LMFDB - Embedded newform 105.8.a.h.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,8,Mod(1,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("105.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	105.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:	$32.8004276758$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 277x^{2} + 80x + 15348 $ x^4 - 2x^3 - 277x^2 + 80*x + 15348
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 5^{2} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-12.8099$ of defining polynomial
Character	$\chi$	$=$	105.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.41438 q^{2} -27.0000 q^{3} -116.342 q^{4} +125.000 q^{5} +92.1883 q^{6} +343.000 q^{7} +834.277 q^{8} +729.000 q^{9} -426.798 q^{10} -3379.63 q^{11} +3141.23 q^{12} -14159.0 q^{13} -1171.13 q^{14} -3375.00 q^{15} +12043.2 q^{16} -19538.0 q^{17} -2489.08 q^{18} -38098.7 q^{19} -14542.8 q^{20} -9261.00 q^{21} +11539.4 q^{22} +103511. q^{23} -22525.5 q^{24} +15625.0 q^{25} +48344.1 q^{26} -19683.0 q^{27} -39905.3 q^{28} +59794.5 q^{29} +11523.5 q^{30} +68349.9 q^{31} -147908. q^{32} +91250.1 q^{33} +66710.3 q^{34} +42875.0 q^{35} -84813.3 q^{36} +266512. q^{37} +130084. q^{38} +382292. q^{39} +104285. q^{40} +655437. q^{41} +31620.6 q^{42} -775223. q^{43} +393193. q^{44} +91125.0 q^{45} -353426. q^{46} -119729. q^{47} -325167. q^{48} +117649. q^{49} -53349.7 q^{50} +527527. q^{51} +1.64728e6 q^{52} +224102. q^{53} +67205.3 q^{54} -422454. q^{55} +286157. q^{56} +1.02867e6 q^{57} -204161. q^{58} -409602. q^{59} +392654. q^{60} +1.42274e6 q^{61} -233373. q^{62} +250047. q^{63} -1.03652e6 q^{64} -1.76987e6 q^{65} -311563. q^{66} +4.22037e6 q^{67} +2.27309e6 q^{68} -2.79479e6 q^{69} -146392. q^{70} +2.17619e6 q^{71} +608188. q^{72} +4.43912e6 q^{73} -909973. q^{74} -421875. q^{75} +4.43248e6 q^{76} -1.15921e6 q^{77} -1.30529e6 q^{78} +1.63306e6 q^{79} +1.50540e6 q^{80} +531441. q^{81} -2.23791e6 q^{82} -3.49903e6 q^{83} +1.07744e6 q^{84} -2.44225e6 q^{85} +2.64691e6 q^{86} -1.61445e6 q^{87} -2.81955e6 q^{88} +2.03583e6 q^{89} -311135. q^{90} -4.85652e6 q^{91} -1.20427e7 q^{92} -1.84545e6 q^{93} +408799. q^{94} -4.76234e6 q^{95} +3.99351e6 q^{96} +1.27049e7 q^{97} -401698. q^{98} -2.46375e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 11 q^{2} - 108 q^{3} + 141 q^{4} + 500 q^{5} - 297 q^{6} + 1372 q^{7} + 2133 q^{8} + 2916 q^{9} + 1375 q^{10} - 2708 q^{11} - 3807 q^{12} - 2212 q^{13} + 3773 q^{14} - 13500 q^{15} - 9599 q^{16} - 17016 q^{17}+ \cdots - 1974132 q^{99}+O(q^{100}) $ 4 * q + 11 * q^2 - 108 * q^3 + 141 * q^4 + 500 * q^5 - 297 * q^6 + 1372 * q^7 + 2133 * q^8 + 2916 * q^9 + 1375 * q^10 - 2708 * q^11 - 3807 * q^12 - 2212 * q^13 + 3773 * q^14 - 13500 * q^15 - 9599 * q^16 - 17016 * q^17 + 8019 * q^18 + 32668 * q^19 + 17625 * q^20 - 37044 * q^21 - 7196 * q^22 + 87696 * q^23 - 57591 * q^24 + 62500 * q^25 + 67354 * q^26 - 78732 * q^27 + 48363 * q^28 + 200488 * q^29 - 37125 * q^30 + 258852 * q^31 + 39445 * q^32 + 73116 * q^33 + 225518 * q^34 + 171500 * q^35 + 102789 * q^36 + 666856 * q^37 + 846556 * q^38 + 59724 * q^39 + 266625 * q^40 + 833000 * q^41 - 101871 * q^42 + 1051896 * q^43 + 1918236 * q^44 + 364500 * q^45 + 1786160 * q^46 + 529824 * q^47 + 259173 * q^48 + 470596 * q^49 + 171875 * q^50 + 459432 * q^51 + 211718 * q^52 + 791764 * q^53 - 216513 * q^54 - 338500 * q^55 + 731619 * q^56 - 882036 * q^57 + 3500242 * q^58 - 3825904 * q^59 - 475875 * q^60 + 212432 * q^61 + 882400 * q^62 + 1000188 * q^63 - 1515063 * q^64 - 276500 * q^65 + 194292 * q^66 + 5165272 * q^67 + 7423202 * q^68 - 2367792 * q^69 + 471625 * q^70 - 623260 * q^71 + 1554957 * q^72 - 2083228 * q^73 + 1059642 * q^74 - 1687500 * q^75 + 6990964 * q^76 - 928844 * q^77 - 1818558 * q^78 - 1325016 * q^79 - 1199875 * q^80 + 2125764 * q^81 + 11798982 * q^82 + 11447616 * q^83 - 1305801 * q^84 - 2127000 * q^85 + 7525948 * q^86 - 5413176 * q^87 + 19484572 * q^88 - 5805808 * q^89 + 1002375 * q^90 - 758716 * q^91 - 2716288 * q^92 - 6989004 * q^93 - 15552560 * q^94 + 4083500 * q^95 - 1065015 * q^96 + 5857516 * q^97 + 1294139 * q^98 - 1974132 * q^99

Coefficient data

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

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

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

$2$	−3.41438	−0.301791	−0.150896	−	0.988550i	$-0.548216\pi$
$2$	−3.41438	−0.301791	−0.150896	+	0.988550i	$0.548216\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	−116.342	−0.908922
$5$	125.000	0.447214
$5$	125.000	0.447214
$6$	92.1883	0.174239
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	834.277	0.576096
$9$	729.000	0.333333
$10$	−426.798	−0.134965
$11$	−3379.63	−0.765588	−0.382794	−	0.923834i	$-0.625038\pi$
$11$	−3379.63	−0.765588	−0.382794	+	0.923834i	$0.625038\pi$
$12$	3141.23	0.524766
$13$	−14159.0	−1.78743	−0.893716	−	0.448633i	$-0.851911\pi$
$13$	−14159.0	−1.78743	−0.893716	+	0.448633i	$0.851911\pi$
$14$	−1171.13	−0.114066
$15$	−3375.00	−0.258199
$16$	12043.2	0.735061
$17$	−19538.0	−0.964516	−0.482258	−	0.876029i	$-0.660183\pi$
$17$	−19538.0	−0.964516	−0.482258	+	0.876029i	$0.660183\pi$
$18$	−2489.08	−0.100597
$19$	−38098.7	−1.27430	−0.637152	−	0.770738i	$-0.719888\pi$
$19$	−38098.7	−1.27430	−0.637152	+	0.770738i	$0.719888\pi$
$20$	−14542.8	−0.406482
$21$	−9261.00	−0.218218
$22$	11539.4	0.231048
$23$	103511.	1.77394	0.886969	−	0.461828i	$-0.152806\pi$
$23$	103511.	1.77394	0.886969	+	0.461828i	$0.152806\pi$
$24$	−22525.5	−0.332609
$25$	15625.0	0.200000
$26$	48344.1	0.539432
$27$	−19683.0	−0.192450
$28$	−39905.3	−0.343540
$29$	59794.5	0.455269	0.227635	−	0.973747i	$-0.426901\pi$
$29$	59794.5	0.455269	0.227635	+	0.973747i	$0.426901\pi$
$30$	11523.5	0.0779222
$31$	68349.9	0.412071	0.206035	−	0.978545i	$-0.433944\pi$
$31$	68349.9	0.412071	0.206035	+	0.978545i	$0.433944\pi$
$32$	−147908.	−0.797931
$33$	91250.1	0.442013
$34$	66710.3	0.291083
$35$	42875.0	0.169031
$36$	−84813.3	−0.302974
$37$	266512.	0.864989	0.432494	−	0.901637i	$-0.357634\pi$
$37$	266512.	0.864989	0.432494	+	0.901637i	$0.357634\pi$
$38$	130084.	0.384574
$39$	382292.	1.03197
$40$	104285.	0.257638
$41$	655437.	1.48521	0.742604	−	0.669730i	$-0.233590\pi$
$41$	655437.	1.48521	0.742604	+	0.669730i	$0.233590\pi$
$42$	31620.6	0.0658563
$43$	−775223.	−1.48692	−0.743459	−	0.668782i	$-0.766816\pi$
$43$	−775223.	−1.48692	−0.743459	+	0.668782i	$0.766816\pi$
$44$	393193.	0.695860
$45$	91125.0	0.149071
$46$	−353426.	−0.535360
$47$	−119729.	−0.168211	−0.0841057	−	0.996457i	$-0.526803\pi$
$47$	−119729.	−0.168211	−0.0841057	+	0.996457i	$0.526803\pi$
$48$	−325167.	−0.424388
$49$	117649.	0.142857
$50$	−53349.7	−0.0603583
$51$	527527.	0.556864
$52$	1.64728e6	1.62464
$53$	224102.	0.206767	0.103383	−	0.994642i	$-0.467033\pi$
$53$	224102.	0.206767	0.103383	+	0.994642i	$0.467033\pi$
$54$	67205.3	0.0580798
$55$	−422454.	−0.342382
$56$	286157.	0.217744
$57$	1.02867e6	0.735720
$58$	−204161.	−0.137396
$59$	−409602.	−0.259645	−0.129823	−	0.991537i	$-0.541441\pi$
$59$	−409602.	−0.259645	−0.129823	+	0.991537i	$0.541441\pi$
$60$	392654.	0.234683
$61$	1.42274e6	0.802548	0.401274	−	0.915958i	$-0.368568\pi$
$61$	1.42274e6	0.802548	0.401274	+	0.915958i	$0.368568\pi$
$62$	−233373.	−0.124359
$63$	250047.	0.125988
$64$	−1.03652e6	−0.494252
$65$	−1.76987e6	−0.799364
$66$	−311563.	−0.133396
$67$	4.22037e6	1.71431	0.857153	−	0.515061i	$-0.172231\pi$
$67$	4.22037e6	1.71431	0.857153	+	0.515061i	$0.172231\pi$
$68$	2.27309e6	0.876670
$69$	−2.79479e6	−1.02418
$70$	−146392.	−0.0510121
$71$	2.17619e6	0.721595	0.360798	−	0.932644i	$-0.382505\pi$
$71$	2.17619e6	0.721595	0.360798	+	0.932644i	$0.382505\pi$
$72$	608188.	0.192032
$73$	4.43912e6	1.33557	0.667785	−	0.744354i	$-0.267242\pi$
$73$	4.43912e6	1.33557	0.667785	+	0.744354i	$0.267242\pi$
$74$	−909973.	−0.261046
$75$	−421875.	−0.115470
$76$	4.43248e6	1.15824
$77$	−1.15921e6	−0.289365
$78$	−1.30529e6	−0.311441
$79$	1.63306e6	0.372656	0.186328	−	0.982488i	$-0.440341\pi$
$79$	1.63306e6	0.372656	0.186328	+	0.982488i	$0.440341\pi$
$80$	1.50540e6	0.328729
$81$	531441.	0.111111
$82$	−2.23791e6	−0.448223
$83$	−3.49903e6	−0.671698	−0.335849	−	0.941916i	$-0.609023\pi$
$83$	−3.49903e6	−0.671698	−0.335849	+	0.941916i	$0.609023\pi$
$84$	1.07744e6	0.198343
$85$	−2.44225e6	−0.431345
$86$	2.64691e6	0.448739
$87$	−1.61445e6	−0.262850
$88$	−2.81955e6	−0.441053
$89$	2.03583e6	0.306110	0.153055	−	0.988218i	$-0.451089\pi$
$89$	2.03583e6	0.306110	0.153055	+	0.988218i	$0.451089\pi$
$90$	−311135.	−0.0449884
$91$	−4.85652e6	−0.675586
$92$	−1.20427e7	−1.61237
$93$	−1.84545e6	−0.237909
$94$	408799.	0.0507648
$95$	−4.76234e6	−0.569886
$96$	3.99351e6	0.460686
$97$	1.27049e7	1.41342	0.706709	−	0.707505i	$-0.250179\pi$
$97$	1.27049e7	1.41342	0.706709	+	0.707505i	$0.250179\pi$
$98$	−401698.	−0.0431131
$99$	−2.46375e6	−0.255196
$100$	−1.81784e6	−0.181784
$101$	−1.86609e7	−1.80222	−0.901110	−	0.433590i	$-0.857247\pi$
$101$	−1.86609e7	−1.80222	−0.901110	+	0.433590i	$0.857247\pi$
$102$	−1.80118e6	−0.168057
$103$	5.30772e6	0.478606	0.239303	−	0.970945i	$-0.423081\pi$
$103$	5.30772e6	0.478606	0.239303	+	0.970945i	$0.423081\pi$
$104$	−1.18125e7	−1.02973
$105$	−1.15762e6	−0.0975900
$106$	−765171.	−0.0624005
$107$	1.74818e7	1.37957	0.689784	−	0.724015i	$-0.257705\pi$
$107$	1.74818e7	1.37957	0.689784	+	0.724015i	$0.257705\pi$
$108$	2.28996e6	0.174922
$109$	467681.	0.0345905	0.0172952	−	0.999850i	$-0.494494\pi$
$109$	467681.	0.0345905	0.0172952	+	0.999850i	$0.494494\pi$
$110$	1.44242e6	0.103328
$111$	−7.19582e6	−0.499401
$112$	4.13083e6	0.277827
$113$	−1.45523e7	−0.948763	−0.474382	−	0.880319i	$-0.657328\pi$
$113$	−1.45523e7	−0.948763	−0.474382	+	0.880319i	$0.657328\pi$
$114$	−3.51226e6	−0.222034
$115$	1.29389e7	0.793329
$116$	−6.95661e6	−0.413804
$117$	−1.03219e7	−0.595811
$118$	1.39854e6	0.0783587
$119$	−6.70154e6	−0.364553
$120$	−2.81568e6	−0.148747
$121$	−8.06524e6	−0.413874
$122$	−4.85777e6	−0.242202
$123$	−1.76968e7	−0.857486
$124$	−7.95196e6	−0.374540
$125$	1.95312e6	0.0894427
$126$	−853756.	−0.0380222
$127$	2.04101e6	0.0884161	0.0442081	−	0.999022i	$-0.485924\pi$
$127$	2.04101e6	0.0884161	0.0442081	+	0.999022i	$0.485924\pi$
$128$	2.24713e7	0.947093
$129$	2.09310e7	0.858472
$130$	6.04301e6	0.241241
$131$	−9.14330e6	−0.355348	−0.177674	−	0.984089i	$-0.556857\pi$
$131$	−9.14330e6	−0.355348	−0.177674	+	0.984089i	$0.556857\pi$
$132$	−1.06162e7	−0.401755
$133$	−1.30679e7	−0.481642
$134$	−1.44099e7	−0.517363
$135$	−2.46038e6	−0.0860663
$136$	−1.63001e7	−0.555654
$137$	3.62725e7	1.20519	0.602596	−	0.798047i	$-0.294133\pi$
$137$	3.62725e7	1.20519	0.602596	+	0.798047i	$0.294133\pi$
$138$	9.54249e6	0.309090
$139$	−2.28823e7	−0.722682	−0.361341	−	0.932434i	$-0.617681\pi$
$139$	−2.28823e7	−0.722682	−0.361341	+	0.932434i	$0.617681\pi$
$140$	−4.98816e6	−0.153636
$141$	3.23267e6	0.0971169
$142$	−7.43036e6	−0.217771
$143$	4.78521e7	1.36844
$144$	8.77952e6	0.245020
$145$	7.47431e6	0.203603
$146$	−1.51568e7	−0.403064
$147$	−3.17652e6	−0.0824786
$148$	−3.10065e7	−0.786207
$149$	−7.18870e7	−1.78032	−0.890161	−	0.455646i	$-0.849408\pi$
$149$	−7.18870e7	−1.78032	−0.890161	+	0.455646i	$0.849408\pi$
$150$	1.44044e6	0.0348479
$151$	6.39974e7	1.51267	0.756333	−	0.654187i	$-0.226989\pi$
$151$	6.39974e7	1.51267	0.756333	+	0.654187i	$0.226989\pi$
$152$	−3.17849e7	−0.734122
$153$	−1.42432e7	−0.321505
$154$	3.95800e6	0.0873280
$155$	8.54374e6	0.184284
$156$	−4.44766e7	−0.937984
$157$	6.00497e6	0.123840	0.0619202	−	0.998081i	$-0.480278\pi$
$157$	6.00497e6	0.123840	0.0619202	+	0.998081i	$0.480278\pi$
$158$	−5.57589e6	−0.112464
$159$	−6.05077e6	−0.119377
$160$	−1.84885e7	−0.356846
$161$	3.55042e7	0.670486
$162$	−1.81454e6	−0.0335324
$163$	9.83028e7	1.77791	0.888954	−	0.457997i	$-0.151433\pi$
$163$	9.83028e7	1.77791	0.888954	+	0.457997i	$0.151433\pi$
$164$	−7.62549e7	−1.34994
$165$	1.14063e7	0.197674
$166$	1.19470e7	0.202713
$167$	5.80791e7	0.964966	0.482483	−	0.875905i	$-0.339735\pi$
$167$	5.80791e7	0.964966	0.482483	+	0.875905i	$0.339735\pi$
$168$	−7.72624e6	−0.125715
$169$	1.37728e8	2.19491
$170$	8.33878e6	0.130176
$171$	−2.77740e7	−0.424768
$172$	9.01909e7	1.35149
$173$	−2.31746e7	−0.340291	−0.170146	−	0.985419i	$-0.554424\pi$
$173$	−2.31746e7	−0.340291	−0.170146	+	0.985419i	$0.554424\pi$
$174$	5.51235e6	0.0793258
$175$	5.35938e6	0.0755929
$176$	−4.07017e7	−0.562754
$177$	1.10593e7	0.149906
$178$	−6.95111e6	−0.0923814
$179$	3.77902e7	0.492486	0.246243	−	0.969208i	$-0.420804\pi$
$179$	3.77902e7	0.492486	0.246243	+	0.969208i	$0.420804\pi$
$180$	−1.06017e7	−0.135494
$181$	−9.09325e6	−0.113984	−0.0569920	−	0.998375i	$-0.518151\pi$
$181$	−9.09325e6	−0.113984	−0.0569920	+	0.998375i	$0.518151\pi$
$182$	1.65820e7	0.203886
$183$	−3.84140e7	−0.463351
$184$	8.63567e7	1.02196
$185$	3.33140e7	0.386835
$186$	6.30106e6	0.0717990
$187$	6.60314e7	0.738422
$188$	1.39295e7	0.152891
$189$	−6.75127e6	−0.0727393
$190$	1.62605e7	0.171987
$191$	−5.34900e7	−0.555464	−0.277732	−	0.960659i	$-0.589583\pi$
$191$	−5.34900e7	−0.555464	−0.277732	+	0.960659i	$0.589583\pi$
$192$	2.79861e7	0.285357
$193$	−8.24940e7	−0.825984	−0.412992	−	0.910735i	$-0.635516\pi$
$193$	−8.24940e7	−0.825984	−0.412992	+	0.910735i	$0.635516\pi$
$194$	−4.33794e7	−0.426557
$195$	4.77865e7	0.461513
$196$	−1.36875e7	−0.129846
$197$	7.55328e7	0.703888	0.351944	−	0.936021i	$-0.385521\pi$
$197$	7.55328e7	0.703888	0.351944	+	0.936021i	$0.385521\pi$
$198$	8.41219e6	0.0770160
$199$	−1.05546e6	−0.00949412	−0.00474706	−	0.999989i	$-0.501511\pi$
$199$	−1.05546e6	−0.00949412	−0.00474706	+	0.999989i	$0.501511\pi$
$200$	1.30356e7	0.115219
$201$	−1.13950e8	−0.989756
$202$	6.37154e7	0.543895
$203$	2.05095e7	0.172076
$204$	−6.13735e7	−0.506146
$205$	8.19296e7	0.664205
$206$	−1.81226e7	−0.144439
$207$	7.54594e7	0.591313
$208$	−1.70520e8	−1.31387
$209$	1.28760e8	0.975593
$210$	3.95257e6	0.0294518
$211$	1.14474e7	0.0838916	0.0419458	−	0.999120i	$-0.486644\pi$
$211$	1.14474e7	0.0838916	0.0419458	+	0.999120i	$0.486644\pi$
$212$	−2.60725e7	−0.187935
$213$	−5.87573e7	−0.416613
$214$	−5.96896e7	−0.416342
$215$	−9.69028e7	−0.664970
$216$	−1.64211e7	−0.110870
$217$	2.34440e7	0.155748
$218$	−1.59684e6	−0.0104391
$219$	−1.19856e8	−0.771092
$220$	4.91492e7	0.311198
$221$	2.76638e8	1.72401
$222$	2.45693e7	0.150715
$223$	2.81598e8	1.70044	0.850222	−	0.526425i	$-0.176468\pi$
$223$	2.81598e8	1.70044	0.850222	+	0.526425i	$0.176468\pi$
$224$	−5.07323e7	−0.301590
$225$	1.13906e7	0.0666667
$226$	4.96872e7	0.286329
$227$	−4.00301e7	−0.227141	−0.113571	−	0.993530i	$-0.536229\pi$
$227$	−4.00301e7	−0.227141	−0.113571	+	0.993530i	$0.536229\pi$
$228$	−1.19677e8	−0.668712
$229$	−1.24592e8	−0.685591	−0.342796	−	0.939410i	$-0.611374\pi$
$229$	−1.24592e8	−0.685591	−0.342796	+	0.939410i	$0.611374\pi$
$230$	−4.41782e7	−0.239420
$231$	3.12988e7	0.167065
$232$	4.98852e7	0.262279
$233$	−3.21485e8	−1.66500	−0.832500	−	0.554025i	$-0.813091\pi$
$233$	−3.21485e8	−1.66500	−0.832500	+	0.554025i	$0.813091\pi$
$234$	3.52428e7	0.179811
$235$	−1.49661e7	−0.0752264
$236$	4.76540e7	0.235997
$237$	−4.40927e7	−0.215153
$238$	2.28816e7	0.110019
$239$	−2.95076e8	−1.39811	−0.699054	−	0.715068i	$-0.746395\pi$
$239$	−2.95076e8	−1.39811	−0.699054	+	0.715068i	$0.746395\pi$
$240$	−4.06459e7	−0.189792
$241$	1.00887e8	0.464273	0.232137	−	0.972683i	$-0.425428\pi$
$241$	1.00887e8	0.464273	0.232137	+	0.972683i	$0.425428\pi$
$242$	2.75378e7	0.124904
$243$	−1.43489e7	−0.0641500
$244$	−1.65524e8	−0.729453
$245$	1.47061e7	0.0638877
$246$	6.04236e7	0.258782
$247$	5.39439e8	2.27773
$248$	5.70227e7	0.237393
$249$	9.44737e7	0.387805
$250$	−6.66871e6	−0.0269931
$251$	−9.30364e7	−0.371360	−0.185680	−	0.982610i	$-0.559449\pi$
$251$	−9.30364e7	−0.371360	−0.185680	+	0.982610i	$0.559449\pi$
$252$	−2.90910e7	−0.114513
$253$	−3.49829e8	−1.35811
$254$	−6.96877e6	−0.0266832
$255$	6.59408e7	0.249037
$256$	5.59493e7	0.208428
$257$	3.64584e8	1.33978	0.669888	−	0.742462i	$-0.266342\pi$
$257$	3.64584e8	1.33978	0.669888	+	0.742462i	$0.266342\pi$
$258$	−7.14664e7	−0.259080
$259$	9.14136e7	0.326935
$260$	2.05910e8	0.726559
$261$	4.35902e7	0.151756
$262$	3.12187e7	0.107241
$263$	1.11633e8	0.378396	0.189198	−	0.981939i	$-0.439411\pi$
$263$	1.11633e8	0.378396	0.189198	+	0.981939i	$0.439411\pi$
$264$	7.61279e7	0.254642
$265$	2.80128e7	0.0924690
$266$	4.46187e7	0.145355
$267$	−5.49675e7	−0.176733
$268$	−4.91006e8	−1.55817
$269$	−1.53396e8	−0.480487	−0.240244	−	0.970713i	$-0.577227\pi$
$269$	−1.53396e8	−0.480487	−0.240244	+	0.970713i	$0.577227\pi$
$270$	8.40066e6	0.0259741
$271$	−4.17128e8	−1.27314	−0.636571	−	0.771218i	$-0.719648\pi$
$271$	−4.17128e8	−1.27314	−0.636571	+	0.771218i	$0.719648\pi$
$272$	−2.35301e8	−0.708978
$273$	1.31126e8	0.390050
$274$	−1.23848e8	−0.363717
$275$	−5.28068e7	−0.153118
$276$	3.25152e8	0.930903
$277$	−4.05683e8	−1.14685	−0.573426	−	0.819257i	$-0.694386\pi$
$277$	−4.05683e8	−1.14685	−0.573426	+	0.819257i	$0.694386\pi$
$278$	7.81288e7	0.218099
$279$	4.98271e7	0.137357
$280$	3.57696e7	0.0973781
$281$	−1.50774e8	−0.405371	−0.202686	−	0.979244i	$-0.564967\pi$
$281$	−1.50774e8	−0.405371	−0.202686	+	0.979244i	$0.564967\pi$
$282$	−1.10376e7	−0.0293091
$283$	−3.69597e7	−0.0969338	−0.0484669	−	0.998825i	$-0.515434\pi$
$283$	−3.69597e7	−0.0969338	−0.0484669	+	0.998825i	$0.515434\pi$
$284$	−2.53183e8	−0.655874
$285$	1.28583e8	0.329024
$286$	−1.63385e8	−0.412983
$287$	2.24815e8	0.561356
$288$	−1.07825e8	−0.265977
$289$	−2.86042e7	−0.0697088
$290$	−2.55202e7	−0.0614455
$291$	−3.43032e8	−0.816037
$292$	−5.16456e8	−1.21393
$293$	−6.00426e8	−1.39451	−0.697257	−	0.716822i	$-0.745596\pi$
$293$	−6.00426e8	−1.39451	−0.697257	+	0.716822i	$0.745596\pi$
$294$	1.08459e7	0.0248913
$295$	−5.12003e7	−0.116117
$296$	2.22345e8	0.498317
$297$	6.65214e7	0.147338
$298$	2.45450e8	0.537286
$299$	−1.46561e9	−3.17079
$300$	4.90818e7	0.104953
$301$	−2.65901e8	−0.562002
$302$	−2.18511e8	−0.456510
$303$	5.03844e8	1.04051
$304$	−4.58832e8	−0.936691
$305$	1.77842e8	0.358910
$306$	4.86318e7	0.0970276
$307$	9.08890e8	1.79278	0.896390	−	0.443267i	$-0.146181\pi$
$307$	9.08890e8	1.79278	0.896390	+	0.443267i	$0.146181\pi$
$308$	1.34865e8	0.263010
$309$	−1.43309e8	−0.276323
$310$	−2.91716e7	−0.0556153
$311$	6.45862e8	1.21753	0.608763	−	0.793352i	$-0.291666\pi$
$311$	6.45862e8	1.21753	0.608763	+	0.793352i	$0.291666\pi$
$312$	3.18937e8	0.594517
$313$	−8.96603e8	−1.65270	−0.826352	−	0.563154i	$-0.809588\pi$
$313$	−8.96603e8	−1.65270	−0.826352	+	0.563154i	$0.809588\pi$
$314$	−2.05033e7	−0.0373740
$315$	3.12559e7	0.0563436
$316$	−1.89994e8	−0.338715
$317$	8.47295e8	1.49392	0.746959	−	0.664870i	$-0.231513\pi$
$317$	8.47295e8	1.49392	0.746959	+	0.664870i	$0.231513\pi$
$318$	2.06596e7	0.0360269
$319$	−2.02084e8	−0.348549
$320$	−1.29565e8	−0.221036
$321$	−4.72009e8	−0.796494
$322$	−1.21225e8	−0.202347
$323$	7.44374e8	1.22909
$324$	−6.18289e7	−0.100991
$325$	−2.21234e8	−0.357486
$326$	−3.35643e8	−0.536557
$327$	−1.26274e7	−0.0199708
$328$	5.46816e8	0.855623
$329$	−4.10669e7	−0.0635779
$330$	−3.89453e7	−0.0596564
$331$	7.42401e8	1.12523	0.562614	−	0.826720i	$-0.309796\pi$
$331$	7.42401e8	1.12523	0.562614	+	0.826720i	$0.309796\pi$
$332$	4.07084e8	0.610521
$333$	1.94287e8	0.288330
$334$	−1.98304e8	−0.291219
$335$	5.27546e8	0.766661
$336$	−1.11532e8	−0.160403
$337$	−7.24512e8	−1.03120	−0.515598	−	0.856831i	$-0.672430\pi$
$337$	−7.24512e8	−1.03120	−0.515598	+	0.856831i	$0.672430\pi$
$338$	−4.70254e8	−0.662406
$339$	3.92913e8	0.547769
$340$	2.84137e8	0.392059
$341$	−2.30998e8	−0.315477
$342$	9.48310e7	0.128191
$343$	4.03536e7	0.0539949
$344$	−6.46750e8	−0.856608
$345$	−3.49349e8	−0.458029
$346$	7.91269e7	0.102697
$347$	5.09846e8	0.655068	0.327534	−	0.944839i	$-0.393782\pi$
$347$	5.09846e8	0.655068	0.327534	+	0.944839i	$0.393782\pi$
$348$	1.87829e8	0.238910
$349$	−8.76052e8	−1.10317	−0.551583	−	0.834120i	$-0.685976\pi$
$349$	−8.76052e8	−1.10317	−0.551583	+	0.834120i	$0.685976\pi$
$350$	−1.82989e7	−0.0228133
$351$	2.78691e8	0.343991
$352$	4.99874e8	0.610887
$353$	1.26670e9	1.53272	0.766358	−	0.642413i	$-0.222067\pi$
$353$	1.26670e9	1.53272	0.766358	+	0.642413i	$0.222067\pi$
$354$	−3.77605e7	−0.0452404
$355$	2.72024e8	0.322707
$356$	−2.36853e8	−0.278230
$357$	1.80942e8	0.210475
$358$	−1.29030e8	−0.148628
$359$	1.66558e9	1.89992	0.949961	−	0.312369i	$-0.101122\pi$
$359$	1.66558e9	1.89992	0.949961	+	0.312369i	$0.101122\pi$
$360$	7.60235e7	0.0858794
$361$	5.57643e8	0.623851
$362$	3.10478e7	0.0343994
$363$	2.17761e8	0.238950
$364$	5.65018e8	0.614055
$365$	5.54890e8	0.597285
$366$	1.31160e8	0.139835
$367$	1.67575e9	1.76961	0.884807	−	0.465957i	$-0.154290\pi$
$367$	1.67575e9	1.76961	0.884807	+	0.465957i	$0.154290\pi$
$368$	1.24661e9	1.30395
$369$	4.77814e8	0.495070
$370$	−1.13747e8	−0.116743
$371$	7.68672e7	0.0781506
$372$	2.14703e8	0.216241
$373$	1.47694e9	1.47360	0.736802	−	0.676109i	$-0.236335\pi$
$373$	1.47694e9	1.47360	0.736802	+	0.676109i	$0.236335\pi$
$374$	−2.25456e8	−0.222850
$375$	−5.27344e7	−0.0516398
$376$	−9.98868e7	−0.0969060
$377$	−8.46628e8	−0.813763
$378$	2.30514e7	0.0219521
$379$	−1.64279e9	−1.55005	−0.775024	−	0.631932i	$-0.782262\pi$
$379$	−1.64279e9	−1.55005	−0.775024	+	0.631932i	$0.782262\pi$
$380$	5.54061e8	0.517982
$381$	−5.51072e7	−0.0510471
$382$	1.82635e8	0.167634
$383$	−1.89784e9	−1.72609	−0.863044	−	0.505129i	$-0.831445\pi$
$383$	−1.89784e9	−1.72609	−0.863044	+	0.505129i	$0.831445\pi$
$384$	−6.06724e8	−0.546804
$385$	−1.44902e8	−0.129408
$386$	2.81666e8	0.249275
$387$	−5.65137e8	−0.495639
$388$	−1.47811e9	−1.28469
$389$	1.05432e9	0.908131	0.454065	−	0.890968i	$-0.349973\pi$
$389$	1.05432e9	0.908131	0.454065	+	0.890968i	$0.349973\pi$
$390$	−1.63161e8	−0.139281
$391$	−2.02240e9	−1.71099
$392$	9.81518e7	0.0822995
$393$	2.46869e8	0.205160
$394$	−2.57898e8	−0.212428
$395$	2.04133e8	0.166657
$396$	2.86638e8	0.231953
$397$	2.96848e8	0.238104	0.119052	−	0.992888i	$-0.462014\pi$
$397$	2.96848e8	0.238104	0.119052	+	0.992888i	$0.462014\pi$
$398$	3.60373e6	0.00286525
$399$	3.52832e8	0.278076
$400$	1.88176e8	0.147012
$401$	−7.79941e8	−0.604028	−0.302014	−	0.953304i	$-0.597659\pi$
$401$	−7.79941e8	−0.604028	−0.302014	+	0.953304i	$0.597659\pi$
$402$	3.89069e8	0.298700
$403$	−9.67763e8	−0.736549
$404$	2.17105e9	1.63808
$405$	6.64301e7	0.0496904
$406$	−7.00273e7	−0.0519310
$407$	−9.00713e8	−0.662225
$408$	4.40103e8	0.320807
$409$	8.75152e8	0.632488	0.316244	−	0.948678i	$-0.397578\pi$
$409$	8.75152e8	0.632488	0.316244	+	0.948678i	$0.397578\pi$
$410$	−2.79739e8	−0.200452
$411$	−9.79359e8	−0.695818
$412$	−6.17511e8	−0.435015
$413$	−1.40494e8	−0.0981367
$414$	−2.57647e8	−0.178453
$415$	−4.37378e8	−0.300392
$416$	2.09422e9	1.42625
$417$	6.17821e8	0.417241
$418$	−4.39635e8	−0.294426
$419$	1.07058e9	0.711000	0.355500	−	0.934676i	$-0.384311\pi$
$419$	1.07058e9	0.711000	0.355500	+	0.934676i	$0.384311\pi$
$420$	1.34680e8	0.0887017
$421$	2.54184e9	1.66020	0.830100	−	0.557614i	$-0.188283\pi$
$421$	2.54184e9	1.66020	0.830100	+	0.557614i	$0.188283\pi$
$422$	−3.90858e7	−0.0253178
$423$	−8.72822e7	−0.0560705
$424$	1.86963e8	0.119118
$425$	−3.05282e8	−0.192903
$426$	2.00620e8	0.125730
$427$	4.87999e8	0.303335
$428$	−2.03387e9	−1.25392
$429$	−1.29201e9	−0.790068
$430$	3.30863e8	0.200682
$431$	8.91747e8	0.536502	0.268251	−	0.963349i	$-0.413554\pi$
$431$	8.91747e8	0.536502	0.268251	+	0.963349i	$0.413554\pi$
$432$	−2.37047e8	−0.141463
$433$	−1.03966e9	−0.615440	−0.307720	−	0.951477i	$-0.599566\pi$
$433$	−1.03966e9	−0.615440	−0.307720	+	0.951477i	$0.599566\pi$
$434$	−8.00468e7	−0.0470035
$435$	−2.01806e8	−0.117550
$436$	−5.44109e7	−0.0314400
$437$	−3.94363e9	−2.26054
$438$	4.09235e8	0.232709
$439$	−1.55931e9	−0.879641	−0.439821	−	0.898086i	$-0.644958\pi$
$439$	−1.55931e9	−0.879641	−0.439821	+	0.898086i	$0.644958\pi$
$440$	−3.52444e8	−0.197245
$441$	8.57661e7	0.0476190
$442$	−9.44548e8	−0.520291
$443$	−2.79970e8	−0.153002	−0.0765012	−	0.997069i	$-0.524375\pi$
$443$	−2.79970e8	−0.153002	−0.0765012	+	0.997069i	$0.524375\pi$
$444$	8.37176e8	0.453917
$445$	2.54479e8	0.136897
$446$	−9.61482e8	−0.513179
$447$	1.94095e9	1.02787
$448$	−3.55527e8	−0.186810
$449$	6.18452e8	0.322436	0.161218	−	0.986919i	$-0.448458\pi$
$449$	6.18452e8	0.322436	0.161218	+	0.986919i	$0.448458\pi$
$450$	−3.88919e7	−0.0201194
$451$	−2.21514e9	−1.13706
$452$	1.69305e9	0.862352
$453$	−1.72793e9	−0.873338
$454$	1.36678e8	0.0685494
$455$	−6.07065e8	−0.302131
$456$	8.58192e8	0.423846
$457$	9.07329e8	0.444691	0.222345	−	0.974968i	$-0.428629\pi$
$457$	9.07329e8	0.444691	0.222345	+	0.974968i	$0.428629\pi$
$458$	4.25404e8	0.206906
$459$	3.84567e8	0.185621
$460$	−1.50533e9	−0.721075
$461$	−2.41729e9	−1.14915	−0.574573	−	0.818453i	$-0.694832\pi$
$461$	−2.41729e9	−1.14915	−0.574573	+	0.818453i	$0.694832\pi$
$462$	−1.06866e8	−0.0504188
$463$	−3.14336e8	−0.147184	−0.0735921	−	0.997288i	$-0.523446\pi$
$463$	−3.14336e8	−0.147184	−0.0735921	+	0.997288i	$0.523446\pi$
$464$	7.20120e8	0.334651
$465$	−2.30681e8	−0.106396
$466$	1.09767e9	0.502483
$467$	4.74332e7	0.0215513	0.0107757	−	0.999942i	$-0.496570\pi$
$467$	4.74332e7	0.0215513	0.0107757	+	0.999942i	$0.496570\pi$
$468$	1.20087e9	0.541545
$469$	1.44759e9	0.647947
$470$	5.10999e7	0.0227027
$471$	−1.62134e8	−0.0714993
$472$	−3.41722e8	−0.149581
$473$	2.61997e9	1.13837
$474$	1.50549e8	0.0649313
$475$	−5.95293e8	−0.254861
$476$	7.79671e8	0.331350
$477$	1.63371e8	0.0689223
$478$	1.00750e9	0.421937
$479$	−2.08794e9	−0.868048	−0.434024	−	0.900901i	$-0.642907\pi$
$479$	−2.08794e9	−0.868048	−0.434024	+	0.900901i	$0.642907\pi$
$480$	4.99188e8	0.206025
$481$	−3.77353e9	−1.54611
$482$	−3.44465e8	−0.140114
$483$	−9.58614e8	−0.387105
$484$	9.38326e8	0.376179
$485$	1.58811e9	0.632099
$486$	4.89926e7	0.0193599
$487$	−2.19273e9	−0.860267	−0.430134	−	0.902765i	$-0.641534\pi$
$487$	−2.19273e9	−0.860267	−0.430134	+	0.902765i	$0.641534\pi$
$488$	1.18696e9	0.462345
$489$	−2.65417e9	−1.02648
$490$	−5.02123e7	−0.0192808
$491$	2.19027e9	0.835050	0.417525	−	0.908666i	$-0.362898\pi$
$491$	2.19027e9	0.835050	0.417525	+	0.908666i	$0.362898\pi$
$492$	2.05888e9	0.779387
$493$	−1.16827e9	−0.439115
$494$	−1.84185e9	−0.687400
$495$	−3.07969e8	−0.114127
$496$	8.23154e8	0.302897
$497$	7.46435e8	0.272737
$498$	−3.22569e8	−0.117036
$499$	6.56737e8	0.236614	0.118307	−	0.992977i	$-0.462253\pi$
$499$	6.56737e8	0.236614	0.118307	+	0.992977i	$0.462253\pi$
$500$	−2.27230e8	−0.0812964
$501$	−1.56813e9	−0.557123
$502$	3.17662e8	0.112073
$503$	−2.58040e9	−0.904065	−0.452033	−	0.892001i	$-0.649301\pi$
$503$	−2.58040e9	−0.904065	−0.452033	+	0.892001i	$0.649301\pi$
$504$	2.08608e8	0.0725813
$505$	−2.33261e9	−0.805977
$506$	1.19445e9	0.409865
$507$	−3.71864e9	−1.26723
$508$	−2.37455e8	−0.0803633
$509$	−2.07943e9	−0.698928	−0.349464	−	0.936950i	$-0.613636\pi$
$509$	−2.07943e9	−0.698928	−0.349464	+	0.936950i	$0.613636\pi$
$510$	−2.25147e8	−0.0751572
$511$	1.52262e9	0.504798
$512$	−3.06735e9	−1.00999
$513$	7.49898e8	0.245240
$514$	−1.24483e9	−0.404333
$515$	6.63465e8	0.214039
$516$	−2.43516e9	−0.780284
$517$	4.04639e8	0.128781
$518$	−3.12121e8	−0.0986662
$519$	6.25714e8	0.196467
$520$	−1.47656e9	−0.460511
$521$	−2.82646e9	−0.875609	−0.437804	−	0.899070i	$-0.644244\pi$
$521$	−2.82646e9	−0.875609	−0.437804	+	0.899070i	$0.644244\pi$
$522$	−1.48834e8	−0.0457988
$523$	4.81610e9	1.47211	0.736055	−	0.676922i	$-0.236687\pi$
$523$	4.81610e9	1.47211	0.736055	+	0.676922i	$0.236687\pi$
$524$	1.06375e9	0.322983
$525$	−1.44703e8	−0.0436436
$526$	−3.81157e8	−0.114197
$527$	−1.33542e9	−0.397449
$528$	1.09895e9	0.324906
$529$	7.30968e9	2.14686
$530$	−9.56464e7	−0.0279064
$531$	−2.98600e8	−0.0865484
$532$	1.52034e9	0.437775
$533$	−9.28030e9	−2.65471
$534$	1.87680e8	0.0533364
$535$	2.18523e9	0.616962
$536$	3.52096e9	0.987606
$537$	−1.02034e9	−0.284337
$538$	5.23754e8	0.145007
$539$	−3.97611e8	−0.109370
$540$	2.86245e8	0.0782275
$541$	1.56108e9	0.423871	0.211936	−	0.977284i	$-0.432023\pi$
$541$	1.56108e9	0.423871	0.211936	+	0.977284i	$0.432023\pi$
$542$	1.42423e9	0.384223
$543$	2.45518e8	0.0658087
$544$	2.88982e9	0.769618
$545$	5.84601e7	0.0154693
$546$	−4.47714e8	−0.117714
$547$	−3.82511e8	−0.0999282	−0.0499641	−	0.998751i	$-0.515911\pi$
$547$	−3.82511e8	−0.0999282	−0.0499641	+	0.998751i	$0.515911\pi$
$548$	−4.22002e9	−1.09543
$549$	1.03718e9	0.267516
$550$	1.80303e8	0.0462096
$551$	−2.27810e9	−0.580152
$552$	−2.33163e9	−0.590029
$553$	5.60140e8	0.140851
$554$	1.38516e9	0.346110
$555$	−8.99477e8	−0.223339
$556$	2.66217e9	0.656861
$557$	−7.35207e9	−1.80267	−0.901335	−	0.433122i	$-0.857412\pi$
$557$	−7.35207e9	−1.80267	−0.901335	+	0.433122i	$0.857412\pi$
$558$	−1.70129e8	−0.0414532
$559$	1.09763e10	2.65776
$560$	5.16354e8	0.124248
$561$	−1.78285e9	−0.426328
$562$	5.14798e8	0.122338
$563$	7.91584e9	1.86947	0.934733	−	0.355352i	$-0.115639\pi$
$563$	7.91584e9	1.86947	0.934733	+	0.355352i	$0.115639\pi$
$564$	−3.76096e8	−0.0882717
$565$	−1.81904e9	−0.424300
$566$	1.26194e8	0.0292538
$567$	1.82284e8	0.0419961
$568$	1.81555e9	0.415708
$569$	4.49464e9	1.02283	0.511414	−	0.859335i	$-0.329122\pi$
$569$	4.49464e9	1.02283	0.511414	+	0.859335i	$0.329122\pi$
$570$	−4.39032e8	−0.0992966
$571$	−2.15052e9	−0.483412	−0.241706	−	0.970350i	$-0.577707\pi$
$571$	−2.15052e9	−0.483412	−0.241706	+	0.970350i	$0.577707\pi$
$572$	−5.56721e9	−1.24380
$573$	1.44423e9	0.320697
$574$	−7.67604e8	−0.169412
$575$	1.61736e9	0.354788
$576$	−7.55624e8	−0.164751
$577$	−1.73438e9	−0.375862	−0.187931	−	0.982182i	$-0.560178\pi$
$577$	−1.73438e9	−0.375862	−0.187931	+	0.982182i	$0.560178\pi$
$578$	9.76656e7	0.0210375
$579$	2.22734e9	0.476882
$580$	−8.69577e8	−0.185059
$581$	−1.20017e9	−0.253878
$582$	1.17124e9	0.246273
$583$	−7.57385e8	−0.158298
$584$	3.70345e9	0.769418
$585$	−1.29024e9	−0.266455
$586$	2.05008e9	0.420852
$587$	−2.98775e9	−0.609692	−0.304846	−	0.952402i	$-0.598605\pi$
$587$	−2.98775e9	−0.609692	−0.304846	+	0.952402i	$0.598605\pi$
$588$	3.69563e8	0.0749666
$589$	−2.60405e9	−0.525104
$590$	1.74817e8	0.0350431
$591$	−2.03939e9	−0.406390
$592$	3.20967e9	0.635819
$593$	5.56485e9	1.09588	0.547938	−	0.836519i	$-0.315413\pi$
$593$	5.56485e9	1.09588	0.547938	+	0.836519i	$0.315413\pi$
$594$	−2.27129e8	−0.0444652
$595$	−8.37693e8	−0.163033
$596$	8.36348e9	1.61817
$597$	2.84973e7	0.00548143
$598$	5.00414e9	0.956919
$599$	−5.39399e9	−1.02545	−0.512727	−	0.858552i	$-0.671365\pi$
$599$	−5.39399e9	−1.02545	−0.512727	+	0.858552i	$0.671365\pi$
$600$	−3.51960e8	−0.0665219
$601$	−5.88616e8	−0.110604	−0.0553021	−	0.998470i	$-0.517612\pi$
$601$	−5.88616e8	−0.110604	−0.0553021	+	0.998470i	$0.517612\pi$
$602$	9.07888e8	0.169607
$603$	3.07665e9	0.571436
$604$	−7.44558e9	−1.37489
$605$	−1.00815e9	−0.185090
$606$	−1.72032e9	−0.314018
$607$	5.38304e9	0.976938	0.488469	−	0.872581i	$-0.337556\pi$
$607$	5.38304e9	0.976938	0.488469	+	0.872581i	$0.337556\pi$
$608$	5.63509e9	1.01681
$609$	−5.53757e8	−0.0993479
$610$	−6.07222e8	−0.108316
$611$	1.69523e9	0.300667
$612$	1.65708e9	0.292223
$613$	8.87502e9	1.55617	0.778086	−	0.628158i	$-0.216191\pi$
$613$	8.87502e9	1.55617	0.778086	+	0.628158i	$0.216191\pi$
$614$	−3.10330e9	−0.541046
$615$	−2.21210e9	−0.383479
$616$	−9.67106e8	−0.166702
$617$	5.94996e6	0.00101980	0.000509901	−	1.00000i	$-0.499838\pi$
$617$	5.94996e6	0.00101980	0.000509901		1.00000i	$0.499838\pi$
$618$	4.89310e8	0.0833920
$619$	8.21425e9	1.39204	0.696019	−	0.718024i	$-0.254953\pi$
$619$	8.21425e9	1.39204	0.696019	+	0.718024i	$0.254953\pi$
$620$	−9.93996e8	−0.167500
$621$	−2.03740e9	−0.341395
$622$	−2.20522e9	−0.367439
$623$	6.98291e8	0.115699
$624$	4.60403e9	0.758564
$625$	2.44141e8	0.0400000
$626$	3.06134e9	0.498772
$627$	−3.47652e9	−0.563259
$628$	−6.98631e8	−0.112561
$629$	−5.20711e9	−0.834295
$630$	−1.06719e8	−0.0170040
$631$	2.53051e9	0.400964	0.200482	−	0.979697i	$-0.435749\pi$
$631$	2.53051e9	0.400964	0.200482	+	0.979697i	$0.435749\pi$
$632$	1.36243e9	0.214686
$633$	−3.09080e8	−0.0484348
$634$	−2.89299e9	−0.450852
$635$	2.55126e8	0.0395409
$636$	7.03958e8	0.108504
$637$	−1.66579e9	−0.255347
$638$	6.89990e8	0.105189
$639$	1.58645e9	0.240532
$640$	2.80891e9	0.423553
$641$	6.96698e9	1.04482	0.522410	−	0.852694i	$-0.325033\pi$
$641$	6.96698e9	1.04482	0.522410	+	0.852694i	$0.325033\pi$
$642$	1.61162e9	0.240375
$643$	1.21823e10	1.80714	0.903572	−	0.428437i	$-0.140936\pi$
$643$	1.21823e10	1.80714	0.903572	+	0.428437i	$0.140936\pi$
$644$	−4.13063e9	−0.609419
$645$	2.61638e9	0.383920
$646$	−2.54158e9	−0.370928
$647$	−9.95454e9	−1.44496	−0.722481	−	0.691391i	$-0.756998\pi$
$647$	−9.95454e9	−1.44496	−0.722481	+	0.691391i	$0.756998\pi$
$648$	4.43369e8	0.0640107
$649$	1.38431e9	0.198781
$650$	7.55376e8	0.107886
$651$	−6.32988e8	−0.0899213
$652$	−1.14367e10	−1.61598
$653$	2.38576e9	0.335297	0.167649	−	0.985847i	$-0.446383\pi$
$653$	2.38576e9	0.335297	0.167649	+	0.985847i	$0.446383\pi$
$654$	4.31147e7	0.00602702
$655$	−1.14291e9	−0.158916
$656$	7.89358e9	1.09172
$657$	3.23612e9	0.445190
$658$	1.40218e8	0.0191873
$659$	1.98573e8	0.0270284	0.0135142	−	0.999909i	$-0.495698\pi$
$659$	1.98573e8	0.0270284	0.0135142	+	0.999909i	$0.495698\pi$
$660$	−1.32703e9	−0.179670
$661$	1.68735e9	0.227247	0.113624	−	0.993524i	$-0.463754\pi$
$661$	1.68735e9	0.227247	0.113624	+	0.993524i	$0.463754\pi$
$662$	−2.53484e9	−0.339584
$663$	−7.46923e9	−0.995356
$664$	−2.91916e9	−0.386963
$665$	−1.63348e9	−0.215397
$666$	−6.63370e8	−0.0870154
$667$	6.18938e9	0.807620
$668$	−6.75704e9	−0.877079
$669$	−7.60314e9	−0.981752
$670$	−1.80124e9	−0.231372
$671$	−4.80834e9	−0.614421
$672$	1.36977e9	0.174123
$673$	−5.02352e9	−0.635266	−0.317633	−	0.948214i	$-0.602888\pi$
$673$	−5.02352e9	−0.635266	−0.317633	+	0.948214i	$0.602888\pi$
$674$	2.47376e9	0.311206
$675$	−3.07547e8	−0.0384900
$676$	−1.60235e10	−1.99501
$677$	−1.03907e10	−1.28702	−0.643510	−	0.765438i	$-0.722523\pi$
$677$	−1.03907e10	−1.28702	−0.643510	+	0.765438i	$0.722523\pi$
$678$	−1.34155e9	−0.165312
$679$	4.35778e9	0.534222
$680$	−2.03751e9	−0.248496
$681$	1.08081e9	0.131140
$682$	7.88714e8	0.0952082
$683$	3.61608e9	0.434276	0.217138	−	0.976141i	$-0.430328\pi$
$683$	3.61608e9	0.434276	0.217138	+	0.976141i	$0.430328\pi$
$684$	3.23128e9	0.386081
$685$	4.53407e9	0.538978
$686$	−1.37783e8	−0.0162952
$687$	3.36398e9	0.395826
$688$	−9.33619e9	−1.09297
$689$	−3.17306e9	−0.369582
$690$	1.19281e9	0.138229
$691$	1.65856e10	1.91231	0.956153	−	0.292869i	$-0.0946100\pi$
$691$	1.65856e10	1.91231	0.956153	+	0.292869i	$0.0946100\pi$
$692$	2.69618e9	0.309298
$693$	−8.45068e8	−0.0964551
$694$	−1.74081e9	−0.197694
$695$	−2.86028e9	−0.323193
$696$	−1.34690e9	−0.151427
$697$	−1.28059e10	−1.43251
$698$	2.99117e9	0.332926
$699$	8.68008e9	0.961289
$700$	−6.23520e8	−0.0687080
$701$	1.42971e10	1.56760	0.783798	−	0.621015i	$-0.213280\pi$
$701$	1.42971e10	1.56760	0.783798	+	0.621015i	$0.213280\pi$
$702$	−9.51556e8	−0.103814
$703$	−1.01538e10	−1.10226
$704$	3.50306e9	0.378394
$705$	4.04084e8	0.0434320
$706$	−4.32499e9	−0.462561
$707$	−6.40069e9	−0.681175
$708$	−1.28666e9	−0.136253
$709$	4.66391e9	0.491460	0.245730	−	0.969338i	$-0.420972\pi$
$709$	4.66391e9	0.491460	0.245730	+	0.969338i	$0.420972\pi$
$710$	−9.28795e8	−0.0973903
$711$	1.19050e9	0.124219
$712$	1.69845e9	0.176349
$713$	7.07496e9	0.730989
$714$	−6.17804e8	−0.0635195
$715$	5.98151e9	0.611984
$716$	−4.39659e9	−0.447631
$717$	7.96705e9	0.807199
$718$	−5.68694e9	−0.573380
$719$	4.82173e9	0.483784	0.241892	−	0.970303i	$-0.422232\pi$
$719$	4.82173e9	0.483784	0.241892	+	0.970303i	$0.422232\pi$
$720$	1.09744e9	0.109576
$721$	1.82055e9	0.180896
$722$	−1.90400e9	−0.188273
$723$	−2.72394e9	−0.268048
$724$	1.05793e9	0.103603
$725$	9.34289e8	0.0910539
$726$	−7.43521e8	−0.0721132
$727$	2.17621e9	0.210054	0.105027	−	0.994469i	$-0.466507\pi$
$727$	2.17621e9	0.210054	0.105027	+	0.994469i	$0.466507\pi$
$728$	−4.05168e9	−0.389203
$729$	3.87420e8	0.0370370
$730$	−1.89461e9	−0.180256
$731$	1.51463e10	1.43416
$732$	4.46916e9	0.421150
$733$	4.65228e9	0.436317	0.218158	−	0.975913i	$-0.429995\pi$
$733$	4.65228e9	0.436317	0.218158	+	0.975913i	$0.429995\pi$
$734$	−5.72166e9	−0.534055
$735$	−3.97065e8	−0.0368856
$736$	−1.53100e10	−1.41548
$737$	−1.42633e10	−1.31245
$738$	−1.63144e9	−0.149408
$739$	4.05338e8	0.0369456	0.0184728	−	0.999829i	$-0.494120\pi$
$739$	4.05338e8	0.0369456	0.0184728	+	0.999829i	$0.494120\pi$
$740$	−3.87581e9	−0.351603
$741$	−1.45648e10	−1.31505
$742$	−2.62454e8	−0.0235852
$743$	1.08140e10	0.967223	0.483611	−	0.875283i	$-0.339325\pi$
$743$	1.08140e10	0.967223	0.483611	+	0.875283i	$0.339325\pi$
$744$	−1.53961e9	−0.137059
$745$	−8.98588e9	−0.796184
$746$	−5.04282e9	−0.444721
$747$	−2.55079e9	−0.223899
$748$	−7.68222e9	−0.671168
$749$	5.99626e9	0.521428
$750$	1.80055e8	0.0155844
$751$	−1.42070e10	−1.22394	−0.611972	−	0.790880i	$-0.709623\pi$
$751$	−1.42070e10	−1.22394	−0.611972	+	0.790880i	$0.709623\pi$
$752$	−1.44192e9	−0.123646
$753$	2.51198e9	0.214405
$754$	2.89071e9	0.245587
$755$	7.99967e9	0.676485
$756$	7.85456e8	0.0661143
$757$	3.78427e9	0.317064	0.158532	−	0.987354i	$-0.449324\pi$
$757$	3.78427e9	0.317064	0.158532	+	0.987354i	$0.449324\pi$
$758$	5.60911e9	0.467791
$759$	9.44538e9	0.784103
$760$	−3.97311e9	−0.328309
$761$	1.01511e10	0.834966	0.417483	−	0.908685i	$-0.362912\pi$
$761$	1.01511e10	0.834966	0.417483	+	0.908685i	$0.362912\pi$
$762$	1.88157e8	0.0154056
$763$	1.60414e8	0.0130740
$764$	6.22314e9	0.504874
$765$	−1.78040e9	−0.143782
$766$	6.47993e9	0.520919
$767$	5.79954e9	0.464098
$768$	−1.51063e9	−0.120336
$769$	−1.31076e10	−1.03939	−0.519696	−	0.854351i	$-0.673955\pi$
$769$	−1.31076e10	−1.03939	−0.519696	+	0.854351i	$0.673955\pi$
$770$	4.94750e8	0.0390543
$771$	−9.84378e9	−0.773520
$772$	9.59751e9	0.750755
$773$	−1.40370e10	−1.09307	−0.546533	−	0.837438i	$-0.684053\pi$
$773$	−1.40370e10	−1.09307	−0.546533	+	0.837438i	$0.684053\pi$
$774$	1.92959e9	0.149580
$775$	1.06797e9	0.0824142
$776$	1.05994e10	0.814265
$777$	−2.46817e9	−0.188756
$778$	−3.59985e9	−0.274066
$779$	−2.49713e10	−1.89261
$780$	−5.55958e9	−0.419479
$781$	−7.35474e9	−0.552445
$782$	6.90524e9	0.516363
$783$	−1.17694e9	−0.0876166
$784$	1.41687e9	0.105009
$785$	7.50622e8	0.0553831
$786$	−8.42905e8	−0.0619155
$787$	−3.87288e9	−0.283219	−0.141610	−	0.989923i	$-0.545228\pi$
$787$	−3.87288e9	−0.283219	−0.141610	+	0.989923i	$0.545228\pi$
$788$	−8.78764e9	−0.639780
$789$	−3.01409e9	−0.218467
$790$	−6.96987e8	−0.0502956
$791$	−4.99145e9	−0.358599
$792$	−2.05545e9	−0.147018
$793$	−2.01445e10	−1.43450
$794$	−1.01355e9	−0.0718578
$795$	−7.56346e8	−0.0533870
$796$	1.22794e8	0.00862942
$797$	−8.56688e9	−0.599403	−0.299701	−	0.954033i	$-0.596887\pi$
$797$	−8.56688e9	−0.599403	−0.299701	+	0.954033i	$0.596887\pi$
$798$	−1.20470e9	−0.0839210
$799$	2.33926e9	0.162243
$800$	−2.31106e9	−0.159586
$801$	1.48412e9	0.102037
$802$	2.66302e9	0.182290
$803$	−1.50026e10	−1.02250
$804$	1.32572e10	0.899611
$805$	4.43803e9	0.299850
$806$	3.30431e9	0.222284
$807$	4.14170e9	0.277410
$808$	−1.55684e10	−1.03825
$809$	−1.49503e10	−0.992731	−0.496365	−	0.868114i	$-0.665332\pi$
$809$	−1.49503e10	−0.992731	−0.496365	+	0.868114i	$0.665332\pi$
$810$	−2.26818e8	−0.0149961
$811$	−8.61940e9	−0.567419	−0.283710	−	0.958910i	$-0.591565\pi$
$811$	−8.61940e9	−0.567419	−0.283710	+	0.958910i	$0.591565\pi$
$812$	−2.38612e9	−0.156403
$813$	1.12625e10	0.735049
$814$	3.07538e9	0.199854
$815$	1.22878e10	0.795104
$816$	6.35313e9	0.409329
$817$	2.95350e10	1.89478
$818$	−2.98810e9	−0.190879
$819$	−3.54041e9	−0.225195
$820$	−9.53186e9	−0.603711
$821$	2.53165e10	1.59663	0.798313	−	0.602243i	$-0.205726\pi$
$821$	2.53165e10	1.59663	0.798313	+	0.602243i	$0.205726\pi$
$822$	3.34390e9	0.209992
$823$	1.51790e9	0.0949171	0.0474586	−	0.998873i	$-0.484888\pi$
$823$	1.51790e9	0.0949171	0.0474586	+	0.998873i	$0.484888\pi$
$824$	4.42811e9	0.275723
$825$	1.42578e9	0.0884025
$826$	4.79699e8	0.0296168
$827$	1.68322e10	1.03484	0.517418	−	0.855733i	$-0.326893\pi$
$827$	1.68322e10	1.03484	0.517418	+	0.855733i	$0.326893\pi$
$828$	−8.77910e9	−0.537457
$829$	−1.54259e10	−0.940396	−0.470198	−	0.882561i	$-0.655818\pi$
$829$	−1.54259e10	−0.940396	−0.470198	+	0.882561i	$0.655818\pi$
$830$	1.49338e9	0.0906559
$831$	1.09534e10	0.662135
$832$	1.46761e10	0.883442
$833$	−2.29863e9	−0.137788
$834$	−2.10948e9	−0.125920
$835$	7.25988e9	0.431546
$836$	−1.49802e10	−0.886737
$837$	−1.34533e9	−0.0793031
$838$	−3.65536e9	−0.214574
$839$	−1.06044e9	−0.0619894	−0.0309947	−	0.999520i	$-0.509868\pi$
$839$	−1.06044e9	−0.0619894	−0.0309947	+	0.999520i	$0.509868\pi$
$840$	−9.65780e8	−0.0562212
$841$	−1.36745e10	−0.792730
$842$	−8.67880e9	−0.501034
$843$	4.07089e9	0.234041
$844$	−1.33181e9	−0.0762509
$845$	1.72159e10	0.981595
$846$	2.98015e8	0.0169216
$847$	−2.76638e9	−0.156430
$848$	2.69892e9	0.151986
$849$	9.97911e8	0.0559648
$850$	1.04235e9	0.0582165
$851$	2.75869e10	1.53444
$852$	6.83594e9	0.378669
$853$	3.03756e10	1.67573	0.837864	−	0.545878i	$-0.183804\pi$
$853$	3.03756e10	1.67573	0.837864	+	0.545878i	$0.183804\pi$
$854$	−1.66622e9	−0.0915438
$855$	−3.47175e9	−0.189962
$856$	1.45847e10	0.794764
$857$	−1.27509e10	−0.692001	−0.346001	−	0.938234i	$-0.612461\pi$
$857$	−1.27509e10	−0.692001	−0.346001	+	0.938234i	$0.612461\pi$
$858$	4.41140e9	0.238436
$859$	1.08205e10	0.582467	0.291233	−	0.956652i	$-0.405934\pi$
$859$	1.08205e10	0.582467	0.291233	+	0.956652i	$0.405934\pi$
$860$	1.12739e10	0.604405
$861$	−6.07000e9	−0.324099
$862$	−3.04476e9	−0.161912
$863$	6.05794e9	0.320839	0.160419	−	0.987049i	$-0.448715\pi$
$863$	6.05794e9	0.320839	0.160419	+	0.987049i	$0.448715\pi$
$864$	2.91127e9	0.153562
$865$	−2.89682e9	−0.152183
$866$	3.54981e9	0.185734
$867$	7.72313e8	0.0402464
$868$	−2.72752e9	−0.141563
$869$	−5.51915e9	−0.285301
$870$	6.89044e8	0.0354756
$871$	−5.97560e10	−3.06421
$872$	3.90175e8	0.0199274
$873$	9.26188e9	0.471139
$874$	1.34651e10	0.682211
$875$	6.69922e8	0.0338062
$876$	1.39443e10	0.700863
$877$	5.64172e9	0.282431	0.141216	−	0.989979i	$-0.454899\pi$
$877$	5.64172e9	0.282431	0.141216	+	0.989979i	$0.454899\pi$
$878$	5.32407e9	0.265468
$879$	1.62115e10	0.805123
$880$	−5.08772e9	−0.251671
$881$	−1.41128e9	−0.0695339	−0.0347669	−	0.999395i	$-0.511069\pi$
$881$	−1.41128e9	−0.0695339	−0.0347669	+	0.999395i	$0.511069\pi$
$882$	−2.92838e8	−0.0143710
$883$	1.83461e10	0.896773	0.448386	−	0.893840i	$-0.351999\pi$
$883$	1.83461e10	0.896773	0.448386	+	0.893840i	$0.351999\pi$
$884$	−3.21846e10	−1.56699
$885$	1.38241e9	0.0670401
$886$	9.55923e8	0.0461748
$887$	6.77821e9	0.326124	0.163062	−	0.986616i	$-0.447863\pi$
$887$	6.77821e9	0.326124	0.163062	+	0.986616i	$0.447863\pi$
$888$	−6.00330e9	−0.287703
$889$	7.00065e8	0.0334182
$890$	−8.68889e8	−0.0413142
$891$	−1.79608e9	−0.0850654
$892$	−3.27617e10	−1.54557
$893$	4.56151e9	0.214353
$894$	−6.62714e9	−0.310202
$895$	4.72378e9	0.220246
$896$	7.70764e9	0.357967
$897$	3.95714e10	1.83066
$898$	−2.11163e9	−0.0973085
$899$	4.08695e9	0.187603
$900$	−1.32521e9	−0.0605948
$901$	−4.37852e9	−0.199430
$902$	7.56332e9	0.343155
$903$	7.17934e9	0.324472
$904$	−1.21407e10	−0.546579
$905$	−1.13666e9	−0.0509752
$906$	5.89981e9	0.263566
$907$	−3.32813e9	−0.148107	−0.0740535	−	0.997254i	$-0.523594\pi$
$907$	−3.32813e9	−0.148107	−0.0740535	+	0.997254i	$0.523594\pi$
$908$	4.65718e9	0.206454
$909$	−1.36038e10	−0.600740
$910$	2.07275e9	0.0911806
$911$	7.48533e9	0.328017	0.164009	−	0.986459i	$-0.447558\pi$
$911$	7.48533e9	0.328017	0.164009	+	0.986459i	$0.447558\pi$
$912$	1.23885e10	0.540799
$913$	1.18254e10	0.514244
$914$	−3.09797e9	−0.134204
$915$	−4.80174e9	−0.207217
$916$	1.44953e10	0.623149
$917$	−3.13615e9	−0.134309
$918$	−1.31306e9	−0.0560189
$919$	3.84326e10	1.63341	0.816705	−	0.577056i	$-0.195799\pi$
$919$	3.84326e10	1.63341	0.816705	+	0.577056i	$0.195799\pi$
$920$	1.07946e10	0.457034
$921$	−2.45400e10	−1.03506
$922$	8.25354e9	0.346802
$923$	−3.08127e10	−1.28980
$924$	−3.64136e9	−0.151849
$925$	4.16425e9	0.172998
$926$	1.07326e9	0.0444189
$927$	3.86933e9	0.159535
$928$	−8.84406e9	−0.363274
$929$	2.74203e10	1.12206	0.561032	−	0.827794i	$-0.310404\pi$
$929$	2.74203e10	1.12206	0.561032	+	0.827794i	$0.310404\pi$
$930$	7.87633e8	0.0321095
$931$	−4.48228e9	−0.182043
$932$	3.74022e10	1.51336
$933$	−1.74383e10	−0.702939
$934$	−1.61955e8	−0.00650400
$935$	8.25392e9	0.330233
$936$	−8.61130e9	−0.343244
$937$	−2.33959e9	−0.0929077	−0.0464539	−	0.998920i	$-0.514792\pi$
$937$	−2.33959e9	−0.0929077	−0.0464539	+	0.998920i	$0.514792\pi$
$938$	−4.94261e9	−0.195545
$939$	2.42083e10	0.954189
$940$	1.74118e9	0.0683750
$941$	−4.04198e10	−1.58136	−0.790680	−	0.612230i	$-0.790273\pi$
$941$	−4.04198e10	−1.58136	−0.790680	+	0.612230i	$0.790273\pi$
$942$	5.53588e8	0.0215779
$943$	6.78449e10	2.63467
$944$	−4.93294e9	−0.190855
$945$	−8.43909e8	−0.0325300
$946$	−8.94557e9	−0.343549
$947$	2.68103e10	1.02583	0.512917	−	0.858438i	$-0.328565\pi$
$947$	2.68103e10	1.02583	0.512917	+	0.858438i	$0.328565\pi$
$948$	5.12983e9	0.195557
$949$	−6.28533e10	−2.38724
$950$	2.03256e9	0.0769148
$951$	−2.28770e10	−0.862514
$952$	−5.59094e9	−0.210018
$953$	−6.72263e9	−0.251602	−0.125801	−	0.992056i	$-0.540150\pi$
$953$	−6.72263e9	−0.251602	−0.125801	+	0.992056i	$0.540150\pi$
$954$	−5.57810e8	−0.0208002
$955$	−6.68625e9	−0.248411
$956$	3.43297e10	1.27077
$957$	5.45626e9	0.201235
$958$	7.12902e9	0.261970
$959$	1.24415e10	0.455520
$960$	3.49826e9	0.127615
$961$	−2.28409e10	−0.830198
$962$	1.28843e10	0.466602
$963$	1.27442e10	0.459856
$964$	−1.17373e10	−0.421988
$965$	−1.03117e10	−0.369391
$966$	3.27307e9	0.116825
$967$	2.39023e10	0.850055	0.425027	−	0.905180i	$-0.360264\pi$
$967$	2.39023e10	0.850055	0.425027	+	0.905180i	$0.360264\pi$
$968$	−6.72864e9	−0.238431
$969$	−2.00981e10	−0.709614
$970$	−5.42242e9	−0.190762
$971$	1.65771e10	0.581088	0.290544	−	0.956862i	$-0.406164\pi$
$971$	1.65771e10	0.581088	0.290544	+	0.956862i	$0.406164\pi$
$972$	1.66938e9	0.0583074
$973$	−7.84862e9	−0.273148
$974$	7.48681e9	0.259621
$975$	5.97331e9	0.206395
$976$	1.71344e10	0.589921
$977$	−2.03177e10	−0.697018	−0.348509	−	0.937305i	$-0.613312\pi$
$977$	−2.03177e10	−0.697018	−0.348509	+	0.937305i	$0.613312\pi$
$978$	9.06236e9	0.309781
$979$	−6.88038e9	−0.234354
$980$	−1.71094e9	−0.0580689
$981$	3.40939e8	0.0115302
$982$	−7.47841e9	−0.252011
$983$	4.78793e10	1.60772	0.803861	−	0.594818i	$-0.202776\pi$
$983$	4.78793e10	1.60772	0.803861	+	0.594818i	$0.202776\pi$
$984$	−1.47640e10	−0.493994
$985$	9.44160e9	0.314788
$986$	3.98891e9	0.132521
$987$	1.10881e9	0.0367067
$988$	−6.27594e10	−2.07028
$989$	−8.02440e10	−2.63770
$990$	1.05152e9	0.0344426
$991$	−1.99787e10	−0.652092	−0.326046	−	0.945354i	$-0.605716\pi$
$991$	−1.99787e10	−0.652092	−0.326046	+	0.945354i	$0.605716\pi$
$992$	−1.01095e10	−0.328804
$993$	−2.00448e10	−0.649650
$994$	−2.54861e9	−0.0823098
$995$	−1.31932e8	−0.00424590
$996$	−1.09913e10	−0.352484
$997$	4.49634e10	1.43690	0.718450	−	0.695579i	$-0.244852\pi$
$997$	4.49634e10	1.43690	0.718450	+	0.695579i	$0.244852\pi$
$998$	−2.24235e9	−0.0714080
$999$	−5.24575e9	−0.166467

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.8.a.h.1.2	✓	4
3.2	odd	2		315.8.a.g.1.3		4
5.4	even	2		525.8.a.i.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.8.a.h.1.2	✓	4	1.1	even	1	trivial
315.8.a.g.1.3		4	3.2	odd	2
525.8.a.i.1.3		4	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	105.a (trivial)

\(f(q)\)	\(=\)	\(q-3.41438 q^{2} -27.0000 q^{3} -116.342 q^{4} +125.000 q^{5} +92.1883 q^{6} +343.000 q^{7} +834.277 q^{8} +729.000 q^{9} -426.798 q^{10} -3379.63 q^{11} +3141.23 q^{12} -14159.0 q^{13} -1171.13 q^{14} -3375.00 q^{15} +12043.2 q^{16} -19538.0 q^{17} -2489.08 q^{18} -38098.7 q^{19} -14542.8 q^{20} -9261.00 q^{21} +11539.4 q^{22} +103511. q^{23} -22525.5 q^{24} +15625.0 q^{25} +48344.1 q^{26} -19683.0 q^{27} -39905.3 q^{28} +59794.5 q^{29} +11523.5 q^{30} +68349.9 q^{31} -147908. q^{32} +91250.1 q^{33} +66710.3 q^{34} +42875.0 q^{35} -84813.3 q^{36} +266512. q^{37} +130084. q^{38} +382292. q^{39} +104285. q^{40} +655437. q^{41} +31620.6 q^{42} -775223. q^{43} +393193. q^{44} +91125.0 q^{45} -353426. q^{46} -119729. q^{47} -325167. q^{48} +117649. q^{49} -53349.7 q^{50} +527527. q^{51} +1.64728e6 q^{52} +224102. q^{53} +67205.3 q^{54} -422454. q^{55} +286157. q^{56} +1.02867e6 q^{57} -204161. q^{58} -409602. q^{59} +392654. q^{60} +1.42274e6 q^{61} -233373. q^{62} +250047. q^{63} -1.03652e6 q^{64} -1.76987e6 q^{65} -311563. q^{66} +4.22037e6 q^{67} +2.27309e6 q^{68} -2.79479e6 q^{69} -146392. q^{70} +2.17619e6 q^{71} +608188. q^{72} +4.43912e6 q^{73} -909973. q^{74} -421875. q^{75} +4.43248e6 q^{76} -1.15921e6 q^{77} -1.30529e6 q^{78} +1.63306e6 q^{79} +1.50540e6 q^{80} +531441. q^{81} -2.23791e6 q^{82} -3.49903e6 q^{83} +1.07744e6 q^{84} -2.44225e6 q^{85} +2.64691e6 q^{86} -1.61445e6 q^{87} -2.81955e6 q^{88} +2.03583e6 q^{89} -311135. q^{90} -4.85652e6 q^{91} -1.20427e7 q^{92} -1.84545e6 q^{93} +408799. q^{94} -4.76234e6 q^{95} +3.99351e6 q^{96} +1.27049e7 q^{97} -401698. q^{98} -2.46375e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 11 q^{2} - 108 q^{3} + 141 q^{4} + 500 q^{5} - 297 q^{6} + 1372 q^{7} + 2133 q^{8} + 2916 q^{9} + 1375 q^{10} - 2708 q^{11} - 3807 q^{12} - 2212 q^{13} + 3773 q^{14} - 13500 q^{15} - 9599 q^{16} - 17016 q^{17}+ \cdots - 1974132 q^{99}+O(q^{100}) \) 4 * q + 11 * q^2 - 108 * q^3 + 141 * q^4 + 500 * q^5 - 297 * q^6 + 1372 * q^7 + 2133 * q^8 + 2916 * q^9 + 1375 * q^10 - 2708 * q^11 - 3807 * q^12 - 2212 * q^13 + 3773 * q^14 - 13500 * q^15 - 9599 * q^16 - 17016 * q^17 + 8019 * q^18 + 32668 * q^19 + 17625 * q^20 - 37044 * q^21 - 7196 * q^22 + 87696 * q^23 - 57591 * q^24 + 62500 * q^25 + 67354 * q^26 - 78732 * q^27 + 48363 * q^28 + 200488 * q^29 - 37125 * q^30 + 258852 * q^31 + 39445 * q^32 + 73116 * q^33 + 225518 * q^34 + 171500 * q^35 + 102789 * q^36 + 666856 * q^37 + 846556 * q^38 + 59724 * q^39 + 266625 * q^40 + 833000 * q^41 - 101871 * q^42 + 1051896 * q^43 + 1918236 * q^44 + 364500 * q^45 + 1786160 * q^46 + 529824 * q^47 + 259173 * q^48 + 470596 * q^49 + 171875 * q^50 + 459432 * q^51 + 211718 * q^52 + 791764 * q^53 - 216513 * q^54 - 338500 * q^55 + 731619 * q^56 - 882036 * q^57 + 3500242 * q^58 - 3825904 * q^59 - 475875 * q^60 + 212432 * q^61 + 882400 * q^62 + 1000188 * q^63 - 1515063 * q^64 - 276500 * q^65 + 194292 * q^66 + 5165272 * q^67 + 7423202 * q^68 - 2367792 * q^69 + 471625 * q^70 - 623260 * q^71 + 1554957 * q^72 - 2083228 * q^73 + 1059642 * q^74 - 1687500 * q^75 + 6990964 * q^76 - 928844 * q^77 - 1818558 * q^78 - 1325016 * q^79 - 1199875 * q^80 + 2125764 * q^81 + 11798982 * q^82 + 11447616 * q^83 - 1305801 * q^84 - 2127000 * q^85 + 7525948 * q^86 - 5413176 * q^87 + 19484572 * q^88 - 5805808 * q^89 + 1002375 * q^90 - 758716 * q^91 - 2716288 * q^92 - 6989004 * q^93 - 15552560 * q^94 + 4083500 * q^95 - 1065015 * q^96 + 5857516 * q^97 + 1294139 * q^98 - 1974132 * q^99

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