LMFDB - Embedded newform 11.10.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [11,10,Mod(1,11)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(11, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("11.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 11 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	11.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:	$5.66539419780$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 1608x^{3} - 7720x^{2} + 616135x + 6122025 $ x^5 - x^4 - 1608x^3 - 7720x^2 + 616135*x + 6122025
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$26.1027$ of defining polynomial
Character	$\chi$	$=$	11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+29.1027 q^{2} -6.46828 q^{3} +334.967 q^{4} +2255.95 q^{5} -188.244 q^{6} +6425.84 q^{7} -5152.14 q^{8} -19641.2 q^{9} +O(q^{10})$	\(q+29.1027 q^{2} -6.46828 q^{3} +334.967 q^{4} +2255.95 q^{5} -188.244 q^{6} +6425.84 q^{7} -5152.14 q^{8} -19641.2 q^{9} +65654.3 q^{10} +14641.0 q^{11} -2166.66 q^{12} -59269.4 q^{13} +187009. q^{14} -14592.1 q^{15} -321444. q^{16} -253740. q^{17} -571611. q^{18} -467456. q^{19} +755669. q^{20} -41564.1 q^{21} +426093. q^{22} +806718. q^{23} +33325.5 q^{24} +3.13619e6 q^{25} -1.72490e6 q^{26} +254360. q^{27} +2.15245e6 q^{28} +3.92951e6 q^{29} -424670. q^{30} -8.97464e6 q^{31} -6.71700e6 q^{32} -94702.1 q^{33} -7.38452e6 q^{34} +1.44964e7 q^{35} -6.57914e6 q^{36} +1.58262e7 q^{37} -1.36042e7 q^{38} +383371. q^{39} -1.16230e7 q^{40} +2.33806e7 q^{41} -1.20963e6 q^{42} -2.21562e7 q^{43} +4.90425e6 q^{44} -4.43095e7 q^{45} +2.34777e7 q^{46} +4.06593e7 q^{47} +2.07919e6 q^{48} +937862. q^{49} +9.12716e7 q^{50} +1.64126e6 q^{51} -1.98533e7 q^{52} -7.38745e7 q^{53} +7.40255e6 q^{54} +3.30294e7 q^{55} -3.31068e7 q^{56} +3.02364e6 q^{57} +1.14359e8 q^{58} -3.71311e7 q^{59} -4.88788e6 q^{60} +3.27516e6 q^{61} -2.61186e8 q^{62} -1.26211e8 q^{63} -3.09034e7 q^{64} -1.33709e8 q^{65} -2.75609e6 q^{66} +1.92567e8 q^{67} -8.49946e7 q^{68} -5.21808e6 q^{69} +4.21884e8 q^{70} -1.94606e8 q^{71} +1.01194e8 q^{72} +3.52547e8 q^{73} +4.60585e8 q^{74} -2.02858e7 q^{75} -1.56582e8 q^{76} +9.40808e7 q^{77} +1.11571e7 q^{78} -4.07144e8 q^{79} -7.25163e8 q^{80} +3.84952e8 q^{81} +6.80439e8 q^{82} +1.91281e7 q^{83} -1.39226e7 q^{84} -5.72425e8 q^{85} -6.44804e8 q^{86} -2.54172e7 q^{87} -7.54324e7 q^{88} +9.43839e8 q^{89} -1.28953e9 q^{90} -3.80856e8 q^{91} +2.70224e8 q^{92} +5.80505e7 q^{93} +1.18330e9 q^{94} -1.05456e9 q^{95} +4.34474e7 q^{96} +8.32562e8 q^{97} +2.72943e7 q^{98} -2.87566e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 16 q^{2} + 112 q^{3} + 708 q^{4} + 1594 q^{5} + 10378 q^{6} + 8400 q^{7} + 40716 q^{8} + 74789 q^{9}+O(q^{10}) $ 5 * q + 16 * q^2 + 112 * q^3 + 708 * q^4 + 1594 * q^5 + 10378 * q^6 + 8400 * q^7 + 40716 * q^8 + 74789 * q^9	\( 5 q + 16 q^{2} + 112 q^{3} + 708 q^{4} + 1594 q^{5} + 10378 q^{6} + 8400 q^{7} + 40716 q^{8} + 74789 q^{9} + 2986 q^{10} + 73205 q^{11} + 110288 q^{12} + 47214 q^{13} - 299852 q^{14} - 559436 q^{15} - 454776 q^{16} - 547238 q^{17} - 822418 q^{18} - 162940 q^{19} - 1913320 q^{20} + 825496 q^{21} + 234256 q^{22} + 3415892 q^{23} + 1435932 q^{24} + 6164943 q^{25} + 5356756 q^{26} + 5240140 q^{27} - 2477216 q^{28} + 5868414 q^{29} - 9766670 q^{30} + 11730396 q^{31} - 18454552 q^{32} + 1639792 q^{33} - 25579352 q^{34} - 6567848 q^{35} - 26683532 q^{36} + 7021250 q^{37} - 22257720 q^{38} + 29114872 q^{39} - 22406796 q^{40} + 5595418 q^{41} - 65554916 q^{42} + 29161940 q^{43} + 10365828 q^{44} + 68008838 q^{45} + 47468978 q^{46} + 33703664 q^{47} + 96997832 q^{48} + 106606605 q^{49} + 84598070 q^{50} - 135853760 q^{51} + 185107192 q^{52} - 88905666 q^{53} - 95103866 q^{54} + 23337754 q^{55} - 78057672 q^{56} - 362541120 q^{57} + 63640668 q^{58} + 13747712 q^{59} - 208875616 q^{60} + 274324430 q^{61} - 161612942 q^{62} - 436710568 q^{63} - 46082368 q^{64} - 658499468 q^{65} + 151944298 q^{66} + 323117752 q^{67} - 679289848 q^{68} - 60345676 q^{69} + 1608436228 q^{70} + 9655356 q^{71} + 1168471200 q^{72} + 159287274 q^{73} + 76718502 q^{74} - 963596116 q^{75} + 483002000 q^{76} + 122984400 q^{77} + 1270322200 q^{78} - 668342072 q^{79} - 424312360 q^{80} + 1578463805 q^{81} + 666585700 q^{82} + 378353820 q^{83} - 2381947456 q^{84} + 1459757140 q^{85} - 2133621276 q^{86} - 2822691048 q^{87} + 596122956 q^{88} + 851774166 q^{89} - 4463334016 q^{90} - 991736368 q^{91} + 1919755168 q^{92} + 1149973204 q^{93} + 2620937360 q^{94} - 2812243800 q^{95} - 1157568712 q^{96} - 240502490 q^{97} - 2298624888 q^{98} + 1094985749 q^{99}+O(q^{100}) \) 5 * q + 16 * q^2 + 112 * q^3 + 708 * q^4 + 1594 * q^5 + 10378 * q^6 + 8400 * q^7 + 40716 * q^8 + 74789 * q^9 + 2986 * q^10 + 73205 * q^11 + 110288 * q^12 + 47214 * q^13 - 299852 * q^14 - 559436 * q^15 - 454776 * q^16 - 547238 * q^17 - 822418 * q^18 - 162940 * q^19 - 1913320 * q^20 + 825496 * q^21 + 234256 * q^22 + 3415892 * q^23 + 1435932 * q^24 + 6164943 * q^25 + 5356756 * q^26 + 5240140 * q^27 - 2477216 * q^28 + 5868414 * q^29 - 9766670 * q^30 + 11730396 * q^31 - 18454552 * q^32 + 1639792 * q^33 - 25579352 * q^34 - 6567848 * q^35 - 26683532 * q^36 + 7021250 * q^37 - 22257720 * q^38 + 29114872 * q^39 - 22406796 * q^40 + 5595418 * q^41 - 65554916 * q^42 + 29161940 * q^43 + 10365828 * q^44 + 68008838 * q^45 + 47468978 * q^46 + 33703664 * q^47 + 96997832 * q^48 + 106606605 * q^49 + 84598070 * q^50 - 135853760 * q^51 + 185107192 * q^52 - 88905666 * q^53 - 95103866 * q^54 + 23337754 * q^55 - 78057672 * q^56 - 362541120 * q^57 + 63640668 * q^58 + 13747712 * q^59 - 208875616 * q^60 + 274324430 * q^61 - 161612942 * q^62 - 436710568 * q^63 - 46082368 * q^64 - 658499468 * q^65 + 151944298 * q^66 + 323117752 * q^67 - 679289848 * q^68 - 60345676 * q^69 + 1608436228 * q^70 + 9655356 * q^71 + 1168471200 * q^72 + 159287274 * q^73 + 76718502 * q^74 - 963596116 * q^75 + 483002000 * q^76 + 122984400 * q^77 + 1270322200 * q^78 - 668342072 * q^79 - 424312360 * q^80 + 1578463805 * q^81 + 666585700 * q^82 + 378353820 * q^83 - 2381947456 * q^84 + 1459757140 * q^85 - 2133621276 * q^86 - 2822691048 * q^87 + 596122956 * q^88 + 851774166 * q^89 - 4463334016 * q^90 - 991736368 * q^91 + 1919755168 * q^92 + 1149973204 * q^93 + 2620937360 * q^94 - 2812243800 * q^95 - 1157568712 * q^96 - 240502490 * q^97 - 2298624888 * q^98 + 1094985749 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	29.1027	1.28617	0.643085	−	0.765795i	$-0.277654\pi$
$2$	29.1027	1.28617	0.643085	+	0.765795i	$0.277654\pi$
$3$	−6.46828	−0.0461045	−0.0230522	−	0.999734i	$-0.507338\pi$
$3$	−6.46828	−0.0461045	−0.0230522	+	0.999734i	$0.507338\pi$
$4$	334.967	0.654232
$5$	2255.95	1.61423	0.807114	−	0.590396i	$-0.201028\pi$
$5$	2255.95	1.61423	0.807114	+	0.590396i	$0.201028\pi$
$6$	−188.244	−0.0592982
$7$	6425.84	1.01155	0.505777	−	0.862664i	$-0.331206\pi$
$7$	6425.84	1.01155	0.505777	+	0.862664i	$0.331206\pi$
$8$	−5152.14	−0.444716
$9$	−19641.2	−0.997874
$10$	65654.3	2.07617
$11$	14641.0	0.301511
$11$	14641.0	0.301511
$12$	−2166.66	−0.0301630
$13$	−59269.4	−0.575553	−0.287777	−	0.957698i	$-0.592916\pi$
$13$	−59269.4	−0.575553	−0.287777	+	0.957698i	$0.592916\pi$
$14$	187009.	1.30103
$15$	−14592.1	−0.0744231
$16$	−321444.	−1.22621
$17$	−253740.	−0.736833	−0.368416	−	0.929661i	$-0.620100\pi$
$17$	−253740.	−0.736833	−0.368416	+	0.929661i	$0.620100\pi$
$18$	−571611.	−1.28344
$19$	−467456.	−0.822905	−0.411453	−	0.911431i	$-0.634978\pi$
$19$	−467456.	−0.822905	−0.411453	+	0.911431i	$0.634978\pi$
$20$	755669.	1.05608
$21$	−41564.1	−0.0466372
$22$	426093.	0.387795
$23$	806718.	0.601100	0.300550	−	0.953766i	$-0.402830\pi$
$23$	806718.	0.601100	0.300550	+	0.953766i	$0.402830\pi$
$24$	33325.5	0.0205034
$25$	3.13619e6	1.60573
$26$	−1.72490e6	−0.740259
$27$	254360.	0.0921110
$28$	2.15245e6	0.661791
$29$	3.92951e6	1.03169	0.515843	−	0.856683i	$-0.327479\pi$
$29$	3.92951e6	1.03169	0.515843	+	0.856683i	$0.327479\pi$
$30$	−424670.	−0.0957207
$31$	−8.97464e6	−1.74538	−0.872689	−	0.488277i	$-0.837626\pi$
$31$	−8.97464e6	−1.74538	−0.872689	+	0.488277i	$0.837626\pi$
$32$	−6.71700e6	−1.13240
$33$	−94702.1	−0.0139010
$34$	−7.38452e6	−0.947692
$35$	1.44964e7	1.63288
$36$	−6.57914e6	−0.652842
$37$	1.58262e7	1.38825	0.694126	−	0.719853i	$-0.255791\pi$
$37$	1.58262e7	1.38825	0.694126	+	0.719853i	$0.255791\pi$
$38$	−1.36042e7	−1.05840
$39$	383371.	0.0265356
$40$	−1.16230e7	−0.717872
$41$	2.33806e7	1.29220	0.646099	−	0.763254i	$-0.276399\pi$
$41$	2.33806e7	1.29220	0.646099	+	0.763254i	$0.276399\pi$
$42$	−1.20963e6	−0.0599833
$43$	−2.21562e7	−0.988295	−0.494147	−	0.869378i	$-0.664520\pi$
$43$	−2.21562e7	−0.988295	−0.494147	+	0.869378i	$0.664520\pi$
$44$	4.90425e6	0.197259
$45$	−4.43095e7	−1.61080
$46$	2.34777e7	0.773117
$47$	4.06593e7	1.21540	0.607701	−	0.794166i	$-0.292092\pi$
$47$	4.06593e7	1.21540	0.607701	+	0.794166i	$0.292092\pi$
$48$	2.07919e6	0.0565339
$49$	937862.	0.0232411
$50$	9.12716e7	2.06524
$51$	1.64126e6	0.0339713
$52$	−1.98533e7	−0.376546
$53$	−7.38745e7	−1.28604	−0.643018	−	0.765851i	$-0.722318\pi$
$53$	−7.38745e7	−1.28604	−0.643018	+	0.765851i	$0.722318\pi$
$54$	7.40255e6	0.118470
$55$	3.30294e7	0.486708
$56$	−3.31068e7	−0.449854
$57$	3.02364e6	0.0379396
$58$	1.14359e8	1.32692
$59$	−3.71311e7	−0.398936	−0.199468	−	0.979904i	$-0.563921\pi$
$59$	−3.71311e7	−0.398936	−0.199468	+	0.979904i	$0.563921\pi$
$60$	−4.88788e6	−0.0486900
$61$	3.27516e6	0.0302864	0.0151432	−	0.999885i	$-0.495180\pi$
$61$	3.27516e6	0.0302864	0.0151432	+	0.999885i	$0.495180\pi$
$62$	−2.61186e8	−2.24485
$63$	−1.26211e8	−1.00940
$64$	−3.09034e7	−0.230248
$65$	−1.33709e8	−0.929074
$66$	−2.75609e6	−0.0178791
$67$	1.92567e8	1.16747	0.583734	−	0.811945i	$-0.301591\pi$
$67$	1.92567e8	1.16747	0.583734	+	0.811945i	$0.301591\pi$
$68$	−8.49946e7	−0.482060
$69$	−5.21808e6	−0.0277134
$70$	4.21884e8	2.10016
$71$	−1.94606e8	−0.908854	−0.454427	−	0.890784i	$-0.650156\pi$
$71$	−1.94606e8	−0.908854	−0.454427	+	0.890784i	$0.650156\pi$
$72$	1.01194e8	0.443770
$73$	3.52547e8	1.45299	0.726497	−	0.687169i	$-0.241147\pi$
$73$	3.52547e8	1.45299	0.726497	+	0.687169i	$0.241147\pi$
$74$	4.60585e8	1.78553
$75$	−2.02858e7	−0.0740314
$76$	−1.56582e8	−0.538371
$77$	9.40808e7	0.304995
$78$	1.11571e7	0.0341293
$79$	−4.07144e8	−1.17605	−0.588025	−	0.808843i	$-0.700094\pi$
$79$	−4.07144e8	−1.17605	−0.588025	+	0.808843i	$0.700094\pi$
$80$	−7.25163e8	−1.97939
$81$	3.84952e8	0.993628
$82$	6.80439e8	1.66198
$83$	1.91281e7	0.0442404	0.0221202	−	0.999755i	$-0.492958\pi$
$83$	1.91281e7	0.0442404	0.0221202	+	0.999755i	$0.492958\pi$
$84$	−1.39226e7	−0.0305115
$85$	−5.72425e8	−1.18942
$86$	−6.44804e8	−1.27111
$87$	−2.54172e7	−0.0475653
$88$	−7.54324e7	−0.134087
$89$	9.43839e8	1.59457	0.797284	−	0.603605i	$-0.206269\pi$
$89$	9.43839e8	1.59457	0.797284	+	0.603605i	$0.206269\pi$
$90$	−1.28953e9	−2.07176
$91$	−3.80856e8	−0.582203
$92$	2.70224e8	0.393259
$93$	5.80505e7	0.0804697
$94$	1.18330e9	1.56321
$95$	−1.05456e9	−1.32836
$96$	4.34474e7	0.0522088
$97$	8.32562e8	0.954870	0.477435	−	0.878667i	$-0.341567\pi$
$97$	8.32562e8	0.954870	0.477435	+	0.878667i	$0.341567\pi$
$98$	2.72943e7	0.0298920
$99$	−2.87566e8	−0.300870
$100$	1.05052e9	1.05052
$101$	−1.31500e9	−1.25742	−0.628708	−	0.777641i	$-0.716416\pi$
$101$	−1.31500e9	−1.25742	−0.628708	+	0.777641i	$0.716416\pi$
$102$	4.77652e7	0.0436929
$103$	1.28477e9	1.12475	0.562377	−	0.826881i	$-0.309887\pi$
$103$	1.28477e9	1.12475	0.562377	+	0.826881i	$0.309887\pi$
$104$	3.05364e8	0.255958
$105$	−9.37667e7	−0.0752830
$106$	−2.14995e9	−1.65406
$107$	5.81507e8	0.428873	0.214436	−	0.976738i	$-0.431209\pi$
$107$	5.81507e8	0.428873	0.214436	+	0.976738i	$0.431209\pi$
$108$	8.52021e7	0.0602620
$109$	7.27470e8	0.493624	0.246812	−	0.969063i	$-0.420617\pi$
$109$	7.27470e8	0.493624	0.246812	+	0.969063i	$0.420617\pi$
$110$	9.61244e8	0.625989
$111$	−1.02368e8	−0.0640047
$112$	−2.06555e9	−1.24038
$113$	1.24110e9	0.716069	0.358035	−	0.933708i	$-0.383447\pi$
$113$	1.24110e9	0.716069	0.358035	+	0.933708i	$0.383447\pi$
$114$	8.79960e7	0.0487968
$115$	1.81992e9	0.970312
$116$	1.31626e9	0.674962
$117$	1.16412e9	0.574330
$118$	−1.08061e9	−0.513100
$119$	−1.63049e9	−0.745346
$120$	7.51806e7	0.0330971
$121$	2.14359e8	0.0909091
$122$	9.53159e7	0.0389535
$123$	−1.51232e8	−0.0595761
$124$	−3.00621e9	−1.14188
$125$	2.66894e9	0.977786
$126$	−3.67308e9	−1.29826
$127$	4.55054e8	0.155219	0.0776097	−	0.996984i	$-0.475271\pi$
$127$	4.55054e8	0.155219	0.0776097	+	0.996984i	$0.475271\pi$
$128$	2.53973e9	0.836263
$129$	1.43312e8	0.0455648
$130$	−3.89129e9	−1.19495
$131$	−5.86035e9	−1.73861	−0.869306	−	0.494274i	$-0.835434\pi$
$131$	−5.86035e9	−1.73861	−0.869306	+	0.494274i	$0.835434\pi$
$132$	−3.17221e7	−0.00909450
$133$	−3.00380e9	−0.832413
$134$	5.60422e9	1.50156
$135$	5.73823e8	0.148688
$136$	1.30730e9	0.327681
$137$	−3.33279e9	−0.808287	−0.404144	−	0.914696i	$-0.632430\pi$
$137$	−3.33279e9	−0.808287	−0.404144	+	0.914696i	$0.632430\pi$
$138$	−1.51860e8	−0.0356441
$139$	−2.29930e9	−0.522431	−0.261216	−	0.965280i	$-0.584123\pi$
$139$	−2.29930e9	−0.522431	−0.261216	+	0.965280i	$0.584123\pi$
$140$	4.85581e9	1.06828
$141$	−2.62996e8	−0.0560355
$142$	−5.66356e9	−1.16894
$143$	−8.67763e8	−0.173536
$144$	6.31354e9	1.22361
$145$	8.86479e9	1.66538
$146$	1.02601e10	1.86880
$147$	−6.06635e6	−0.00107152
$148$	5.30125e9	0.908240
$149$	6.37313e9	1.05929	0.529645	−	0.848220i	$-0.322325\pi$
$149$	6.37313e9	1.05929	0.529645	+	0.848220i	$0.322325\pi$
$150$	−5.90370e8	−0.0952169
$151$	−8.49068e9	−1.32906	−0.664532	−	0.747260i	$-0.731369\pi$
$151$	−8.49068e9	−1.32906	−0.664532	+	0.747260i	$0.731369\pi$
$152$	2.40840e9	0.365959
$153$	4.98375e9	0.735267
$154$	2.73800e9	0.392275
$155$	−2.02463e10	−2.81744
$156$	1.28417e8	0.0173604
$157$	−1.60026e8	−0.0210204	−0.0105102	−	0.999945i	$-0.503346\pi$
$157$	−1.60026e8	−0.0210204	−0.0105102	+	0.999945i	$0.503346\pi$
$158$	−1.18490e10	−1.51260
$159$	4.77841e8	0.0592921
$160$	−1.51532e10	−1.82795
$161$	5.18385e9	0.608045
$162$	1.12031e10	1.27797
$163$	1.18027e9	0.130959	0.0654796	−	0.997854i	$-0.479142\pi$
$163$	1.18027e9	0.130959	0.0654796	+	0.997854i	$0.479142\pi$
$164$	7.83174e9	0.845397
$165$	−2.13643e8	−0.0224394
$166$	5.56678e8	0.0569007
$167$	−1.22731e10	−1.22104	−0.610521	−	0.792000i	$-0.709040\pi$
$167$	−1.22731e10	−1.22104	−0.610521	+	0.792000i	$0.709040\pi$
$168$	2.14144e8	0.0207403
$169$	−7.09164e9	−0.668739
$170$	−1.66591e10	−1.52979
$171$	9.18139e9	0.821156
$172$	−7.42158e9	−0.646575
$173$	−9.80811e9	−0.832488	−0.416244	−	0.909253i	$-0.636654\pi$
$173$	−9.80811e9	−0.832488	−0.416244	+	0.909253i	$0.636654\pi$
$174$	−7.39708e8	−0.0611771
$175$	2.01527e10	1.62428
$176$	−4.70626e9	−0.369717
$177$	2.40174e8	0.0183927
$178$	2.74683e10	2.05088
$179$	6.86609e9	0.499886	0.249943	−	0.968261i	$-0.419588\pi$
$179$	6.86609e9	0.499886	0.249943	+	0.968261i	$0.419588\pi$
$180$	−1.48422e10	−1.05384
$181$	1.20777e10	0.836432	0.418216	−	0.908348i	$-0.362655\pi$
$181$	1.20777e10	0.836432	0.418216	+	0.908348i	$0.362655\pi$
$182$	−1.10839e10	−0.748812
$183$	−2.11846e7	−0.00139634
$184$	−4.15632e9	−0.267319
$185$	3.57031e10	2.24096
$186$	1.68943e9	0.103498
$187$	−3.71501e9	−0.222163
$188$	1.36195e10	0.795155
$189$	1.63448e9	0.0931752
$190$	−3.06905e10	−1.70849
$191$	1.61990e10	0.880722	0.440361	−	0.897821i	$-0.354850\pi$
$191$	1.61990e10	0.880722	0.440361	+	0.897821i	$0.354850\pi$
$192$	1.99892e8	0.0106155
$193$	−3.36439e10	−1.74542	−0.872708	−	0.488243i	$-0.837638\pi$
$193$	−3.36439e10	−1.74542	−0.872708	+	0.488243i	$0.837638\pi$
$194$	2.42298e10	1.22812
$195$	8.64866e8	0.0428345
$196$	3.14153e8	0.0152051
$197$	−2.07027e10	−0.979331	−0.489666	−	0.871910i	$-0.662881\pi$
$197$	−2.07027e10	−0.979331	−0.489666	+	0.871910i	$0.662881\pi$
$198$	−8.36895e9	−0.386970
$199$	1.05093e10	0.475045	0.237523	−	0.971382i	$-0.423665\pi$
$199$	1.05093e10	0.475045	0.237523	+	0.971382i	$0.423665\pi$
$200$	−1.61581e10	−0.714094
$201$	−1.24558e9	−0.0538255
$202$	−3.82700e10	−1.61725
$203$	2.52504e10	1.04361
$204$	5.49769e8	0.0222251
$205$	5.27456e10	2.08590
$206$	3.73903e10	1.44663
$207$	−1.58449e10	−0.599822
$208$	1.90518e10	0.705750
$209$	−6.84403e9	−0.248115
$210$	−2.72886e9	−0.0968267
$211$	−9.58512e9	−0.332910	−0.166455	−	0.986049i	$-0.553232\pi$
$211$	−9.58512e9	−0.332910	−0.166455	+	0.986049i	$0.553232\pi$
$212$	−2.47455e10	−0.841367
$213$	1.25877e9	0.0419022
$214$	1.69234e10	0.551603
$215$	−4.99832e10	−1.59533
$216$	−1.31050e9	−0.0409632
$217$	−5.76696e10	−1.76554
$218$	2.11713e10	0.634884
$219$	−2.28037e9	−0.0669896
$220$	1.10638e10	0.318420
$221$	1.50390e10	0.424087
$222$	−2.97919e9	−0.0823209
$223$	1.35200e10	0.366104	0.183052	−	0.983103i	$-0.441402\pi$
$223$	1.35200e10	0.366104	0.183052	+	0.983103i	$0.441402\pi$
$224$	−4.31624e10	−1.14548
$225$	−6.15985e10	−1.60232
$226$	3.61195e10	0.920987
$227$	−5.06876e10	−1.26703	−0.633513	−	0.773732i	$-0.718388\pi$
$227$	−5.06876e10	−1.26703	−0.633513	+	0.773732i	$0.718388\pi$
$228$	1.01282e9	0.0248213
$229$	2.16237e10	0.519601	0.259801	−	0.965662i	$-0.416343\pi$
$229$	2.16237e10	0.519601	0.259801	+	0.965662i	$0.416343\pi$
$230$	5.29645e10	1.24799
$231$	−6.08541e8	−0.0140616
$232$	−2.02454e10	−0.458807
$233$	3.52657e10	0.783883	0.391941	−	0.919990i	$-0.371804\pi$
$233$	3.52657e10	0.783883	0.391941	+	0.919990i	$0.371804\pi$
$234$	3.38790e10	0.738686
$235$	9.17255e10	1.96194
$236$	−1.24377e10	−0.260997
$237$	2.63352e9	0.0542212
$238$	−4.74518e10	−0.958642
$239$	−5.84001e9	−0.115777	−0.0578886	−	0.998323i	$-0.518437\pi$
$239$	−5.84001e9	−0.115777	−0.0578886	+	0.998323i	$0.518437\pi$
$240$	4.69055e9	0.0912585
$241$	1.87636e10	0.358294	0.179147	−	0.983822i	$-0.442666\pi$
$241$	1.87636e10	0.358294	0.179147	+	0.983822i	$0.442666\pi$
$242$	6.23842e9	0.116925
$243$	−7.49654e9	−0.137922
$244$	1.09707e9	0.0198144
$245$	2.11577e9	0.0375164
$246$	−4.40127e9	−0.0766249
$247$	2.77059e10	0.473626
$248$	4.62386e10	0.776197
$249$	−1.23726e8	−0.00203968
$250$	7.76734e10	1.25760
$251$	−1.72838e10	−0.274858	−0.137429	−	0.990512i	$-0.543884\pi$
$251$	−1.72838e10	−0.274858	−0.137429	+	0.990512i	$0.543884\pi$
$252$	−4.22765e10	−0.660385
$253$	1.18112e10	0.181238
$254$	1.32433e10	0.199639
$255$	3.70261e9	0.0548374
$256$	8.97356e10	1.30582
$257$	−7.81257e10	−1.11711	−0.558554	−	0.829468i	$-0.688643\pi$
$257$	−7.81257e10	−1.11711	−0.558554	+	0.829468i	$0.688643\pi$
$258$	4.17077e9	0.0586041
$259$	1.01697e11	1.40429
$260$	−4.47881e10	−0.607830
$261$	−7.71802e10	−1.02949
$262$	−1.70552e11	−2.23615
$263$	−1.47823e11	−1.90520	−0.952600	−	0.304226i	$-0.901602\pi$
$263$	−1.47823e11	−1.90520	−0.952600	+	0.304226i	$0.901602\pi$
$264$	4.87918e8	0.00618200
$265$	−1.66657e11	−2.07596
$266$	−8.74187e10	−1.07062
$267$	−6.10501e9	−0.0735167
$268$	6.45035e10	0.763795
$269$	5.46285e10	0.636112	0.318056	−	0.948072i	$-0.396970\pi$
$269$	5.46285e10	0.636112	0.318056	+	0.948072i	$0.396970\pi$
$270$	1.66998e10	0.191238
$271$	6.40268e10	0.721107	0.360554	−	0.932738i	$-0.382588\pi$
$271$	6.40268e10	0.721107	0.360554	+	0.932738i	$0.382588\pi$
$272$	8.15633e10	0.903514
$273$	2.46348e9	0.0268422
$274$	−9.69933e10	−1.03959
$275$	4.59170e10	0.484146
$276$	−1.74788e9	−0.0181310
$277$	8.27883e10	0.844909	0.422454	−	0.906384i	$-0.361169\pi$
$277$	8.27883e10	0.844909	0.422454	+	0.906384i	$0.361169\pi$
$278$	−6.69158e10	−0.671935
$279$	1.76272e11	1.74167
$280$	−7.46874e10	−0.726167
$281$	6.37543e9	0.0610001	0.0305001	−	0.999535i	$-0.490290\pi$
$281$	6.37543e9	0.0610001	0.0305001	+	0.999535i	$0.490290\pi$
$282$	−7.65389e9	−0.0720711
$283$	6.21108e9	0.0575610	0.0287805	−	0.999586i	$-0.490838\pi$
$283$	6.21108e9	0.0575610	0.0287805	+	0.999586i	$0.490838\pi$
$284$	−6.51866e10	−0.594602
$285$	6.82118e9	0.0612432
$286$	−2.52543e10	−0.223197
$287$	1.50240e11	1.30713
$288$	1.31930e11	1.12999
$289$	−5.42038e10	−0.457077
$290$	2.57989e11	2.14196
$291$	−5.38525e9	−0.0440238
$292$	1.18092e11	0.950596
$293$	−1.17426e11	−0.930806	−0.465403	−	0.885099i	$-0.654091\pi$
$293$	−1.17426e11	−0.930806	−0.465403	+	0.885099i	$0.654091\pi$
$294$	−1.76547e8	−0.00137815
$295$	−8.37659e10	−0.643974
$296$	−8.15387e10	−0.617378
$297$	3.72408e9	0.0277725
$298$	1.85475e11	1.36243
$299$	−4.78137e10	−0.345965
$300$	−6.79506e9	−0.0484337
$301$	−1.42372e11	−0.999713
$302$	−2.47102e11	−1.70940
$303$	8.50578e9	0.0579725
$304$	1.50261e11	1.00906
$305$	7.38859e9	0.0488892
$306$	1.45041e11	0.945678
$307$	1.47331e11	0.946613	0.473306	−	0.880898i	$-0.343060\pi$
$307$	1.47331e11	0.946613	0.473306	+	0.880898i	$0.343060\pi$
$308$	3.15140e10	0.199538
$309$	−8.31025e9	−0.0518562
$310$	−5.89223e11	−3.62370
$311$	4.67522e10	0.283387	0.141694	−	0.989911i	$-0.454745\pi$
$311$	4.67522e10	0.283387	0.141694	+	0.989911i	$0.454745\pi$
$312$	−1.97518e9	−0.0118008
$313$	2.38944e11	1.40717	0.703585	−	0.710611i	$-0.251581\pi$
$313$	2.38944e11	1.40717	0.703585	+	0.710611i	$0.251581\pi$
$314$	−4.65718e9	−0.0270358
$315$	−2.84726e11	−1.62941
$316$	−1.36380e11	−0.769410
$317$	6.12150e10	0.340480	0.170240	−	0.985403i	$-0.445546\pi$
$317$	6.12150e10	0.340480	0.170240	+	0.985403i	$0.445546\pi$
$318$	1.39065e10	0.0762596
$319$	5.75320e10	0.311065
$320$	−6.97165e10	−0.371673
$321$	−3.76135e9	−0.0197729
$322$	1.50864e11	0.782049
$323$	1.18612e11	0.606344
$324$	1.28946e11	0.650063
$325$	−1.85880e11	−0.924183
$326$	3.43490e10	0.168436
$327$	−4.70548e9	−0.0227583
$328$	−1.20460e11	−0.574660
$329$	2.61271e11	1.22944
$330$	−6.21760e9	−0.0288609
$331$	9.43195e10	0.431892	0.215946	−	0.976405i	$-0.430716\pi$
$331$	9.43195e10	0.431892	0.215946	+	0.976405i	$0.430716\pi$
$332$	6.40727e9	0.0289435
$333$	−3.10845e11	−1.38530
$334$	−3.57181e11	−1.57047
$335$	4.34421e11	1.88456
$336$	1.33606e10	0.0571871
$337$	3.22100e10	0.136037	0.0680183	−	0.997684i	$-0.478332\pi$
$337$	3.22100e10	0.136037	0.0680183	+	0.997684i	$0.478332\pi$
$338$	−2.06386e11	−0.860111
$339$	−8.02781e9	−0.0330140
$340$	−1.91744e11	−0.778155
$341$	−1.31398e11	−0.526251
$342$	2.67203e11	1.05615
$343$	−2.53279e11	−0.988044
$344$	1.14152e11	0.439510
$345$	−1.17717e10	−0.0447357
$346$	−2.85442e11	−1.07072
$347$	9.79208e10	0.362570	0.181285	−	0.983431i	$-0.441974\pi$
$347$	9.79208e10	0.362570	0.181285	+	0.983431i	$0.441974\pi$
$348$	−8.51391e9	−0.0311188
$349$	3.11903e11	1.12539	0.562697	−	0.826663i	$-0.309764\pi$
$349$	3.11903e11	1.12539	0.562697	+	0.826663i	$0.309764\pi$
$350$	5.86497e11	2.08910
$351$	−1.50757e10	−0.0530148
$352$	−9.83436e10	−0.341432
$353$	2.85828e10	0.0979758	0.0489879	−	0.998799i	$-0.484400\pi$
$353$	2.85828e10	0.0979758	0.0489879	+	0.998799i	$0.484400\pi$
$354$	6.98972e9	0.0236562
$355$	−4.39022e11	−1.46710
$356$	3.16155e11	1.04322
$357$	1.05465e10	0.0343638
$358$	1.99822e11	0.642938
$359$	−3.36785e11	−1.07011	−0.535055	−	0.844817i	$-0.679709\pi$
$359$	−3.36785e11	−1.07011	−0.535055	+	0.844817i	$0.679709\pi$
$360$	2.28289e11	0.716346
$361$	−1.04172e11	−0.322827
$362$	3.51494e11	1.07579
$363$	−1.38653e9	−0.00419132
$364$	−1.27574e11	−0.380896
$365$	7.95329e11	2.34546
$366$	−6.16530e8	−0.00179593
$367$	−1.97061e11	−0.567027	−0.283513	−	0.958968i	$-0.591500\pi$
$367$	−1.97061e11	−0.567027	−0.283513	+	0.958968i	$0.591500\pi$
$368$	−2.59315e11	−0.737076
$369$	−4.59223e11	−1.28945
$370$	1.03906e12	2.88225
$371$	−4.74706e11	−1.30090
$372$	1.94450e10	0.0526459
$373$	1.08765e11	0.290937	0.145469	−	0.989363i	$-0.453531\pi$
$373$	1.08765e11	0.290937	0.145469	+	0.989363i	$0.453531\pi$
$374$	−1.08117e11	−0.285740
$375$	−1.72635e10	−0.0450803
$376$	−2.09482e11	−0.540508
$377$	−2.32900e11	−0.593790
$378$	4.75676e10	0.119839
$379$	3.52379e10	0.0877270	0.0438635	−	0.999038i	$-0.486033\pi$
$379$	3.52379e10	0.0877270	0.0438635	+	0.999038i	$0.486033\pi$
$380$	−3.53242e11	−0.869054
$381$	−2.94342e9	−0.00715631
$382$	4.71435e11	1.13276
$383$	−2.18098e11	−0.517913	−0.258956	−	0.965889i	$-0.583379\pi$
$383$	−2.18098e11	−0.517913	−0.258956	+	0.965889i	$0.583379\pi$
$384$	−1.64277e10	−0.0385555
$385$	2.12242e11	0.492331
$386$	−9.79129e11	−2.24490
$387$	4.35173e11	0.986194
$388$	2.78881e11	0.624707
$389$	−3.83970e11	−0.850205	−0.425103	−	0.905145i	$-0.639762\pi$
$389$	−3.83970e11	−0.850205	−0.425103	+	0.905145i	$0.639762\pi$
$390$	2.51699e10	0.0550924
$391$	−2.04697e11	−0.442910
$392$	−4.83199e9	−0.0103357
$393$	3.79064e10	0.0801578
$394$	−6.02505e11	−1.25959
$395$	−9.18497e11	−1.89841
$396$	−9.63252e10	−0.196839
$397$	−1.01749e11	−0.205576	−0.102788	−	0.994703i	$-0.532776\pi$
$397$	−1.01749e11	−0.205576	−0.102788	+	0.994703i	$0.532776\pi$
$398$	3.05849e11	0.610989
$399$	1.94294e10	0.0383780
$400$	−1.00811e12	−1.96897
$401$	−3.49624e11	−0.675230	−0.337615	−	0.941284i	$-0.609620\pi$
$401$	−3.49624e11	−0.675230	−0.337615	+	0.941284i	$0.609620\pi$
$402$	−3.62496e10	−0.0692287
$403$	5.31921e11	1.00456
$404$	−4.40481e11	−0.822642
$405$	8.68432e11	1.60394
$406$	7.34855e11	1.34225
$407$	2.31711e11	0.418574
$408$	−8.45601e9	−0.0151076
$409$	6.41874e11	1.13421	0.567107	−	0.823644i	$-0.308063\pi$
$409$	6.41874e11	1.13421	0.567107	+	0.823644i	$0.308063\pi$
$410$	1.53504e12	2.68282
$411$	2.15574e10	0.0372657
$412$	4.30356e11	0.735851
$413$	−2.38599e11	−0.403545
$414$	−4.61129e11	−0.771473
$415$	4.31520e10	0.0714141
$416$	3.98113e11	0.651757
$417$	1.48725e10	0.0240864
$418$	−1.99180e11	−0.319118
$419$	9.72234e11	1.54102	0.770509	−	0.637429i	$-0.220002\pi$
$419$	9.72234e11	1.54102	0.770509	+	0.637429i	$0.220002\pi$
$420$	−3.14088e10	−0.0492526
$421$	1.10496e12	1.71427	0.857135	−	0.515092i	$-0.172242\pi$
$421$	1.10496e12	1.71427	0.857135	+	0.515092i	$0.172242\pi$
$422$	−2.78953e11	−0.428178
$423$	−7.98597e11	−1.21282
$424$	3.80612e11	0.571921
$425$	−7.95778e11	−1.18315
$426$	3.66335e10	0.0538934
$427$	2.10456e10	0.0306363
$428$	1.94786e11	0.280582
$429$	5.61294e9	0.00800078
$430$	−1.45465e12	−2.05187
$431$	1.06311e12	1.48399	0.741995	−	0.670406i	$-0.233880\pi$
$431$	1.06311e12	1.48399	0.741995	+	0.670406i	$0.233880\pi$
$432$	−8.17624e10	−0.112948
$433$	1.00353e11	0.137194	0.0685968	−	0.997644i	$-0.478148\pi$
$433$	1.00353e11	0.137194	0.0685968	+	0.997644i	$0.478148\pi$
$434$	−1.67834e12	−2.27079
$435$	−5.73399e10	−0.0767813
$436$	2.43678e11	0.322945
$437$	−3.77106e11	−0.494648
$438$	−6.63650e10	−0.0861599
$439$	6.59302e11	0.847216	0.423608	−	0.905846i	$-0.360763\pi$
$439$	6.59302e11	0.847216	0.423608	+	0.905846i	$0.360763\pi$
$440$	−1.70172e11	−0.216447
$441$	−1.84207e10	−0.0231917
$442$	4.37676e11	0.545447
$443$	−8.55891e11	−1.05585	−0.527925	−	0.849291i	$-0.677030\pi$
$443$	−8.55891e11	−1.05585	−0.527925	+	0.849291i	$0.677030\pi$
$444$	−3.42900e10	−0.0418739
$445$	2.12926e12	2.57399
$446$	3.93468e11	0.470871
$447$	−4.12232e10	−0.0488380
$448$	−1.98580e11	−0.232908
$449$	−1.21238e12	−1.40777	−0.703885	−	0.710314i	$-0.748553\pi$
$449$	−1.21238e12	−1.40777	−0.703885	+	0.710314i	$0.748553\pi$
$450$	−1.79268e12	−2.06085
$451$	3.42316e11	0.389612
$452$	4.15729e11	0.468476
$453$	5.49201e10	0.0612758
$454$	−1.47515e12	−1.62961
$455$	−8.59193e11	−0.939808
$456$	−1.55782e10	−0.0168723
$457$	−6.81720e11	−0.731111	−0.365555	−	0.930790i	$-0.619121\pi$
$457$	−6.81720e11	−0.731111	−0.365555	+	0.930790i	$0.619121\pi$
$458$	6.29308e11	0.668295
$459$	−6.45413e10	−0.0678704
$460$	6.09612e11	0.634810
$461$	1.10310e12	1.13752	0.568762	−	0.822502i	$-0.307423\pi$
$461$	1.10310e12	1.13752	0.568762	+	0.822502i	$0.307423\pi$
$462$	−1.77102e10	−0.0180856
$463$	−1.84917e12	−1.87009	−0.935045	−	0.354529i	$-0.884641\pi$
$463$	−1.84917e12	−1.87009	−0.935045	+	0.354529i	$0.884641\pi$
$464$	−1.26312e12	−1.26507
$465$	1.30959e11	0.129896
$466$	1.02633e12	1.00821
$467$	3.87624e11	0.377124	0.188562	−	0.982061i	$-0.439617\pi$
$467$	3.87624e11	0.377124	0.188562	+	0.982061i	$0.439617\pi$
$468$	3.89942e11	0.375745
$469$	1.23740e12	1.18096
$470$	2.66946e12	2.52338
$471$	1.03509e9	0.000969134 0
$472$	1.91304e11	0.177413
$473$	−3.24388e11	−0.297982
$474$	7.66425e10	0.0697376
$475$	−1.46603e12	−1.32136
$476$	−5.46162e11	−0.487630
$477$	1.45098e12	1.28330
$478$	−1.69960e11	−0.148909
$479$	−1.14162e11	−0.0990860	−0.0495430	−	0.998772i	$-0.515776\pi$
$479$	−1.14162e11	−0.0990860	−0.0495430	+	0.998772i	$0.515776\pi$
$480$	9.80153e10	0.0842768
$481$	−9.38009e11	−0.799013
$482$	5.46071e11	0.460826
$483$	−3.35306e10	−0.0280336
$484$	7.18032e10	0.0594757
$485$	1.87822e12	1.54138
$486$	−2.18169e11	−0.177391
$487$	−9.91126e11	−0.798452	−0.399226	−	0.916853i	$-0.630721\pi$
$487$	−9.91126e11	−0.798452	−0.399226	+	0.916853i	$0.630721\pi$
$488$	−1.68741e10	−0.0134688
$489$	−7.63430e9	−0.00603781
$490$	6.15746e10	0.0482525
$491$	−2.00990e12	−1.56066	−0.780330	−	0.625367i	$-0.784949\pi$
$491$	−2.00990e12	−1.56066	−0.780330	+	0.625367i	$0.784949\pi$
$492$	−5.06579e10	−0.0389766
$493$	−9.97075e11	−0.760180
$494$	8.06315e11	0.609163
$495$	−6.48735e11	−0.485673
$496$	2.88485e12	2.14020
$497$	−1.25051e12	−0.919354
$498$	−3.60075e9	−0.00262338
$499$	1.05096e12	0.758811	0.379406	−	0.925230i	$-0.376128\pi$
$499$	1.05096e12	0.758811	0.379406	+	0.925230i	$0.376128\pi$
$500$	8.94007e11	0.639700
$501$	7.93860e10	0.0562955
$502$	−5.03006e11	−0.353514
$503$	−1.95563e11	−0.136217	−0.0681083	−	0.997678i	$-0.521696\pi$
$503$	−1.95563e11	−0.136217	−0.0681083	+	0.997678i	$0.521696\pi$
$504$	6.50257e11	0.448898
$505$	−2.96657e12	−2.02976
$506$	3.43737e11	0.233103
$507$	4.58707e10	0.0308318
$508$	1.52428e11	0.101550
$509$	−5.05921e11	−0.334082	−0.167041	−	0.985950i	$-0.553421\pi$
$509$	−5.05921e11	−0.334082	−0.167041	+	0.985950i	$0.553421\pi$
$510$	1.07756e11	0.0705302
$511$	2.26541e12	1.46978
$512$	1.31120e12	0.843249
$513$	−1.18902e11	−0.0757986
$514$	−2.27367e12	−1.43679
$515$	2.89838e12	1.81561
$516$	4.80049e10	0.0298100
$517$	5.95293e11	0.366457
$518$	2.95965e12	1.80616
$519$	6.34416e10	0.0383814
$520$	6.88887e11	0.413174
$521$	6.18107e11	0.367531	0.183765	−	0.982970i	$-0.441171\pi$
$521$	6.18107e11	0.367531	0.183765	+	0.982970i	$0.441171\pi$
$522$	−2.24615e12	−1.32410
$523$	−5.22467e10	−0.0305352	−0.0152676	−	0.999883i	$-0.504860\pi$
$523$	−5.22467e10	−0.0305352	−0.0152676	+	0.999883i	$0.504860\pi$
$524$	−1.96302e12	−1.13746
$525$	−1.30353e11	−0.0748867
$526$	−4.30204e12	−2.45041
$527$	2.27723e12	1.28605
$528$	3.04414e10	0.0170456
$529$	−1.15036e12	−0.638679
$530$	−4.85018e12	−2.67003
$531$	7.29297e11	0.398088
$532$	−1.00617e12	−0.544592
$533$	−1.38576e12	−0.743728
$534$	−1.77672e11	−0.0945550
$535$	1.31185e12	0.692298
$536$	−9.92131e11	−0.519191
$537$	−4.44118e10	−0.0230470
$538$	1.58984e12	0.818148
$539$	1.37312e10	0.00700745
$540$	1.92212e11	0.0972765
$541$	−2.94333e12	−1.47724	−0.738620	−	0.674122i	$-0.764522\pi$
$541$	−2.94333e12	−1.47724	−0.738620	+	0.674122i	$0.764522\pi$
$542$	1.86335e12	0.927466
$543$	−7.81220e10	−0.0385633
$544$	1.70437e12	0.834391
$545$	1.64114e12	0.796821
$546$	7.16940e10	0.0345236
$547$	−9.41728e11	−0.449762	−0.224881	−	0.974386i	$-0.572199\pi$
$547$	−9.41728e11	−0.449762	−0.224881	+	0.974386i	$0.572199\pi$
$548$	−1.11638e12	−0.528808
$549$	−6.43279e10	−0.0302220
$550$	1.33631e12	0.622694
$551$	−1.83688e12	−0.848980
$552$	2.68843e10	0.0123246
$553$	−2.61624e12	−1.18964
$554$	2.40936e12	1.08670
$555$	−2.30938e11	−0.103318
$556$	−7.70190e11	−0.341791
$557$	−1.13307e12	−0.498781	−0.249390	−	0.968403i	$-0.580230\pi$
$557$	−1.13307e12	−0.498781	−0.249390	+	0.968403i	$0.580230\pi$
$558$	5.13000e12	2.24008
$559$	1.31318e12	0.568816
$560$	−4.65978e12	−2.00226
$561$	2.40297e10	0.0102427
$562$	1.85542e11	0.0784565
$563$	2.74095e12	1.14977	0.574887	−	0.818233i	$-0.305046\pi$
$563$	2.74095e12	1.14977	0.574887	+	0.818233i	$0.305046\pi$
$564$	−8.80950e10	−0.0366602
$565$	2.79987e12	1.15590
$566$	1.80759e11	0.0740332
$567$	2.47364e12	1.00511
$568$	1.00264e12	0.404182
$569$	−5.80323e11	−0.232094	−0.116047	−	0.993244i	$-0.537022\pi$
$569$	−5.80323e11	−0.232094	−0.116047	+	0.993244i	$0.537022\pi$
$570$	1.98515e11	0.0787691
$571$	−7.04079e11	−0.277178	−0.138589	−	0.990350i	$-0.544257\pi$
$571$	−7.04079e11	−0.277178	−0.138589	+	0.990350i	$0.544257\pi$
$572$	−2.90672e11	−0.113533
$573$	−1.04780e11	−0.0406052
$574$	4.37240e12	1.68119
$575$	2.53002e12	0.965204
$576$	6.06978e11	0.229759
$577$	−7.82091e11	−0.293742	−0.146871	−	0.989156i	$-0.546920\pi$
$577$	−7.82091e11	−0.293742	−0.146871	+	0.989156i	$0.546920\pi$
$578$	−1.57748e12	−0.587879
$579$	2.17618e11	0.0804715
$580$	2.96941e12	1.08954
$581$	1.22914e11	0.0447516
$582$	−1.56725e11	−0.0566220
$583$	−1.08160e12	−0.387755
$584$	−1.81637e12	−0.646170
$585$	2.62620e12	0.927099
$586$	−3.41741e12	−1.19718
$587$	1.57632e12	0.547991	0.273995	−	0.961731i	$-0.411655\pi$
$587$	1.57632e12	0.547991	0.273995	+	0.961731i	$0.411655\pi$
$588$	−2.03203e9	−0.000701022 0
$589$	4.19525e12	1.43628
$590$	−2.43781e12	−0.828260
$591$	1.33911e11	0.0451515
$592$	−5.08724e12	−1.70229
$593$	−1.45482e12	−0.483129	−0.241565	−	0.970385i	$-0.577661\pi$
$593$	−1.45482e12	−0.483129	−0.241565	+	0.970385i	$0.577661\pi$
$594$	1.08381e11	0.0357201
$595$	−3.67832e12	−1.20316
$596$	2.13479e12	0.693022
$597$	−6.79771e10	−0.0219017
$598$	−1.39151e12	−0.444970
$599$	−2.48554e12	−0.788861	−0.394430	−	0.918926i	$-0.629058\pi$
$599$	−2.48554e12	−0.788861	−0.394430	+	0.918926i	$0.629058\pi$
$600$	1.04515e11	0.0329229
$601$	−2.43906e12	−0.762584	−0.381292	−	0.924455i	$-0.624521\pi$
$601$	−2.43906e12	−0.762584	−0.381292	+	0.924455i	$0.624521\pi$
$602$	−4.14341e12	−1.28580
$603$	−3.78224e12	−1.16499
$604$	−2.84410e12	−0.869517
$605$	4.83583e11	0.146748
$606$	2.47541e11	0.0745625
$607$	1.10333e12	0.329881	0.164941	−	0.986303i	$-0.447257\pi$
$607$	1.10333e12	0.329881	0.164941	+	0.986303i	$0.447257\pi$
$608$	3.13990e12	0.931859
$609$	−1.63327e11	−0.0481149
$610$	2.15028e11	0.0628798
$611$	−2.40985e12	−0.699529
$612$	1.66939e12	0.481035
$613$	−2.33157e11	−0.0666925	−0.0333463	−	0.999444i	$-0.510616\pi$
$613$	−2.33157e11	−0.0666925	−0.0333463	+	0.999444i	$0.510616\pi$
$614$	4.28774e12	1.21750
$615$	−3.41173e11	−0.0961693
$616$	−4.84717e11	−0.135636
$617$	−2.92926e12	−0.813719	−0.406859	−	0.913491i	$-0.633376\pi$
$617$	−2.92926e12	−0.813719	−0.406859	+	0.913491i	$0.633376\pi$
$618$	−2.41851e11	−0.0666959
$619$	6.26421e12	1.71498	0.857488	−	0.514503i	$-0.172024\pi$
$619$	6.26421e12	1.71498	0.857488	+	0.514503i	$0.172024\pi$
$620$	−6.78186e12	−1.84326
$621$	2.05197e11	0.0553679
$622$	1.36061e12	0.364484
$623$	6.06496e12	1.61299
$624$	−1.23232e11	−0.0325383
$625$	−1.04372e11	−0.0273606
$626$	6.95391e12	1.80986
$627$	4.42691e10	0.0114392
$628$	−5.36033e10	−0.0137522
$629$	−4.01574e12	−1.02291
$630$	−8.28629e12	−2.09569
$631$	−6.02555e12	−1.51309	−0.756544	−	0.653943i	$-0.773114\pi$
$631$	−6.02555e12	−1.51309	−0.756544	+	0.653943i	$0.773114\pi$
$632$	2.09766e12	0.523008
$633$	6.19992e10	0.0153486
$634$	1.78152e12	0.437914
$635$	1.02658e12	0.250560
$636$	1.60061e11	0.0387908
$637$	−5.55865e10	−0.0133765
$638$	1.67434e12	0.400082
$639$	3.82229e12	0.906922
$640$	5.72951e12	1.34992
$641$	8.16296e12	1.90979	0.954897	−	0.296938i	$-0.0959656\pi$
$641$	8.16296e12	1.90979	0.954897	+	0.296938i	$0.0959656\pi$
$642$	−1.09465e11	−0.0254314
$643$	5.42510e11	0.125158	0.0625789	−	0.998040i	$-0.480067\pi$
$643$	5.42510e11	0.125158	0.0625789	+	0.998040i	$0.480067\pi$
$644$	1.73642e12	0.397803
$645$	3.23305e11	0.0735520
$646$	3.45194e12	0.779861
$647$	5.22729e12	1.17275	0.586377	−	0.810038i	$-0.300554\pi$
$647$	5.22729e12	1.17275	0.586377	+	0.810038i	$0.300554\pi$
$648$	−1.98332e12	−0.441882
$649$	−5.43636e11	−0.120284
$650$	−5.40962e12	−1.18866
$651$	3.73023e11	0.0813994
$652$	3.95351e11	0.0856778
$653$	3.23629e12	0.696527	0.348264	−	0.937397i	$-0.386771\pi$
$653$	3.23629e12	0.696527	0.348264	+	0.937397i	$0.386771\pi$
$654$	−1.36942e11	−0.0292710
$655$	−1.32207e13	−2.80652
$656$	−7.51557e12	−1.58451
$657$	−6.92443e12	−1.44991
$658$	7.60368e12	1.58127
$659$	3.14006e12	0.648566	0.324283	−	0.945960i	$-0.394877\pi$
$659$	3.14006e12	0.648566	0.324283	+	0.945960i	$0.394877\pi$
$660$	−7.15634e10	−0.0146806
$661$	5.53149e12	1.12703	0.563515	−	0.826106i	$-0.309449\pi$
$661$	5.53149e12	1.12703	0.563515	+	0.826106i	$0.309449\pi$
$662$	2.74495e12	0.555487
$663$	−9.72766e10	−0.0195523
$664$	−9.85504e10	−0.0196744
$665$	−6.77643e12	−1.34370
$666$	−9.04642e12	−1.78173
$667$	3.17001e12	0.620146
$668$	−4.11109e12	−0.798846
$669$	−8.74510e10	−0.0168790
$670$	1.26428e13	2.42386
$671$	4.79516e10	0.00913170
$672$	2.79186e11	0.0528120
$673$	−5.00712e12	−0.940850	−0.470425	−	0.882440i	$-0.655899\pi$
$673$	−5.00712e12	−0.940850	−0.470425	+	0.882440i	$0.655899\pi$
$674$	9.37398e11	0.174966
$675$	7.97721e11	0.147905
$676$	−2.37546e12	−0.437510
$677$	−6.52042e11	−0.119296	−0.0596481	−	0.998219i	$-0.518998\pi$
$677$	−6.52042e11	−0.119296	−0.0596481	+	0.998219i	$0.518998\pi$
$678$	−2.33631e11	−0.0424616
$679$	5.34992e12	0.965902
$680$	2.94921e12	0.528952
$681$	3.27862e11	0.0584155
$682$	−3.82403e12	−0.676848
$683$	2.51755e12	0.442676	0.221338	−	0.975197i	$-0.428958\pi$
$683$	2.51755e12	0.442676	0.221338	+	0.975197i	$0.428958\pi$
$684$	3.07546e12	0.537227
$685$	−7.51862e12	−1.30476
$686$	−7.37111e12	−1.27079
$687$	−1.39868e11	−0.0239559
$688$	7.12197e12	1.21186
$689$	4.37850e12	0.740183
$690$	−3.42589e11	−0.0575377
$691$	−7.90711e10	−0.0131937	−0.00659685	−	0.999978i	$-0.502100\pi$
$691$	−7.90711e10	−0.0131937	−0.00659685	+	0.999978i	$0.502100\pi$
$692$	−3.28539e12	−0.544640
$693$	−1.84786e12	−0.304347
$694$	2.84976e12	0.466327
$695$	−5.18711e12	−0.843323
$696$	1.30953e11	0.0211531
$697$	−5.93260e12	−0.952133
$698$	9.07721e12	1.44745
$699$	−2.28109e11	−0.0361405
$700$	6.75048e12	1.06266
$701$	5.21330e12	0.815420	0.407710	−	0.913111i	$-0.366327\pi$
$701$	5.21330e12	0.815420	0.407710	+	0.913111i	$0.366327\pi$
$702$	−4.38745e11	−0.0681860
$703$	−7.39805e12	−1.14240
$704$	−4.52456e11	−0.0694224
$705$	−5.93306e11	−0.0904540
$706$	8.31837e11	0.126013
$707$	−8.44997e12	−1.27194
$708$	8.04504e10	0.0120331
$709$	−1.11426e12	−0.165606	−0.0828032	−	0.996566i	$-0.526387\pi$
$709$	−1.11426e12	−0.165606	−0.0828032	+	0.996566i	$0.526387\pi$
$710$	−1.27767e13	−1.88694
$711$	7.99678e12	1.17355
$712$	−4.86279e12	−0.709129
$713$	−7.24001e12	−1.04915
$714$	3.06931e11	0.0441977
$715$	−1.95763e12	−0.280126
$716$	2.29991e12	0.327042
$717$	3.77748e10	0.00533785
$718$	−9.80137e12	−1.37634
$719$	−1.29076e13	−1.80121	−0.900604	−	0.434640i	$-0.856876\pi$
$719$	−1.29076e13	−1.80121	−0.900604	+	0.434640i	$0.856876\pi$
$720$	1.42430e13	1.97518
$721$	8.25573e12	1.13775
$722$	−3.03169e12	−0.415210
$723$	−1.21368e11	−0.0165189
$724$	4.04563e12	0.547221
$725$	1.23237e13	1.65661
$726$	−4.03519e10	−0.00539074
$727$	−4.87575e11	−0.0647347	−0.0323673	−	0.999476i	$-0.510305\pi$
$727$	−4.87575e11	−0.0647347	−0.0323673	+	0.999476i	$0.510305\pi$
$728$	1.96222e12	0.258915
$729$	−7.52851e12	−0.987269
$730$	2.31462e13	3.01666
$731$	5.62191e12	0.728208
$732$	−7.09615e9	−0.000913530 0
$733$	4.58153e12	0.586196	0.293098	−	0.956082i	$-0.405314\pi$
$733$	4.58153e12	0.586196	0.293098	+	0.956082i	$0.405314\pi$
$734$	−5.73501e12	−0.729293
$735$	−1.36854e10	−0.00172967
$736$	−5.41873e12	−0.680686
$737$	2.81937e12	0.352005
$738$	−1.33646e13	−1.65845
$739$	−6.69937e11	−0.0826292	−0.0413146	−	0.999146i	$-0.513155\pi$
$739$	−6.69937e11	−0.0826292	−0.0413146	+	0.999146i	$0.513155\pi$
$740$	1.19594e13	1.46611
$741$	−1.79209e11	−0.0218363
$742$	−1.38152e13	−1.67317
$743$	6.71335e12	0.808145	0.404073	−	0.914727i	$-0.367594\pi$
$743$	6.71335e12	0.808145	0.404073	+	0.914727i	$0.367594\pi$
$744$	−2.99084e11	−0.0357861
$745$	1.43775e13	1.70993
$746$	3.16535e12	0.374195
$747$	−3.75697e11	−0.0441464
$748$	−1.24441e12	−0.145347
$749$	3.73668e12	0.433828
$750$	−5.02413e11	−0.0579810
$751$	1.25035e13	1.43434	0.717170	−	0.696898i	$-0.245437\pi$
$751$	1.25035e13	1.43434	0.717170	+	0.696898i	$0.245437\pi$
$752$	−1.30697e13	−1.49034
$753$	1.11797e11	0.0126722
$754$	−6.77801e12	−0.763715
$755$	−1.91546e13	−2.14541
$756$	5.47495e11	0.0609582
$757$	1.66054e13	1.83788	0.918940	−	0.394398i	$-0.129047\pi$
$757$	1.66054e13	1.83788	0.918940	+	0.394398i	$0.129047\pi$
$758$	1.02552e12	0.112832
$759$	−7.63979e10	−0.00835590
$760$	5.43323e12	0.590741
$761$	5.87109e12	0.634582	0.317291	−	0.948328i	$-0.397227\pi$
$761$	5.87109e12	0.634582	0.317291	+	0.948328i	$0.397227\pi$
$762$	−8.56614e10	−0.00920423
$763$	4.67461e12	0.499327
$764$	5.42614e12	0.576197
$765$	1.12431e13	1.18689
$766$	−6.34723e12	−0.666124
$767$	2.20074e12	0.229609
$768$	−5.80435e11	−0.0602044
$769$	−6.39550e12	−0.659487	−0.329743	−	0.944071i	$-0.606962\pi$
$769$	−6.39550e12	−0.659487	−0.329743	+	0.944071i	$0.606962\pi$
$770$	6.17681e12	0.633221
$771$	5.05339e11	0.0515036
$772$	−1.12696e13	−1.14191
$773$	4.09471e12	0.412492	0.206246	−	0.978500i	$-0.433875\pi$
$773$	4.09471e12	0.412492	0.206246	+	0.978500i	$0.433875\pi$
$774$	1.26647e13	1.26841
$775$	−2.81462e13	−2.80261
$776$	−4.28948e12	−0.424645
$777$	−6.57802e11	−0.0647442
$778$	−1.11746e13	−1.09351
$779$	−1.09294e13	−1.06336
$780$	2.89702e11	0.0280237
$781$	−2.84923e12	−0.274030
$782$	−5.95723e12	−0.569658
$783$	9.99509e11	0.0950296
$784$	−3.01470e11	−0.0284985
$785$	−3.61010e11	−0.0339317
$786$	1.10318e12	0.103097
$787$	2.51798e12	0.233973	0.116987	−	0.993133i	$-0.462677\pi$
$787$	2.51798e12	0.233973	0.116987	+	0.993133i	$0.462677\pi$
$788$	−6.93473e12	−0.640710
$789$	9.56159e11	0.0878382
$790$	−2.67307e13	−2.44168
$791$	7.97514e12	0.724343
$792$	1.48158e12	0.133802
$793$	−1.94117e11	−0.0174314
$794$	−2.96117e12	−0.264406
$795$	1.07799e12	0.0957109
$796$	3.52027e12	0.310790
$797$	2.14274e12	0.188108	0.0940539	−	0.995567i	$-0.470017\pi$
$797$	2.14274e12	0.188108	0.0940539	+	0.995567i	$0.470017\pi$
$798$	5.65449e11	0.0493606
$799$	−1.03169e13	−0.895548
$800$	−2.10658e13	−1.81833
$801$	−1.85381e13	−1.59118
$802$	−1.01750e13	−0.868460
$803$	5.16164e12	0.438094
$804$	−4.17227e11	−0.0352144
$805$	1.16945e13	0.981523
$806$	1.54803e13	1.29203
$807$	−3.53352e11	−0.0293276
$808$	6.77505e12	0.559193
$809$	6.30008e12	0.517104	0.258552	−	0.965997i	$-0.416755\pi$
$809$	6.30008e12	0.517104	0.258552	+	0.965997i	$0.416755\pi$
$810$	2.52737e13	2.06294
$811$	1.77348e13	1.43957	0.719785	−	0.694197i	$-0.244240\pi$
$811$	1.77348e13	1.43957	0.719785	+	0.694197i	$0.244240\pi$
$812$	8.45806e12	0.682761
$813$	−4.14143e11	−0.0332463
$814$	6.74342e12	0.538357
$815$	2.66263e12	0.211398
$816$	−5.27574e11	−0.0416560
$817$	1.03570e13	0.813273
$818$	1.86803e13	1.45879
$819$	7.48045e12	0.580965
$820$	1.76680e13	1.36466
$821$	−5.89436e12	−0.452785	−0.226393	−	0.974036i	$-0.572693\pi$
$821$	−5.89436e12	−0.452785	−0.226393	+	0.974036i	$0.572693\pi$
$822$	6.27380e11	0.0479300
$823$	6.01678e12	0.457156	0.228578	−	0.973526i	$-0.426592\pi$
$823$	6.01678e12	0.457156	0.228578	+	0.973526i	$0.426592\pi$
$824$	−6.61931e12	−0.500196
$825$	−2.97004e11	−0.0223213
$826$	−6.94386e12	−0.519028
$827$	−2.04581e13	−1.52086	−0.760432	−	0.649418i	$-0.775013\pi$
$827$	−2.04581e13	−1.52086	−0.760432	+	0.649418i	$0.775013\pi$
$828$	−5.30751e12	−0.392423
$829$	−7.23437e12	−0.531992	−0.265996	−	0.963974i	$-0.585701\pi$
$829$	−7.23437e12	−0.531992	−0.265996	+	0.963974i	$0.585701\pi$
$830$	1.25584e12	0.0918507
$831$	−5.35498e11	−0.0389541
$832$	1.83162e12	0.132520
$833$	−2.37973e11	−0.0171248
$834$	4.32830e11	0.0309792
$835$	−2.76876e13	−1.97104
$836$	−2.29252e12	−0.162325
$837$	−2.28279e12	−0.160768
$838$	2.82946e13	1.98201
$839$	6.35467e11	0.0442756	0.0221378	−	0.999755i	$-0.492953\pi$
$839$	6.35467e11	0.0442756	0.0221378	+	0.999755i	$0.492953\pi$
$840$	4.83099e11	0.0334795
$841$	9.33910e11	0.0643758
$842$	3.21575e13	2.20484
$843$	−4.12380e10	−0.00281238
$844$	−3.21070e12	−0.217800
$845$	−1.59984e13	−1.07950
$846$	−2.32413e13	−1.55989
$847$	1.37744e12	0.0919594
$848$	2.37465e13	1.57695
$849$	−4.01750e10	−0.00265382
$850$	−2.31593e13	−1.52174
$851$	1.27673e13	0.834479
$852$	4.21645e11	0.0274138
$853$	−2.12280e13	−1.37290	−0.686450	−	0.727177i	$-0.740832\pi$
$853$	−2.12280e13	−1.37290	−0.686450	+	0.727177i	$0.740832\pi$
$854$	6.12485e11	0.0394035
$855$	2.07128e13	1.32553
$856$	−2.99601e12	−0.190726
$857$	1.04035e13	0.658817	0.329408	−	0.944188i	$-0.393151\pi$
$857$	1.04035e13	0.658817	0.329408	+	0.944188i	$0.393151\pi$
$858$	1.63352e11	0.0102904
$859$	−6.19031e12	−0.387921	−0.193961	−	0.981009i	$-0.562133\pi$
$859$	−6.19031e12	−0.387921	−0.193961	+	0.981009i	$0.562133\pi$
$860$	−1.67427e13	−1.04372
$861$	−9.71796e11	−0.0602644
$862$	3.09394e13	1.90866
$863$	−1.10977e13	−0.681058	−0.340529	−	0.940234i	$-0.610606\pi$
$863$	−1.10977e13	−0.681058	−0.340529	+	0.940234i	$0.610606\pi$
$864$	−1.70853e12	−0.104307
$865$	−2.21266e13	−1.34382
$866$	2.92054e12	0.176454
$867$	3.50605e11	0.0210733
$868$	−1.93174e13	−1.15508
$869$	−5.96099e12	−0.354593
$870$	−1.66875e12	−0.0987537
$871$	−1.14133e13	−0.671940
$872$	−3.74803e12	−0.219522
$873$	−1.63525e13	−0.952840
$874$	−1.09748e13	−0.636202
$875$	1.71502e13	0.989084
$876$	−7.63849e11	−0.0438267
$877$	1.57725e13	0.900331	0.450165	−	0.892945i	$-0.351365\pi$
$877$	1.57725e13	0.900331	0.450165	+	0.892945i	$0.351365\pi$
$878$	1.91875e13	1.08966
$879$	7.59543e11	0.0429143
$880$	−1.06171e13	−0.596807
$881$	−2.12008e12	−0.118566	−0.0592832	−	0.998241i	$-0.518881\pi$
$881$	−2.12008e12	−0.118566	−0.0592832	+	0.998241i	$0.518881\pi$
$882$	−5.36092e11	−0.0298284
$883$	−3.21938e13	−1.78217	−0.891084	−	0.453838i	$-0.850055\pi$
$883$	−3.21938e13	−1.78217	−0.891084	+	0.453838i	$0.850055\pi$
$884$	5.03758e12	0.277451
$885$	5.41821e11	0.0296901
$886$	−2.49088e13	−1.35800
$887$	1.85783e13	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$887$	1.85783e13	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$888$	5.27415e11	0.0284639
$889$	2.92411e12	0.157013
$890$	6.19671e13	3.31059
$891$	5.63608e12	0.299590
$892$	4.52875e12	0.239517
$893$	−1.90065e13	−1.00016
$894$	−1.19971e12	−0.0628139
$895$	1.54896e13	0.806930
$896$	1.63199e13	0.845925
$897$	3.09272e11	0.0159505
$898$	−3.52837e13	−1.81063
$899$	−3.52659e13	−1.80068
$900$	−2.06334e13	−1.04829
$901$	1.87449e13	0.947594
$902$	9.96231e12	0.501107
$903$	9.20902e11	0.0460913
$904$	−6.39434e12	−0.318447
$905$	2.72467e13	1.35019
$906$	1.59832e12	0.0788111
$907$	3.67870e13	1.80494	0.902468	−	0.430758i	$-0.141754\pi$
$907$	3.67870e13	1.80494	0.902468	+	0.430758i	$0.141754\pi$
$908$	−1.69787e13	−0.828929
$909$	2.58281e13	1.25474
$910$	−2.50048e13	−1.20875
$911$	−2.95783e12	−0.142279	−0.0711394	−	0.997466i	$-0.522664\pi$
$911$	−2.95783e12	−0.142279	−0.0711394	+	0.997466i	$0.522664\pi$
$912$	−9.71931e11	−0.0465220
$913$	2.80054e11	0.0133390
$914$	−1.98399e13	−0.940333
$915$	−4.77915e10	−0.00225401
$916$	7.24322e12	0.339940
$917$	−3.76577e13	−1.75870
$918$	−1.87832e12	−0.0872928
$919$	3.19254e13	1.47644	0.738222	−	0.674558i	$-0.235666\pi$
$919$	3.19254e13	1.47644	0.738222	+	0.674558i	$0.235666\pi$
$920$	−9.37647e12	−0.431513
$921$	−9.52980e11	−0.0436431
$922$	3.21032e13	1.46305
$923$	1.15342e13	0.523094
$924$	−2.03841e11	−0.00919958
$925$	4.96340e13	2.22916
$926$	−5.38158e13	−2.40525
$927$	−2.52344e13	−1.12236
$928$	−2.63945e13	−1.16828
$929$	−2.63363e13	−1.16007	−0.580034	−	0.814592i	$-0.696961\pi$
$929$	−2.63363e13	−1.16007	−0.580034	+	0.814592i	$0.696961\pi$
$930$	3.81126e12	0.167069
$931$	−4.38409e11	−0.0191252
$932$	1.18129e13	0.512842
$933$	−3.02406e11	−0.0130654
$934$	1.12809e13	0.485046
$935$	−8.38088e12	−0.358622
$936$	−5.99771e12	−0.255413
$937$	3.90562e13	1.65524	0.827622	−	0.561286i	$-0.189693\pi$
$937$	3.90562e13	1.65524	0.827622	+	0.561286i	$0.189693\pi$
$938$	3.60118e13	1.51891
$939$	−1.54556e12	−0.0648768
$940$	3.07250e13	1.28356
$941$	−4.31390e13	−1.79356	−0.896782	−	0.442474i	$-0.854101\pi$
$941$	−4.31390e13	−1.79356	−0.896782	+	0.442474i	$0.854101\pi$
$942$	3.01239e10	0.00124647
$943$	1.88616e13	0.776740
$944$	1.19356e13	0.489181
$945$	3.68730e12	0.150406
$946$	−9.44058e12	−0.383256
$947$	2.05301e13	0.829499	0.414750	−	0.909936i	$-0.363869\pi$
$947$	2.05301e13	0.829499	0.414750	+	0.909936i	$0.363869\pi$
$948$	8.82142e11	0.0354733
$949$	−2.08952e13	−0.836276
$950$	−4.26655e13	−1.69950
$951$	−3.95956e11	−0.0156976
$952$	8.40053e12	0.331467
$953$	2.97284e13	1.16749	0.583745	−	0.811937i	$-0.301587\pi$
$953$	2.97284e13	1.16749	0.583745	+	0.811937i	$0.301587\pi$
$954$	4.22275e13	1.65055
$955$	3.65442e13	1.42169
$956$	−1.95621e12	−0.0757452
$957$	−3.72133e11	−0.0143415
$958$	−3.32243e12	−0.127441
$959$	−2.14160e13	−0.817626
$960$	4.50946e11	0.0171358
$961$	5.41045e13	2.04634
$962$	−2.72986e13	−1.02767
$963$	−1.14215e13	−0.427961
$964$	6.28518e12	0.234407
$965$	−7.58991e13	−2.81750
$966$	−9.75830e11	−0.0360560
$967$	−3.32193e13	−1.22172	−0.610860	−	0.791738i	$-0.709176\pi$
$967$	−3.32193e13	−1.22172	−0.610860	+	0.791738i	$0.709176\pi$
$968$	−1.10441e12	−0.0404287
$969$	−7.67218e11	−0.0279552
$970$	5.46613e13	1.98247
$971$	2.43945e13	0.880653	0.440326	−	0.897838i	$-0.354863\pi$
$971$	2.43945e13	0.880653	0.440326	+	0.897838i	$0.354863\pi$
$972$	−2.51109e12	−0.0902328
$973$	−1.47749e13	−0.528467
$974$	−2.88444e13	−1.02694
$975$	1.20233e12	0.0426090
$976$	−1.05278e12	−0.0371376
$977$	2.28184e13	0.801234	0.400617	−	0.916246i	$-0.368796\pi$
$977$	2.28184e13	0.801234	0.400617	+	0.916246i	$0.368796\pi$
$978$	−2.22179e11	−0.00776564
$979$	1.38187e13	0.480780
$980$	7.08713e11	0.0245444
$981$	−1.42884e13	−0.492574
$982$	−5.84936e13	−2.00727
$983$	−2.53488e13	−0.865897	−0.432949	−	0.901419i	$-0.642527\pi$
$983$	−2.53488e13	−0.865897	−0.432949	+	0.901419i	$0.642527\pi$
$984$	7.79170e11	0.0264944
$985$	−4.67043e13	−1.58086
$986$	−2.90176e13	−0.977721
$987$	−1.68997e12	−0.0566829
$988$	9.28055e12	0.309861
$989$	−1.78738e13	−0.594064
$990$	−1.88800e13	−0.624658
$991$	−2.60279e13	−0.857249	−0.428625	−	0.903483i	$-0.641002\pi$
$991$	−2.60279e13	−0.857249	−0.428625	+	0.903483i	$0.641002\pi$
$992$	6.02826e13	1.97647
$993$	−6.10085e11	−0.0199122
$994$	−3.63932e13	−1.18245
$995$	2.37085e13	0.766831
$996$	−4.14440e10	−0.00133443
$997$	2.82518e13	0.905563	0.452781	−	0.891622i	$-0.350432\pi$
$997$	2.82518e13	0.905563	0.452781	+	0.891622i	$0.350432\pi$
$998$	3.05858e13	0.975960
$999$	4.02554e12	0.127873

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.10.a.b.1.4	✓	5
3.2	odd	2		99.10.a.f.1.2		5
4.3	odd	2		176.10.a.j.1.3		5
5.4	even	2		275.10.a.b.1.2		5
11.10	odd	2		121.10.a.c.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.10.a.b.1.4	✓	5	1.1	even	1	trivial
99.10.a.f.1.2		5	3.2	odd	2
121.10.a.c.1.2		5	11.10	odd	2
176.10.a.j.1.3		5	4.3	odd	2
275.10.a.b.1.2		5	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	11.a (trivial)

\(f(q)\)	\(=\)	\(q+29.1027 q^{2} -6.46828 q^{3} +334.967 q^{4} +2255.95 q^{5} -188.244 q^{6} +6425.84 q^{7} -5152.14 q^{8} -19641.2 q^{9} +O(q^{10})\)	\(q+29.1027 q^{2} -6.46828 q^{3} +334.967 q^{4} +2255.95 q^{5} -188.244 q^{6} +6425.84 q^{7} -5152.14 q^{8} -19641.2 q^{9} +65654.3 q^{10} +14641.0 q^{11} -2166.66 q^{12} -59269.4 q^{13} +187009. q^{14} -14592.1 q^{15} -321444. q^{16} -253740. q^{17} -571611. q^{18} -467456. q^{19} +755669. q^{20} -41564.1 q^{21} +426093. q^{22} +806718. q^{23} +33325.5 q^{24} +3.13619e6 q^{25} -1.72490e6 q^{26} +254360. q^{27} +2.15245e6 q^{28} +3.92951e6 q^{29} -424670. q^{30} -8.97464e6 q^{31} -6.71700e6 q^{32} -94702.1 q^{33} -7.38452e6 q^{34} +1.44964e7 q^{35} -6.57914e6 q^{36} +1.58262e7 q^{37} -1.36042e7 q^{38} +383371. q^{39} -1.16230e7 q^{40} +2.33806e7 q^{41} -1.20963e6 q^{42} -2.21562e7 q^{43} +4.90425e6 q^{44} -4.43095e7 q^{45} +2.34777e7 q^{46} +4.06593e7 q^{47} +2.07919e6 q^{48} +937862. q^{49} +9.12716e7 q^{50} +1.64126e6 q^{51} -1.98533e7 q^{52} -7.38745e7 q^{53} +7.40255e6 q^{54} +3.30294e7 q^{55} -3.31068e7 q^{56} +3.02364e6 q^{57} +1.14359e8 q^{58} -3.71311e7 q^{59} -4.88788e6 q^{60} +3.27516e6 q^{61} -2.61186e8 q^{62} -1.26211e8 q^{63} -3.09034e7 q^{64} -1.33709e8 q^{65} -2.75609e6 q^{66} +1.92567e8 q^{67} -8.49946e7 q^{68} -5.21808e6 q^{69} +4.21884e8 q^{70} -1.94606e8 q^{71} +1.01194e8 q^{72} +3.52547e8 q^{73} +4.60585e8 q^{74} -2.02858e7 q^{75} -1.56582e8 q^{76} +9.40808e7 q^{77} +1.11571e7 q^{78} -4.07144e8 q^{79} -7.25163e8 q^{80} +3.84952e8 q^{81} +6.80439e8 q^{82} +1.91281e7 q^{83} -1.39226e7 q^{84} -5.72425e8 q^{85} -6.44804e8 q^{86} -2.54172e7 q^{87} -7.54324e7 q^{88} +9.43839e8 q^{89} -1.28953e9 q^{90} -3.80856e8 q^{91} +2.70224e8 q^{92} +5.80505e7 q^{93} +1.18330e9 q^{94} -1.05456e9 q^{95} +4.34474e7 q^{96} +8.32562e8 q^{97} +2.72943e7 q^{98} -2.87566e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 16 q^{2} + 112 q^{3} + 708 q^{4} + 1594 q^{5} + 10378 q^{6} + 8400 q^{7} + 40716 q^{8} + 74789 q^{9}+O(q^{10}) \) 5 * q + 16 * q^2 + 112 * q^3 + 708 * q^4 + 1594 * q^5 + 10378 * q^6 + 8400 * q^7 + 40716 * q^8 + 74789 * q^9	\( 5 q + 16 q^{2} + 112 q^{3} + 708 q^{4} + 1594 q^{5} + 10378 q^{6} + 8400 q^{7} + 40716 q^{8} + 74789 q^{9} + 2986 q^{10} + 73205 q^{11} + 110288 q^{12} + 47214 q^{13} - 299852 q^{14} - 559436 q^{15} - 454776 q^{16} - 547238 q^{17} - 822418 q^{18} - 162940 q^{19} - 1913320 q^{20} + 825496 q^{21} + 234256 q^{22} + 3415892 q^{23} + 1435932 q^{24} + 6164943 q^{25} + 5356756 q^{26} + 5240140 q^{27} - 2477216 q^{28} + 5868414 q^{29} - 9766670 q^{30} + 11730396 q^{31} - 18454552 q^{32} + 1639792 q^{33} - 25579352 q^{34} - 6567848 q^{35} - 26683532 q^{36} + 7021250 q^{37} - 22257720 q^{38} + 29114872 q^{39} - 22406796 q^{40} + 5595418 q^{41} - 65554916 q^{42} + 29161940 q^{43} + 10365828 q^{44} + 68008838 q^{45} + 47468978 q^{46} + 33703664 q^{47} + 96997832 q^{48} + 106606605 q^{49} + 84598070 q^{50} - 135853760 q^{51} + 185107192 q^{52} - 88905666 q^{53} - 95103866 q^{54} + 23337754 q^{55} - 78057672 q^{56} - 362541120 q^{57} + 63640668 q^{58} + 13747712 q^{59} - 208875616 q^{60} + 274324430 q^{61} - 161612942 q^{62} - 436710568 q^{63} - 46082368 q^{64} - 658499468 q^{65} + 151944298 q^{66} + 323117752 q^{67} - 679289848 q^{68} - 60345676 q^{69} + 1608436228 q^{70} + 9655356 q^{71} + 1168471200 q^{72} + 159287274 q^{73} + 76718502 q^{74} - 963596116 q^{75} + 483002000 q^{76} + 122984400 q^{77} + 1270322200 q^{78} - 668342072 q^{79} - 424312360 q^{80} + 1578463805 q^{81} + 666585700 q^{82} + 378353820 q^{83} - 2381947456 q^{84} + 1459757140 q^{85} - 2133621276 q^{86} - 2822691048 q^{87} + 596122956 q^{88} + 851774166 q^{89} - 4463334016 q^{90} - 991736368 q^{91} + 1919755168 q^{92} + 1149973204 q^{93} + 2620937360 q^{94} - 2812243800 q^{95} - 1157568712 q^{96} - 240502490 q^{97} - 2298624888 q^{98} + 1094985749 q^{99}+O(q^{100}) \) 5 * q + 16 * q^2 + 112 * q^3 + 708 * q^4 + 1594 * q^5 + 10378 * q^6 + 8400 * q^7 + 40716 * q^8 + 74789 * q^9 + 2986 * q^10 + 73205 * q^11 + 110288 * q^12 + 47214 * q^13 - 299852 * q^14 - 559436 * q^15 - 454776 * q^16 - 547238 * q^17 - 822418 * q^18 - 162940 * q^19 - 1913320 * q^20 + 825496 * q^21 + 234256 * q^22 + 3415892 * q^23 + 1435932 * q^24 + 6164943 * q^25 + 5356756 * q^26 + 5240140 * q^27 - 2477216 * q^28 + 5868414 * q^29 - 9766670 * q^30 + 11730396 * q^31 - 18454552 * q^32 + 1639792 * q^33 - 25579352 * q^34 - 6567848 * q^35 - 26683532 * q^36 + 7021250 * q^37 - 22257720 * q^38 + 29114872 * q^39 - 22406796 * q^40 + 5595418 * q^41 - 65554916 * q^42 + 29161940 * q^43 + 10365828 * q^44 + 68008838 * q^45 + 47468978 * q^46 + 33703664 * q^47 + 96997832 * q^48 + 106606605 * q^49 + 84598070 * q^50 - 135853760 * q^51 + 185107192 * q^52 - 88905666 * q^53 - 95103866 * q^54 + 23337754 * q^55 - 78057672 * q^56 - 362541120 * q^57 + 63640668 * q^58 + 13747712 * q^59 - 208875616 * q^60 + 274324430 * q^61 - 161612942 * q^62 - 436710568 * q^63 - 46082368 * q^64 - 658499468 * q^65 + 151944298 * q^66 + 323117752 * q^67 - 679289848 * q^68 - 60345676 * q^69 + 1608436228 * q^70 + 9655356 * q^71 + 1168471200 * q^72 + 159287274 * q^73 + 76718502 * q^74 - 963596116 * q^75 + 483002000 * q^76 + 122984400 * q^77 + 1270322200 * q^78 - 668342072 * q^79 - 424312360 * q^80 + 1578463805 * q^81 + 666585700 * q^82 + 378353820 * q^83 - 2381947456 * q^84 + 1459757140 * q^85 - 2133621276 * q^86 - 2822691048 * q^87 + 596122956 * q^88 + 851774166 * q^89 - 4463334016 * q^90 - 991736368 * q^91 + 1919755168 * q^92 + 1149973204 * q^93 + 2620937360 * q^94 - 2812243800 * q^95 - 1157568712 * q^96 - 240502490 * q^97 - 2298624888 * q^98 + 1094985749 * q^99

Introduction

L-functions

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