.4580	1.69636
$263$	21.6544	1.33527	0.667633	−	0.744491i	$-0.267308\pi$
$263$	21.6544	1.33527	0.667633	+	0.744491i	$0.267308\pi$
$264$	15.7415	0.968824
$265$	−2.40925	−0.147999
$266$	−32.2227	−1.97570
$267$	9.35939	0.572785
$268$	14.7576	0.901463
$269$	−14.0081	−0.854087	−0.427044	−	0.904231i	$-0.640445\pi$
$269$	−14.0081	−0.854087	−0.427044	+	0.904231i	$0.640445\pi$
$270$	−8.38238	−0.510136
$271$	−15.2549	−0.926669	−0.463335	−	0.886183i	$-0.653347\pi$
$271$	−15.2549	−0.926669	−0.463335	+	0.886183i	$0.653347\pi$
$272$	−8.26010	−0.500842
$273$	−10.7576	−0.651082
$274$	−38.7110	−2.33862
$275$	17.0149	1.02603
$276$	−19.3767	−1.16634
$277$	15.0193	0.902422	0.451211	−	0.892417i	$-0.350992\pi$
$277$	15.0193	0.902422	0.451211	+	0.892417i	$0.350992\pi$
$278$	−22.5569	−1.35288
$279$	−6.58421	−0.394186
$280$	4.50071	0.268969
$281$	21.2300	1.26648	0.633239	−	0.773957i	$-0.281725\pi$
$281$	21.2300	1.26648	0.633239	+	0.773957i	$0.281725\pi$
$282$	24.7970	1.47664
$283$	−10.6216	−0.631389	−0.315694	−	0.948861i	$-0.602237\pi$
$283$	−10.6216	−0.631389	−0.315694	+	0.948861i	$0.602237\pi$
$284$	4.47812	0.265727
$285$	−6.00084	−0.355459
$286$	−59.3617	−3.51013
$287$	−0.145971	−0.00861640
$288$	−5.02012	−0.295813
$289$	−4.57640	−0.269200
$290$	−4.25225	−0.249701
$291$	4.98823	0.292415
$292$	38.2306	2.23728
$293$	−28.7086	−1.67718	−0.838589	−	0.544765i	$-0.816619\pi$
$293$	−28.7086	−1.67718	−0.838589	+	0.544765i	$0.816619\pi$
$294$	10.9247	0.637144
$295$	−7.85240	−0.457184
$296$	6.03461	0.350755
$297$	19.0784	1.10704
$298$	3.01778	0.174815
$299$	33.6780	1.94765
$300$	−17.1712	−0.991380
$301$	−1.11865	−0.0644781
$302$	4.58083	0.263597
$303$	18.1631	1.04345
$304$	19.8517	1.13857
$305$	−7.10669	−0.406928
$306$	−16.4402	−0.939826
$307$	12.9693	0.740197	0.370098	−	0.928993i	$-0.379324\pi$
$307$	12.9693	0.740197	0.370098	+	0.928993i	$0.379324\pi$
$308$	−22.2254	−1.26641
$309$	0.817068	0.0464814
$310$	5.57743	0.316777
$311$	12.5848	0.713619	0.356810	−	0.934177i	$-0.383864\pi$
$311$	12.5848	0.713619	0.356810	+	0.934177i	$0.383864\pi$
$312$	27.6112	1.56318
$313$	8.14618	0.460450	0.230225	−	0.973137i	$-0.426054\pi$
$313$	8.14618	0.460450	0.230225	+	0.973137i	$0.426054\pi$
$314$	43.9577	2.48068
$315$	2.15016	0.121148
$316$	37.2026	2.09281
$317$	−0.127186	−0.00714347	−0.00357174	−	0.999994i	$-0.501137\pi$
$317$	−0.127186	−0.00714347	−0.00357174	+	0.999994i	$0.501137\pi$
$318$	−8.51718	−0.477620
$319$	9.67819	0.541874
$320$	7.49574	0.419025
$321$	−16.7594	−0.935421
$322$	19.4069	1.08150
$323$	−29.8579	−1.66134
$324$	2.47088	0.137271
$325$	29.8447	1.65549
$326$	−2.33593	−0.129375
$327$	3.44913	0.190737
$328$	0.374658	0.0206870
$329$	−16.1365	−0.889633
$330$	−6.37041	−0.350680
$331$	−22.3024	−1.22585	−0.612925	−	0.790141i	$-0.710007\pi$
$331$	−22.3024	−1.22585	−0.612925	+	0.790141i	$0.710007\pi$
$332$	41.2444	2.26358
$333$	2.88297	0.157986
$334$	0.0641678	0.00351111
$335$	−2.75260	−0.150390
$336$	3.81912	0.208350
$337$	−29.0862	−1.58442	−0.792212	−	0.610246i	$-0.791071\pi$
$337$	−29.0862	−1.58442	−0.792212	+	0.610246i	$0.791071\pi$
$338$	−73.0587	−3.97387
$339$	−18.6273	−1.01170
$340$	9.04840	0.490719
$341$	−12.6943	−0.687437
$342$	39.5112	2.13652
$343$	−18.2524	−0.985538
$344$	2.87121	0.154805
$345$	3.61416	0.194580
$346$	0.127947	0.00687846
$347$	−21.7671	−1.16852	−0.584260	−	0.811566i	$-0.698615\pi$
$347$	−21.7671	−1.16852	−0.584260	+	0.811566i	$0.698615\pi$
$348$	−9.76712	−0.523573
$349$	7.87393	0.421482	0.210741	−	0.977542i	$-0.432412\pi$
$349$	7.87393	0.421482	0.210741	+	0.977542i	$0.432412\pi$
$350$	17.1980	0.919271
$351$	33.4643	1.78619
$352$	−9.67877	−0.515880
$353$	−6.28135	−0.334323	−0.167161	−	0.985930i	$-0.553460\pi$
$353$	−6.28135	−0.334323	−0.167161	+	0.985930i	$0.553460\pi$
$354$	−27.7599	−1.47542
$355$	−0.835262	−0.0443311
$356$	33.9171	1.79760
$357$	−5.74414	−0.304012
$358$	−6.62266	−0.350019
$359$	−13.4265	−0.708625	−0.354312	−	0.935127i	$-0.615285\pi$
$359$	−13.4265	−0.708625	−0.354312	+	0.935127i	$0.615285\pi$
$360$	−5.51873	−0.290863
$361$	52.7581	2.77674
$362$	0.375457	0.0197336
$363$	3.23804	0.169953
$364$	−38.9842	−2.04333
$365$	−7.13080	−0.373243
$366$	−25.1236	−1.31323
$367$	16.3491	0.853417	0.426708	−	0.904389i	$-0.359673\pi$
$367$	16.3491	0.853417	0.426708	+	0.904389i	$0.359673\pi$
$368$	−11.9562	−0.623258
$369$	0.178989	0.00931777
$370$	−2.44214	−0.126961
$371$	5.54250	0.287752
$372$	12.8110	0.664218
$373$	11.2437	0.582177	0.291089	−	0.956696i	$-0.405983\pi$
$373$	11.2437	0.582177	0.291089	+	0.956696i	$0.405983\pi$
$374$	−31.6967	−1.63900
$375$	6.74477	0.348299
$376$	41.4169	2.13591
$377$	16.9759	0.874303
$378$	19.2838	0.991850
$379$	32.1363	1.65073	0.825366	−	0.564598i	$-0.190969\pi$
$379$	32.1363	1.65073	0.825366	+	0.564598i	$0.190969\pi$
$380$	−21.7462	−1.11556
$381$	17.4155	0.892226
$382$	−2.09174	−0.107023
$383$	1.61818	0.0826852	0.0413426	−	0.999145i	$-0.486836\pi$
$383$	1.61818	0.0826852	0.0413426	+	0.999145i	$0.486836\pi$
$384$	21.2332	1.08355
$385$	4.14550	0.211274
$386$	−32.5174	−1.65509
$387$	1.37168	0.0697266
$388$	18.0766	0.917702
$389$	26.4362	1.34037	0.670183	−	0.742196i	$-0.266216\pi$
$389$	26.4362	1.34037	0.670183	+	0.742196i	$0.266216\pi$
$390$	−11.1739	−0.565814
$391$	17.9827	0.909422
$392$	18.2469	0.921608
$393$	−11.7637	−0.593400
$394$	−44.9619	−2.26515
$395$	−6.93906	−0.349142
$396$	27.2526	1.36950
$397$	16.5300	0.829618	0.414809	−	0.909908i	$-0.363848\pi$
$397$	16.5300	0.829618	0.414809	+	0.909908i	$0.363848\pi$
$398$	34.0976	1.70916
$399$	13.8050	0.691115
$400$	−10.5953	−0.529765
$401$	17.7641	0.887098	0.443549	−	0.896250i	$-0.353719\pi$
$401$	17.7641	0.887098	0.443549	+	0.896250i	$0.353719\pi$
$402$	−9.73100	−0.485338
$403$	−22.2663	−1.10917
$404$	65.8207	3.27470
$405$	−0.460871	−0.0229009
$406$	9.78235	0.485490
$407$	5.55835	0.275517
$408$	14.7433	0.729900
$409$	−18.1025	−0.895112	−0.447556	−	0.894256i	$-0.647705\pi$
$409$	−18.1025	−0.895112	−0.447556	+	0.894256i	$0.647705\pi$
$410$	−0.151620	−0.00748797
$411$	16.5848	0.818067
$412$	2.96094	0.145875
$413$	18.0645	0.888898
$414$	−23.7966	−1.16954
$415$	−7.69294	−0.377632
$416$	−16.9769	−0.832362
$417$	9.66397	0.473247
$418$	76.1774	3.72596
$419$	9.75815	0.476717	0.238358	−	0.971177i	$-0.423391\pi$
$419$	9.75815	0.476717	0.238358	+	0.971177i	$0.423391\pi$
$420$	−4.18359	−0.204139
$421$	13.7003	0.667709	0.333855	−	0.942625i	$-0.391651\pi$
$421$	13.7003	0.667709	0.333855	+	0.942625i	$0.391651\pi$
$422$	41.1704	2.00414
$423$	19.7864	0.962049
$424$	−14.2257	−0.690862
$425$	15.9358	0.773002
$426$	−2.95282	−0.143065
$427$	16.3490	0.791184
$428$	−60.7339	−2.93568
$429$	25.4321	1.22787
$430$	−1.16194	−0.0560339
$431$	5.57834	0.268699	0.134350	−	0.990934i	$-0.457105\pi$
$431$	5.57834	0.268699	0.134350	+	0.990934i	$0.457105\pi$
$432$	−11.8803	−0.571591
$433$	−9.29506	−0.446692	−0.223346	−	0.974739i	$-0.571698\pi$
$433$	−9.29506	−0.446692	−0.223346	+	0.974739i	$0.571698\pi$
$434$	−12.8310	−0.615905
$435$	1.82177	0.0873472
$436$	12.4992	0.598602
$437$	−43.2181	−2.06740
$438$	−25.2089	−1.20453
$439$	2.26624	0.108162	0.0540809	−	0.998537i	$-0.482777\pi$
$439$	2.26624	0.108162	0.0540809	+	0.998537i	$0.482777\pi$
$440$	−10.6401	−0.507247
$441$	8.71725	0.415107
$442$	−55.5972	−2.64449
$443$	41.7013	1.98129	0.990644	−	0.136473i	$-0.0435767\pi$
$443$	41.7013	1.98129	0.990644	+	0.136473i	$0.0435767\pi$
$444$	−5.60942	−0.266211
$445$	−6.32625	−0.299893
$446$	2.35671	0.111594
$447$	−1.29289	−0.0611518
$448$	−17.2441	−0.814705
$449$	−24.6243	−1.16209	−0.581046	−	0.813871i	$-0.697356\pi$
$449$	−24.6243	−1.16209	−0.581046	+	0.813871i	$0.697356\pi$
$450$	−21.0880	−0.994099
$451$	0.345089	0.0162496
$452$	−67.5029	−3.17507
$453$	−1.96255	−0.0922084
$454$	35.1070	1.64765
$455$	7.27136	0.340887
$456$	−35.4328	−1.65929
$457$	2.68355	0.125531	0.0627655	−	0.998028i	$-0.480008\pi$
$457$	2.68355	0.125531	0.0627655	+	0.998028i	$0.480008\pi$
$458$	−64.2817	−3.00368
$459$	17.8686	0.834033
$460$	13.0972	0.610660
$461$	−23.1757	−1.07940	−0.539699	−	0.841858i	$-0.681462\pi$
$461$	−23.1757	−1.07940	−0.539699	+	0.841858i	$0.681462\pi$
$462$	14.6552	0.681822
$463$	−20.8861	−0.970658	−0.485329	−	0.874332i	$-0.661300\pi$
$463$	−20.8861	−0.970658	−0.485329	+	0.874332i	$0.661300\pi$
$464$	−6.02668	−0.279782
$465$	−2.38951	−0.110811
$466$	−0.717482	−0.0332367
$467$	40.3437	1.86688	0.933441	−	0.358731i	$-0.116790\pi$
$467$	40.3437	1.86688	0.933441	+	0.358731i	$0.116790\pi$
$468$	47.8021	2.20965
$469$	6.33238	0.292402
$470$	−16.7609	−0.773124
$471$	−18.8326	−0.867761
$472$	−46.3655	−2.13415
$473$	2.64460	0.121599
$474$	−24.5310	−1.12675
$475$	−38.2989	−1.75728
$476$	−20.8160	−0.954098
$477$	−6.79617	−0.311175
$478$	54.3194	2.48451
$479$	29.6590	1.35515	0.677577	−	0.735452i	$-0.263030\pi$
$479$	29.6590	1.35515	0.677577	+	0.735452i	$0.263030\pi$
$480$	−1.82188	−0.0831571
$481$	9.74955	0.444541
$482$	65.3003	2.97435
$483$	−8.31441	−0.378319
$484$	11.7342	0.533373
$485$	−3.37167	−0.153100
$486$	−37.9706	−1.72238
$487$	3.27381	0.148350	0.0741752	−	0.997245i	$-0.476368\pi$
$487$	3.27381	0.148350	0.0741752	+	0.997245i	$0.476368\pi$
$488$	−41.9624	−1.89955
$489$	1.00077	0.0452566
$490$	−7.38431	−0.333589
$491$	0.893860	0.0403393	0.0201697	−	0.999797i	$-0.493579\pi$
$491$	0.893860	0.0403393	0.0201697	+	0.999797i	$0.493579\pi$
$492$	−0.348260	−0.0157008
$493$	9.06443	0.408242
$494$	133.618	6.01176
$495$	−5.08318	−0.228472
$496$	7.90486	0.354939
$497$	1.92153	0.0861924
$498$	−27.1962	−1.21869
$499$	−3.18500	−0.142580	−0.0712902	−	0.997456i	$-0.522712\pi$
$499$	−3.18500	−0.142580	−0.0712902	+	0.997456i	$0.522712\pi$
$500$	24.4421	1.09309
$501$	−0.0274911	−0.00122821
$502$	40.3990	1.80310
$503$	−26.9720	−1.20262	−0.601310	−	0.799016i	$-0.705354\pi$
$503$	−26.9720	−1.20262	−0.601310	+	0.799016i	$0.705354\pi$
$504$	12.6959	0.565521
$505$	−12.2769	−0.546316
$506$	−45.8797	−2.03960
$507$	31.3002	1.39009
$508$	63.1115	2.80012
$509$	9.87918	0.437887	0.218944	−	0.975738i	$-0.429739\pi$
$509$	9.87918	0.437887	0.218944	+	0.975738i	$0.429739\pi$
$510$	−5.96642	−0.264198
$511$	16.4045	0.725692
$512$	25.1772	1.11269
$513$	−42.9439	−1.89602
$514$	23.7154	1.04604
$515$	−0.552277	−0.0243362
$516$	−2.66890	−0.117492
$517$	38.1481	1.67775
$518$	5.61817	0.246848
$519$	−0.0548157	−0.00240614
$520$	−18.6631	−0.818432
$521$	−37.6895	−1.65121	−0.825604	−	0.564250i	$-0.809165\pi$
$521$	−37.6895	−1.65121	−0.825604	+	0.564250i	$0.809165\pi$
$522$	−11.9950	−0.525008
$523$	2.65860	0.116252	0.0581262	−	0.998309i	$-0.481487\pi$
$523$	2.65860	0.116252	0.0581262	+	0.998309i	$0.481487\pi$
$524$	−42.6300	−1.86230
$525$	−7.36805	−0.321568
$526$	−51.7439	−2.25614
$527$	−11.8893	−0.517906
$528$	−9.02875	−0.392926
$529$	3.02917	0.131703
$530$	5.75698	0.250067
$531$	−22.1506	−0.961254
$532$	50.0274	2.16896
$533$	0.605299	0.0262184
$534$	−22.3646	−0.967811
$535$	11.3281	0.489758
$536$	−16.2531	−0.702026
$537$	2.83732	0.122439
$538$	33.4728	1.44311
$539$	16.8068	0.723921
$540$	13.0141	0.560038
$541$	35.0639	1.50752	0.753758	−	0.657152i	$-0.228239\pi$
$541$	35.0639	1.50752	0.753758	+	0.657152i	$0.228239\pi$
$542$	36.4521	1.56575
$543$	−0.160855	−0.00690296
$544$	−9.06498	−0.388658
$545$	−2.33136	−0.0998643
$546$	25.7058	1.10011
$547$	−16.0956	−0.688198	−0.344099	−	0.938933i	$-0.611816\pi$
$547$	−16.0956	−0.688198	−0.344099	+	0.938933i	$0.611816\pi$
$548$	60.1009	2.56738
$549$	−20.0470	−0.855587
$550$	−40.6576	−1.73365
$551$	−21.7847	−0.928061
$552$	21.3403	0.908302
$553$	15.9634	0.678833
$554$	−35.8892	−1.52478
$555$	1.04627	0.0444118
$556$	35.0209	1.48522
$557$	−22.9718	−0.973345	−0.486673	−	0.873584i	$-0.661790\pi$
$557$	−22.9718	−0.973345	−0.486673	+	0.873584i	$0.661790\pi$
$558$	15.7332	0.666040
$559$	4.63873	0.196197
$560$	−2.58144	−0.109086
$561$	13.5797	0.573335
$562$	−50.7299	−2.13991
$563$	−2.64631	−0.111529	−0.0557644	−	0.998444i	$-0.517760\pi$
$563$	−2.64631	−0.111529	−0.0557644	+	0.998444i	$0.517760\pi$
$564$	−38.4987	−1.62109
$565$	12.5907	0.529695
$566$	25.3807	1.06683
$567$	1.06024	0.0445258
$568$	−4.93192	−0.206939
$569$	31.7026	1.32904	0.664522	−	0.747269i	$-0.268635\pi$
$569$	31.7026	1.32904	0.664522	+	0.747269i	$0.268635\pi$
$570$	14.3392	0.600604
$571$	33.8474	1.41647	0.708235	−	0.705977i	$-0.249492\pi$
$571$	33.8474	1.41647	0.708235	+	0.705977i	$0.249492\pi$
$572$	92.1623	3.85350
$573$	0.896153	0.0374373
$574$	0.348803	0.0145588
$575$	23.0665	0.961939
$576$	21.1445	0.881022
$577$	33.5613	1.39717	0.698587	−	0.715525i	$-0.253813\pi$
$577$	33.5613	1.39717	0.698587	+	0.715525i	$0.253813\pi$
$578$	10.9355	0.454856
$579$	13.9313	0.578964
$580$	6.60184	0.274127
$581$	17.6977	0.734225
$582$	−11.9196	−0.494081
$583$	−13.1030	−0.542670
$584$	−42.1048	−1.74231
$585$	−8.91609	−0.368635
$586$	68.6004	2.83386
$587$	−29.2482	−1.20720	−0.603602	−	0.797286i	$-0.706268\pi$
$587$	−29.2482	−1.20720	−0.603602	+	0.797286i	$0.706268\pi$
$588$	−16.9613	−0.699470
$589$	28.5738	1.17736
$590$	18.7636	0.772485
$591$	19.2628	0.792367
$592$	−3.46123	−0.142256
$593$	−4.86929	−0.199958	−0.0999789	−	0.994990i	$-0.531878\pi$
$593$	−4.86929	−0.199958	−0.0999789	+	0.994990i	$0.531878\pi$
$594$	−45.5887	−1.87053
$595$	3.88261	0.159171
$596$	−4.68527	−0.191916
$597$	−14.6083	−0.597877
$598$	−80.4748	−3.29086
$599$	−19.0420	−0.778036	−0.389018	−	0.921230i	$-0.627186\pi$
$599$	−19.0420	−0.778036	−0.389018	+	0.921230i	$0.627186\pi$
$600$	18.9113	0.772050
$601$	19.4782	0.794532	0.397266	−	0.917704i	$-0.369959\pi$
$601$	19.4782	0.794532	0.397266	+	0.917704i	$0.369959\pi$
$602$	2.67306	0.108946
$603$	−7.76472	−0.316204
$604$	−7.11199	−0.289383
$605$	−2.18867	−0.0889823
$606$	−43.4015	−1.76307
$607$	10.1934	0.413739	0.206869	−	0.978369i	$-0.433672\pi$
$607$	10.1934	0.413739	0.206869	+	0.978369i	$0.433672\pi$
$608$	21.7861	0.883541
$609$	−4.19101	−0.169828
$610$	16.9817	0.687568
$611$	66.9133	2.70702
$612$	25.5244	1.03176
$613$	−38.1356	−1.54028	−0.770141	−	0.637874i	$-0.779814\pi$
$613$	−38.1356	−1.54028	−0.770141	+	0.637874i	$0.779814\pi$
$614$	−30.9906	−1.25068
$615$	0.0649578	0.00261935
$616$	24.4777	0.986233
$617$	19.5485	0.786993	0.393497	−	0.919326i	$-0.371265\pi$
$617$	19.5485	0.786993	0.393497	+	0.919326i	$0.371265\pi$
$618$	−1.95241	−0.0785376
$619$	35.8732	1.44186	0.720932	−	0.693006i	$-0.243714\pi$
$619$	35.8732	1.44186	0.720932	+	0.693006i	$0.243714\pi$
$620$	−8.65927	−0.347765
$621$	25.8640	1.03789
$622$	−30.0719	−1.20577
$623$	14.5536	0.583078
$624$	−15.8368	−0.633978
$625$	18.0469	0.721877
$626$	−19.4656	−0.778002
$627$	−32.6363	−1.30337
$628$	−68.2467	−2.72334
$629$	5.20586	0.207571
$630$	−5.13789	−0.204698
$631$	20.6698	0.822852	0.411426	−	0.911443i	$-0.365031\pi$
$631$	20.6698	0.822852	0.411426	+	0.911443i	$0.365031\pi$
$632$	−40.9726	−1.62980
$633$	−17.6385	−0.701066
$634$	0.303915	0.0120700
$635$	−11.7716	−0.467142
$636$	13.2234	0.524341
$637$	29.4798	1.16803
$638$	−23.1264	−0.915582
$639$	−2.35617	−0.0932085
$640$	−14.3521	−0.567316
$641$	21.3885	0.844796	0.422398	−	0.906410i	$-0.361188\pi$
$641$	21.3885	0.844796	0.422398	+	0.906410i	$0.361188\pi$
$642$	40.0473	1.58054
$643$	−34.6540	−1.36662	−0.683310	−	0.730128i	$-0.739460\pi$
$643$	−34.6540	−1.36662	−0.683310	+	0.730128i	$0.739460\pi$
$644$	−30.1303	−1.18730
$645$	0.497806	0.0196011
$646$	71.3465	2.80709
$647$	−21.1529	−0.831606	−0.415803	−	0.909455i	$-0.636499\pi$
$647$	−21.1529	−0.831606	−0.415803	+	0.909455i	$0.636499\pi$
$648$	−2.72127	−0.106902
$649$	−42.7063	−1.67637
$650$	−71.3150	−2.79721
$651$	5.49711	0.215449
$652$	3.62667	0.142031
$653$	39.0203	1.52698	0.763492	−	0.645817i	$-0.223483\pi$
$653$	39.0203	1.52698	0.763492	+	0.645817i	$0.223483\pi$
$654$	−8.24183	−0.322281
$655$	7.95139	0.310686
$656$	−0.214890	−0.00839004
$657$	−20.1151	−0.784764
$658$	38.5587	1.50318
$659$	−24.0817	−0.938090	−0.469045	−	0.883174i	$-0.655402\pi$
$659$	−24.0817	−0.938090	−0.469045	+	0.883174i	$0.655402\pi$
$660$	9.89041	0.384984
$661$	−4.27710	−0.166360	−0.0831801	−	0.996535i	$-0.526508\pi$
$661$	−4.27710	−0.166360	−0.0831801	+	0.996535i	$0.526508\pi$
$662$	53.2924	2.07127
$663$	23.8193	0.925064
$664$	−45.4240	−1.76279
$665$	−9.33116	−0.361847
$666$	−6.88895	−0.266941
$667$	13.1204	0.508024
$668$	−0.0996241	−0.00385457
$669$	−1.00968	−0.0390363
$670$	6.57743	0.254108
$671$	−38.6506	−1.49209
$672$	4.19126	0.161681
$673$	37.4545	1.44376	0.721882	−	0.692016i	$-0.243277\pi$
$673$	37.4545	1.44376	0.721882	+	0.692016i	$0.243277\pi$
$674$	69.5024	2.67713
$675$	22.9202	0.882197
$676$	113.428	4.36260
$677$	−0.845317	−0.0324882	−0.0162441	−	0.999868i	$-0.505171\pi$
$677$	−0.845317	−0.0324882	−0.0162441	+	0.999868i	$0.505171\pi$
$678$	44.5107	1.70942
$679$	7.75657	0.297670
$680$	−9.96534	−0.382153
$681$	−15.0407	−0.576362
$682$	30.3336	1.16153
$683$	23.0532	0.882105	0.441053	−	0.897481i	$-0.354605\pi$
$683$	23.0532	0.882105	0.441053	+	0.897481i	$0.354605\pi$
$684$	−61.3433	−2.34552
$685$	−11.2101	−0.428315
$686$	43.6148	1.66522
$687$	27.5399	1.05071
$688$	−1.64682	−0.0627842
$689$	−22.9831	−0.875587
$690$	−8.63616	−0.328773
$691$	−24.7034	−0.939760	−0.469880	−	0.882730i	$-0.655703\pi$
$691$	−24.7034	−0.939760	−0.469880	+	0.882730i	$0.655703\pi$
$692$	−0.198644	−0.00755132
$693$	11.6939	0.444215
$694$	52.0133	1.97440
$695$	−6.53212	−0.247778
$696$	10.7569	0.407739
$697$	0.323205	0.0122423
$698$	−18.8150	−0.712160
$699$	0.307388	0.0116265
$700$	−26.7008	−1.00920
$701$	32.6233	1.23217	0.616083	−	0.787681i	$-0.288719\pi$
$701$	32.6233	1.23217	0.616083	+	0.787681i	$0.288719\pi$
$702$	−79.9642	−3.01805
$703$	−12.5113	−0.471874
$704$	40.7666	1.53645
$705$	7.18081	0.270445
$706$	15.0095	0.564891
$707$	28.2432	1.06220
$708$	43.0987	1.61975
$709$	−7.32179	−0.274975	−0.137488	−	0.990503i	$-0.543903\pi$
$709$	−7.32179	−0.274975	−0.137488	+	0.990503i	$0.543903\pi$
$710$	1.99589	0.0749044
$711$	−19.5742	−0.734090
$712$	−37.3542	−1.39991
$713$	−17.2093	−0.644493
$714$	13.7258	0.513676
$715$	−17.1902	−0.642877
$716$	10.2820	0.384258
$717$	−23.2718	−0.869101
$718$	32.0832	1.19733
$719$	40.6923	1.51757	0.758784	−	0.651342i	$-0.225794\pi$
$719$	40.6923	1.51757	0.758784	+	0.651342i	$0.225794\pi$
$720$	3.16534	0.117965
$721$	1.27052	0.0473166
$722$	−126.067	−4.69174
$723$	−27.9763	−1.04045
$724$	−0.582917	−0.0216640
$725$	11.6270	0.431817
$726$	−7.73742	−0.287163
$727$	3.63658	0.134873	0.0674367	−	0.997724i	$-0.478518\pi$
$727$	3.63658	0.134873	0.0674367	+	0.997724i	$0.478518\pi$
$728$	42.9348	1.59127
$729$	14.2695	0.528500
$730$	17.0393	0.630653
$731$	2.47689	0.0916112
$732$	39.0058	1.44169
$733$	46.5311	1.71866	0.859332	−	0.511418i	$-0.170880\pi$
$733$	46.5311	1.71866	0.859332	+	0.511418i	$0.170880\pi$
$734$	−39.0668	−1.44198
$735$	3.16363	0.116692
$736$	−13.1212	−0.483654
$737$	−14.9703	−0.551440
$738$	−0.427700	−0.0157438
$739$	21.8017	0.801988	0.400994	−	0.916081i	$-0.368665\pi$
$739$	21.8017	0.801988	0.400994	+	0.916081i	$0.368665\pi$
$740$	3.79155	0.139380
$741$	−57.2454	−2.10296
$742$	−13.2440	−0.486203
$743$	17.1929	0.630748	0.315374	−	0.948967i	$-0.397870\pi$
$743$	17.1929	0.630748	0.315374	+	0.948967i	$0.397870\pi$
$744$	−14.1092	−0.517269
$745$	0.873900	0.0320172
$746$	−26.8673	−0.983680
$747$	−21.7008	−0.793991
$748$	49.2109	1.79933
$749$	−26.0605	−0.952230
$750$	−16.1169	−0.588505
$751$	18.6753	0.681470	0.340735	−	0.940159i	$-0.389324\pi$
$751$	18.6753	0.681470	0.340735	+	0.940159i	$0.389324\pi$
$752$	−23.7552	−0.866262
$753$	−17.3080	−0.630738
$754$	−40.5645	−1.47727
$755$	1.32653	0.0482775
$756$	−29.9391	−1.08888
$757$	17.5354	0.637335	0.318668	−	0.947867i	$-0.396765\pi$
$757$	17.5354	0.637335	0.318668	+	0.947867i	$0.396765\pi$
$758$	−76.7910	−2.78917
$759$	19.6560	0.713469
$760$	23.9499	0.868755
$761$	−36.1741	−1.31131	−0.655655	−	0.755061i	$-0.727607\pi$
$761$	−36.1741	−1.31131	−0.655655	+	0.755061i	$0.727607\pi$
$762$	−41.6151	−1.50756
$763$	5.36331	0.194165
$764$	3.24754	0.117492
$765$	−4.76083	−0.172128
$766$	−3.86670	−0.139710
$767$	−74.9084	−2.70478
$768$	−28.5584	−1.03051
$769$	42.0671	1.51698	0.758488	−	0.651687i	$-0.225938\pi$
$769$	42.0671	1.51698	0.758488	+	0.651687i	$0.225938\pi$
$770$	−9.90583	−0.356981
$771$	−10.1603	−0.365913
$772$	50.4850	1.81699
$773$	−29.1123	−1.04710	−0.523548	−	0.851996i	$-0.675392\pi$
$773$	−29.1123	−1.04710	−0.523548	+	0.851996i	$0.675392\pi$
$774$	−3.27769	−0.117814
$775$	−15.2505	−0.547814
$776$	−19.9085	−0.714673
$777$	−2.40697	−0.0863494
$778$	−63.1702	−2.26476
$779$	−0.776765	−0.0278305
$780$	17.3481	0.621163
$781$	−4.54268	−0.162550
$782$	−42.9702	−1.53661
$783$	13.0372	0.465910
$784$	−10.4657	−0.373776
$785$	12.7294	0.454333
$786$	28.1098	1.00264
$787$	−16.2086	−0.577775	−0.288887	−	0.957363i	$-0.593285\pi$
$787$	−16.2086	−0.577775	−0.288887	+	0.957363i	$0.593285\pi$
$788$	69.8059	2.48673
$789$	22.1684	0.789216
$790$	16.5811	0.589931
$791$	−28.9650	−1.02988
$792$	−30.0143	−1.06651
$793$	−67.7946	−2.40746
$794$	−39.4991	−1.40177
$795$	−2.46644	−0.0874755
$796$	−52.9383	−1.87635
$797$	−13.2231	−0.468384	−0.234192	−	0.972190i	$-0.575245\pi$
$797$	−13.2231	−0.468384	−0.234192	+	0.972190i	$0.575245\pi$
$798$	−32.9876	−1.16775
$799$	35.7289	1.26400
$800$	−11.6277	−0.411102
$801$	−17.8455	−0.630541
$802$	−42.4480	−1.49889
$803$	−38.7818	−1.36858
$804$	15.1079	0.532815
$805$	5.61992	0.198076
$806$	53.2062	1.87411
$807$	−14.3406	−0.504813
$808$	−72.4908	−2.55022
$809$	−31.9751	−1.12418	−0.562092	−	0.827075i	$-0.690003\pi$
$809$	−31.9751	−1.12418	−0.562092	+	0.827075i	$0.690003\pi$
$810$	1.10127	0.0386946
$811$	−6.19389	−0.217497	−0.108748	−	0.994069i	$-0.534684\pi$
$811$	−6.19389	−0.217497	−0.108748	+	0.994069i	$0.534684\pi$
$812$	−15.1876	−0.532981
$813$	−15.6170	−0.547713
$814$	−13.2819	−0.465529
$815$	−0.676448	−0.0236950
$816$	−8.45618	−0.296025
$817$	−5.95277	−0.208261
$818$	43.2566	1.51243
$819$	20.5116	0.716732
$820$	0.235398	0.00822045
$821$	−13.5354	−0.472390	−0.236195	−	0.971706i	$-0.575900\pi$
$821$	−13.5354	−0.472390	−0.236195	+	0.971706i	$0.575900\pi$
$822$	−39.6299	−1.38225
$823$	13.8750	0.483651	0.241825	−	0.970320i	$-0.422254\pi$
$823$	13.8750	0.483651	0.241825	+	0.970320i	$0.422254\pi$
$824$	−3.26099	−0.113602
$825$	17.4188	0.606444
$826$	−43.1659	−1.50193
$827$	11.9531	0.415650	0.207825	−	0.978166i	$-0.433362\pi$
$827$	11.9531	0.415650	0.207825	+	0.978166i	$0.433362\pi$
$828$	36.9455	1.28395
$829$	−54.1876	−1.88201	−0.941007	−	0.338387i	$-0.890119\pi$
$829$	−54.1876	−1.88201	−0.941007	+	0.338387i	$0.890119\pi$
$830$	18.3826	0.638068
$831$	15.3758	0.533382
$832$	71.5061	2.47903
$833$	15.7410	0.545393
$834$	−23.0924	−0.799625
$835$	0.0185820	0.000643055 0
$836$	−118.270	−4.09044
$837$	−17.1001	−0.591066
$838$	−23.3174	−0.805488
$839$	39.5974	1.36706	0.683528	−	0.729925i	$-0.260445\pi$
$839$	39.5974	1.36706	0.683528	+	0.729925i	$0.260445\pi$
$840$	4.60755	0.158976
$841$	−22.3865	−0.771947
$842$	−32.7373	−1.12820
$843$	21.7340	0.748558
$844$	−63.9193	−2.20019
$845$	−21.1566	−0.727810
$846$	−47.2804	−1.62553
$847$	5.03507	0.173007
$848$	8.15933	0.280193
$849$	−10.8737	−0.373186
$850$	−38.0793	−1.30611
$851$	7.53527	0.258306
$852$	4.58442	0.157060
$853$	−55.8668	−1.91284	−0.956421	−	0.291992i	$-0.905682\pi$
$853$	−55.8668	−1.91284	−0.956421	+	0.291992i	$0.905682\pi$
$854$	−39.0666	−1.33683
$855$	11.4418	0.391301
$856$	66.8885	2.28620
$857$	−1.28388	−0.0438566	−0.0219283	−	0.999760i	$-0.506981\pi$
$857$	−1.28388	−0.0438566	−0.0219283	+	0.999760i	$0.506981\pi$
$858$	−60.7709	−2.07468
$859$	−3.50058	−0.119438	−0.0597191	−	0.998215i	$-0.519020\pi$
$859$	−3.50058	−0.119438	−0.0597191	+	0.998215i	$0.519020\pi$
$860$	1.80398	0.0615152
$861$	−0.149436	−0.00509277
$862$	−13.3297	−0.454010
$863$	11.6133	0.395320	0.197660	−	0.980271i	$-0.436666\pi$
$863$	11.6133	0.395320	0.197660	+	0.980271i	$0.436666\pi$
$864$	−13.0379	−0.443560
$865$	0.0370513	0.00125978
$866$	22.2109	0.754757
$867$	−4.68504	−0.159112
$868$	19.9208	0.676154
$869$	−37.7390	−1.28021
$870$	−4.35319	−0.147587
$871$	−26.2586	−0.889737
$872$	−13.7658	−0.466169
$873$	−9.51104	−0.321900
$874$	103.271	3.49320
$875$	10.4880	0.354557
$876$	39.1381	1.32236
$877$	−55.5236	−1.87490	−0.937449	−	0.348124i	$-0.886819\pi$
$877$	−55.5236	−1.87490	−0.937449	+	0.348124i	$0.886819\pi$
$878$	−5.41526	−0.182756
$879$	−29.3901	−0.991305
$880$	6.10276	0.205724
$881$	47.2257	1.59107	0.795537	−	0.605905i	$-0.207189\pi$
$881$	47.2257	1.59107	0.795537	+	0.605905i	$0.207189\pi$
$882$	−20.8302	−0.701389
$883$	−17.4833	−0.588361	−0.294181	−	0.955750i	$-0.595047\pi$
$883$	−17.4833	−0.588361	−0.294181	+	0.955750i	$0.595047\pi$
$884$	86.3177	2.90318
$885$	−8.03880	−0.270221
$886$	−99.6467	−3.34770
$887$	27.3403	0.917997	0.458999	−	0.888437i	$-0.348208\pi$
$887$	27.3403	0.917997	0.458999	+	0.888437i	$0.348208\pi$
$888$	6.17786	0.207316
$889$	27.0807	0.908259
$890$	15.1168	0.506716
$891$	−2.50650	−0.0839710
$892$	−3.65892	−0.122510
$893$	−85.8681	−2.87347
$894$	3.08942	0.103326
$895$	−1.91781	−0.0641055
$896$	33.0172	1.10303
$897$	34.4774	1.15117
$898$	58.8406	1.96354
$899$	−8.67461	−0.289314
$900$	32.7403	1.09134
$901$	−12.2720	−0.408841
$902$	−0.824603	−0.0274563
$903$	−1.14521	−0.0381102
$904$	74.3435	2.47263
$905$	0.108726	0.00361418
$906$	4.68957	0.155801
$907$	−21.1427	−0.702033	−0.351016	−	0.936369i	$-0.614164\pi$
$907$	−21.1427	−0.702033	−0.351016	+	0.936369i	$0.614164\pi$
$908$	−54.5055	−1.80883
$909$	−34.6316	−1.14866
$910$	−17.3752	−0.575982
$911$	4.25567	0.140997	0.0704983	−	0.997512i	$-0.477541\pi$
$911$	4.25567	0.140997	0.0704983	+	0.997512i	$0.477541\pi$
$912$	20.3229	0.672959
$913$	−41.8390	−1.38467
$914$	−6.41243	−0.212104
$915$	−7.27539	−0.240517
$916$	99.8008	3.29751
$917$	−18.2923	−0.604064
$918$	−42.6976	−1.40923
$919$	1.61472	0.0532646	0.0266323	−	0.999645i	$-0.491522\pi$
$919$	1.61472	0.0532646	0.0266323	+	0.999645i	$0.491522\pi$
$920$	−14.4244	−0.475560
$921$	13.2772	0.437497
$922$	55.3791	1.82381
$923$	−7.96803	−0.262271
$924$	−22.7530	−0.748519
$925$	6.67759	0.219558
$926$	49.9080	1.64008
$927$	−1.55790	−0.0511682
$928$	−6.61394	−0.217113
$929$	−23.7427	−0.778971	−0.389486	−	0.921033i	$-0.627347\pi$
$929$	−23.7427	−0.778971	−0.389486	+	0.921033i	$0.627347\pi$
$930$	5.70983	0.187233
$931$	−37.8307	−1.23985
$932$	1.11393	0.0364880
$933$	12.8836	0.421789
$934$	−96.4027	−3.15439
$935$	−9.17885	−0.300181
$936$	−52.6463	−1.72080
$937$	−3.09828	−0.101216	−0.0506082	−	0.998719i	$-0.516116\pi$
$937$	−3.09828	−0.101216	−0.0506082	+	0.998719i	$0.516116\pi$
$938$	−15.1315	−0.494060
$939$	8.33956	0.272151
$940$	26.0222	0.848752
$941$	40.0969	1.30712	0.653561	−	0.756874i	$-0.273274\pi$
$941$	40.0969	1.30712	0.653561	+	0.756874i	$0.273274\pi$
$942$	45.0012	1.46622
$943$	0.467826	0.0152345
$944$	26.5935	0.865546
$945$	5.58427	0.181656
$946$	−6.31937	−0.205461
$947$	9.86792	0.320664	0.160332	−	0.987063i	$-0.448743\pi$
$947$	9.86792	0.320664	0.160332	+	0.987063i	$0.448743\pi$
$948$	38.0858	1.23697
$949$	−68.0247	−2.20817
$950$	91.5167	2.96920
$951$	−0.130205	−0.00422219
$952$	22.9254	0.743016
$953$	29.7987	0.965273	0.482637	−	0.875821i	$-0.339679\pi$
$953$	29.7987	0.965273	0.482637	+	0.875821i	$0.339679\pi$
$954$	16.2397	0.525779
$955$	−0.605733	−0.0196011
$956$	−84.3338	−2.72755
$957$	9.90793	0.320278
$958$	−70.8713	−2.28975
$959$	25.7889	0.832767
$960$	7.67368	0.247667
$961$	−19.6220	−0.632968
$962$	−23.2969	−0.751122
$963$	31.9552	1.02974
$964$	−101.382	−3.26530
$965$	−9.41650	−0.303128
$966$	19.8676	0.639229
$967$	23.0918	0.742581	0.371290	−	0.928517i	$-0.378915\pi$
$967$	23.0918	0.742581	0.371290	+	0.928517i	$0.378915\pi$
$968$	−12.9233	−0.415371
$969$	−30.5667	−0.981943
$970$	8.05673	0.258686
$971$	−2.89017	−0.0927501	−0.0463750	−	0.998924i	$-0.514767\pi$
$971$	−2.89017	−0.0927501	−0.0463750	+	0.998924i	$0.514767\pi$
$972$	58.9515	1.89087
$973$	15.0272	0.481751
$974$	−7.82288	−0.250661
$975$	30.5532	0.978485
$976$	24.0680	0.770399
$977$	34.4450	1.10199	0.550996	−	0.834508i	$-0.314248\pi$
$977$	34.4450	1.10199	0.550996	+	0.834508i	$0.314248\pi$
$978$	−2.39139	−0.0764681
$979$	−34.4061	−1.09962
$980$	11.4645	0.366221
$981$	−6.57645	−0.209970
$982$	−2.13591	−0.0681597
$983$	23.7644	0.757967	0.378984	−	0.925403i	$-0.376274\pi$
$983$	23.7644	0.757967	0.378984	+	0.925403i	$0.376274\pi$
$984$	0.383552	0.0122272
$985$	−13.0202	−0.414859
$986$	−21.6598	−0.689788
$987$	−16.5195	−0.525823
$988$	−207.449	−6.59984
$989$	3.58520	0.114003
$990$	12.1464	0.386039
$991$	−42.1420	−1.33868	−0.669342	−	0.742955i	$-0.733424\pi$
$991$	−42.1420	−1.33868	−0.669342	+	0.742955i	$0.733424\pi$
$992$	8.67513	0.275436
$993$	−22.8318	−0.724545
$994$	−4.59157	−0.145636
$995$	9.87410	0.313030
$996$	42.2235	1.33790
$997$	37.0304	1.17276	0.586382	−	0.810034i	$-0.300552\pi$
$997$	37.0304	1.17276	0.586382	+	0.810034i	$0.300552\pi$
$998$	7.61068	0.240912
$999$	7.48746	0.236893

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4001.2.a.b.1.19	✓	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4001.2.a.b.1.19	✓	184	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 $\F_{q}$

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Newspace parameters

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Embedding invariants

$q$ -expansion

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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.b.1.19

Level	$4001$
Weight	$2$
Character	4001.1
Self dual	yes
Analytic conductor	$31.948$
Analytic rank	$0$
Dimension	$184$
CM	no
Inner twists	$1$