LMFDB - Embedded newform 289.10.a.e.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,10,Mod(1,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, 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("289.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	289.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:	$148.845356651$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5 x^{11} - 4542 x^{10} + 30079 x^{9} + 7481825 x^{8} - 58373994 x^{7} - 5553197164 x^{6} + \cdots + 245077910606835 $ x^12 - 5x^11 - 4542x^10 + 30079x^9 + 7481825x^8 - 58373994x^7 - 5553197164x^6 + 45662797046x^5 + 1825619566875x^4 - 13493392282513x^3 - 214257360688838x^2 + 1064197876989579*x + 245077910606835
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{5}\cdot 17 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-14.2275$ of defining polynomial
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-13.2275 q^{2} +162.576 q^{3} -337.033 q^{4} +1690.93 q^{5} -2150.48 q^{6} -10426.0 q^{7} +11230.6 q^{8} +6748.01 q^{9} +O(q^{10})$	\(q-13.2275 q^{2} +162.576 q^{3} -337.033 q^{4} +1690.93 q^{5} -2150.48 q^{6} -10426.0 q^{7} +11230.6 q^{8} +6748.01 q^{9} -22366.8 q^{10} +27908.0 q^{11} -54793.5 q^{12} -147572. q^{13} +137910. q^{14} +274906. q^{15} +24008.3 q^{16} -89259.3 q^{18} -505938. q^{19} -569901. q^{20} -1.69502e6 q^{21} -369153. q^{22} +1.59404e6 q^{23} +1.82583e6 q^{24} +906135. q^{25} +1.95201e6 q^{26} -2.10292e6 q^{27} +3.51390e6 q^{28} +3.23512e6 q^{29} -3.63632e6 q^{30} -5.16741e6 q^{31} -6.06763e6 q^{32} +4.53717e6 q^{33} -1.76296e7 q^{35} -2.27430e6 q^{36} -1.45073e7 q^{37} +6.69229e6 q^{38} -2.39917e7 q^{39} +1.89902e7 q^{40} +3.32642e7 q^{41} +2.24208e7 q^{42} +2.69905e6 q^{43} -9.40592e6 q^{44} +1.14104e7 q^{45} -2.10851e7 q^{46} +9.23270e6 q^{47} +3.90317e6 q^{48} +6.83475e7 q^{49} -1.19859e7 q^{50} +4.97366e7 q^{52} +6.19599e7 q^{53} +2.78164e7 q^{54} +4.71906e7 q^{55} -1.17090e8 q^{56} -8.22534e7 q^{57} -4.27926e7 q^{58} +9.85359e7 q^{59} -9.26523e7 q^{60} -2.07595e8 q^{61} +6.83519e7 q^{62} -7.03546e7 q^{63} +6.79674e7 q^{64} -2.49534e8 q^{65} -6.00155e7 q^{66} +5.69266e7 q^{67} +2.59152e8 q^{69} +2.33196e8 q^{70} +1.84556e8 q^{71} +7.57841e7 q^{72} +3.74402e8 q^{73} +1.91895e8 q^{74} +1.47316e8 q^{75} +1.70518e8 q^{76} -2.90968e8 q^{77} +3.17350e8 q^{78} -1.08255e8 q^{79} +4.05964e7 q^{80} -4.74706e8 q^{81} -4.40002e8 q^{82} +4.94434e8 q^{83} +5.71276e8 q^{84} -3.57017e7 q^{86} +5.25954e8 q^{87} +3.13423e8 q^{88} -1.69740e8 q^{89} -1.50932e8 q^{90} +1.53858e9 q^{91} -5.37243e8 q^{92} -8.40098e8 q^{93} -1.22126e8 q^{94} -8.55507e8 q^{95} -9.86452e8 q^{96} -7.68005e8 q^{97} -9.04066e8 q^{98} +1.88323e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 17 q^{2} + 74 q^{3} + 2987 q^{4} + 454 q^{5} + 2674 q^{6} - 5524 q^{7} - 12036 q^{8} + 71898 q^{9}+O(q^{10}) $ 12 * q + 17 * q^2 + 74 * q^3 + 2987 * q^4 + 454 * q^5 + 2674 * q^6 - 5524 * q^7 - 12036 * q^8 + 71898 * q^9	\( 12 q + 17 q^{2} + 74 q^{3} + 2987 q^{4} + 454 q^{5} + 2674 q^{6} - 5524 q^{7} - 12036 q^{8} + 71898 q^{9} - 2449 q^{10} + 152886 q^{11} + 41717 q^{12} + 23478 q^{13} + 492839 q^{14} - 149346 q^{15} + 272743 q^{16} + 1610378 q^{18} + 1053982 q^{19} - 2477218 q^{20} - 1395256 q^{21} + 2391095 q^{22} + 2012428 q^{23} + 708393 q^{24} + 6123166 q^{25} - 733144 q^{26} + 3231638 q^{27} - 5978216 q^{28} + 12772842 q^{29} + 181633 q^{30} + 5535814 q^{31} - 5277485 q^{32} - 16526054 q^{33} + 23712622 q^{35} - 37692723 q^{36} + 1352872 q^{37} + 3704404 q^{38} - 1380780 q^{39} + 44739331 q^{40} + 40941240 q^{41} - 73649073 q^{42} - 14142490 q^{43} + 148233417 q^{44} - 79449336 q^{45} + 31855859 q^{46} + 133558002 q^{47} - 80444894 q^{48} + 184488050 q^{49} + 103322437 q^{50} + 179597031 q^{52} - 299319258 q^{53} - 50215469 q^{54} - 91197532 q^{55} + 267350757 q^{56} + 49507694 q^{57} + 367048088 q^{58} - 106431852 q^{59} + 103650215 q^{60} + 262041240 q^{61} - 314328847 q^{62} + 218532626 q^{63} + 595820098 q^{64} + 330279796 q^{65} - 117450322 q^{66} - 489635100 q^{67} + 661586712 q^{69} - 226277420 q^{70} + 204290852 q^{71} - 208030791 q^{72} + 673538852 q^{73} + 1274510282 q^{74} + 588895258 q^{75} - 403517977 q^{76} - 705301770 q^{77} + 165043245 q^{78} + 434002980 q^{79} + 599590757 q^{80} - 389011392 q^{81} - 180073450 q^{82} + 411781442 q^{83} - 475971445 q^{84} + 492988379 q^{86} + 1513399800 q^{87} - 262108460 q^{88} + 911678128 q^{89} - 2734590475 q^{90} - 560105446 q^{91} - 847049266 q^{92} - 1228562570 q^{93} + 2009871759 q^{94} - 1116511966 q^{95} + 2204198979 q^{96} - 3589270998 q^{97} - 2677144485 q^{98} + 2056683494 q^{99}+O(q^{100}) \) 12 * q + 17 * q^2 + 74 * q^3 + 2987 * q^4 + 454 * q^5 + 2674 * q^6 - 5524 * q^7 - 12036 * q^8 + 71898 * q^9 - 2449 * q^10 + 152886 * q^11 + 41717 * q^12 + 23478 * q^13 + 492839 * q^14 - 149346 * q^15 + 272743 * q^16 + 1610378 * q^18 + 1053982 * q^19 - 2477218 * q^20 - 1395256 * q^21 + 2391095 * q^22 + 2012428 * q^23 + 708393 * q^24 + 6123166 * q^25 - 733144 * q^26 + 3231638 * q^27 - 5978216 * q^28 + 12772842 * q^29 + 181633 * q^30 + 5535814 * q^31 - 5277485 * q^32 - 16526054 * q^33 + 23712622 * q^35 - 37692723 * q^36 + 1352872 * q^37 + 3704404 * q^38 - 1380780 * q^39 + 44739331 * q^40 + 40941240 * q^41 - 73649073 * q^42 - 14142490 * q^43 + 148233417 * q^44 - 79449336 * q^45 + 31855859 * q^46 + 133558002 * q^47 - 80444894 * q^48 + 184488050 * q^49 + 103322437 * q^50 + 179597031 * q^52 - 299319258 * q^53 - 50215469 * q^54 - 91197532 * q^55 + 267350757 * q^56 + 49507694 * q^57 + 367048088 * q^58 - 106431852 * q^59 + 103650215 * q^60 + 262041240 * q^61 - 314328847 * q^62 + 218532626 * q^63 + 595820098 * q^64 + 330279796 * q^65 - 117450322 * q^66 - 489635100 * q^67 + 661586712 * q^69 - 226277420 * q^70 + 204290852 * q^71 - 208030791 * q^72 + 673538852 * q^73 + 1274510282 * q^74 + 588895258 * q^75 - 403517977 * q^76 - 705301770 * q^77 + 165043245 * q^78 + 434002980 * q^79 + 599590757 * q^80 - 389011392 * q^81 - 180073450 * q^82 + 411781442 * q^83 - 475971445 * q^84 + 492988379 * q^86 + 1513399800 * q^87 - 262108460 * q^88 + 911678128 * q^89 - 2734590475 * q^90 - 560105446 * q^91 - 847049266 * q^92 - 1228562570 * q^93 + 2009871759 * q^94 - 1116511966 * q^95 + 2204198979 * q^96 - 3589270998 * q^97 - 2677144485 * q^98 + 2056683494 * 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 $

$2$	−13.2275	−0.584579	−0.292289	−	0.956330i	$-0.594417\pi$
$2$	−13.2275	−0.584579	−0.292289	+	0.956330i	$0.594417\pi$
$3$	162.576	1.15881	0.579404	−	0.815041i	$-0.303286\pi$
$3$	162.576	1.15881	0.579404	+	0.815041i	$0.303286\pi$
$4$	−337.033	−0.658268
$5$	1690.93	1.20993	0.604967	−	0.796250i	$-0.293186\pi$
$5$	1690.93	1.20993	0.604967	+	0.796250i	$0.293186\pi$
$6$	−2150.48	−0.677414
$7$	−10426.0	−1.64125	−0.820627	−	0.571464i	$-0.806376\pi$
$7$	−10426.0	−1.64125	−0.820627	+	0.571464i	$0.806376\pi$
$8$	11230.6	0.969388
$9$	6748.01	0.342834
$10$	−22366.8	−0.707302
$11$	27908.0	0.574727	0.287363	−	0.957822i	$-0.407221\pi$
$11$	27908.0	0.574727	0.287363	+	0.957822i	$0.407221\pi$
$12$	−54793.5	−0.762806
$13$	−147572.	−1.43304	−0.716520	−	0.697566i	$-0.754266\pi$
$13$	−147572.	−1.43304	−0.716520	+	0.697566i	$0.754266\pi$
$14$	137910.	0.959442
$15$	274906.	1.40208
$16$	24008.3	0.0915842
$17$	0	0
$17$	0	0
$18$	−89259.3	−0.200414
$19$	−505938.	−0.890647	−0.445324	−	0.895370i	$-0.646911\pi$
$19$	−505938.	−0.890647	−0.445324	+	0.895370i	$0.646911\pi$
$20$	−569901.	−0.796461
$21$	−1.69502e6	−1.90190
$22$	−369153.	−0.335973
$23$	1.59404e6	1.18774	0.593872	−	0.804560i	$-0.297599\pi$
$23$	1.59404e6	1.18774	0.593872	+	0.804560i	$0.297599\pi$
$24$	1.82583e6	1.12333
$25$	906135.	0.463941
$26$	1.95201e6	0.837725
$27$	−2.10292e6	−0.761528
$28$	3.51390e6	1.08038
$29$	3.23512e6	0.849376	0.424688	−	0.905340i	$-0.360384\pi$
$29$	3.23512e6	0.849376	0.424688	+	0.905340i	$0.360384\pi$
$30$	−3.63632e6	−0.819626
$31$	−5.16741e6	−1.00495	−0.502476	−	0.864591i	$-0.667577\pi$
$31$	−5.16741e6	−1.00495	−0.502476	+	0.864591i	$0.667577\pi$
$32$	−6.06763e6	−1.02293
$33$	4.53717e6	0.665998
$34$	0	0
$35$	−1.76296e7	−1.98581
$36$	−2.27430e6	−0.225677
$37$	−1.45073e7	−1.27256	−0.636281	−	0.771457i	$-0.719528\pi$
$37$	−1.45073e7	−1.27256	−0.636281	+	0.771457i	$0.719528\pi$
$38$	6.69229e6	0.520653
$39$	−2.39917e7	−1.66062
$40$	1.89902e7	1.17290
$41$	3.32642e7	1.83844	0.919219	−	0.393746i	$-0.128821\pi$
$41$	3.32642e7	1.83844	0.919219	+	0.393746i	$0.128821\pi$
$42$	2.24208e7	1.11181
$43$	2.69905e6	0.120393	0.0601967	−	0.998187i	$-0.480827\pi$
$43$	2.69905e6	0.120393	0.0601967	+	0.998187i	$0.480827\pi$
$44$	−9.40592e6	−0.378324
$45$	1.14104e7	0.414807
$46$	−2.10851e7	−0.694329
$47$	9.23270e6	0.275987	0.137993	−	0.990433i	$-0.455935\pi$
$47$	9.23270e6	0.275987	0.137993	+	0.990433i	$0.455935\pi$
$48$	3.90317e6	0.106128
$49$	6.83475e7	1.69371
$50$	−1.19859e7	−0.271210
$51$	0	0
$52$	4.97366e7	0.943324
$53$	6.19599e7	1.07862	0.539311	−	0.842107i	$-0.318685\pi$
$53$	6.19599e7	1.07862	0.539311	+	0.842107i	$0.318685\pi$
$54$	2.78164e7	0.445173
$55$	4.71906e7	0.695382
$56$	−1.17090e8	−1.59101
$57$	−8.22534e7	−1.03209
$58$	−4.27926e7	−0.496527
$59$	9.85359e7	1.05867	0.529335	−	0.848413i	$-0.322441\pi$
$59$	9.85359e7	1.05867	0.529335	+	0.848413i	$0.322441\pi$
$60$	−9.26523e7	−0.922945
$61$	−2.07595e8	−1.91969	−0.959847	−	0.280525i	$-0.909491\pi$
$61$	−2.07595e8	−1.91969	−0.959847	+	0.280525i	$0.909491\pi$
$62$	6.83519e7	0.587474
$63$	−7.03546e7	−0.562678
$64$	6.79674e7	0.506397
$65$	−2.49534e8	−1.73388
$66$	−6.00155e7	−0.389328
$67$	5.69266e7	0.345127	0.172563	−	0.984998i	$-0.444795\pi$
$67$	5.69266e7	0.345127	0.172563	+	0.984998i	$0.444795\pi$
$68$	0	0
$69$	2.59152e8	1.37637
$70$	2.33196e8	1.16086
$71$	1.84556e8	0.861919	0.430960	−	0.902371i	$-0.358175\pi$
$71$	1.84556e8	0.861919	0.430960	+	0.902371i	$0.358175\pi$
$72$	7.57841e7	0.332340
$73$	3.74402e8	1.54307	0.771535	−	0.636187i	$-0.219489\pi$
$73$	3.74402e8	1.54307	0.771535	+	0.636187i	$0.219489\pi$
$74$	1.91895e8	0.743913
$75$	1.47316e8	0.537618
$76$	1.70518e8	0.586284
$77$	−2.90968e8	−0.943272
$78$	3.17350e8	0.970762
$79$	−1.08255e8	−0.312699	−0.156349	−	0.987702i	$-0.549973\pi$
$79$	−1.08255e8	−0.312699	−0.156349	+	0.987702i	$0.549973\pi$
$80$	4.05964e7	0.110811
$81$	−4.74706e8	−1.22530
$82$	−4.40002e8	−1.07471
$83$	4.94434e8	1.14356	0.571778	−	0.820409i	$-0.306254\pi$
$83$	4.94434e8	1.14356	0.571778	+	0.820409i	$0.306254\pi$
$84$	5.71276e8	1.25196
$85$	0	0
$86$	−3.57017e7	−0.0703794
$87$	5.25954e8	0.984263
$88$	3.13423e8	0.557133
$89$	−1.69740e8	−0.286767	−0.143383	−	0.989667i	$-0.545798\pi$
$89$	−1.69740e8	−0.286767	−0.143383	+	0.989667i	$0.545798\pi$
$90$	−1.50932e8	−0.242487
$91$	1.53858e9	2.35198
$92$	−5.37243e8	−0.781853
$93$	−8.40098e8	−1.16455
$94$	−1.22126e8	−0.161336
$95$	−8.55507e8	−1.07762
$96$	−9.86452e8	−1.18537
$97$	−7.68005e8	−0.880828	−0.440414	−	0.897795i	$-0.645168\pi$
$97$	−7.68005e8	−0.880828	−0.440414	+	0.897795i	$0.645168\pi$
$98$	−9.04066e8	−0.990109
$99$	1.88323e8	0.197036
$100$	−3.05397e8	−0.305397
$101$	7.28489e8	0.696589	0.348295	−	0.937385i	$-0.386761\pi$
$101$	7.28489e8	0.696589	0.348295	+	0.937385i	$0.386761\pi$
$102$	0	0
$103$	1.02779e8	0.0899780	0.0449890	−	0.998987i	$-0.485675\pi$
$103$	1.02779e8	0.0899780	0.0449890	+	0.998987i	$0.485675\pi$
$104$	−1.65732e9	−1.38917
$105$	−2.86616e9	−2.30117
$106$	−8.19575e8	−0.630540
$107$	3.63658e8	0.268204	0.134102	−	0.990968i	$-0.457185\pi$
$107$	3.63658e8	0.268204	0.134102	+	0.990968i	$0.457185\pi$
$108$	7.08754e8	0.501290
$109$	1.71212e9	1.16175	0.580876	−	0.813992i	$-0.302710\pi$
$109$	1.71212e9	1.16175	0.580876	+	0.813992i	$0.302710\pi$
$110$	−6.24214e8	−0.406505
$111$	−2.35854e9	−1.47465
$112$	−2.50310e8	−0.150313
$113$	1.38464e8	0.0798887	0.0399444	−	0.999202i	$-0.487282\pi$
$113$	1.38464e8	0.0798887	0.0399444	+	0.999202i	$0.487282\pi$
$114$	1.08801e9	0.603337
$115$	2.69541e9	1.43709
$116$	−1.09034e9	−0.559117
$117$	−9.95816e8	−0.491295
$118$	−1.30338e9	−0.618876
$119$	0	0
$120$	3.08735e9	1.35916
$121$	−1.57909e9	−0.669689
$122$	2.74596e9	1.12221
$123$	5.40796e9	2.13040
$124$	1.74159e9	0.661528
$125$	−1.77039e9	−0.648596
$126$	9.30616e8	0.328930
$127$	9.57226e8	0.326511	0.163255	−	0.986584i	$-0.447801\pi$
$127$	9.57226e8	0.326511	0.163255	+	0.986584i	$0.447801\pi$
$128$	2.20759e9	0.726898
$129$	4.38801e8	0.139513
$130$	3.30072e9	1.01359
$131$	−5.31655e9	−1.57728	−0.788640	−	0.614855i	$-0.789215\pi$
$131$	−5.31655e9	−1.57728	−0.788640	+	0.614855i	$0.789215\pi$
$132$	−1.52918e9	−0.438405
$133$	5.27489e9	1.46178
$134$	−7.52997e8	−0.201754
$135$	−3.55590e9	−0.921399
$136$	0	0
$137$	−2.22736e9	−0.540191	−0.270096	−	0.962834i	$-0.587055\pi$
$137$	−2.22736e9	−0.540191	−0.270096	+	0.962834i	$0.587055\pi$
$138$	−3.42794e9	−0.804594
$139$	−6.00076e9	−1.36345	−0.681726	−	0.731608i	$-0.738770\pi$
$139$	−6.00076e9	−1.36345	−0.681726	+	0.731608i	$0.738770\pi$
$140$	5.94178e9	1.30719
$141$	1.50102e9	0.319816
$142$	−2.44122e9	−0.503860
$143$	−4.11843e9	−0.823607
$144$	1.62008e8	0.0313982
$145$	5.47038e9	1.02769
$146$	−4.95241e9	−0.902045
$147$	1.11117e10	1.96269
$148$	4.88944e9	0.837687
$149$	3.19033e9	0.530270	0.265135	−	0.964211i	$-0.414583\pi$
$149$	3.19033e9	0.530270	0.265135	+	0.964211i	$0.414583\pi$
$150$	−1.94862e9	−0.314280
$151$	7.14958e9	1.11914	0.559570	−	0.828783i	$-0.310966\pi$
$151$	7.14958e9	1.11914	0.559570	+	0.828783i	$0.310966\pi$
$152$	−5.68198e9	−0.863383
$153$	0	0
$154$	3.84878e9	0.551417
$155$	−8.73775e9	−1.21593
$156$	8.08598e9	1.09313
$157$	7.67405e9	1.00804	0.504018	−	0.863693i	$-0.331855\pi$
$157$	7.67405e9	1.00804	0.504018	+	0.863693i	$0.331855\pi$
$158$	1.43194e9	0.182797
$159$	1.00732e10	1.24992
$160$	−1.02600e10	−1.23767
$161$	−1.66194e10	−1.94939
$162$	6.27918e9	0.716284
$163$	−1.02613e10	−1.13857	−0.569283	−	0.822142i	$-0.692779\pi$
$163$	−1.02613e10	−1.13857	−0.569283	+	0.822142i	$0.692779\pi$
$164$	−1.12111e10	−1.21018
$165$	7.67206e9	0.805813
$166$	−6.54013e9	−0.668498
$167$	8.99357e9	0.894763	0.447382	−	0.894343i	$-0.352357\pi$
$167$	8.99357e9	0.894763	0.447382	+	0.894343i	$0.352357\pi$
$168$	−1.90360e10	−1.84368
$169$	1.11729e10	1.05360
$170$	0	0
$171$	−3.41407e9	−0.305344
$172$	−9.09668e8	−0.0792510
$173$	7.25497e9	0.615784	0.307892	−	0.951421i	$-0.400376\pi$
$173$	7.25497e9	0.615784	0.307892	+	0.951421i	$0.400376\pi$
$174$	−6.95706e9	−0.575379
$175$	−9.44734e9	−0.761445
$176$	6.70022e8	0.0526359
$177$	1.60196e10	1.22679
$178$	2.24524e9	0.167638
$179$	1.13634e10	0.827315	0.413657	−	0.910433i	$-0.364251\pi$
$179$	1.13634e10	0.827315	0.413657	+	0.910433i	$0.364251\pi$
$180$	−3.84570e9	−0.273054
$181$	1.75389e10	1.21465	0.607323	−	0.794455i	$-0.292244\pi$
$181$	1.75389e10	1.21465	0.607323	+	0.794455i	$0.292244\pi$
$182$	−2.03516e10	−1.37492
$183$	−3.37499e10	−2.22455
$184$	1.79020e10	1.15138
$185$	−2.45309e10	−1.53972
$186$	1.11124e10	0.680769
$187$	0	0
$188$	−3.11173e9	−0.181673
$189$	2.19250e10	1.24986
$190$	1.13162e10	0.629956
$191$	6.77140e9	0.368153	0.184076	−	0.982912i	$-0.441071\pi$
$191$	6.77140e9	0.368153	0.184076	+	0.982912i	$0.441071\pi$
$192$	1.10499e10	0.586816
$193$	2.72304e10	1.41269	0.706343	−	0.707869i	$-0.250344\pi$
$193$	2.72304e10	1.41269	0.706343	+	0.707869i	$0.250344\pi$
$194$	1.01588e10	0.514913
$195$	−4.05683e10	−2.00924
$196$	−2.30354e10	−1.11492
$197$	4.54510e9	0.215003	0.107502	−	0.994205i	$-0.465715\pi$
$197$	4.54510e9	0.215003	0.107502	+	0.994205i	$0.465715\pi$
$198$	−2.49105e9	−0.115183
$199$	−1.59981e10	−0.723152	−0.361576	−	0.932343i	$-0.617761\pi$
$199$	−1.59981e10	−0.723152	−0.361576	+	0.932343i	$0.617761\pi$
$200$	1.01764e10	0.449739
$201$	9.25491e9	0.399936
$202$	−9.63609e9	−0.407211
$203$	−3.37293e10	−1.39404
$204$	0	0
$205$	5.62475e10	2.22439
$206$	−1.35951e9	−0.0525992
$207$	1.07566e10	0.407199
$208$	−3.54294e9	−0.131244
$209$	−1.41197e10	−0.511879
$210$	3.79122e10	1.34521
$211$	1.63246e10	0.566984	0.283492	−	0.958975i	$-0.408507\pi$
$211$	1.63246e10	0.566984	0.283492	+	0.958975i	$0.408507\pi$
$212$	−2.08825e10	−0.710022
$213$	3.00045e10	0.998798
$214$	−4.81028e9	−0.156786
$215$	4.56391e9	0.145668
$216$	−2.36170e10	−0.738216
$217$	5.38753e10	1.64938
$218$	−2.26470e10	−0.679136
$219$	6.08689e10	1.78812
$220$	−1.59048e10	−0.457747
$221$	0	0
$222$	3.11976e10	0.862051
$223$	5.70751e10	1.54552	0.772761	−	0.634698i	$-0.218875\pi$
$223$	5.70751e10	1.54552	0.772761	+	0.634698i	$0.218875\pi$
$224$	6.32610e10	1.67888
$225$	6.11460e9	0.159055
$226$	−1.83154e9	−0.0467012
$227$	2.05843e10	0.514541	0.257270	−	0.966339i	$-0.417177\pi$
$227$	2.05843e10	0.514541	0.257270	+	0.966339i	$0.417177\pi$
$228$	2.77221e10	0.679391
$229$	−4.57633e9	−0.109966	−0.0549829	−	0.998487i	$-0.517510\pi$
$229$	−4.57633e9	−0.109966	−0.0549829	+	0.998487i	$0.517510\pi$
$230$	−3.56535e10	−0.840093
$231$	−4.73045e10	−1.09307
$232$	3.63323e10	0.823375
$233$	5.69299e10	1.26543	0.632715	−	0.774384i	$-0.281940\pi$
$233$	5.69299e10	1.26543	0.632715	+	0.774384i	$0.281940\pi$
$234$	1.31722e10	0.287201
$235$	1.56119e10	0.333926
$236$	−3.32099e10	−0.696888
$237$	−1.75997e10	−0.362358
$238$	0	0
$239$	6.52563e10	1.29370	0.646848	−	0.762619i	$-0.276087\pi$
$239$	6.52563e10	1.29370	0.646848	+	0.762619i	$0.276087\pi$
$240$	6.60001e9	0.128409
$241$	8.61216e10	1.64451	0.822253	−	0.569122i	$-0.192717\pi$
$241$	8.61216e10	1.64451	0.822253	+	0.569122i	$0.192717\pi$
$242$	2.08874e10	0.391486
$243$	−3.57841e10	−0.658357
$244$	6.99663e10	1.26367
$245$	1.15571e11	2.04928
$246$	−7.15338e10	−1.24538
$247$	7.46621e10	1.27633
$248$	−5.80331e10	−0.974188
$249$	8.03832e10	1.32516
$250$	2.34179e10	0.379156
$251$	5.22016e9	0.0830142	0.0415071	−	0.999138i	$-0.486784\pi$
$251$	5.22016e9	0.0830142	0.0415071	+	0.999138i	$0.486784\pi$
$252$	2.37118e10	0.370393
$253$	4.44863e10	0.682628
$254$	−1.26617e10	−0.190871
$255$	0	0
$256$	−6.40002e10	−0.931325
$257$	−1.08824e11	−1.55606	−0.778031	−	0.628226i	$-0.783781\pi$
$257$	−1.08824e11	−1.55606	−0.778031	+	0.628226i	$0.783781\pi$
$258$	−5.80424e9	−0.0815561
$259$	1.51253e11	2.08860
$260$	8.41013e10	1.14136
$261$	2.18306e10	0.291195
$262$	7.03247e10	0.922045
$263$	1.28662e11	1.65825	0.829125	−	0.559064i	$-0.188839\pi$
$263$	1.28662e11	1.65825	0.829125	+	0.559064i	$0.188839\pi$
$264$	5.09551e10	0.645610
$265$	1.04770e11	1.30506
$266$	−6.97737e10	−0.854524
$267$	−2.75957e10	−0.332308
$268$	−1.91862e10	−0.227186
$269$	−5.69926e9	−0.0663641	−0.0331820	−	0.999449i	$-0.510564\pi$
$269$	−5.69926e9	−0.0663641	−0.0331820	+	0.999449i	$0.510564\pi$
$270$	4.70357e10	0.538630
$271$	1.43579e11	1.61707	0.808537	−	0.588445i	$-0.200260\pi$
$271$	1.43579e11	1.61707	0.808537	+	0.588445i	$0.200260\pi$
$272$	0	0
$273$	2.50137e11	2.72549
$274$	2.94624e10	0.315784
$275$	2.52884e10	0.266639
$276$	−8.73428e10	−0.906017
$277$	−1.36201e11	−1.39002	−0.695011	−	0.718999i	$-0.744601\pi$
$277$	−1.36201e11	−1.39002	−0.695011	+	0.718999i	$0.744601\pi$
$278$	7.93751e10	0.797044
$279$	−3.48697e10	−0.344532
$280$	−1.97991e11	−1.92502
$281$	1.12477e11	1.07618	0.538089	−	0.842888i	$-0.319146\pi$
$281$	1.12477e11	1.07618	0.538089	+	0.842888i	$0.319146\pi$
$282$	−1.98547e10	−0.186957
$283$	1.20925e11	1.12067	0.560336	−	0.828265i	$-0.310672\pi$
$283$	1.20925e11	1.12067	0.560336	+	0.828265i	$0.310672\pi$
$284$	−6.22016e10	−0.567374
$285$	−1.39085e11	−1.24876
$286$	5.44766e10	0.481463
$287$	−3.46811e11	−3.01734
$288$	−4.09444e10	−0.350694
$289$	0	0
$290$	−7.23595e10	−0.600765
$291$	−1.24859e11	−1.02071
$292$	−1.26186e11	−1.01575
$293$	−4.42742e10	−0.350951	−0.175475	−	0.984484i	$-0.556146\pi$
$293$	−4.42742e10	−0.350951	−0.175475	+	0.984484i	$0.556146\pi$
$294$	−1.46980e11	−1.14735
$295$	1.66618e11	1.28092
$296$	−1.62926e11	−1.23361
$297$	−5.86883e10	−0.437671
$298$	−4.22001e10	−0.309985
$299$	−2.35235e11	−1.70208
$300$	−4.96503e10	−0.353897
$301$	−2.81402e10	−0.197596
$302$	−9.45711e10	−0.654225
$303$	1.18435e11	0.807213
$304$	−1.21467e10	−0.0815692
$305$	−3.51029e11	−2.32270
$306$	0	0
$307$	−2.79424e11	−1.79532	−0.897658	−	0.440692i	$-0.854733\pi$
$307$	−2.79424e11	−1.79532	−0.897658	+	0.440692i	$0.854733\pi$
$308$	9.80659e10	0.620926
$309$	1.67094e10	0.104267
$310$	1.15579e11	0.710804
$311$	1.84625e11	1.11910	0.559549	−	0.828797i	$-0.310974\pi$
$311$	1.84625e11	1.11910	0.559549	+	0.828797i	$0.310974\pi$
$312$	−2.69441e11	−1.60978
$313$	−1.58481e11	−0.933313	−0.466657	−	0.884439i	$-0.654542\pi$
$313$	−1.58481e11	−0.933313	−0.466657	+	0.884439i	$0.654542\pi$
$314$	−1.01508e11	−0.589276
$315$	−1.18965e11	−0.680804
$316$	3.64855e10	0.205839
$317$	4.35550e10	0.242254	0.121127	−	0.992637i	$-0.461349\pi$
$317$	4.35550e10	0.242254	0.121127	+	0.992637i	$0.461349\pi$
$318$	−1.33243e11	−0.730674
$319$	9.02858e10	0.488159
$320$	1.14928e11	0.612707
$321$	5.91220e10	0.310797
$322$	2.19833e11	1.13957
$323$	0	0
$324$	1.59992e11	0.806575
$325$	−1.33720e11	−0.664846
$326$	1.35731e11	0.665581
$327$	2.78349e11	1.34625
$328$	3.73576e11	1.78216
$329$	−9.62600e10	−0.452965
$330$	−1.01482e11	−0.471061
$331$	−6.42279e10	−0.294102	−0.147051	−	0.989129i	$-0.546978\pi$
$331$	−6.42279e10	−0.294102	−0.147051	+	0.989129i	$0.546978\pi$
$332$	−1.66641e11	−0.752766
$333$	−9.78954e10	−0.436278
$334$	−1.18963e11	−0.523059
$335$	9.62592e10	0.417581
$336$	−4.06944e10	−0.174184
$337$	1.30865e11	0.552698	0.276349	−	0.961057i	$-0.410875\pi$
$337$	1.30865e11	0.552698	0.276349	+	0.961057i	$0.410875\pi$
$338$	−1.47790e11	−0.615915
$339$	2.25110e10	0.0925756
$340$	0	0
$341$	−1.44212e11	−0.577573
$342$	4.51596e10	0.178498
$343$	−2.91863e11	−1.13856
$344$	3.03119e10	0.116708
$345$	4.38209e11	1.66531
$346$	−9.59652e10	−0.359974
$347$	2.14010e11	0.792413	0.396207	−	0.918161i	$-0.370326\pi$
$347$	2.14010e11	0.792413	0.396207	+	0.918161i	$0.370326\pi$
$348$	−1.77264e11	−0.647908
$349$	−7.69184e10	−0.277534	−0.138767	−	0.990325i	$-0.544314\pi$
$349$	−7.69184e10	−0.277534	−0.138767	+	0.990325i	$0.544314\pi$
$350$	1.24965e11	0.445124
$351$	3.10332e11	1.09130
$352$	−1.69335e11	−0.587903
$353$	2.30925e10	0.0791560	0.0395780	−	0.999216i	$-0.487399\pi$
$353$	2.30925e10	0.0791560	0.0395780	+	0.999216i	$0.487399\pi$
$354$	−2.11899e11	−0.717158
$355$	3.12073e11	1.04287
$356$	5.72080e10	0.188769
$357$	0	0
$358$	−1.50310e11	−0.483630
$359$	4.58231e10	0.145599	0.0727996	−	0.997347i	$-0.476807\pi$
$359$	4.58231e10	0.145599	0.0727996	+	0.997347i	$0.476807\pi$
$360$	1.28146e11	0.402109
$361$	−6.67149e10	−0.206748
$362$	−2.31996e11	−0.710056
$363$	−2.56723e11	−0.776041
$364$	−5.18553e11	−1.54823
$365$	6.33089e11	1.86701
$366$	4.46428e11	1.30043
$367$	−2.58359e11	−0.743406	−0.371703	−	0.928352i	$-0.621226\pi$
$367$	−2.58359e11	−0.743406	−0.371703	+	0.928352i	$0.621226\pi$
$368$	3.82700e10	0.108779
$369$	2.24467e11	0.630280
$370$	3.24483e11	0.900085
$371$	−6.45993e11	−1.77029
$372$	2.83141e11	0.766583
$373$	−1.52288e11	−0.407357	−0.203678	−	0.979038i	$-0.565290\pi$
$373$	−1.52288e11	−0.407357	−0.203678	+	0.979038i	$0.565290\pi$
$374$	0	0
$375$	−2.87824e11	−0.751598
$376$	1.03689e11	0.267538
$377$	−4.77413e11	−1.21719
$378$	−2.90013e11	−0.730642
$379$	−4.41214e11	−1.09843	−0.549215	−	0.835681i	$-0.685073\pi$
$379$	−4.41214e11	−1.09843	−0.549215	+	0.835681i	$0.685073\pi$
$380$	2.88334e11	0.709365
$381$	1.55622e11	0.378363
$382$	−8.95687e10	−0.215214
$383$	−2.29999e11	−0.546175	−0.273087	−	0.961989i	$-0.588045\pi$
$383$	−2.29999e11	−0.546175	−0.273087	+	0.961989i	$0.588045\pi$
$384$	3.58901e11	0.842334
$385$	−4.92008e11	−1.14130
$386$	−3.60190e11	−0.825826
$387$	1.82132e10	0.0412750
$388$	2.58843e11	0.579821
$389$	−1.45947e11	−0.323163	−0.161582	−	0.986859i	$-0.551659\pi$
$389$	−1.45947e11	−0.323163	−0.161582	+	0.986859i	$0.551659\pi$
$390$	5.36618e11	1.17456
$391$	0	0
$392$	7.67582e11	1.64187
$393$	−8.64344e11	−1.82776
$394$	−6.01203e10	−0.125686
$395$	−1.83052e11	−0.378345
$396$	−6.34712e10	−0.129703
$397$	1.51733e11	0.306565	0.153283	−	0.988182i	$-0.451016\pi$
$397$	1.51733e11	0.306565	0.153283	+	0.988182i	$0.451016\pi$
$398$	2.11615e11	0.422739
$399$	8.57572e11	1.69392
$400$	2.17547e10	0.0424897
$401$	5.23476e11	1.01099	0.505495	−	0.862829i	$-0.331310\pi$
$401$	5.23476e11	1.01099	0.505495	+	0.862829i	$0.331310\pi$
$402$	−1.22419e11	−0.233794
$403$	7.62564e11	1.44014
$404$	−2.45525e11	−0.458542
$405$	−8.02697e11	−1.48253
$406$	4.46155e11	0.814927
$407$	−4.04870e11	−0.731375
$408$	0	0
$409$	4.55257e10	0.0804455	0.0402228	−	0.999191i	$-0.487193\pi$
$409$	4.55257e10	0.0804455	0.0402228	+	0.999191i	$0.487193\pi$
$410$	−7.44014e11	−1.30033
$411$	−3.62115e11	−0.625977
$412$	−3.46399e10	−0.0592296
$413$	−1.02733e12	−1.73755
$414$	−1.42283e11	−0.238040
$415$	8.36056e11	1.38363
$416$	8.95412e11	1.46589
$417$	−9.75580e11	−1.57998
$418$	1.86768e11	0.299233
$419$	−1.02772e12	−1.62896	−0.814479	−	0.580193i	$-0.802977\pi$
$419$	−1.02772e12	−1.62896	−0.814479	+	0.580193i	$0.802977\pi$
$420$	9.65991e11	1.51479
$421$	−2.02257e11	−0.313786	−0.156893	−	0.987616i	$-0.550148\pi$
$421$	−2.02257e11	−0.313786	−0.156893	+	0.987616i	$0.550148\pi$
$422$	−2.15933e11	−0.331447
$423$	6.23024e10	0.0946178
$424$	6.95846e11	1.04560
$425$	0	0
$426$	−3.96884e11	−0.583876
$427$	2.16438e12	3.15070
$428$	−1.22565e11	−0.176550
$429$	−6.69559e11	−0.954401
$430$	−6.03692e10	−0.0851544
$431$	−1.48533e11	−0.207336	−0.103668	−	0.994612i	$-0.533058\pi$
$431$	−1.48533e11	−0.207336	−0.103668	+	0.994612i	$0.533058\pi$
$432$	−5.04875e10	−0.0697440
$433$	3.95179e11	0.540255	0.270127	−	0.962825i	$-0.412934\pi$
$433$	3.95179e11	0.540255	0.270127	+	0.962825i	$0.412934\pi$
$434$	−7.12636e11	−0.964193
$435$	8.89354e11	1.19089
$436$	−5.77040e11	−0.764745
$437$	−8.06482e11	−1.05786
$438$	−8.05143e11	−1.04530
$439$	6.20307e11	0.797106	0.398553	−	0.917145i	$-0.369512\pi$
$439$	6.20307e11	0.797106	0.398553	+	0.917145i	$0.369512\pi$
$440$	5.29978e11	0.674095
$441$	4.61209e11	0.580663
$442$	0	0
$443$	−5.92208e11	−0.730563	−0.365282	−	0.930897i	$-0.619027\pi$
$443$	−5.92208e11	−0.730563	−0.365282	+	0.930897i	$0.619027\pi$
$444$	7.94907e11	0.970717
$445$	−2.87019e11	−0.346969
$446$	−7.54961e11	−0.903479
$447$	5.18672e11	0.614481
$448$	−7.08627e11	−0.831125
$449$	−2.83563e10	−0.0329261	−0.0164630	−	0.999864i	$-0.505241\pi$
$449$	−2.83563e10	−0.0329261	−0.0164630	+	0.999864i	$0.505241\pi$
$450$	−8.08810e10	−0.0929801
$451$	9.28336e11	1.05660
$452$	−4.66671e10	−0.0525882
$453$	1.16235e12	1.29687
$454$	−2.72279e11	−0.300790
$455$	2.60164e12	2.84574
$456$	−9.23754e11	−1.00049
$457$	−2.62498e10	−0.0281516	−0.0140758	−	0.999901i	$-0.504481\pi$
$457$	−2.62498e10	−0.0281516	−0.0140758	+	0.999901i	$0.504481\pi$
$458$	6.05334e10	0.0642837
$459$	0	0
$460$	−9.08442e11	−0.945991
$461$	1.29684e12	1.33731	0.668653	−	0.743574i	$-0.266871\pi$
$461$	1.29684e12	1.33731	0.668653	+	0.743574i	$0.266871\pi$
$462$	6.25720e11	0.638986
$463$	−6.64207e10	−0.0671722	−0.0335861	−	0.999436i	$-0.510693\pi$
$463$	−6.64207e10	−0.0671722	−0.0335861	+	0.999436i	$0.510693\pi$
$464$	7.76697e10	0.0777894
$465$	−1.42055e12	−1.40902
$466$	−7.53040e11	−0.739744
$467$	−7.96403e11	−0.774831	−0.387415	−	0.921905i	$-0.626632\pi$
$467$	−7.96403e11	−0.774831	−0.387415	+	0.921905i	$0.626632\pi$
$468$	3.35623e11	0.323404
$469$	−5.93516e11	−0.566441
$470$	−2.06506e11	−0.195206
$471$	1.24762e12	1.16812
$472$	1.10662e12	1.02626
$473$	7.53250e10	0.0691933
$474$	2.32800e11	0.211826
$475$	−4.58447e11	−0.413208
$476$	0	0
$477$	4.18106e11	0.369789
$478$	−8.63178e11	−0.756267
$479$	5.78197e11	0.501841	0.250921	−	0.968008i	$-0.419267\pi$
$479$	5.78197e11	0.501841	0.250921	+	0.968008i	$0.419267\pi$
$480$	−1.66803e12	−1.43423
$481$	2.14087e12	1.82363
$482$	−1.13917e12	−0.961343
$483$	−2.70191e12	−2.25897
$484$	5.32206e11	0.440835
$485$	−1.29865e12	−1.06574
$486$	4.73334e11	0.384861
$487$	−1.55619e12	−1.25367	−0.626834	−	0.779152i	$-0.715650\pi$
$487$	−1.55619e12	−1.25367	−0.626834	+	0.779152i	$0.715650\pi$
$488$	−2.33141e12	−1.86093
$489$	−1.66824e12	−1.31938
$490$	−1.52872e12	−1.19797
$491$	6.58358e11	0.511205	0.255603	−	0.966782i	$-0.417726\pi$
$491$	6.58358e11	0.511205	0.255603	+	0.966782i	$0.417726\pi$
$492$	−1.82266e12	−1.40237
$493$	0	0
$494$	−9.87594e11	−0.746117
$495$	3.18442e11	0.238401
$496$	−1.24061e11	−0.0920378
$497$	−1.92418e12	−1.41463
$498$	−1.06327e12	−0.774660
$499$	4.76335e11	0.343922	0.171961	−	0.985104i	$-0.444990\pi$
$499$	4.76335e11	0.343922	0.171961	+	0.985104i	$0.444990\pi$
$500$	5.96681e11	0.426950
$501$	1.46214e12	1.03686
$502$	−6.90497e10	−0.0485283
$503$	2.43679e12	1.69731	0.848656	−	0.528945i	$-0.177412\pi$
$503$	2.43679e12	1.69731	0.848656	+	0.528945i	$0.177412\pi$
$504$	−7.90124e11	−0.545453
$505$	1.23183e12	0.842827
$506$	−5.88443e11	−0.399050
$507$	1.81646e12	1.22092
$508$	−3.22617e11	−0.214932
$509$	1.43148e12	0.945266	0.472633	−	0.881259i	$-0.343304\pi$
$509$	1.43148e12	0.945266	0.472633	+	0.881259i	$0.343304\pi$
$510$	0	0
$511$	−3.90351e12	−2.53257
$512$	−2.83722e11	−0.182465
$513$	1.06395e12	0.678253
$514$	1.43947e12	0.909641
$515$	1.73792e11	0.108867
$516$	−1.47890e11	−0.0918367
$517$	2.57666e11	0.158617
$518$	−2.00070e12	−1.22095
$519$	1.17949e12	0.713575
$520$	−2.80242e12	−1.68081
$521$	3.25365e12	1.93465	0.967323	−	0.253547i	$-0.0815974\pi$
$521$	3.25365e12	1.93465	0.967323	+	0.253547i	$0.0815974\pi$
$522$	−2.88765e11	−0.170226
$523$	−1.21455e12	−0.709835	−0.354918	−	0.934898i	$-0.615491\pi$
$523$	−1.21455e12	−0.709835	−0.354918	+	0.934898i	$0.615491\pi$
$524$	1.79185e12	1.03827
$525$	−1.53591e12	−0.882368
$526$	−1.70188e12	−0.969377
$527$	0	0
$528$	1.08930e11	0.0609949
$529$	7.39795e11	0.410734
$530$	−1.38585e12	−0.762911
$531$	6.64921e11	0.362948
$532$	−1.77781e12	−0.962241
$533$	−4.90885e12	−2.63456
$534$	3.65022e11	0.194260
$535$	6.14921e11	0.324509
$536$	6.39320e11	0.334562
$537$	1.84742e12	0.958698
$538$	7.53870e10	0.0387950
$539$	1.90744e12	0.973423
$540$	1.19846e12	0.606527
$541$	3.69419e11	0.185409	0.0927047	−	0.995694i	$-0.470449\pi$
$541$	3.69419e11	0.185409	0.0927047	+	0.995694i	$0.470449\pi$
$542$	−1.89920e12	−0.945307
$543$	2.85141e12	1.40754
$544$	0	0
$545$	2.89507e12	1.40564
$546$	−3.30868e12	−1.59327
$547$	−2.58892e12	−1.23645	−0.618225	−	0.786001i	$-0.712148\pi$
$547$	−2.58892e12	−1.23645	−0.618225	+	0.786001i	$0.712148\pi$
$548$	7.50693e11	0.355590
$549$	−1.40085e12	−0.658137
$550$	−3.34502e11	−0.155872
$551$	−1.63677e12	−0.756494
$552$	2.91043e12	1.33423
$553$	1.12866e12	0.513218
$554$	1.80160e12	0.812578
$555$	−3.98814e12	−1.78423
$556$	2.02245e12	0.897516
$557$	−3.75988e12	−1.65510	−0.827552	−	0.561390i	$-0.810267\pi$
$557$	−3.75988e12	−1.65510	−0.827552	+	0.561390i	$0.810267\pi$
$558$	4.61240e11	0.201406
$559$	−3.98303e11	−0.172528
$560$	−4.23257e11	−0.181869
$561$	0	0
$562$	−1.48779e12	−0.629111
$563$	−1.81478e12	−0.761267	−0.380633	−	0.924726i	$-0.624294\pi$
$563$	−1.81478e12	−0.761267	−0.380633	+	0.924726i	$0.624294\pi$
$564$	−5.05893e11	−0.210524
$565$	2.34134e11	0.0966601
$566$	−1.59954e12	−0.655121
$567$	4.94927e12	2.01103
$568$	2.07268e12	0.835534
$569$	−2.85565e12	−1.14209	−0.571044	−	0.820919i	$-0.693461\pi$
$569$	−2.85565e12	−1.14209	−0.571044	+	0.820919i	$0.693461\pi$
$570$	1.83975e12	0.729998
$571$	8.21370e11	0.323352	0.161676	−	0.986844i	$-0.448310\pi$
$571$	8.21370e11	0.323352	0.161676	+	0.986844i	$0.448310\pi$
$572$	1.38805e12	0.542154
$573$	1.10087e12	0.426618
$574$	4.58745e12	1.76388
$575$	1.44441e12	0.551043
$576$	4.58645e11	0.173610
$577$	−1.44262e12	−0.541828	−0.270914	−	0.962604i	$-0.587326\pi$
$577$	−1.44262e12	−0.541828	−0.270914	+	0.962604i	$0.587326\pi$
$578$	0	0
$579$	4.42701e12	1.63703
$580$	−1.84370e12	−0.676494
$581$	−5.15496e12	−1.87686
$582$	1.65158e12	0.596685
$583$	1.72918e12	0.619913
$584$	4.20476e12	1.49583
$585$	−1.68386e12	−0.594435
$586$	5.85637e11	0.205158
$587$	1.58591e12	0.551324	0.275662	−	0.961255i	$-0.411103\pi$
$587$	1.58591e12	0.551324	0.275662	+	0.961255i	$0.411103\pi$
$588$	−3.74500e12	−1.29197
$589$	2.61439e12	0.895058
$590$	−2.20394e12	−0.748799
$591$	7.38925e11	0.249147
$592$	−3.48295e11	−0.116547
$593$	9.83115e11	0.326481	0.163241	−	0.986586i	$-0.447805\pi$
$593$	9.83115e11	0.326481	0.163241	+	0.986586i	$0.447805\pi$
$594$	7.76300e11	0.255853
$595$	0	0
$596$	−1.07525e12	−0.349060
$597$	−2.60091e12	−0.837994
$598$	3.11157e12	0.995002
$599$	3.87791e12	1.23077	0.615385	−	0.788226i	$-0.289000\pi$
$599$	3.87791e12	1.23077	0.615385	+	0.788226i	$0.289000\pi$
$600$	1.65444e12	0.521161
$601$	−1.63204e12	−0.510266	−0.255133	−	0.966906i	$-0.582119\pi$
$601$	−1.63204e12	−0.510266	−0.255133	+	0.966906i	$0.582119\pi$
$602$	3.72225e11	0.115510
$603$	3.84141e11	0.118321
$604$	−2.40965e12	−0.736694
$605$	−2.67014e12	−0.810280
$606$	−1.56660e12	−0.471879
$607$	−4.21961e12	−1.26160	−0.630802	−	0.775944i	$-0.717274\pi$
$607$	−4.21961e12	−1.26160	−0.630802	+	0.775944i	$0.717274\pi$
$608$	3.06984e12	0.911066
$609$	−5.48358e12	−1.61542
$610$	4.64324e12	1.35780
$611$	−1.36249e12	−0.395500
$612$	0	0
$613$	−5.46165e10	−0.0156226	−0.00781128	−	0.999969i	$-0.502486\pi$
$613$	−5.46165e10	−0.0156226	−0.00781128	+	0.999969i	$0.502486\pi$
$614$	3.69608e12	1.04950
$615$	9.14450e12	2.57764
$616$	−3.26774e12	−0.914397
$617$	3.86551e12	1.07380	0.536900	−	0.843646i	$-0.319595\pi$
$617$	3.86551e12	1.07380	0.536900	+	0.843646i	$0.319595\pi$
$618$	−2.21023e11	−0.0609523
$619$	6.41780e12	1.75703	0.878513	−	0.477718i	$-0.158536\pi$
$619$	6.41780e12	1.75703	0.878513	+	0.477718i	$0.158536\pi$
$620$	2.94491e12	0.800405
$621$	−3.35213e12	−0.904500
$622$	−2.44212e12	−0.654201
$623$	1.76971e12	0.470657
$624$	−5.75998e11	−0.152086
$625$	−4.76341e12	−1.24870
$626$	2.09631e12	0.545595
$627$	−2.29553e12	−0.593169
$628$	−2.58641e12	−0.663557
$629$	0	0
$630$	1.57361e12	0.397983
$631$	2.84108e12	0.713431	0.356716	−	0.934213i	$-0.383897\pi$
$631$	2.84108e12	0.713431	0.356716	+	0.934213i	$0.383897\pi$
$632$	−1.21577e12	−0.303126
$633$	2.65399e12	0.657025
$634$	−5.76124e11	−0.141617
$635$	1.61861e12	0.395057
$636$	−3.39500e12	−0.822779
$637$	−1.00862e13	−2.42716
$638$	−1.19426e12	−0.285367
$639$	1.24539e12	0.295495
$640$	3.73289e12	0.879498
$641$	−2.08823e12	−0.488560	−0.244280	−	0.969705i	$-0.578552\pi$
$641$	−2.08823e12	−0.488560	−0.244280	+	0.969705i	$0.578552\pi$
$642$	−7.82037e11	−0.181685
$643$	−2.66139e12	−0.613987	−0.306993	−	0.951712i	$-0.599323\pi$
$643$	−2.66139e12	−0.613987	−0.306993	+	0.951712i	$0.599323\pi$
$644$	5.60128e12	1.28322
$645$	7.41983e11	0.168801
$646$	0	0
$647$	4.94078e12	1.10848	0.554238	−	0.832358i	$-0.313010\pi$
$647$	4.94078e12	1.10848	0.554238	+	0.832358i	$0.313010\pi$
$648$	−5.33123e12	−1.18779
$649$	2.74994e12	0.608446
$650$	1.76878e12	0.388655
$651$	8.75884e12	1.91131
$652$	3.45840e12	0.749481
$653$	5.54623e12	1.19368	0.596841	−	0.802359i	$-0.296422\pi$
$653$	5.54623e12	1.19368	0.596841	+	0.802359i	$0.296422\pi$
$654$	−3.68186e12	−0.786988
$655$	−8.98994e12	−1.90841
$656$	7.98615e11	0.168372
$657$	2.52647e12	0.529017
$658$	1.27328e12	0.264793
$659$	2.33637e12	0.482566	0.241283	−	0.970455i	$-0.422432\pi$
$659$	2.33637e12	0.482566	0.241283	+	0.970455i	$0.422432\pi$
$660$	−2.58574e12	−0.530441
$661$	−5.46597e12	−1.11368	−0.556840	−	0.830620i	$-0.687986\pi$
$661$	−5.46597e12	−1.11368	−0.556840	+	0.830620i	$0.687986\pi$
$662$	8.49575e11	0.171926
$663$	0	0
$664$	5.55279e12	1.10855
$665$	8.91950e12	1.76866
$666$	1.29491e12	0.255039
$667$	5.15690e12	1.00884
$668$	−3.03113e12	−0.588994
$669$	9.27905e12	1.79096
$670$	−1.27327e12	−0.244109
$671$	−5.79355e12	−1.10330
$672$	1.02847e13	1.94550
$673$	−4.62101e12	−0.868299	−0.434149	−	0.900841i	$-0.642951\pi$
$673$	−4.62101e12	−0.868299	−0.434149	+	0.900841i	$0.642951\pi$
$674$	−1.73101e12	−0.323095
$675$	−1.90553e12	−0.353304
$676$	−3.76565e12	−0.693554
$677$	4.87496e12	0.891912	0.445956	−	0.895055i	$-0.352864\pi$
$677$	4.87496e12	0.891912	0.445956	+	0.895055i	$0.352864\pi$
$678$	−2.97765e11	−0.0541177
$679$	8.00720e12	1.44566
$680$	0	0
$681$	3.34652e12	0.596254
$682$	1.90757e12	0.337637
$683$	−8.52711e12	−1.49937	−0.749685	−	0.661795i	$-0.769795\pi$
$683$	−8.52711e12	−1.49937	−0.749685	+	0.661795i	$0.769795\pi$
$684$	1.15065e12	0.200998
$685$	−3.76632e12	−0.653596
$686$	3.86062e12	0.665578
$687$	−7.44002e11	−0.127429
$688$	6.47994e10	0.0110261
$689$	−9.14354e12	−1.54571
$690$	−5.79642e12	−0.973506
$691$	−1.58080e12	−0.263770	−0.131885	−	0.991265i	$-0.542103\pi$
$691$	−1.58080e12	−0.263770	−0.131885	+	0.991265i	$0.542103\pi$
$692$	−2.44517e12	−0.405351
$693$	−1.96346e12	−0.323386
$694$	−2.83082e12	−0.463228
$695$	−1.01469e13	−1.64969
$696$	5.90677e12	0.954132
$697$	0	0
$698$	1.01744e12	0.162240
$699$	9.25544e12	1.46639
$700$	3.18407e12	0.501235
$701$	−7.52831e12	−1.17751	−0.588757	−	0.808310i	$-0.700383\pi$
$701$	−7.52831e12	−1.17751	−0.588757	+	0.808310i	$0.700383\pi$
$702$	−4.10492e12	−0.637951
$703$	7.33979e12	1.13340
$704$	1.89683e12	0.291040
$705$	2.53812e12	0.386956
$706$	−3.05456e11	−0.0462729
$707$	−7.59521e12	−1.14328
$708$	−5.39913e12	−0.807559
$709$	−9.73509e12	−1.44688	−0.723439	−	0.690388i	$-0.757440\pi$
$709$	−9.73509e12	−1.44688	−0.723439	+	0.690388i	$0.757440\pi$
$710$	−4.12794e12	−0.609637
$711$	−7.30506e11	−0.107204
$712$	−1.90628e12	−0.277988
$713$	−8.23703e12	−1.19363
$714$	0	0
$715$	−6.96400e12	−0.996510
$716$	−3.82985e12	−0.544594
$717$	1.06091e13	1.49914
$718$	−6.06125e11	−0.0851142
$719$	−5.11859e12	−0.714283	−0.357142	−	0.934050i	$-0.616249\pi$
$719$	−5.11859e12	−0.714283	−0.357142	+	0.934050i	$0.616249\pi$
$720$	2.73945e11	0.0379898
$721$	−1.07157e12	−0.147677
$722$	8.82472e11	0.120860
$723$	1.40013e13	1.90567
$724$	−5.91120e12	−0.799562
$725$	2.93146e12	0.394060
$726$	3.39580e12	0.453657
$727$	−2.98745e12	−0.396639	−0.198320	−	0.980137i	$-0.563548\pi$
$727$	−2.98745e12	−0.396639	−0.198320	+	0.980137i	$0.563548\pi$
$728$	1.72792e13	2.27998
$729$	3.52600e12	0.462390
$730$	−8.37419e12	−1.09142
$731$	0	0
$732$	1.13748e13	1.46435
$733$	−1.43419e13	−1.83501	−0.917504	−	0.397727i	$-0.869799\pi$
$733$	−1.43419e13	−1.83501	−0.917504	+	0.397727i	$0.869799\pi$
$734$	3.41744e12	0.434579
$735$	1.87891e13	2.37472
$736$	−9.67202e12	−1.21497
$737$	1.58871e12	0.198354
$738$	−2.96914e12	−0.368448
$739$	9.31228e12	1.14857	0.574283	−	0.818657i	$-0.305281\pi$
$739$	9.31228e12	1.14857	0.574283	+	0.818657i	$0.305281\pi$
$740$	8.26773e12	1.01355
$741$	1.21383e13	1.47902
$742$	8.54487e12	1.03488
$743$	1.06547e13	1.28260	0.641300	−	0.767290i	$-0.278395\pi$
$743$	1.06547e13	1.28260	0.641300	+	0.767290i	$0.278395\pi$
$744$	−9.43479e12	−1.12890
$745$	5.39464e12	0.641592
$746$	2.01439e12	0.238132
$747$	3.33645e12	0.392050
$748$	0	0
$749$	−3.79149e12	−0.440191
$750$	3.80719e12	0.439368
$751$	2.96169e12	0.339750	0.169875	−	0.985466i	$-0.445664\pi$
$751$	2.96169e12	0.339750	0.169875	+	0.985466i	$0.445664\pi$
$752$	2.21661e11	0.0252761
$753$	8.48674e11	0.0961974
$754$	6.31498e12	0.711543
$755$	1.20895e13	1.35409
$756$	−7.38946e12	−0.822743
$757$	5.93614e12	0.657011	0.328506	−	0.944502i	$-0.393455\pi$
$757$	5.93614e12	0.657011	0.328506	+	0.944502i	$0.393455\pi$
$758$	5.83616e12	0.642119
$759$	7.23241e12	0.791034
$760$	−9.60785e12	−1.04464
$761$	8.11063e12	0.876645	0.438322	−	0.898818i	$-0.355573\pi$
$761$	8.11063e12	0.876645	0.438322	+	0.898818i	$0.355573\pi$
$762$	−2.05849e12	−0.221183
$763$	−1.78505e13	−1.90673
$764$	−2.28219e12	−0.242343
$765$	0	0
$766$	3.04231e12	0.319282
$767$	−1.45411e13	−1.51712
$768$	−1.04049e13	−1.07923
$769$	−1.33952e13	−1.38128	−0.690640	−	0.723199i	$-0.742671\pi$
$769$	−1.33952e13	−1.38128	−0.690640	+	0.723199i	$0.742671\pi$
$770$	6.50804e12	0.667178
$771$	−1.76922e13	−1.80318
$772$	−9.17754e12	−0.929926
$773$	−1.80918e13	−1.82253	−0.911264	−	0.411822i	$-0.864893\pi$
$773$	−1.80918e13	−1.82253	−0.911264	+	0.411822i	$0.864893\pi$
$774$	−2.40915e11	−0.0241285
$775$	−4.68237e12	−0.466238
$776$	−8.62514e12	−0.853864
$777$	2.45901e13	2.42028
$778$	1.93051e12	0.188914
$779$	−1.68296e13	−1.63740
$780$	1.36729e13	1.32262
$781$	5.15060e12	0.495368
$782$	0	0
$783$	−6.80321e12	−0.646824
$784$	1.64090e12	0.155117
$785$	1.29763e13	1.21966
$786$	1.14331e13	1.06847
$787$	1.17741e13	1.09406	0.547030	−	0.837113i	$-0.315758\pi$
$787$	1.17741e13	1.09406	0.547030	+	0.837113i	$0.315758\pi$
$788$	−1.53185e12	−0.141530
$789$	2.09174e13	1.92159
$790$	2.42132e12	0.221172
$791$	−1.44363e12	−0.131118
$792$	2.11498e12	0.191004
$793$	3.06351e13	2.75100
$794$	−2.00705e12	−0.179211
$795$	1.70331e13	1.51232
$796$	5.39189e12	0.476028
$797$	9.65087e12	0.847235	0.423618	−	0.905841i	$-0.360760\pi$
$797$	9.65087e12	0.847235	0.423618	+	0.905841i	$0.360760\pi$
$798$	−1.13435e13	−0.990229
$799$	0	0
$800$	−5.49809e12	−0.474577
$801$	−1.14541e12	−0.0983136
$802$	−6.92428e12	−0.591004
$803$	1.04488e13	0.886843
$804$	−3.11921e12	−0.263265
$805$	−2.81023e13	−2.35863
$806$	−1.00868e13	−0.841873
$807$	−9.26564e11	−0.0769032
$808$	8.18136e12	0.675265
$809$	−1.12770e13	−0.925604	−0.462802	−	0.886462i	$-0.653156\pi$
$809$	−1.12770e13	−0.925604	−0.462802	+	0.886462i	$0.653156\pi$
$810$	1.06177e13	0.866656
$811$	−1.52478e13	−1.23769	−0.618847	−	0.785512i	$-0.712400\pi$
$811$	−1.52478e13	−1.23769	−0.618847	+	0.785512i	$0.712400\pi$
$812$	1.13679e13	0.917652
$813$	2.33426e13	1.87388
$814$	5.35542e12	0.427546
$815$	−1.73512e13	−1.37759
$816$	0	0
$817$	−1.36555e12	−0.107228
$818$	−6.02192e11	−0.0470267
$819$	1.03824e13	0.806341
$820$	−1.89573e13	−1.46424
$821$	−4.82791e12	−0.370864	−0.185432	−	0.982657i	$-0.559368\pi$
$821$	−4.82791e12	−0.370864	−0.185432	+	0.982657i	$0.559368\pi$
$822$	4.78988e12	0.365933
$823$	−5.22318e12	−0.396858	−0.198429	−	0.980115i	$-0.563584\pi$
$823$	−5.22318e12	−0.396858	−0.198429	+	0.980115i	$0.563584\pi$
$824$	1.15427e12	0.0872235
$825$	4.11129e12	0.308984
$826$	1.35891e13	1.01573
$827$	−1.93970e13	−1.44198	−0.720990	−	0.692945i	$-0.756313\pi$
$827$	−1.93970e13	−1.44198	−0.720990	+	0.692945i	$0.756313\pi$
$828$	−3.62532e12	−0.268046
$829$	2.38824e12	0.175624	0.0878119	−	0.996137i	$-0.472013\pi$
$829$	2.38824e12	0.175624	0.0878119	+	0.996137i	$0.472013\pi$
$830$	−1.10589e13	−0.808839
$831$	−2.21431e13	−1.61077
$832$	−1.00301e13	−0.725687
$833$	0	0
$834$	1.29045e13	0.923621
$835$	1.52075e13	1.08260
$836$	4.75881e12	0.336953
$837$	1.08667e13	0.765299
$838$	1.35941e13	0.952254
$839$	1.16067e13	0.808687	0.404344	−	0.914607i	$-0.367500\pi$
$839$	1.16067e13	0.808687	0.404344	+	0.914607i	$0.367500\pi$
$840$	−3.21887e13	−2.23073
$841$	−4.04112e12	−0.278561
$842$	2.67536e12	0.183433
$843$	1.82860e13	1.24708
$844$	−5.50192e12	−0.373227
$845$	1.88927e13	1.27479
$846$	−8.24105e11	−0.0553116
$847$	1.64636e13	1.09913
$848$	1.48755e12	0.0987848
$849$	1.96596e13	1.29864
$850$	0	0
$851$	−2.31252e13	−1.51148
$852$	−1.01125e13	−0.657477
$853$	−2.31967e13	−1.50022	−0.750111	−	0.661312i	$-0.770000\pi$
$853$	−2.31967e13	−1.50022	−0.750111	+	0.661312i	$0.770000\pi$
$854$	−2.86293e13	−1.84183
$855$	−5.77297e12	−0.369447
$856$	4.08409e12	0.259994
$857$	2.78721e13	1.76505	0.882523	−	0.470269i	$-0.155843\pi$
$857$	2.78721e13	1.76505	0.882523	+	0.470269i	$0.155843\pi$
$858$	8.85660e12	0.557923
$859$	−4.65756e12	−0.291870	−0.145935	−	0.989294i	$-0.546619\pi$
$859$	−4.65756e12	−0.291870	−0.145935	+	0.989294i	$0.546619\pi$
$860$	−1.53819e12	−0.0958885
$861$	−5.63833e13	−3.49652
$862$	1.96472e12	0.121204
$863$	3.55944e12	0.218441	0.109220	−	0.994018i	$-0.465165\pi$
$863$	3.55944e12	0.218441	0.109220	+	0.994018i	$0.465165\pi$
$864$	1.27598e13	0.778987
$865$	1.22677e13	0.745058
$866$	−5.22724e12	−0.315822
$867$	0	0
$868$	−1.81578e13	−1.08573
$869$	−3.02118e12	−0.179716
$870$	−1.17639e13	−0.696171
$871$	−8.40077e12	−0.494581
$872$	1.92281e13	1.12619
$873$	−5.18250e12	−0.301978
$874$	1.06677e13	0.618403
$875$	1.84581e13	1.06451
$876$	−2.05148e13	−1.17706
$877$	1.26085e13	0.719724	0.359862	−	0.933005i	$-0.382824\pi$
$877$	1.26085e13	0.719724	0.359862	+	0.933005i	$0.382824\pi$
$878$	−8.20511e12	−0.465971
$879$	−7.19793e12	−0.406684
$880$	1.13296e12	0.0636860
$881$	−6.09559e12	−0.340898	−0.170449	−	0.985366i	$-0.554522\pi$
$881$	−6.09559e12	−0.340898	−0.170449	+	0.985366i	$0.554522\pi$
$882$	−6.10065e12	−0.339443
$883$	6.22930e12	0.344839	0.172419	−	0.985024i	$-0.444842\pi$
$883$	6.22930e12	0.344839	0.172419	+	0.985024i	$0.444842\pi$
$884$	0	0
$885$	2.70881e13	1.48434
$886$	7.83344e12	0.427072
$887$	1.24863e13	0.677292	0.338646	−	0.940914i	$-0.390031\pi$
$887$	1.24863e13	0.677292	0.338646	+	0.940914i	$0.390031\pi$
$888$	−2.64878e13	−1.42951
$889$	−9.98002e12	−0.535887
$890$	3.79655e12	0.202831
$891$	−1.32481e13	−0.704212
$892$	−1.92362e13	−1.01737
$893$	−4.67117e12	−0.245807
$894$	−6.86073e12	−0.359213
$895$	1.92148e13	1.00100
$896$	−2.30163e13	−1.19302
$897$	−3.82436e13	−1.97239
$898$	3.75082e11	0.0192479
$899$	−1.67172e13	−0.853582
$900$	−2.06082e12	−0.104701
$901$	0	0
$902$	−1.22796e13	−0.617666
$903$	−4.57493e12	−0.228976
$904$	1.55504e12	0.0774432
$905$	2.96572e13	1.46964
$906$	−1.53750e13	−0.758121
$907$	−1.47898e13	−0.725655	−0.362827	−	0.931856i	$-0.618189\pi$
$907$	−1.47898e13	−0.725655	−0.362827	+	0.931856i	$0.618189\pi$
$908$	−6.93759e12	−0.338706
$909$	4.91585e12	0.238815
$910$	−3.44132e13	−1.66356
$911$	1.93502e13	0.930793	0.465396	−	0.885102i	$-0.345912\pi$
$911$	1.93502e13	0.930793	0.465396	+	0.885102i	$0.345912\pi$
$912$	−1.97476e12	−0.0945230
$913$	1.37987e13	0.657232
$914$	3.47219e11	0.0164568
$915$	−5.70689e13	−2.69157
$916$	1.54237e12	0.0723870
$917$	5.54302e13	2.58872
$918$	0	0
$919$	6.14623e12	0.284243	0.142121	−	0.989849i	$-0.454608\pi$
$919$	6.14623e12	0.284243	0.142121	+	0.989849i	$0.454608\pi$
$920$	3.02710e13	1.39310
$921$	−4.54277e13	−2.08043
$922$	−1.71539e13	−0.781761
$923$	−2.72353e13	−1.23516
$924$	1.59432e13	0.719533
$925$	−1.31456e13	−0.590394
$926$	8.78581e11	0.0392674
$927$	6.93552e11	0.0308475
$928$	−1.96295e13	−0.868849
$929$	2.99979e12	0.132136	0.0660679	−	0.997815i	$-0.478955\pi$
$929$	2.99979e12	0.132136	0.0660679	+	0.997815i	$0.478955\pi$
$930$	1.87903e13	0.823685
$931$	−3.45795e13	−1.50850
$932$	−1.91872e13	−0.832992
$933$	3.00156e13	1.29682
$934$	1.05344e13	0.452950
$935$	0	0
$936$	−1.11836e13	−0.476256
$937$	3.61606e13	1.53253	0.766263	−	0.642527i	$-0.222114\pi$
$937$	3.61606e13	1.53253	0.766263	+	0.642527i	$0.222114\pi$
$938$	7.85073e12	0.331129
$939$	−2.57652e13	−1.08153
$940$	−5.26173e12	−0.219813
$941$	−3.36752e13	−1.40009	−0.700046	−	0.714097i	$-0.746837\pi$
$941$	−3.36752e13	−1.40009	−0.700046	+	0.714097i	$0.746837\pi$
$942$	−1.65029e13	−0.682858
$943$	5.30242e13	2.18359
$944$	2.36568e12	0.0969575
$945$	3.70738e13	1.51225
$946$	−9.96361e11	−0.0404489
$947$	2.50881e13	1.01366	0.506830	−	0.862046i	$-0.330817\pi$
$947$	2.50881e13	1.01366	0.506830	+	0.862046i	$0.330817\pi$
$948$	5.93168e12	0.238528
$949$	−5.52512e13	−2.21128
$950$	6.06412e12	0.241552
$951$	7.08100e12	0.280726
$952$	0	0
$953$	−2.40784e13	−0.945604	−0.472802	−	0.881169i	$-0.656757\pi$
$953$	−2.40784e13	−0.945604	−0.472802	+	0.881169i	$0.656757\pi$
$954$	−5.53050e12	−0.216171
$955$	1.14500e13	0.445441
$956$	−2.19935e13	−0.851598
$957$	1.46783e13	0.565682
$958$	−7.64811e12	−0.293366
$959$	2.32224e13	0.886591
$960$	1.86846e13	0.710009
$961$	2.62508e11	0.00992857
$962$	−2.83184e13	−1.06606
$963$	2.45396e12	0.0919496
$964$	−2.90258e13	−1.08253
$965$	4.60448e13	1.70926
$966$	3.57396e13	1.32054
$967$	−4.05243e11	−0.0149038	−0.00745189	−	0.999972i	$-0.502372\pi$
$967$	−4.05243e11	−0.0149038	−0.00745189	+	0.999972i	$0.502372\pi$
$968$	−1.77341e13	−0.649189
$969$	0	0
$970$	1.71778e13	0.623011
$971$	−3.48606e13	−1.25848	−0.629242	−	0.777209i	$-0.716635\pi$
$971$	−3.48606e13	−1.25848	−0.629242	+	0.777209i	$0.716635\pi$
$972$	1.20604e13	0.433375
$973$	6.25638e13	2.23777
$974$	2.05845e13	0.732868
$975$	−2.17397e13	−0.770428
$976$	−4.98399e12	−0.175814
$977$	3.41692e13	1.19980	0.599901	−	0.800074i	$-0.295207\pi$
$977$	3.41692e13	1.19980	0.599901	+	0.800074i	$0.295207\pi$
$978$	2.20667e13	0.771280
$979$	−4.73710e12	−0.164813
$980$	−3.89513e13	−1.34898
$981$	1.15534e13	0.398289
$982$	−8.70844e12	−0.298840
$983$	−1.39724e13	−0.477288	−0.238644	−	0.971107i	$-0.576703\pi$
$983$	−1.39724e13	−0.477288	−0.238644	+	0.971107i	$0.576703\pi$
$984$	6.07346e13	2.06518
$985$	7.68546e12	0.260140
$986$	0	0
$987$	−1.56496e13	−0.524899
$988$	−2.51636e13	−0.840169
$989$	4.30238e12	0.142996
$990$	−4.21220e12	−0.139364
$991$	−1.22242e12	−0.0402614	−0.0201307	−	0.999797i	$-0.506408\pi$
$991$	−1.22242e12	−0.0402614	−0.0201307	+	0.999797i	$0.506408\pi$
$992$	3.13539e13	1.02799
$993$	−1.04419e13	−0.340807
$994$	2.54521e13	0.826961
$995$	−2.70517e13	−0.874966
$996$	−2.70918e13	−0.872310
$997$	2.99277e13	0.959280	0.479640	−	0.877465i	$-0.340767\pi$
$997$	2.99277e13	0.959280	0.479640	+	0.877465i	$0.340767\pi$
$998$	−6.30073e12	−0.201050
$999$	3.05077e13	0.969092

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.e.1.5	yes	12
17.16	even	2		289.10.a.d.1.5	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.d.1.5	✓	12	17.16	even	2
289.10.a.e.1.5	yes	12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q-13.2275 q^{2} +162.576 q^{3} -337.033 q^{4} +1690.93 q^{5} -2150.48 q^{6} -10426.0 q^{7} +11230.6 q^{8} +6748.01 q^{9} +O(q^{10})\)	\(q-13.2275 q^{2} +162.576 q^{3} -337.033 q^{4} +1690.93 q^{5} -2150.48 q^{6} -10426.0 q^{7} +11230.6 q^{8} +6748.01 q^{9} -22366.8 q^{10} +27908.0 q^{11} -54793.5 q^{12} -147572. q^{13} +137910. q^{14} +274906. q^{15} +24008.3 q^{16} -89259.3 q^{18} -505938. q^{19} -569901. q^{20} -1.69502e6 q^{21} -369153. q^{22} +1.59404e6 q^{23} +1.82583e6 q^{24} +906135. q^{25} +1.95201e6 q^{26} -2.10292e6 q^{27} +3.51390e6 q^{28} +3.23512e6 q^{29} -3.63632e6 q^{30} -5.16741e6 q^{31} -6.06763e6 q^{32} +4.53717e6 q^{33} -1.76296e7 q^{35} -2.27430e6 q^{36} -1.45073e7 q^{37} +6.69229e6 q^{38} -2.39917e7 q^{39} +1.89902e7 q^{40} +3.32642e7 q^{41} +2.24208e7 q^{42} +2.69905e6 q^{43} -9.40592e6 q^{44} +1.14104e7 q^{45} -2.10851e7 q^{46} +9.23270e6 q^{47} +3.90317e6 q^{48} +6.83475e7 q^{49} -1.19859e7 q^{50} +4.97366e7 q^{52} +6.19599e7 q^{53} +2.78164e7 q^{54} +4.71906e7 q^{55} -1.17090e8 q^{56} -8.22534e7 q^{57} -4.27926e7 q^{58} +9.85359e7 q^{59} -9.26523e7 q^{60} -2.07595e8 q^{61} +6.83519e7 q^{62} -7.03546e7 q^{63} +6.79674e7 q^{64} -2.49534e8 q^{65} -6.00155e7 q^{66} +5.69266e7 q^{67} +2.59152e8 q^{69} +2.33196e8 q^{70} +1.84556e8 q^{71} +7.57841e7 q^{72} +3.74402e8 q^{73} +1.91895e8 q^{74} +1.47316e8 q^{75} +1.70518e8 q^{76} -2.90968e8 q^{77} +3.17350e8 q^{78} -1.08255e8 q^{79} +4.05964e7 q^{80} -4.74706e8 q^{81} -4.40002e8 q^{82} +4.94434e8 q^{83} +5.71276e8 q^{84} -3.57017e7 q^{86} +5.25954e8 q^{87} +3.13423e8 q^{88} -1.69740e8 q^{89} -1.50932e8 q^{90} +1.53858e9 q^{91} -5.37243e8 q^{92} -8.40098e8 q^{93} -1.22126e8 q^{94} -8.55507e8 q^{95} -9.86452e8 q^{96} -7.68005e8 q^{97} -9.04066e8 q^{98} +1.88323e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 17 q^{2} + 74 q^{3} + 2987 q^{4} + 454 q^{5} + 2674 q^{6} - 5524 q^{7} - 12036 q^{8} + 71898 q^{9}+O(q^{10}) \) 12 * q + 17 * q^2 + 74 * q^3 + 2987 * q^4 + 454 * q^5 + 2674 * q^6 - 5524 * q^7 - 12036 * q^8 + 71898 * q^9	\( 12 q + 17 q^{2} + 74 q^{3} + 2987 q^{4} + 454 q^{5} + 2674 q^{6} - 5524 q^{7} - 12036 q^{8} + 71898 q^{9} - 2449 q^{10} + 152886 q^{11} + 41717 q^{12} + 23478 q^{13} + 492839 q^{14} - 149346 q^{15} + 272743 q^{16} + 1610378 q^{18} + 1053982 q^{19} - 2477218 q^{20} - 1395256 q^{21} + 2391095 q^{22} + 2012428 q^{23} + 708393 q^{24} + 6123166 q^{25} - 733144 q^{26} + 3231638 q^{27} - 5978216 q^{28} + 12772842 q^{29} + 181633 q^{30} + 5535814 q^{31} - 5277485 q^{32} - 16526054 q^{33} + 23712622 q^{35} - 37692723 q^{36} + 1352872 q^{37} + 3704404 q^{38} - 1380780 q^{39} + 44739331 q^{40} + 40941240 q^{41} - 73649073 q^{42} - 14142490 q^{43} + 148233417 q^{44} - 79449336 q^{45} + 31855859 q^{46} + 133558002 q^{47} - 80444894 q^{48} + 184488050 q^{49} + 103322437 q^{50} + 179597031 q^{52} - 299319258 q^{53} - 50215469 q^{54} - 91197532 q^{55} + 267350757 q^{56} + 49507694 q^{57} + 367048088 q^{58} - 106431852 q^{59} + 103650215 q^{60} + 262041240 q^{61} - 314328847 q^{62} + 218532626 q^{63} + 595820098 q^{64} + 330279796 q^{65} - 117450322 q^{66} - 489635100 q^{67} + 661586712 q^{69} - 226277420 q^{70} + 204290852 q^{71} - 208030791 q^{72} + 673538852 q^{73} + 1274510282 q^{74} + 588895258 q^{75} - 403517977 q^{76} - 705301770 q^{77} + 165043245 q^{78} + 434002980 q^{79} + 599590757 q^{80} - 389011392 q^{81} - 180073450 q^{82} + 411781442 q^{83} - 475971445 q^{84} + 492988379 q^{86} + 1513399800 q^{87} - 262108460 q^{88} + 911678128 q^{89} - 2734590475 q^{90} - 560105446 q^{91} - 847049266 q^{92} - 1228562570 q^{93} + 2009871759 q^{94} - 1116511966 q^{95} + 2204198979 q^{96} - 3589270998 q^{97} - 2677144485 q^{98} + 2056683494 q^{99}+O(q^{100}) \) 12 * q + 17 * q^2 + 74 * q^3 + 2987 * q^4 + 454 * q^5 + 2674 * q^6 - 5524 * q^7 - 12036 * q^8 + 71898 * q^9 - 2449 * q^10 + 152886 * q^11 + 41717 * q^12 + 23478 * q^13 + 492839 * q^14 - 149346 * q^15 + 272743 * q^16 + 1610378 * q^18 + 1053982 * q^19 - 2477218 * q^20 - 1395256 * q^21 + 2391095 * q^22 + 2012428 * q^23 + 708393 * q^24 + 6123166 * q^25 - 733144 * q^26 + 3231638 * q^27 - 5978216 * q^28 + 12772842 * q^29 + 181633 * q^30 + 5535814 * q^31 - 5277485 * q^32 - 16526054 * q^33 + 23712622 * q^35 - 37692723 * q^36 + 1352872 * q^37 + 3704404 * q^38 - 1380780 * q^39 + 44739331 * q^40 + 40941240 * q^41 - 73649073 * q^42 - 14142490 * q^43 + 148233417 * q^44 - 79449336 * q^45 + 31855859 * q^46 + 133558002 * q^47 - 80444894 * q^48 + 184488050 * q^49 + 103322437 * q^50 + 179597031 * q^52 - 299319258 * q^53 - 50215469 * q^54 - 91197532 * q^55 + 267350757 * q^56 + 49507694 * q^57 + 367048088 * q^58 - 106431852 * q^59 + 103650215 * q^60 + 262041240 * q^61 - 314328847 * q^62 + 218532626 * q^63 + 595820098 * q^64 + 330279796 * q^65 - 117450322 * q^66 - 489635100 * q^67 + 661586712 * q^69 - 226277420 * q^70 + 204290852 * q^71 - 208030791 * q^72 + 673538852 * q^73 + 1274510282 * q^74 + 588895258 * q^75 - 403517977 * q^76 - 705301770 * q^77 + 165043245 * q^78 + 434002980 * q^79 + 599590757 * q^80 - 389011392 * q^81 - 180073450 * q^82 + 411781442 * q^83 - 475971445 * q^84 + 492988379 * q^86 + 1513399800 * q^87 - 262108460 * q^88 + 911678128 * q^89 - 2734590475 * q^90 - 560105446 * q^91 - 847049266 * q^92 - 1228562570 * q^93 + 2009871759 * q^94 - 1116511966 * q^95 + 2204198979 * q^96 - 3589270998 * q^97 - 2677144485 * q^98 + 2056683494 * q^99

Introduction

L-functions

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