LMFDB - Embedded newform 11.10.a.a.1.3

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:	$1$
Dimension:	$3$
Coefficient field:	3.3.2659452.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 306x - 836 $ x^3 - 306*x - 836
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-15.9214$ 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)

$f(q)$	$=$	$q+31.8429 q^{2} -261.882 q^{3} +501.969 q^{4} -1908.19 q^{5} -8339.07 q^{6} +3060.06 q^{7} -319.425 q^{8} +48899.1 q^{9} +O(q^{10})$	\(q+31.8429 q^{2} -261.882 q^{3} +501.969 q^{4} -1908.19 q^{5} -8339.07 q^{6} +3060.06 q^{7} -319.425 q^{8} +48899.1 q^{9} -60762.2 q^{10} -14641.0 q^{11} -131457. q^{12} -100860. q^{13} +97441.1 q^{14} +499720. q^{15} -267179. q^{16} +141383. q^{17} +1.55709e6 q^{18} -491244. q^{19} -957851. q^{20} -801374. q^{21} -466212. q^{22} +1.02113e6 q^{23} +83651.6 q^{24} +1.68806e6 q^{25} -3.21167e6 q^{26} -7.65118e6 q^{27} +1.53605e6 q^{28} -1.58245e6 q^{29} +1.59125e7 q^{30} -2.39728e6 q^{31} -8.34421e6 q^{32} +3.83421e6 q^{33} +4.50205e6 q^{34} -5.83917e6 q^{35} +2.45458e7 q^{36} -1.40297e7 q^{37} -1.56426e7 q^{38} +2.64134e7 q^{39} +609523. q^{40} -8.90588e6 q^{41} -2.55181e7 q^{42} +3.79365e7 q^{43} -7.34932e6 q^{44} -9.33088e7 q^{45} +3.25158e7 q^{46} +3.02797e7 q^{47} +6.99694e7 q^{48} -3.09896e7 q^{49} +5.37527e7 q^{50} -3.70257e7 q^{51} -5.06286e7 q^{52} -1.24582e6 q^{53} -2.43635e8 q^{54} +2.79378e7 q^{55} -977459. q^{56} +1.28648e8 q^{57} -5.03897e7 q^{58} +1.27784e8 q^{59} +2.50844e8 q^{60} -6.35208e7 q^{61} -7.63362e7 q^{62} +1.49634e8 q^{63} -1.28908e8 q^{64} +1.92460e8 q^{65} +1.22092e8 q^{66} +7.51979e7 q^{67} +7.09700e7 q^{68} -2.67416e8 q^{69} -1.85936e8 q^{70} -9.00530e7 q^{71} -1.56196e7 q^{72} -1.51420e8 q^{73} -4.46747e8 q^{74} -4.42072e8 q^{75} -2.46589e8 q^{76} -4.48023e7 q^{77} +8.41079e8 q^{78} -5.42941e8 q^{79} +5.09829e8 q^{80} +1.04122e9 q^{81} -2.83589e8 q^{82} +4.30849e8 q^{83} -4.02265e8 q^{84} -2.69786e8 q^{85} +1.20801e9 q^{86} +4.14414e8 q^{87} +4.67670e6 q^{88} -5.75029e8 q^{89} -2.97122e9 q^{90} -3.08638e8 q^{91} +5.12577e8 q^{92} +6.27804e8 q^{93} +9.64194e8 q^{94} +9.37386e8 q^{95} +2.18520e9 q^{96} -2.55198e8 q^{97} -9.86799e8 q^{98} -7.15932e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 186 q^{3} + 912 q^{4} - 1824 q^{5} - 10956 q^{6} - 7260 q^{7} - 20064 q^{8} + 14553 q^{9}+O(q^{10}) $ 3 * q - 186 * q^3 + 912 * q^4 - 1824 * q^5 - 10956 * q^6 - 7260 * q^7 - 20064 * q^8 + 14553 * q^9	\( 3 q - 186 q^{3} + 912 q^{4} - 1824 q^{5} - 10956 q^{6} - 7260 q^{7} - 20064 q^{8} + 14553 q^{9} - 86724 q^{10} - 43923 q^{11} - 71040 q^{12} - 93258 q^{13} + 324264 q^{14} + 540330 q^{15} + 22656 q^{16} + 18678 q^{17} + 1997028 q^{18} - 1027356 q^{19} - 156576 q^{20} - 1287924 q^{21} + 1674690 q^{23} - 947232 q^{24} - 1560729 q^{25} - 2162088 q^{26} - 10285434 q^{27} - 2570304 q^{28} - 2693658 q^{29} + 14272500 q^{30} - 4525302 q^{31} + 160512 q^{32} + 2723226 q^{33} + 19899408 q^{34} - 7933860 q^{35} + 20908368 q^{36} - 8820204 q^{37} + 23297712 q^{38} + 24922920 q^{39} - 5145888 q^{40} - 9771102 q^{41} - 8130360 q^{42} + 18795744 q^{43} - 13352592 q^{44} - 91915398 q^{45} - 68671020 q^{46} - 31155816 q^{47} + 76391808 q^{48} - 54229677 q^{49} + 103405236 q^{50} - 62110884 q^{51} - 86345952 q^{52} + 47500122 q^{53} - 153828180 q^{54} + 26705184 q^{55} + 113407680 q^{56} + 62103096 q^{57} - 120644760 q^{58} + 332138370 q^{59} + 290804160 q^{60} - 49031730 q^{61} - 86992620 q^{62} + 319652784 q^{63} - 421220352 q^{64} + 161689572 q^{65} + 160406796 q^{66} + 330560082 q^{67} - 382273056 q^{68} - 104664822 q^{69} - 22907160 q^{70} - 57835050 q^{71} + 302075136 q^{72} - 458816886 q^{73} - 528939708 q^{74} - 562184580 q^{75} - 1324671744 q^{76} + 106293660 q^{77} + 903869520 q^{78} - 798908748 q^{79} + 442084224 q^{80} + 1544572395 q^{81} - 376730664 q^{82} + 1239784920 q^{83} - 809016384 q^{84} - 632001744 q^{85} + 627638088 q^{86} + 505901880 q^{87} + 293757024 q^{88} - 699523368 q^{89} - 2575080288 q^{90} - 268926960 q^{91} + 3537302976 q^{92} + 614745786 q^{93} + 3327514080 q^{94} + 107303856 q^{95} + 2520807168 q^{96} - 2207436012 q^{97} - 1261919472 q^{98} - 213070473 q^{99}+O(q^{100}) \) 3 * q - 186 * q^3 + 912 * q^4 - 1824 * q^5 - 10956 * q^6 - 7260 * q^7 - 20064 * q^8 + 14553 * q^9 - 86724 * q^10 - 43923 * q^11 - 71040 * q^12 - 93258 * q^13 + 324264 * q^14 + 540330 * q^15 + 22656 * q^16 + 18678 * q^17 + 1997028 * q^18 - 1027356 * q^19 - 156576 * q^20 - 1287924 * q^21 + 1674690 * q^23 - 947232 * q^24 - 1560729 * q^25 - 2162088 * q^26 - 10285434 * q^27 - 2570304 * q^28 - 2693658 * q^29 + 14272500 * q^30 - 4525302 * q^31 + 160512 * q^32 + 2723226 * q^33 + 19899408 * q^34 - 7933860 * q^35 + 20908368 * q^36 - 8820204 * q^37 + 23297712 * q^38 + 24922920 * q^39 - 5145888 * q^40 - 9771102 * q^41 - 8130360 * q^42 + 18795744 * q^43 - 13352592 * q^44 - 91915398 * q^45 - 68671020 * q^46 - 31155816 * q^47 + 76391808 * q^48 - 54229677 * q^49 + 103405236 * q^50 - 62110884 * q^51 - 86345952 * q^52 + 47500122 * q^53 - 153828180 * q^54 + 26705184 * q^55 + 113407680 * q^56 + 62103096 * q^57 - 120644760 * q^58 + 332138370 * q^59 + 290804160 * q^60 - 49031730 * q^61 - 86992620 * q^62 + 319652784 * q^63 - 421220352 * q^64 + 161689572 * q^65 + 160406796 * q^66 + 330560082 * q^67 - 382273056 * q^68 - 104664822 * q^69 - 22907160 * q^70 - 57835050 * q^71 + 302075136 * q^72 - 458816886 * q^73 - 528939708 * q^74 - 562184580 * q^75 - 1324671744 * q^76 + 106293660 * q^77 + 903869520 * q^78 - 798908748 * q^79 + 442084224 * q^80 + 1544572395 * q^81 - 376730664 * q^82 + 1239784920 * q^83 - 809016384 * q^84 - 632001744 * q^85 + 627638088 * q^86 + 505901880 * q^87 + 293757024 * q^88 - 699523368 * q^89 - 2575080288 * q^90 - 268926960 * q^91 + 3537302976 * q^92 + 614745786 * q^93 + 3327514080 * q^94 + 107303856 * q^95 + 2520807168 * q^96 - 2207436012 * q^97 - 1261919472 * q^98 - 213070473 * 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 $

$2$	31.8429	1.40727	0.703635	−	0.710562i	$-0.251559\pi$
$2$	31.8429	1.40727	0.703635	+	0.710562i	$0.251559\pi$
$3$	−261.882	−1.86664	−0.933318	−	0.359050i	$-0.883101\pi$
$3$	−261.882	−1.86664	−0.933318	+	0.359050i	$0.883101\pi$
$4$	501.969	0.980408
$5$	−1908.19	−1.36539	−0.682694	−	0.730704i	$-0.739192\pi$
$5$	−1908.19	−1.36539	−0.682694	+	0.730704i	$0.739192\pi$
$6$	−8339.07	−2.62686
$7$	3060.06	0.481713	0.240857	−	0.970561i	$-0.422572\pi$
$7$	3060.06	0.481713	0.240857	+	0.970561i	$0.422572\pi$
$8$	−319.425	−0.0275717
$9$	48899.1	2.48433
$10$	−60762.2	−1.92147
$11$	−14641.0	−0.301511
$11$	−14641.0	−0.301511
$12$	−131457.	−1.83007
$13$	−100860.	−0.979431	−0.489716	−	0.871882i	$-0.662899\pi$
$13$	−100860.	−0.979431	−0.489716	+	0.871882i	$0.662899\pi$
$14$	97441.1	0.677901
$15$	499720.	2.54869
$16$	−267179.	−1.01921
$17$	141383.	0.410561	0.205281	−	0.978703i	$-0.434189\pi$
$17$	141383.	0.410561	0.205281	+	0.978703i	$0.434189\pi$
$18$	1.55709e6	3.49613
$19$	−491244.	−0.864780	−0.432390	−	0.901687i	$-0.642330\pi$
$19$	−491244.	−0.864780	−0.432390	+	0.901687i	$0.642330\pi$
$20$	−957851.	−1.33864
$21$	−801374.	−0.899184
$22$	−466212.	−0.424308
$23$	1.02113e6	0.760864	0.380432	−	0.924809i	$-0.375775\pi$
$23$	1.02113e6	0.760864	0.380432	+	0.924809i	$0.375775\pi$
$24$	83651.6	0.0514664
$25$	1.68806e6	0.864287
$26$	−3.21167e6	−1.37832
$27$	−7.65118e6	−2.77071
$28$	1.53605e6	0.472275
$29$	−1.58245e6	−0.415469	−0.207734	−	0.978185i	$-0.566609\pi$
$29$	−1.58245e6	−0.415469	−0.207734	+	0.978185i	$0.566609\pi$
$30$	1.59125e7	3.58669
$31$	−2.39728e6	−0.466220	−0.233110	−	0.972450i	$-0.574890\pi$
$31$	−2.39728e6	−0.466220	−0.233110	+	0.972450i	$0.574890\pi$
$32$	−8.34421e6	−1.40673
$33$	3.83421e6	0.562812
$34$	4.50205e6	0.577770
$35$	−5.83917e6	−0.657726
$36$	2.45458e7	2.43566
$37$	−1.40297e7	−1.23067	−0.615335	−	0.788266i	$-0.710979\pi$
$37$	−1.40297e7	−1.23067	−0.615335	+	0.788266i	$0.710979\pi$
$38$	−1.56426e7	−1.21698
$39$	2.64134e7	1.82824
$40$	609523.	0.0376461
$41$	−8.90588e6	−0.492209	−0.246104	−	0.969243i	$-0.579151\pi$
$41$	−8.90588e6	−0.492209	−0.246104	+	0.969243i	$0.579151\pi$
$42$	−2.55181e7	−1.26539
$43$	3.79365e7	1.69219	0.846095	−	0.533032i	$-0.178947\pi$
$43$	3.79365e7	1.69219	0.846095	+	0.533032i	$0.178947\pi$
$44$	−7.34932e6	−0.295604
$45$	−9.33088e7	−3.39208
$46$	3.25158e7	1.07074
$47$	3.02797e7	0.905131	0.452566	−	0.891731i	$-0.350509\pi$
$47$	3.02797e7	0.905131	0.452566	+	0.891731i	$0.350509\pi$
$48$	6.99694e7	1.90249
$49$	−3.09896e7	−0.767952
$50$	5.37527e7	1.21628
$51$	−3.70257e7	−0.766369
$52$	−5.06286e7	−0.960242
$53$	−1.24582e6	−0.0216877	−0.0108439	−	0.999941i	$-0.503452\pi$
$53$	−1.24582e6	−0.0216877	−0.0108439	+	0.999941i	$0.503452\pi$
$54$	−2.43635e8	−3.89914
$55$	2.79378e7	0.411680
$56$	−977459.	−0.0132817
$57$	1.28648e8	1.61423
$58$	−5.03897e7	−0.584676
$59$	1.27784e8	1.37291	0.686457	−	0.727170i	$-0.259165\pi$
$59$	1.27784e8	1.37291	0.686457	+	0.727170i	$0.259165\pi$
$60$	2.50844e8	2.49875
$61$	−6.35208e7	−0.587397	−0.293699	−	0.955898i	$-0.594886\pi$
$61$	−6.35208e7	−0.587397	−0.293699	+	0.955898i	$0.594886\pi$
$62$	−7.63362e7	−0.656097
$63$	1.49634e8	1.19674
$64$	−1.28908e8	−0.960439
$65$	1.92460e8	1.33730
$66$	1.22092e8	0.792028
$67$	7.51979e7	0.455900	0.227950	−	0.973673i	$-0.426798\pi$
$67$	7.51979e7	0.455900	0.227950	+	0.973673i	$0.426798\pi$
$68$	7.09700e7	0.402517
$69$	−2.67416e8	−1.42026
$70$	−1.85936e8	−0.925598
$71$	−9.00530e7	−0.420567	−0.210284	−	0.977640i	$-0.567439\pi$
$71$	−9.00530e7	−0.420567	−0.210284	+	0.977640i	$0.567439\pi$
$72$	−1.56196e7	−0.0684973
$73$	−1.51420e8	−0.624064	−0.312032	−	0.950072i	$-0.601010\pi$
$73$	−1.51420e8	−0.624064	−0.312032	+	0.950072i	$0.601010\pi$
$74$	−4.46747e8	−1.73188
$75$	−4.42072e8	−1.61331
$76$	−2.46589e8	−0.847837
$77$	−4.48023e7	−0.145242
$78$	8.41079e8	2.57283
$79$	−5.42941e8	−1.56831	−0.784153	−	0.620568i	$-0.786902\pi$
$79$	−5.42941e8	−1.56831	−0.784153	+	0.620568i	$0.786902\pi$
$80$	5.09829e8	1.39162
$81$	1.04122e9	2.68758
$82$	−2.83589e8	−0.692671
$83$	4.30849e8	0.996493	0.498246	−	0.867036i	$-0.333978\pi$
$83$	4.30849e8	0.996493	0.498246	+	0.867036i	$0.333978\pi$
$84$	−4.02265e8	−0.881567
$85$	−2.69786e8	−0.560576
$86$	1.20801e9	2.38137
$87$	4.14414e8	0.775529
$88$	4.67670e6	0.00831319
$89$	−5.75029e8	−0.971481	−0.485741	−	0.874103i	$-0.661450\pi$
$89$	−5.75029e8	−0.971481	−0.485741	+	0.874103i	$0.661450\pi$
$90$	−2.97122e9	−4.77357
$91$	−3.08638e8	−0.471805
$92$	5.12577e8	0.745957
$93$	6.27804e8	0.870263
$94$	9.64194e8	1.27376
$95$	9.37386e8	1.18076
$96$	2.18520e9	2.62585
$97$	−2.55198e8	−0.292688	−0.146344	−	0.989234i	$-0.546751\pi$
$97$	−2.55198e8	−0.292688	−0.146344	+	0.989234i	$0.546751\pi$
$98$	−9.86799e8	−1.08072
$99$	−7.15932e8	−0.749055
$100$	8.47353e8	0.847353
$101$	−4.27427e8	−0.408711	−0.204355	−	0.978897i	$-0.565510\pi$
$101$	−4.27427e8	−0.408711	−0.204355	+	0.978897i	$0.565510\pi$
$102$	−1.17901e9	−1.07849
$103$	−1.39676e9	−1.22280	−0.611398	−	0.791323i	$-0.709393\pi$
$103$	−1.39676e9	−1.22280	−0.611398	+	0.791323i	$0.709393\pi$
$104$	3.22172e7	0.0270046
$105$	1.52917e9	1.22774
$106$	−3.96705e7	−0.0305205
$107$	−9.29417e8	−0.685463	−0.342731	−	0.939433i	$-0.611352\pi$
$107$	−9.29417e8	−0.685463	−0.342731	+	0.939433i	$0.611352\pi$
$108$	−3.84065e9	−2.71643
$109$	7.01297e8	0.475864	0.237932	−	0.971282i	$-0.423530\pi$
$109$	7.01297e8	0.475864	0.237932	+	0.971282i	$0.423530\pi$
$110$	8.89620e8	0.579345
$111$	3.67413e9	2.29721
$112$	−8.17585e8	−0.490966
$113$	−2.10978e9	−1.21726	−0.608632	−	0.793453i	$-0.708281\pi$
$113$	−2.10978e9	−1.21726	−0.608632	+	0.793453i	$0.708281\pi$
$114$	4.09652e9	2.27166
$115$	−1.94852e9	−1.03888
$116$	−7.94339e8	−0.407329
$117$	−4.93197e9	−2.43323
$118$	4.06902e9	1.93206
$119$	4.32641e8	0.197773
$120$	−1.59623e8	−0.0702716
$121$	2.14359e8	0.0909091
$122$	−2.02269e9	−0.826626
$123$	2.33229e9	0.918775
$124$	−1.20336e9	−0.457086
$125$	5.05794e8	0.185301
$126$	4.76479e9	1.68413
$127$	1.87148e9	0.638364	0.319182	−	0.947693i	$-0.396592\pi$
$127$	1.87148e9	0.638364	0.319182	+	0.947693i	$0.396592\pi$
$128$	1.67439e8	0.0551329
$129$	−9.93488e9	−3.15871
$130$	6.12848e9	1.88195
$131$	−4.26732e9	−1.26600	−0.633000	−	0.774151i	$-0.718177\pi$
$131$	−4.26732e9	−1.26600	−0.633000	+	0.774151i	$0.718177\pi$
$132$	1.92465e9	0.551785
$133$	−1.50324e9	−0.416576
$134$	2.39452e9	0.641574
$135$	1.45999e10	3.78310
$136$	−4.51613e7	−0.0113199
$137$	1.99943e9	0.484912	0.242456	−	0.970162i	$-0.422047\pi$
$137$	1.99943e9	0.484912	0.242456	+	0.970162i	$0.422047\pi$
$138$	−8.51530e9	−1.99868
$139$	8.48158e9	1.92713	0.963563	−	0.267482i	$-0.0861917\pi$
$139$	8.48158e9	1.92713	0.963563	+	0.267482i	$0.0861917\pi$
$140$	−2.93108e9	−0.644840
$141$	−7.92971e9	−1.68955
$142$	−2.86755e9	−0.591852
$143$	1.47669e9	0.295310
$144$	−1.30648e10	−2.53205
$145$	3.01961e9	0.567276
$146$	−4.82164e9	−0.878226
$147$	8.11563e9	1.43349
$148$	−7.04249e9	−1.20656
$149$	5.84044e9	0.970750	0.485375	−	0.874306i	$-0.338683\pi$
$149$	5.84044e9	0.970750	0.485375	+	0.874306i	$0.338683\pi$
$150$	−1.40769e10	−2.27036
$151$	−9.81916e9	−1.53701	−0.768507	−	0.639841i	$-0.779000\pi$
$151$	−9.81916e9	−1.53701	−0.768507	+	0.639841i	$0.779000\pi$
$152$	1.56915e8	0.0238435
$153$	6.91352e9	1.01997
$154$	−1.42664e9	−0.204395
$155$	4.57446e9	0.636572
$156$	1.32587e10	1.79242
$157$	−3.96402e9	−0.520699	−0.260350	−	0.965514i	$-0.583838\pi$
$157$	−3.96402e9	−0.520699	−0.260350	+	0.965514i	$0.583838\pi$
$158$	−1.72888e10	−2.20703
$159$	3.26258e8	0.0404831
$160$	1.59223e10	1.92073
$161$	3.12473e9	0.366518
$162$	3.31555e10	3.78215
$163$	−7.99417e9	−0.887011	−0.443506	−	0.896272i	$-0.646265\pi$
$163$	−7.99417e9	−0.887011	−0.443506	+	0.896272i	$0.646265\pi$
$164$	−4.47047e9	−0.482565
$165$	−7.31640e9	−0.768458
$166$	1.37195e10	1.40233
$167$	8.68656e9	0.864218	0.432109	−	0.901821i	$-0.357770\pi$
$167$	8.68656e9	0.864218	0.432109	+	0.901821i	$0.357770\pi$
$168$	2.55979e8	0.0247920
$169$	−4.31756e8	−0.0407144
$170$	−8.59076e9	−0.788881
$171$	−2.40214e10	−2.14840
$172$	1.90429e10	1.65904
$173$	2.03589e10	1.72802	0.864008	−	0.503478i	$-0.167947\pi$
$173$	2.03589e10	1.72802	0.864008	+	0.503478i	$0.167947\pi$
$174$	1.31961e10	1.09138
$175$	5.16556e9	0.416339
$176$	3.91177e9	0.307303
$177$	−3.34644e10	−2.56273
$178$	−1.83106e10	−1.36714
$179$	−7.88673e9	−0.574193	−0.287097	−	0.957902i	$-0.592690\pi$
$179$	−7.88673e9	−0.574193	−0.287097	+	0.957902i	$0.592690\pi$
$180$	−4.68381e10	−3.32562
$181$	−1.95626e10	−1.35479	−0.677397	−	0.735618i	$-0.736892\pi$
$181$	−1.95626e10	−1.35479	−0.677397	+	0.735618i	$0.736892\pi$
$182$	−9.82791e9	−0.663957
$183$	1.66350e10	1.09646
$184$	−3.26175e8	−0.0209783
$185$	2.67714e10	1.68034
$186$	1.99911e10	1.22470
$187$	−2.06999e9	−0.123789
$188$	1.51995e10	0.887398
$189$	−2.34131e10	−1.33469
$190$	2.98491e10	1.66165
$191$	2.31782e10	1.26017	0.630084	−	0.776527i	$-0.283020\pi$
$191$	2.31782e10	1.26017	0.630084	+	0.776527i	$0.283020\pi$
$192$	3.37587e10	1.79279
$193$	1.09736e10	0.569299	0.284650	−	0.958632i	$-0.408123\pi$
$193$	1.09736e10	0.569299	0.284650	+	0.958632i	$0.408123\pi$
$194$	−8.12624e9	−0.411891
$195$	−5.04018e10	−2.49626
$196$	−1.55558e10	−0.752906
$197$	1.75456e9	0.0829985	0.0414992	−	0.999139i	$-0.486787\pi$
$197$	1.75456e9	0.0829985	0.0414992	+	0.999139i	$0.486787\pi$
$198$	−2.27973e10	−1.05412
$199$	8.46058e9	0.382438	0.191219	−	0.981547i	$-0.438756\pi$
$199$	8.46058e9	0.382438	0.191219	+	0.981547i	$0.438756\pi$
$200$	−5.39208e8	−0.0238299
$201$	−1.96930e10	−0.850999
$202$	−1.36105e10	−0.575166
$203$	−4.84238e9	−0.200137
$204$	−1.85858e10	−0.751354
$205$	1.69941e10	0.672057
$206$	−4.44768e10	−1.72080
$207$	4.99325e10	1.89024
$208$	2.69477e10	0.998245
$209$	7.19230e9	0.260741
$210$	4.86933e10	1.72776
$211$	−4.27314e9	−0.148414	−0.0742072	−	0.997243i	$-0.523643\pi$
$211$	−4.27314e9	−0.148414	−0.0742072	+	0.997243i	$0.523643\pi$
$212$	−6.25363e8	−0.0212628
$213$	2.35833e10	0.785047
$214$	−2.95953e10	−0.964631
$215$	−7.23900e10	−2.31050
$216$	2.44398e9	0.0763933
$217$	−7.33582e9	−0.224584
$218$	2.23313e10	0.669669
$219$	3.96541e10	1.16490
$220$	1.40239e10	0.403614
$221$	−1.42599e10	−0.402116
$222$	1.16995e11	3.23280
$223$	−1.61882e9	−0.0438357	−0.0219179	−	0.999760i	$-0.506977\pi$
$223$	−1.61882e9	−0.0438357	−0.0219179	+	0.999760i	$0.506977\pi$
$224$	−2.55338e10	−0.677640
$225$	8.25447e10	2.14718
$226$	−6.71816e10	−1.71302
$227$	−3.11808e10	−0.779419	−0.389709	−	0.920938i	$-0.627425\pi$
$227$	−3.11808e10	−0.779419	−0.389709	+	0.920938i	$0.627425\pi$
$228$	6.45772e10	1.58260
$229$	−1.26852e10	−0.304816	−0.152408	−	0.988318i	$-0.548703\pi$
$229$	−1.26852e10	−0.304816	−0.152408	+	0.988318i	$0.548703\pi$
$230$	−6.20463e10	−1.46198
$231$	1.17329e10	0.271114
$232$	5.05473e8	0.0114552
$233$	−3.31367e10	−0.736560	−0.368280	−	0.929715i	$-0.620053\pi$
$233$	−3.31367e10	−0.736560	−0.368280	+	0.929715i	$0.620053\pi$
$234$	−1.57048e11	−3.42422
$235$	−5.77794e10	−1.23586
$236$	6.41437e10	1.34602
$237$	1.42186e11	2.92746
$238$	1.37765e10	0.278320
$239$	3.78058e10	0.749494	0.374747	−	0.927127i	$-0.377730\pi$
$239$	3.78058e10	0.749494	0.374747	+	0.927127i	$0.377730\pi$
$240$	−1.33515e11	−2.59764
$241$	−7.74983e10	−1.47984	−0.739921	−	0.672693i	$-0.765137\pi$
$241$	−7.74983e10	−1.47984	−0.739921	+	0.672693i	$0.765137\pi$
$242$	6.82580e9	0.127934
$243$	−1.22079e11	−2.24602
$244$	−3.18855e10	−0.575889
$245$	5.91341e10	1.04855
$246$	7.42668e10	1.29296
$247$	4.95469e10	0.846993
$248$	7.65751e8	0.0128545
$249$	−1.12832e11	−1.86009
$250$	1.61059e10	0.260769
$251$	8.75828e10	1.39279	0.696397	−	0.717656i	$-0.254785\pi$
$251$	8.75828e10	1.39279	0.696397	+	0.717656i	$0.254785\pi$
$252$	7.51117e10	1.17329
$253$	−1.49504e10	−0.229409
$254$	5.95933e10	0.898351
$255$	7.06521e10	1.04639
$256$	7.13326e10	1.03803
$257$	1.20379e11	1.72128	0.860642	−	0.509210i	$-0.170062\pi$
$257$	1.20379e11	1.72128	0.860642	+	0.509210i	$0.170062\pi$
$258$	−3.16355e11	−4.44515
$259$	−4.29318e10	−0.592830
$260$	9.66089e10	1.31110
$261$	−7.73803e10	−1.03216
$262$	−1.35884e11	−1.78160
$263$	−7.85018e10	−1.01176	−0.505881	−	0.862603i	$-0.668833\pi$
$263$	−7.85018e10	−1.01176	−0.505881	+	0.862603i	$0.668833\pi$
$264$	−1.22474e9	−0.0155177
$265$	2.37726e9	0.0296122
$266$	−4.78673e10	−0.586235
$267$	1.50590e11	1.81340
$268$	3.77470e10	0.446967
$269$	1.29798e10	0.151141	0.0755704	−	0.997140i	$-0.475922\pi$
$269$	1.29798e10	0.151141	0.0755704	+	0.997140i	$0.475922\pi$
$270$	4.64902e11	5.32384
$271$	4.57046e10	0.514752	0.257376	−	0.966311i	$-0.417142\pi$
$271$	4.57046e10	0.514752	0.257376	+	0.966311i	$0.417142\pi$
$272$	−3.77747e10	−0.418447
$273$	8.08266e10	0.880689
$274$	6.36675e10	0.682402
$275$	−2.47149e10	−0.260592
$276$	−1.34235e11	−1.39243
$277$	2.82209e10	0.288013	0.144007	−	0.989577i	$-0.454001\pi$
$277$	2.82209e10	0.288013	0.144007	+	0.989577i	$0.454001\pi$
$278$	2.70078e11	2.71199
$279$	−1.17225e11	−1.15825
$280$	1.86518e9	0.0181346
$281$	−1.57238e11	−1.50445	−0.752227	−	0.658904i	$-0.771020\pi$
$281$	−1.57238e11	−1.50445	−0.752227	+	0.658904i	$0.771020\pi$
$282$	−2.52505e11	−2.37765
$283$	3.28799e10	0.304713	0.152357	−	0.988326i	$-0.451314\pi$
$283$	3.28799e10	0.304713	0.152357	+	0.988326i	$0.451314\pi$
$284$	−4.52038e10	−0.412328
$285$	−2.45484e11	−2.20405
$286$	4.70221e10	0.415580
$287$	−2.72525e10	−0.237104
$288$	−4.08025e11	−3.49478
$289$	−9.85987e10	−0.831440
$290$	9.61530e10	0.798310
$291$	6.68318e10	0.546342
$292$	−7.60079e10	−0.611837
$293$	1.67616e11	1.32865	0.664325	−	0.747444i	$-0.268719\pi$
$293$	1.67616e11	1.32865	0.664325	+	0.747444i	$0.268719\pi$
$294$	2.58425e11	2.01730
$295$	−2.43837e11	−1.87456
$296$	4.48145e9	0.0339317
$297$	1.12021e11	0.835401
$298$	1.85976e11	1.36611
$299$	−1.02992e11	−0.745214
$300$	−2.21907e11	−1.58170
$301$	1.16088e11	0.815151
$302$	−3.12670e11	−2.16299
$303$	1.11935e11	0.762914
$304$	1.31250e11	0.881391
$305$	1.21210e11	0.802026
$306$	2.20146e11	1.43537
$307$	5.05294e10	0.324655	0.162327	−	0.986737i	$-0.448100\pi$
$307$	5.05294e10	0.324655	0.162327	+	0.986737i	$0.448100\pi$
$308$	−2.24894e10	−0.142396
$309$	3.65786e11	2.28252
$310$	1.45664e11	0.895828
$311$	−2.01786e11	−1.22312	−0.611562	−	0.791197i	$-0.709458\pi$
$311$	−2.01786e11	−1.22312	−0.611562	+	0.791197i	$0.709458\pi$
$312$	−8.43710e9	−0.0504078
$313$	2.35263e11	1.38549	0.692745	−	0.721182i	$-0.256401\pi$
$313$	2.35263e11	1.38549	0.692745	+	0.721182i	$0.256401\pi$
$314$	−1.26226e11	−0.732764
$315$	−2.85530e11	−1.63401
$316$	−2.72539e11	−1.53758
$317$	−2.79980e11	−1.55725	−0.778627	−	0.627487i	$-0.784084\pi$
$317$	−2.79980e11	−1.55725	−0.778627	+	0.627487i	$0.784084\pi$
$318$	1.03890e10	0.0569707
$319$	2.31686e10	0.125268
$320$	2.45981e11	1.31137
$321$	2.43398e11	1.27951
$322$	9.95003e10	0.515790
$323$	−6.94536e10	−0.355045
$324$	5.22661e11	2.63492
$325$	−1.70258e11	−0.846510
$326$	−2.54557e11	−1.24826
$327$	−1.83657e11	−0.888265
$328$	2.84476e9	0.0135710
$329$	9.26578e10	0.436014
$330$	−2.32975e11	−1.08143
$331$	−6.27497e10	−0.287333	−0.143666	−	0.989626i	$-0.545889\pi$
$331$	−6.27497e10	−0.287333	−0.143666	+	0.989626i	$0.545889\pi$
$332$	2.16273e11	0.976969
$333$	−6.86042e11	−3.05739
$334$	2.76605e11	1.21619
$335$	−1.43492e11	−0.622480
$336$	2.14111e11	0.916456
$337$	2.93367e11	1.23902	0.619509	−	0.784990i	$-0.287332\pi$
$337$	2.93367e11	1.23902	0.619509	+	0.784990i	$0.287332\pi$
$338$	−1.37483e10	−0.0572961
$339$	5.52514e11	2.27219
$340$	−1.35424e11	−0.549593
$341$	3.50986e10	0.140571
$342$	−7.64910e11	−3.02338
$343$	−2.18315e11	−0.851646
$344$	−1.21179e10	−0.0466566
$345$	5.10281e11	1.93920
$346$	6.48287e11	2.43178
$347$	−1.03009e11	−0.381411	−0.190705	−	0.981647i	$-0.561077\pi$
$347$	−1.03009e11	−0.381411	−0.190705	+	0.981647i	$0.561077\pi$
$348$	2.08023e11	0.760334
$349$	−5.27531e11	−1.90341	−0.951707	−	0.307008i	$-0.900672\pi$
$349$	−5.27531e11	−1.90341	−0.951707	+	0.307008i	$0.900672\pi$
$350$	1.64486e11	0.585901
$351$	7.71698e11	2.71372
$352$	1.22168e11	0.424145
$353$	3.36826e11	1.15457	0.577283	−	0.816544i	$-0.304113\pi$
$353$	3.36826e11	1.15457	0.577283	+	0.816544i	$0.304113\pi$
$354$	−1.06560e12	−3.60645
$355$	1.71838e11	0.574238
$356$	−2.88646e11	−0.952448
$357$	−1.13301e11	−0.369170
$358$	−2.51136e11	−0.808045
$359$	−5.96607e11	−1.89567	−0.947837	−	0.318757i	$-0.896735\pi$
$359$	−5.96607e11	−1.89567	−0.947837	+	0.318757i	$0.896735\pi$
$360$	2.98052e10	0.0935255
$361$	−8.13673e10	−0.252155
$362$	−6.22929e11	−1.90656
$363$	−5.61367e10	−0.169694
$364$	−1.54926e11	−0.462561
$365$	2.88937e11	0.852090
$366$	5.29705e11	1.54301
$367$	−6.72622e11	−1.93541	−0.967706	−	0.252081i	$-0.918885\pi$
$367$	−6.72622e11	−1.93541	−0.967706	+	0.252081i	$0.918885\pi$
$368$	−2.72826e11	−0.775479
$369$	−4.35490e11	−1.22281
$370$	8.52478e11	2.36470
$371$	−3.81229e9	−0.0104473
$372$	3.15138e11	0.853213
$373$	3.52239e11	0.942210	0.471105	−	0.882077i	$-0.343855\pi$
$373$	3.52239e11	0.942210	0.471105	+	0.882077i	$0.343855\pi$
$374$	−6.59145e10	−0.174204
$375$	−1.32458e11	−0.345890
$376$	−9.67210e9	−0.0249560
$377$	1.59606e11	0.406923
$378$	−7.45539e11	−1.87827
$379$	2.19985e11	0.547668	0.273834	−	0.961777i	$-0.411708\pi$
$379$	2.19985e11	0.547668	0.273834	+	0.961777i	$0.411708\pi$
$380$	4.70538e11	1.15763
$381$	−4.90107e11	−1.19159
$382$	7.38059e11	1.77340
$383$	7.62271e10	0.181015	0.0905075	−	0.995896i	$-0.471151\pi$
$383$	7.62271e10	0.181015	0.0905075	+	0.995896i	$0.471151\pi$
$384$	−4.38491e10	−0.102913
$385$	8.54913e10	0.198312
$386$	3.49430e11	0.801158
$387$	1.85506e12	4.20397
$388$	−1.28101e11	−0.286953
$389$	1.23109e11	0.272593	0.136297	−	0.990668i	$-0.456480\pi$
$389$	1.23109e11	0.272593	0.136297	+	0.990668i	$0.456480\pi$
$390$	−1.60494e12	−3.51291
$391$	1.44371e11	0.312381
$392$	9.89886e9	0.0211738
$393$	1.11753e12	2.36316
$394$	5.58702e10	0.116801
$395$	1.03603e12	2.14135
$396$	−3.59376e11	−0.734379
$397$	8.76959e9	0.0177183	0.00885915	−	0.999961i	$-0.497180\pi$
$397$	8.76959e9	0.0177183	0.00885915	+	0.999961i	$0.497180\pi$
$398$	2.69409e11	0.538194
$399$	3.93670e11	0.777597
$400$	−4.51015e11	−0.880888
$401$	−6.43426e11	−1.24265	−0.621325	−	0.783553i	$-0.713405\pi$
$401$	−6.43426e11	−1.24265	−0.621325	+	0.783553i	$0.713405\pi$
$402$	−6.27081e11	−1.19759
$403$	2.41790e11	0.456630
$404$	−2.14555e11	−0.400703
$405$	−1.98685e12	−3.66959
$406$	−1.54195e11	−0.281646
$407$	2.05409e11	0.371061
$408$	1.18269e10	0.0211301
$409$	−7.47574e11	−1.32099	−0.660495	−	0.750831i	$-0.729653\pi$
$409$	−7.47574e11	−1.32099	−0.660495	+	0.750831i	$0.729653\pi$
$410$	5.41141e11	0.945765
$411$	−5.23614e11	−0.905154
$412$	−7.01130e11	−1.19884
$413$	3.91027e11	0.661351
$414$	1.59000e12	2.66008
$415$	−8.22142e11	−1.36060
$416$	8.41598e11	1.37779
$417$	−2.22117e12	−3.59724
$418$	2.29023e11	0.366933
$419$	5.19760e11	0.823834	0.411917	−	0.911221i	$-0.364859\pi$
$419$	5.19760e11	0.823834	0.411917	+	0.911221i	$0.364859\pi$
$420$	7.67597e11	1.20368
$421$	−7.71612e11	−1.19710	−0.598549	−	0.801086i	$-0.704256\pi$
$421$	−7.71612e11	−1.19710	−0.598549	+	0.801086i	$0.704256\pi$
$422$	−1.36069e11	−0.208859
$423$	1.48065e12	2.24865
$424$	3.97946e8	0.000597968 0
$425$	2.38663e11	0.354843
$426$	7.50959e11	1.10477
$427$	−1.94378e11	−0.282957
$428$	−4.66538e11	−0.672033
$429$	−3.86719e11	−0.551236
$430$	−2.30511e12	−3.25149
$431$	−1.03436e10	−0.0144385	−0.00721925	−	0.999974i	$-0.502298\pi$
$431$	−1.03436e10	−0.0144385	−0.00721925	+	0.999974i	$0.502298\pi$
$432$	2.04424e12	2.82393
$433$	−2.25800e11	−0.308694	−0.154347	−	0.988017i	$-0.549327\pi$
$433$	−2.25800e11	−0.308694	−0.154347	+	0.988017i	$0.549327\pi$
$434$	−2.33593e11	−0.316051
$435$	−7.90781e11	−1.05890
$436$	3.52029e11	0.466541
$437$	−5.01625e11	−0.657980
$438$	1.26270e12	1.63933
$439$	−1.42993e11	−0.183749	−0.0918746	−	0.995771i	$-0.529286\pi$
$439$	−1.42993e11	−0.183749	−0.0918746	+	0.995771i	$0.529286\pi$
$440$	−8.92403e9	−0.0113507
$441$	−1.51537e12	−1.90785
$442$	−4.54077e11	−0.565886
$443$	−5.10506e11	−0.629773	−0.314887	−	0.949129i	$-0.601967\pi$
$443$	−5.10506e11	−0.629773	−0.314887	+	0.949129i	$0.601967\pi$
$444$	1.84430e12	2.25221
$445$	1.09726e12	1.32645
$446$	−5.15480e10	−0.0616887
$447$	−1.52951e12	−1.81204
$448$	−3.94466e11	−0.462656
$449$	1.18647e12	1.37768	0.688840	−	0.724914i	$-0.258120\pi$
$449$	1.18647e12	1.37768	0.688840	+	0.724914i	$0.258120\pi$
$450$	2.62846e12	3.02166
$451$	1.30391e11	0.148407
$452$	−1.05905e12	−1.19342
$453$	2.57146e12	2.86905
$454$	−9.92886e11	−1.09685
$455$	5.88939e11	0.644198
$456$	−4.10933e10	−0.0445071
$457$	1.62840e12	1.74637	0.873187	−	0.487386i	$-0.162049\pi$
$457$	1.62840e12	1.74637	0.873187	+	0.487386i	$0.162049\pi$
$458$	−4.03934e11	−0.428959
$459$	−1.08175e12	−1.13755
$460$	−9.78094e11	−1.01852
$461$	6.48086e11	0.668310	0.334155	−	0.942518i	$-0.391549\pi$
$461$	6.48086e11	0.668310	0.334155	+	0.942518i	$0.391549\pi$
$462$	3.73610e11	0.381531
$463$	8.75084e11	0.884983	0.442492	−	0.896773i	$-0.354095\pi$
$463$	8.75084e11	0.884983	0.442492	+	0.896773i	$0.354095\pi$
$464$	4.22797e11	0.423449
$465$	−1.19797e12	−1.18825
$466$	−1.05517e12	−1.03654
$467$	−3.98808e11	−0.388005	−0.194003	−	0.981001i	$-0.562147\pi$
$467$	−3.98808e11	−0.388005	−0.194003	+	0.981001i	$0.562147\pi$
$468$	−2.47569e12	−2.38556
$469$	2.30110e11	0.219613
$470$	−1.83986e12	−1.73918
$471$	1.03810e12	0.971956
$472$	−4.08175e10	−0.0378536
$473$	−5.55428e11	−0.510215
$474$	4.52762e12	4.11972
$475$	−8.29249e11	−0.747418
$476$	2.17172e11	0.193898
$477$	−6.09196e10	−0.0538796
$478$	1.20385e12	1.05474
$479$	5.45258e11	0.473252	0.236626	−	0.971601i	$-0.423958\pi$
$479$	5.45258e11	0.473252	0.236626	+	0.971601i	$0.423958\pi$
$480$	−4.16977e12	−3.58531
$481$	1.41504e12	1.20536
$482$	−2.46777e12	−2.08254
$483$	−8.18310e11	−0.684157
$484$	1.07601e11	0.0891280
$485$	4.86966e11	0.399633
$486$	−3.88736e12	−3.16076
$487$	8.71948e11	0.702442	0.351221	−	0.936293i	$-0.385767\pi$
$487$	8.71948e11	0.702442	0.351221	+	0.936293i	$0.385767\pi$
$488$	2.02901e10	0.0161956
$489$	2.09353e12	1.65573
$490$	1.88300e12	1.47560
$491$	−8.11526e11	−0.630138	−0.315069	−	0.949069i	$-0.602028\pi$
$491$	−8.11526e11	−0.630138	−0.315069	+	0.949069i	$0.602028\pi$
$492$	1.17074e12	0.900774
$493$	−2.23731e11	−0.170575
$494$	1.57771e12	1.19195
$495$	1.36613e12	1.02275
$496$	6.40503e11	0.475175
$497$	−2.75568e11	−0.202593
$498$	−3.59288e12	−2.61765
$499$	−1.08433e12	−0.782902	−0.391451	−	0.920199i	$-0.628027\pi$
$499$	−1.08433e12	−0.782902	−0.391451	+	0.920199i	$0.628027\pi$
$500$	2.53893e11	0.181671
$501$	−2.27485e12	−1.61318
$502$	2.78889e12	1.96004
$503$	−9.51403e11	−0.662687	−0.331344	−	0.943510i	$-0.607502\pi$
$503$	−9.51403e11	−0.662687	−0.331344	+	0.943510i	$0.607502\pi$
$504$	−4.77969e10	−0.0329961
$505$	8.15612e11	0.558049
$506$	−4.76064e11	−0.322841
$507$	1.13069e11	0.0759990
$508$	9.39425e11	0.625857
$509$	−2.00693e12	−1.32526	−0.662630	−	0.748947i	$-0.730560\pi$
$509$	−2.00693e12	−1.32526	−0.662630	+	0.748947i	$0.730560\pi$
$510$	2.24976e12	1.47255
$511$	−4.63353e11	−0.300620
$512$	2.18571e12	1.40565
$513$	3.75859e12	2.39606
$514$	3.83322e12	2.42231
$515$	2.66528e12	1.66959
$516$	−4.98700e12	−3.09682
$517$	−4.43325e11	−0.272907
$518$	−1.36707e12	−0.834272
$519$	−5.33164e12	−3.22558
$520$	−6.14765e10	−0.0368718
$521$	1.17032e12	0.695881	0.347940	−	0.937517i	$-0.386881\pi$
$521$	1.17032e12	0.695881	0.347940	+	0.937517i	$0.386881\pi$
$522$	−2.46401e12	−1.45253
$523$	−2.82109e12	−1.64877	−0.824383	−	0.566033i	$-0.808477\pi$
$523$	−2.82109e12	−1.64877	−0.824383	+	0.566033i	$0.808477\pi$
$524$	−2.14206e12	−1.24120
$525$	−1.35277e12	−0.777153
$526$	−2.49972e12	−1.42382
$527$	−3.38935e11	−0.191412
$528$	−1.02442e12	−0.573623
$529$	−7.58440e11	−0.421086
$530$	7.56989e10	0.0416724
$531$	6.24854e12	3.41078
$532$	−7.54577e11	−0.408415
$533$	8.98247e11	0.482085
$534$	4.79521e12	2.55195
$535$	1.77350e12	0.935923
$536$	−2.40201e10	−0.0125699
$537$	2.06539e12	1.07181
$538$	4.13313e11	0.212696
$539$	4.53719e11	0.231546
$540$	7.32869e12	3.70898
$541$	−1.80357e12	−0.905204	−0.452602	−	0.891713i	$-0.649504\pi$
$541$	−1.80357e12	−0.905204	−0.452602	+	0.891713i	$0.649504\pi$
$542$	1.45537e12	0.724395
$543$	5.12309e12	2.52891
$544$	−1.17973e12	−0.577548
$545$	−1.33821e12	−0.649739
$546$	2.57375e12	1.23937
$547$	−7.55493e11	−0.360817	−0.180409	−	0.983592i	$-0.557742\pi$
$547$	−7.55493e11	−0.360817	−0.180409	+	0.983592i	$0.557742\pi$
$548$	1.00365e12	0.475411
$549$	−3.10611e12	−1.45929
$550$	−7.86993e11	−0.366724
$551$	7.77367e11	0.359289
$552$	8.54194e10	0.0391589
$553$	−1.66143e12	−0.755474
$554$	8.98636e11	0.405312
$555$	−7.01094e12	−3.13659
$556$	4.25749e12	1.88937
$557$	−3.70605e12	−1.63141	−0.815705	−	0.578469i	$-0.803650\pi$
$557$	−3.70605e12	−1.63141	−0.815705	+	0.578469i	$0.803650\pi$
$558$	−3.73278e12	−1.62996
$559$	−3.82628e12	−1.65738
$560$	1.56011e12	0.670360
$561$	5.42094e11	0.231069
$562$	−5.00691e12	−2.11717
$563$	−2.29296e12	−0.961852	−0.480926	−	0.876761i	$-0.659699\pi$
$563$	−2.29296e12	−0.961852	−0.480926	+	0.876761i	$0.659699\pi$
$564$	−3.98047e12	−1.65645
$565$	4.02587e12	1.66204
$566$	1.04699e12	0.428813
$567$	3.18620e12	1.29464
$568$	2.87652e10	0.0115958
$569$	4.25409e12	1.70138	0.850689	−	0.525669i	$-0.176185\pi$
$569$	4.25409e12	1.70138	0.850689	+	0.525669i	$0.176185\pi$
$570$	−7.81693e12	−3.10170
$571$	4.18735e12	1.64845	0.824226	−	0.566261i	$-0.191611\pi$
$571$	4.18735e12	1.64845	0.824226	+	0.566261i	$0.191611\pi$
$572$	7.41253e11	0.289524
$573$	−6.06994e12	−2.35228
$574$	−8.67799e11	−0.333669
$575$	1.72373e12	0.657605
$576$	−6.30349e12	−2.38605
$577$	2.65468e12	0.997061	0.498531	−	0.866872i	$-0.333873\pi$
$577$	2.65468e12	0.997061	0.498531	+	0.866872i	$0.333873\pi$
$578$	−3.13966e12	−1.17006
$579$	−2.87378e12	−1.06268
$580$	1.51575e12	0.556162
$581$	1.31843e12	0.480024
$582$	2.12812e12	0.768850
$583$	1.82401e10	0.00653910
$584$	4.83672e10	0.0172065
$585$	9.41113e12	3.32231
$586$	5.33737e12	1.86977
$587$	−5.43516e12	−1.88948	−0.944738	−	0.327827i	$-0.893684\pi$
$587$	−5.43516e12	−1.88948	−0.944738	+	0.327827i	$0.893684\pi$
$588$	4.07379e12	1.40540
$589$	1.17765e12	0.403178
$590$	−7.76446e12	−2.63801
$591$	−4.59487e11	−0.154928
$592$	3.74845e12	1.25431
$593$	−3.38016e12	−1.12251	−0.561256	−	0.827643i	$-0.689682\pi$
$593$	−3.38016e12	−1.12251	−0.561256	+	0.827643i	$0.689682\pi$
$594$	3.56707e12	1.17563
$595$	−8.25561e11	−0.270037
$596$	2.93172e12	0.951730
$597$	−2.21567e12	−0.713873
$598$	−3.27955e12	−1.04872
$599$	3.36234e12	1.06714	0.533570	−	0.845756i	$-0.320850\pi$
$599$	3.36234e12	1.06714	0.533570	+	0.845756i	$0.320850\pi$
$600$	1.41209e11	0.0444817
$601$	1.96759e12	0.615176	0.307588	−	0.951520i	$-0.400478\pi$
$601$	1.96759e12	0.615176	0.307588	+	0.951520i	$0.400478\pi$
$602$	3.69657e12	1.14714
$603$	3.67711e12	1.13261
$604$	−4.92891e12	−1.50690
$605$	−4.09037e11	−0.124126
$606$	3.56435e12	1.07363
$607$	−1.37391e12	−0.410779	−0.205389	−	0.978680i	$-0.565846\pi$
$607$	−1.37391e12	−0.410779	−0.205389	+	0.978680i	$0.565846\pi$
$608$	4.09904e12	1.21651
$609$	1.26813e12	0.373583
$610$	3.85967e12	1.12867
$611$	−3.05401e12	−0.886514
$612$	3.47037e12	0.999987
$613$	−2.55628e10	−0.00731199	−0.00365599	−	0.999993i	$-0.501164\pi$
$613$	−2.55628e10	−0.00731199	−0.00365599	+	0.999993i	$0.501164\pi$
$614$	1.60900e12	0.456877
$615$	−4.45045e12	−1.25449
$616$	1.43110e10	0.00400457
$617$	−7.94152e11	−0.220608	−0.110304	−	0.993898i	$-0.535182\pi$
$617$	−7.94152e11	−0.220608	−0.110304	+	0.993898i	$0.535182\pi$
$618$	1.16477e13	3.21212
$619$	−4.99808e11	−0.136834	−0.0684172	−	0.997657i	$-0.521795\pi$
$619$	−4.99808e11	−0.136834	−0.0684172	+	0.997657i	$0.521795\pi$
$620$	2.29624e12	0.624100
$621$	−7.81287e12	−2.10813
$622$	−6.42546e12	−1.72126
$623$	−1.75962e12	−0.467976
$624$	−7.05712e12	−1.86336
$625$	−4.26214e12	−1.11730
$626$	7.49144e12	1.94976
$627$	−1.88353e12	−0.486709
$628$	−1.98981e12	−0.510497
$629$	−1.98357e12	−0.505265
$630$	−9.09211e12	−2.29949
$631$	5.33753e12	1.34032	0.670159	−	0.742217i	$-0.266226\pi$
$631$	5.33753e12	1.34032	0.670159	+	0.742217i	$0.266226\pi$
$632$	1.73429e11	0.0432409
$633$	1.11906e12	0.277036
$634$	−8.91535e12	−2.19148
$635$	−3.57114e12	−0.871616
$636$	1.63771e11	0.0396900
$637$	3.12562e12	0.752156
$638$	7.37755e11	0.176287
$639$	−4.40351e12	−1.04483
$640$	−3.19504e11	−0.0752778
$641$	2.26413e12	0.529713	0.264857	−	0.964288i	$-0.414675\pi$
$641$	2.26413e12	0.529713	0.264857	+	0.964288i	$0.414675\pi$
$642$	7.75048e12	1.80062
$643$	3.67937e12	0.848838	0.424419	−	0.905466i	$-0.360478\pi$
$643$	3.67937e12	0.848838	0.424419	+	0.905466i	$0.360478\pi$
$644$	1.56852e12	0.359337
$645$	1.89576e13	4.31286
$646$	−2.21160e12	−0.499644
$647$	3.26628e11	0.0732798	0.0366399	−	0.999329i	$-0.488335\pi$
$647$	3.26628e11	0.0732798	0.0366399	+	0.999329i	$0.488335\pi$
$648$	−3.32593e11	−0.0741012
$649$	−1.87089e12	−0.413949
$650$	−5.42150e12	−1.19127
$651$	1.92112e12	0.419218
$652$	−4.01282e12	−0.869633
$653$	−7.00657e12	−1.50798	−0.753991	−	0.656884i	$-0.771874\pi$
$653$	−7.00657e12	−1.50798	−0.753991	+	0.656884i	$0.771874\pi$
$654$	−5.84817e12	−1.25003
$655$	8.14285e12	1.72858
$656$	2.37947e12	0.501663
$657$	−7.40429e12	−1.55038
$658$	2.95049e12	0.613589
$659$	−2.96242e12	−0.611874	−0.305937	−	0.952052i	$-0.598970\pi$
$659$	−2.96242e12	−0.611874	−0.305937	+	0.952052i	$0.598970\pi$
$660$	−3.67261e12	−0.753402
$661$	3.75411e12	0.764893	0.382447	−	0.923978i	$-0.375082\pi$
$661$	3.75411e12	0.764893	0.382447	+	0.923978i	$0.375082\pi$
$662$	−1.99813e12	−0.404355
$663$	3.73441e12	0.750605
$664$	−1.37624e11	−0.0274750
$665$	2.86846e12	0.568789
$666$	−2.18455e13	−4.30258
$667$	−1.61589e12	−0.316115
$668$	4.36038e12	0.847286
$669$	4.23941e11	0.0818253
$670$	−4.56919e12	−0.875998
$671$	9.30009e11	0.177107
$672$	6.68684e12	1.26491
$673$	5.15215e12	0.968101	0.484051	−	0.875040i	$-0.339165\pi$
$673$	5.15215e12	0.968101	0.484051	+	0.875040i	$0.339165\pi$
$674$	9.34166e12	1.74363
$675$	−1.29156e13	−2.39469
$676$	−2.16728e11	−0.0399167
$677$	2.22445e12	0.406981	0.203491	−	0.979077i	$-0.434771\pi$
$677$	2.22445e12	0.406981	0.203491	+	0.979077i	$0.434771\pi$
$678$	1.75936e13	3.19758
$679$	−7.80922e11	−0.140992
$680$	8.61764e10	0.0154560
$681$	8.16569e12	1.45489
$682$	1.11764e12	0.197821
$683$	2.37597e12	0.417780	0.208890	−	0.977939i	$-0.433015\pi$
$683$	2.37597e12	0.417780	0.208890	+	0.977939i	$0.433015\pi$
$684$	−1.20580e13	−2.10631
$685$	−3.81528e12	−0.662093
$686$	−6.95176e12	−1.19850
$687$	3.32203e12	0.568982
$688$	−1.01359e13	−1.72470
$689$	1.25654e11	0.0212417
$690$	1.62488e13	2.72898
$691$	2.15841e12	0.360150	0.180075	−	0.983653i	$-0.442366\pi$
$691$	2.15841e12	0.360150	0.180075	+	0.983653i	$0.442366\pi$
$692$	1.02196e13	1.69416
$693$	−2.19080e12	−0.360830
$694$	−3.28010e12	−0.536748
$695$	−1.61845e13	−2.63128
$696$	−1.32374e11	−0.0213827
$697$	−1.25914e12	−0.202082
$698$	−1.67981e13	−2.67862
$699$	8.67791e12	1.37489
$700$	2.59295e12	0.408181
$701$	7.87897e12	1.23236	0.616181	−	0.787605i	$-0.288679\pi$
$701$	7.87897e12	1.23236	0.616181	+	0.787605i	$0.288679\pi$
$702$	2.45731e13	3.81894
$703$	6.89202e12	1.06426
$704$	1.88734e12	0.289583
$705$	1.51314e13	2.30689
$706$	1.07255e13	1.62479
$707$	−1.30795e12	−0.196881
$708$	−1.67981e13	−2.51252
$709$	−1.08295e13	−1.60954	−0.804770	−	0.593587i	$-0.797711\pi$
$709$	−1.08295e13	−1.60954	−0.804770	+	0.593587i	$0.797711\pi$
$710$	5.47182e12	0.808108
$711$	−2.65493e13	−3.89619
$712$	1.83678e11	0.0267854
$713$	−2.44794e12	−0.354730
$714$	−3.60783e12	−0.519522
$715$	−2.81781e12	−0.403212
$716$	−3.95889e12	−0.562944
$717$	−9.90066e12	−1.39903
$718$	−1.89977e13	−2.66772
$719$	8.27693e12	1.15502	0.577510	−	0.816384i	$-0.304025\pi$
$719$	8.27693e12	1.15502	0.577510	+	0.816384i	$0.304025\pi$
$720$	2.49302e13	3.45724
$721$	−4.27417e12	−0.589037
$722$	−2.59097e12	−0.354850
$723$	2.02954e13	2.76233
$724$	−9.81981e12	−1.32825
$725$	−2.67127e12	−0.359084
$726$	−1.78755e12	−0.238806
$727$	1.29556e13	1.72010	0.860048	−	0.510214i	$-0.170434\pi$
$727$	1.29556e13	1.72010	0.860048	+	0.510214i	$0.170434\pi$
$728$	9.85866e10	0.0130085
$729$	1.14760e13	1.50493
$730$	9.20059e12	1.19912
$731$	5.36359e12	0.694748
$732$	8.35023e12	1.07498
$733$	−4.94196e12	−0.632312	−0.316156	−	0.948707i	$-0.602392\pi$
$733$	−4.94196e12	−0.632312	−0.316156	+	0.948707i	$0.602392\pi$
$734$	−2.14182e13	−2.72365
$735$	−1.54861e13	−1.95727
$736$	−8.52055e12	−1.07033
$737$	−1.10097e12	−0.137459
$738$	−1.38672e13	−1.72082
$739$	1.30939e13	1.61499	0.807493	−	0.589877i	$-0.200824\pi$
$739$	1.30939e13	1.61499	0.807493	+	0.589877i	$0.200824\pi$
$740$	1.34384e13	1.64742
$741$	−1.29754e13	−1.58103
$742$	−1.21394e11	−0.0147021
$743$	1.33666e12	0.160906	0.0804528	−	0.996758i	$-0.474363\pi$
$743$	1.33666e12	0.160906	0.0804528	+	0.996758i	$0.474363\pi$
$744$	−2.00536e11	−0.0239947
$745$	−1.11447e13	−1.32545
$746$	1.12163e13	1.32594
$747$	2.10682e13	2.47562
$748$	−1.03907e12	−0.121364
$749$	−2.84407e12	−0.330196
$750$	−4.21785e12	−0.486761
$751$	−4.14031e12	−0.474956	−0.237478	−	0.971393i	$-0.576321\pi$
$751$	−4.14031e12	−0.474956	−0.237478	+	0.971393i	$0.576321\pi$
$752$	−8.09012e12	−0.922518
$753$	−2.29364e13	−2.59984
$754$	5.08230e12	0.572650
$755$	1.87368e13	2.09862
$756$	−1.17526e13	−1.30854
$757$	−1.31787e12	−0.145862	−0.0729310	−	0.997337i	$-0.523235\pi$
$757$	−1.31787e12	−0.145862	−0.0729310	+	0.997337i	$0.523235\pi$
$758$	7.00497e12	0.770716
$759$	3.91524e12	0.428224
$760$	−2.99424e11	−0.0325556
$761$	2.12057e12	0.229204	0.114602	−	0.993411i	$-0.463441\pi$
$761$	2.12057e12	0.229204	0.114602	+	0.993411i	$0.463441\pi$
$762$	−1.56064e13	−1.67689
$763$	2.14601e12	0.229230
$764$	1.16347e13	1.23548
$765$	−1.31923e13	−1.39266
$766$	2.42729e12	0.254737
$767$	−1.28883e13	−1.34467
$768$	−1.86807e13	−1.93762
$769$	−8.33503e12	−0.859485	−0.429743	−	0.902951i	$-0.641396\pi$
$769$	−8.33503e12	−0.859485	−0.429743	+	0.902951i	$0.641396\pi$
$770$	2.72229e12	0.279078
$771$	−3.15252e13	−3.21301
$772$	5.50840e12	0.558145
$773$	7.53909e11	0.0759471	0.0379736	−	0.999279i	$-0.487910\pi$
$773$	7.53909e11	0.0759471	0.0379736	+	0.999279i	$0.487910\pi$
$774$	5.90705e13	5.91611
$775$	−4.04675e12	−0.402948
$776$	8.15166e10	0.00806991
$777$	1.12431e13	1.10660
$778$	3.92013e12	0.383612
$779$	4.37496e12	0.425653
$780$	−2.53001e13	−2.44735
$781$	1.31847e12	0.126806
$782$	4.59719e12	0.439605
$783$	1.21076e13	1.15114
$784$	8.27979e12	0.782703
$785$	7.56409e12	0.710957
$786$	3.55855e13	3.32561
$787$	−8.60478e12	−0.799565	−0.399782	−	0.916610i	$-0.630914\pi$
$787$	−8.60478e12	−0.799565	−0.399782	+	0.916610i	$0.630914\pi$
$788$	8.80734e11	0.0813723
$789$	2.05582e13	1.88859
$790$	3.29903e13	3.01345
$791$	−6.45606e12	−0.586372
$792$	2.28687e11	0.0206527
$793$	6.40671e12	0.575315
$794$	2.79249e11	0.0249344
$795$	−6.22562e11	−0.0552752
$796$	4.24695e12	0.374945
$797$	2.39246e12	0.210031	0.105015	−	0.994471i	$-0.466511\pi$
$797$	2.39246e12	0.210031	0.105015	+	0.994471i	$0.466511\pi$
$798$	1.25356e13	1.09429
$799$	4.28105e12	0.371612
$800$	−1.40855e13	−1.21582
$801$	−2.81184e13	−2.41348
$802$	−2.04885e13	−1.74874
$803$	2.21693e12	0.188162
$804$	−9.88526e12	−0.834326
$805$	−5.96257e12	−0.500440
$806$	7.69928e12	0.642602
$807$	−3.39917e12	−0.282125
$808$	1.36531e11	0.0112689
$809$	1.69064e13	1.38766	0.693830	−	0.720139i	$-0.255922\pi$
$809$	1.69064e13	1.38766	0.693830	+	0.720139i	$0.255922\pi$
$810$	−6.32670e13	−5.16410
$811$	1.63650e13	1.32838	0.664189	−	0.747564i	$-0.268777\pi$
$811$	1.63650e13	1.32838	0.664189	+	0.747564i	$0.268777\pi$
$812$	−2.43072e12	−0.196216
$813$	−1.19692e13	−0.960855
$814$	6.54082e12	0.522183
$815$	1.52544e13	1.21112
$816$	9.89251e12	0.781089
$817$	−1.86361e13	−1.46337
$818$	−2.38049e13	−1.85899
$819$	−1.50921e13	−1.17212
$820$	8.53051e12	0.658889
$821$	−1.89805e13	−1.45802	−0.729011	−	0.684503i	$-0.760019\pi$
$821$	−1.89805e13	−1.45802	−0.729011	+	0.684503i	$0.760019\pi$
$822$	−1.66734e13	−1.27380
$823$	1.46185e13	1.11072	0.555359	−	0.831611i	$-0.312581\pi$
$823$	1.46185e13	1.11072	0.555359	+	0.831611i	$0.312581\pi$
$824$	4.46160e11	0.0337146
$825$	6.47238e12	0.486431
$826$	1.24514e13	0.930699
$827$	4.31794e11	0.0320998	0.0160499	−	0.999871i	$-0.494891\pi$
$827$	4.31794e11	0.0320998	0.0160499	+	0.999871i	$0.494891\pi$
$828$	2.50646e13	1.85321
$829$	1.67176e13	1.22936	0.614678	−	0.788778i	$-0.289286\pi$
$829$	1.67176e13	1.22936	0.614678	+	0.788778i	$0.289286\pi$
$830$	−2.61794e13	−1.91473
$831$	−7.39055e12	−0.537616
$832$	1.30017e13	0.940684
$833$	−4.38142e12	−0.315291
$834$	−7.07285e13	−5.06229
$835$	−1.65756e13	−1.17999
$836$	3.61031e12	0.255633
$837$	1.83420e13	1.29176
$838$	1.65507e13	1.15936
$839$	−3.98860e12	−0.277902	−0.138951	−	0.990299i	$-0.544373\pi$
$839$	−3.98860e12	−0.277902	−0.138951	+	0.990299i	$0.544373\pi$
$840$	−4.88456e11	−0.0338508
$841$	−1.20030e13	−0.827386
$842$	−2.45703e13	−1.68464
$843$	4.11778e13	2.80827
$844$	−2.14498e12	−0.145507
$845$	8.23872e11	0.0555910
$846$	4.71482e13	3.16445
$847$	6.55951e11	0.0437921
$848$	3.32858e11	0.0221043
$849$	−8.61064e12	−0.568789
$850$	7.59973e12	0.499359
$851$	−1.43262e13	−0.936373
$852$	1.18381e13	0.769666
$853$	1.40187e13	0.906648	0.453324	−	0.891346i	$-0.350238\pi$
$853$	1.40187e13	0.906648	0.453324	+	0.891346i	$0.350238\pi$
$854$	−6.18954e12	−0.398197
$855$	4.58374e13	2.93340
$856$	2.96879e11	0.0188994
$857$	2.48555e13	1.57401	0.787007	−	0.616943i	$-0.211629\pi$
$857$	2.48555e13	1.57401	0.787007	+	0.616943i	$0.211629\pi$
$858$	−1.23142e13	−0.775737
$859$	1.40520e13	0.880578	0.440289	−	0.897856i	$-0.354876\pi$
$859$	1.40520e13	0.880578	0.440289	+	0.897856i	$0.354876\pi$
$860$	−3.63375e13	−2.26523
$861$	7.13694e12	0.442586
$862$	−3.29369e11	−0.0203189
$863$	−1.38569e13	−0.850392	−0.425196	−	0.905101i	$-0.639795\pi$
$863$	−1.38569e13	−0.850392	−0.425196	+	0.905101i	$0.639795\pi$
$864$	6.38431e13	3.89764
$865$	−3.88487e13	−2.35941
$866$	−7.19013e12	−0.434416
$867$	2.58212e13	1.55200
$868$	−3.68235e12	−0.220184
$869$	7.94920e12	0.472862
$870$	−2.51807e13	−1.49016
$871$	−7.58446e12	−0.446522
$872$	−2.24012e11	−0.0131204
$873$	−1.24790e13	−0.727134
$874$	−1.59732e13	−0.925956
$875$	1.54776e12	0.0892621
$876$	1.99051e13	1.14208
$877$	−1.74955e12	−0.0998683	−0.0499342	−	0.998753i	$-0.515901\pi$
$877$	−1.74955e12	−0.0998683	−0.0499342	+	0.998753i	$0.515901\pi$
$878$	−4.55332e12	−0.258585
$879$	−4.38955e13	−2.48011
$880$	−7.46440e12	−0.419588
$881$	−8.03990e12	−0.449634	−0.224817	−	0.974401i	$-0.572178\pi$
$881$	−8.03990e12	−0.449634	−0.224817	+	0.974401i	$0.572178\pi$
$882$	−4.82536e13	−2.68486
$883$	1.83709e13	1.01697	0.508485	−	0.861071i	$-0.330206\pi$
$883$	1.83709e13	1.01697	0.508485	+	0.861071i	$0.330206\pi$
$884$	−7.15803e12	−0.394238
$885$	6.38564e13	3.49913
$886$	−1.62560e13	−0.886261
$887$	−2.59814e12	−0.140931	−0.0704653	−	0.997514i	$-0.522448\pi$
$887$	−2.59814e12	−0.140931	−0.0704653	+	0.997514i	$0.522448\pi$
$888$	−1.17361e12	−0.0633381
$889$	5.72684e12	0.307509
$890$	3.49400e13	1.86667
$891$	−1.52445e13	−0.810335
$892$	−8.12599e11	−0.0429769
$893$	−1.48747e13	−0.782740
$894$	−4.87038e13	−2.55002
$895$	1.50494e13	0.783997
$896$	5.12372e11	0.0265582
$897$	2.69716e13	1.39104
$898$	3.77806e13	1.93877
$899$	3.79357e12	0.193700
$900$	4.14348e13	2.10511
$901$	−1.76138e11	−0.00890415
$902$	4.15202e12	0.208848
$903$	−3.04013e13	−1.52159
$904$	6.73917e11	0.0335621
$905$	3.73291e13	1.84982
$906$	8.18827e13	4.03752
$907$	−2.95257e13	−1.44867	−0.724333	−	0.689451i	$-0.757852\pi$
$907$	−2.95257e13	−1.44867	−0.724333	+	0.689451i	$0.757852\pi$
$908$	−1.56518e13	−0.764148
$909$	−2.09008e13	−1.01537
$910$	1.87535e13	0.906560
$911$	−1.45008e13	−0.697524	−0.348762	−	0.937211i	$-0.613398\pi$
$911$	−1.45008e13	−0.697524	−0.348762	+	0.937211i	$0.613398\pi$
$912$	−3.43721e13	−1.64524
$913$	−6.30807e12	−0.300454
$914$	5.18528e13	2.45762
$915$	−3.17426e13	−1.49709
$916$	−6.36758e12	−0.298844
$917$	−1.30582e13	−0.609850
$918$	−3.44460e13	−1.60083
$919$	−2.13868e13	−0.989067	−0.494533	−	0.869159i	$-0.664661\pi$
$919$	−2.13868e13	−0.989067	−0.494533	+	0.869159i	$0.664661\pi$
$920$	6.22404e11	0.0286436
$921$	−1.32327e13	−0.606012
$922$	2.06369e13	0.940493
$923$	9.08275e12	0.411917
$924$	5.88956e12	0.265802
$925$	−2.36830e13	−1.06365
$926$	2.78652e13	1.24541
$927$	−6.83003e13	−3.03783
$928$	1.32043e13	0.584452
$929$	1.80507e13	0.795103	0.397551	−	0.917580i	$-0.369860\pi$
$929$	1.80507e13	0.795103	0.397551	+	0.917580i	$0.369860\pi$
$930$	−3.81468e13	−1.67219
$931$	1.52235e13	0.664110
$932$	−1.66336e13	−0.722129
$933$	5.28442e13	2.28313
$934$	−1.26992e13	−0.546028
$935$	3.94994e12	0.169020
$936$	1.57539e12	0.0670884
$937$	−1.02099e13	−0.432704	−0.216352	−	0.976315i	$-0.569416\pi$
$937$	−1.02099e13	−0.432704	−0.216352	+	0.976315i	$0.569416\pi$
$938$	7.32737e12	0.309055
$939$	−6.16110e13	−2.58621
$940$	−2.90035e13	−1.21164
$941$	−1.04407e13	−0.434086	−0.217043	−	0.976162i	$-0.569641\pi$
$941$	−1.04407e13	−0.434086	−0.217043	+	0.976162i	$0.569641\pi$
$942$	3.30562e13	1.36780
$943$	−9.09409e12	−0.374504
$944$	−3.41413e13	−1.39929
$945$	4.46765e13	1.82237
$946$	−1.76864e13	−0.718010
$947$	2.76761e13	1.11823	0.559113	−	0.829091i	$-0.311142\pi$
$947$	2.76761e13	1.11823	0.559113	+	0.829091i	$0.311142\pi$
$948$	7.13731e13	2.87010
$949$	1.52722e13	0.611228
$950$	−2.64057e13	−1.05182
$951$	7.33216e13	2.90683
$952$	−1.38196e11	−0.00545294
$953$	−1.07620e13	−0.422642	−0.211321	−	0.977417i	$-0.567777\pi$
$953$	−1.07620e13	−0.422642	−0.211321	+	0.977417i	$0.567777\pi$
$954$	−1.93986e12	−0.0758231
$955$	−4.42283e13	−1.72062
$956$	1.89773e13	0.734809
$957$	−6.06744e12	−0.233831
$958$	1.73626e13	0.665993
$959$	6.11836e12	0.233589
$960$	−6.44179e13	−2.44786
$961$	−2.06927e13	−0.782639
$962$	4.50589e13	1.69626
$963$	−4.54477e13	−1.70292
$964$	−3.89017e13	−1.45085
$965$	−2.09397e13	−0.777315
$966$	−2.60573e13	−0.962793
$967$	−3.62374e13	−1.33272	−0.666358	−	0.745632i	$-0.732148\pi$
$967$	−3.62374e13	−1.33272	−0.666358	+	0.745632i	$0.732148\pi$
$968$	−6.84716e10	−0.00250652
$969$	1.81887e13	0.662740
$970$	1.55064e13	0.562391
$971$	2.76476e13	0.998093	0.499046	−	0.866575i	$-0.333684\pi$
$971$	2.76476e13	0.998093	0.499046	+	0.866575i	$0.333684\pi$
$972$	−6.12800e13	−2.20202
$973$	2.59541e13	0.928322
$974$	2.77653e13	0.988525
$975$	4.45874e13	1.58013
$976$	1.69715e13	0.598680
$977$	−2.20582e13	−0.774541	−0.387271	−	0.921966i	$-0.626582\pi$
$977$	−2.20582e13	−0.774541	−0.387271	+	0.921966i	$0.626582\pi$
$978$	6.66640e13	2.33006
$979$	8.41900e12	0.292913
$980$	2.96835e13	1.02801
$981$	3.42928e13	1.18220
$982$	−2.58413e13	−0.886774
$983$	2.90064e13	0.990838	0.495419	−	0.868654i	$-0.335015\pi$
$983$	2.90064e13	0.990838	0.495419	+	0.868654i	$0.335015\pi$
$984$	−7.44991e11	−0.0253322
$985$	−3.34803e12	−0.113325
$986$	−7.12425e12	−0.240045
$987$	−2.42654e13	−0.813880
$988$	2.48710e13	0.830398
$989$	3.87382e13	1.28753
$990$	4.35016e13	1.43929
$991$	1.59884e13	0.526590	0.263295	−	0.964715i	$-0.415191\pi$
$991$	1.59884e13	0.526590	0.263295	+	0.964715i	$0.415191\pi$
$992$	2.00034e13	0.655845
$993$	1.64330e13	0.536346
$994$	−8.77486e12	−0.285103
$995$	−1.61444e13	−0.522177
$996$	−5.66380e13	−1.82365
$997$	−4.29994e13	−1.37827	−0.689135	−	0.724633i	$-0.742009\pi$
$997$	−4.29994e13	−1.37827	−0.689135	+	0.724633i	$0.742009\pi$
$998$	−3.45281e13	−1.10175
$999$	1.07344e14	3.40983

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.10.a.a.1.3	✓	3
3.2	odd	2		99.10.a.b.1.1		3
4.3	odd	2		176.10.a.g.1.3		3
5.4	even	2		275.10.a.a.1.1		3
11.10	odd	2		121.10.a.b.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.10.a.a.1.3	✓	3	1.1	even	1	trivial
99.10.a.b.1.1		3	3.2	odd	2
121.10.a.b.1.1		3	11.10	odd	2
176.10.a.g.1.3		3	4.3	odd	2
275.10.a.a.1.1		3	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)

\(f(q)\)	\(=\)	\(q+31.8429 q^{2} -261.882 q^{3} +501.969 q^{4} -1908.19 q^{5} -8339.07 q^{6} +3060.06 q^{7} -319.425 q^{8} +48899.1 q^{9} +O(q^{10})\)	\(q+31.8429 q^{2} -261.882 q^{3} +501.969 q^{4} -1908.19 q^{5} -8339.07 q^{6} +3060.06 q^{7} -319.425 q^{8} +48899.1 q^{9} -60762.2 q^{10} -14641.0 q^{11} -131457. q^{12} -100860. q^{13} +97441.1 q^{14} +499720. q^{15} -267179. q^{16} +141383. q^{17} +1.55709e6 q^{18} -491244. q^{19} -957851. q^{20} -801374. q^{21} -466212. q^{22} +1.02113e6 q^{23} +83651.6 q^{24} +1.68806e6 q^{25} -3.21167e6 q^{26} -7.65118e6 q^{27} +1.53605e6 q^{28} -1.58245e6 q^{29} +1.59125e7 q^{30} -2.39728e6 q^{31} -8.34421e6 q^{32} +3.83421e6 q^{33} +4.50205e6 q^{34} -5.83917e6 q^{35} +2.45458e7 q^{36} -1.40297e7 q^{37} -1.56426e7 q^{38} +2.64134e7 q^{39} +609523. q^{40} -8.90588e6 q^{41} -2.55181e7 q^{42} +3.79365e7 q^{43} -7.34932e6 q^{44} -9.33088e7 q^{45} +3.25158e7 q^{46} +3.02797e7 q^{47} +6.99694e7 q^{48} -3.09896e7 q^{49} +5.37527e7 q^{50} -3.70257e7 q^{51} -5.06286e7 q^{52} -1.24582e6 q^{53} -2.43635e8 q^{54} +2.79378e7 q^{55} -977459. q^{56} +1.28648e8 q^{57} -5.03897e7 q^{58} +1.27784e8 q^{59} +2.50844e8 q^{60} -6.35208e7 q^{61} -7.63362e7 q^{62} +1.49634e8 q^{63} -1.28908e8 q^{64} +1.92460e8 q^{65} +1.22092e8 q^{66} +7.51979e7 q^{67} +7.09700e7 q^{68} -2.67416e8 q^{69} -1.85936e8 q^{70} -9.00530e7 q^{71} -1.56196e7 q^{72} -1.51420e8 q^{73} -4.46747e8 q^{74} -4.42072e8 q^{75} -2.46589e8 q^{76} -4.48023e7 q^{77} +8.41079e8 q^{78} -5.42941e8 q^{79} +5.09829e8 q^{80} +1.04122e9 q^{81} -2.83589e8 q^{82} +4.30849e8 q^{83} -4.02265e8 q^{84} -2.69786e8 q^{85} +1.20801e9 q^{86} +4.14414e8 q^{87} +4.67670e6 q^{88} -5.75029e8 q^{89} -2.97122e9 q^{90} -3.08638e8 q^{91} +5.12577e8 q^{92} +6.27804e8 q^{93} +9.64194e8 q^{94} +9.37386e8 q^{95} +2.18520e9 q^{96} -2.55198e8 q^{97} -9.86799e8 q^{98} -7.15932e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 186 q^{3} + 912 q^{4} - 1824 q^{5} - 10956 q^{6} - 7260 q^{7} - 20064 q^{8} + 14553 q^{9}+O(q^{10}) \) 3 * q - 186 * q^3 + 912 * q^4 - 1824 * q^5 - 10956 * q^6 - 7260 * q^7 - 20064 * q^8 + 14553 * q^9	\( 3 q - 186 q^{3} + 912 q^{4} - 1824 q^{5} - 10956 q^{6} - 7260 q^{7} - 20064 q^{8} + 14553 q^{9} - 86724 q^{10} - 43923 q^{11} - 71040 q^{12} - 93258 q^{13} + 324264 q^{14} + 540330 q^{15} + 22656 q^{16} + 18678 q^{17} + 1997028 q^{18} - 1027356 q^{19} - 156576 q^{20} - 1287924 q^{21} + 1674690 q^{23} - 947232 q^{24} - 1560729 q^{25} - 2162088 q^{26} - 10285434 q^{27} - 2570304 q^{28} - 2693658 q^{29} + 14272500 q^{30} - 4525302 q^{31} + 160512 q^{32} + 2723226 q^{33} + 19899408 q^{34} - 7933860 q^{35} + 20908368 q^{36} - 8820204 q^{37} + 23297712 q^{38} + 24922920 q^{39} - 5145888 q^{40} - 9771102 q^{41} - 8130360 q^{42} + 18795744 q^{43} - 13352592 q^{44} - 91915398 q^{45} - 68671020 q^{46} - 31155816 q^{47} + 76391808 q^{48} - 54229677 q^{49} + 103405236 q^{50} - 62110884 q^{51} - 86345952 q^{52} + 47500122 q^{53} - 153828180 q^{54} + 26705184 q^{55} + 113407680 q^{56} + 62103096 q^{57} - 120644760 q^{58} + 332138370 q^{59} + 290804160 q^{60} - 49031730 q^{61} - 86992620 q^{62} + 319652784 q^{63} - 421220352 q^{64} + 161689572 q^{65} + 160406796 q^{66} + 330560082 q^{67} - 382273056 q^{68} - 104664822 q^{69} - 22907160 q^{70} - 57835050 q^{71} + 302075136 q^{72} - 458816886 q^{73} - 528939708 q^{74} - 562184580 q^{75} - 1324671744 q^{76} + 106293660 q^{77} + 903869520 q^{78} - 798908748 q^{79} + 442084224 q^{80} + 1544572395 q^{81} - 376730664 q^{82} + 1239784920 q^{83} - 809016384 q^{84} - 632001744 q^{85} + 627638088 q^{86} + 505901880 q^{87} + 293757024 q^{88} - 699523368 q^{89} - 2575080288 q^{90} - 268926960 q^{91} + 3537302976 q^{92} + 614745786 q^{93} + 3327514080 q^{94} + 107303856 q^{95} + 2520807168 q^{96} - 2207436012 q^{97} - 1261919472 q^{98} - 213070473 q^{99}+O(q^{100}) \) 3 * q - 186 * q^3 + 912 * q^4 - 1824 * q^5 - 10956 * q^6 - 7260 * q^7 - 20064 * q^8 + 14553 * q^9 - 86724 * q^10 - 43923 * q^11 - 71040 * q^12 - 93258 * q^13 + 324264 * q^14 + 540330 * q^15 + 22656 * q^16 + 18678 * q^17 + 1997028 * q^18 - 1027356 * q^19 - 156576 * q^20 - 1287924 * q^21 + 1674690 * q^23 - 947232 * q^24 - 1560729 * q^25 - 2162088 * q^26 - 10285434 * q^27 - 2570304 * q^28 - 2693658 * q^29 + 14272500 * q^30 - 4525302 * q^31 + 160512 * q^32 + 2723226 * q^33 + 19899408 * q^34 - 7933860 * q^35 + 20908368 * q^36 - 8820204 * q^37 + 23297712 * q^38 + 24922920 * q^39 - 5145888 * q^40 - 9771102 * q^41 - 8130360 * q^42 + 18795744 * q^43 - 13352592 * q^44 - 91915398 * q^45 - 68671020 * q^46 - 31155816 * q^47 + 76391808 * q^48 - 54229677 * q^49 + 103405236 * q^50 - 62110884 * q^51 - 86345952 * q^52 + 47500122 * q^53 - 153828180 * q^54 + 26705184 * q^55 + 113407680 * q^56 + 62103096 * q^57 - 120644760 * q^58 + 332138370 * q^59 + 290804160 * q^60 - 49031730 * q^61 - 86992620 * q^62 + 319652784 * q^63 - 421220352 * q^64 + 161689572 * q^65 + 160406796 * q^66 + 330560082 * q^67 - 382273056 * q^68 - 104664822 * q^69 - 22907160 * q^70 - 57835050 * q^71 + 302075136 * q^72 - 458816886 * q^73 - 528939708 * q^74 - 562184580 * q^75 - 1324671744 * q^76 + 106293660 * q^77 + 903869520 * q^78 - 798908748 * q^79 + 442084224 * q^80 + 1544572395 * q^81 - 376730664 * q^82 + 1239784920 * q^83 - 809016384 * q^84 - 632001744 * q^85 + 627638088 * q^86 + 505901880 * q^87 + 293757024 * q^88 - 699523368 * q^89 - 2575080288 * q^90 - 268926960 * q^91 + 3537302976 * q^92 + 614745786 * q^93 + 3327514080 * q^94 + 107303856 * q^95 + 2520807168 * q^96 - 2207436012 * q^97 - 1261919472 * q^98 - 213070473 * q^99

Introduction

L-functions

Modular forms

Varieties

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