LMFDB - Embedded newform 91.8.a.e.1.6

Newspace parameters

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	91.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$28.4270373191$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
Defining polynomial:	$ x^{12} - 6 x^{11} - 1243 x^{10} + 5598 x^{9} + 567554 x^{8} - 1739560 x^{7} - 117081910 x^{6} + 186018392 x^{5} + 10752389517 x^{4} + 491049966 x^{3} + \cdots + 59402280000 $ x^12 - 6x^11 - 1243x^10 + 5598x^9 + 567554x^8 - 1739560x^7 - 117081910x^6 + 186018392x^5 + 10752389517x^4 + 491049966x^3 - 344602049215x^2 - 835334324470*x + 59402280000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.0691404$ of defining polynomial
Character	$\chi$	$=$	91.1

$q$-expansion

$f(q)$	$=$	$q+0.930860 q^{2} +23.4478 q^{3} -127.134 q^{4} -494.625 q^{5} +21.8266 q^{6} +343.000 q^{7} -237.493 q^{8} -1637.20 q^{9} +O(q^{10})$	\(q+0.930860 q^{2} +23.4478 q^{3} -127.134 q^{4} -494.625 q^{5} +21.8266 q^{6} +343.000 q^{7} -237.493 q^{8} -1637.20 q^{9} -460.427 q^{10} -2424.00 q^{11} -2981.00 q^{12} +2197.00 q^{13} +319.285 q^{14} -11597.9 q^{15} +16052.0 q^{16} +3893.57 q^{17} -1524.00 q^{18} -4518.07 q^{19} +62883.5 q^{20} +8042.60 q^{21} -2256.40 q^{22} +66046.1 q^{23} -5568.70 q^{24} +166529. q^{25} +2045.10 q^{26} -89669.1 q^{27} -43606.8 q^{28} +6156.48 q^{29} -10796.0 q^{30} +17664.1 q^{31} +45341.3 q^{32} -56837.5 q^{33} +3624.37 q^{34} -169657. q^{35} +208143. q^{36} -516218. q^{37} -4205.69 q^{38} +51514.8 q^{39} +117470. q^{40} +470707. q^{41} +7486.53 q^{42} -10789.1 q^{43} +308172. q^{44} +809801. q^{45} +61479.6 q^{46} +326569. q^{47} +376385. q^{48} +117649. q^{49} +155015. q^{50} +91295.7 q^{51} -279312. q^{52} +1.91089e6 q^{53} -83469.3 q^{54} +1.19897e6 q^{55} -81460.3 q^{56} -105939. q^{57} +5730.82 q^{58} +558449. q^{59} +1.47448e6 q^{60} -1.32987e6 q^{61} +16442.8 q^{62} -561560. q^{63} -2.01245e6 q^{64} -1.08669e6 q^{65} -52907.7 q^{66} +2.71304e6 q^{67} -495004. q^{68} +1.54864e6 q^{69} -157926. q^{70} -2.18693e6 q^{71} +388824. q^{72} -2.12208e6 q^{73} -480527. q^{74} +3.90475e6 q^{75} +574398. q^{76} -831432. q^{77} +47953.1 q^{78} -3.62059e6 q^{79} -7.93974e6 q^{80} +1.47801e6 q^{81} +438162. q^{82} +8.69991e6 q^{83} -1.02248e6 q^{84} -1.92586e6 q^{85} -10043.1 q^{86} +144356. q^{87} +575684. q^{88} -2.94631e6 q^{89} +753811. q^{90} +753571. q^{91} -8.39667e6 q^{92} +414184. q^{93} +303990. q^{94} +2.23475e6 q^{95} +1.06315e6 q^{96} -1.35540e7 q^{97} +109515. q^{98} +3.96857e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} + 82 q^{3} + 986 q^{4} + 1026 q^{5} + 309 q^{6} + 4116 q^{7} + 228 q^{8} + 10902 q^{9}+O(q^{10}) $ 12 * q + 6 * q^2 + 82 * q^3 + 986 * q^4 + 1026 * q^5 + 309 * q^6 + 4116 * q^7 + 228 * q^8 + 10902 * q^9	\( 12 q + 6 q^{2} + 82 q^{3} + 986 q^{4} + 1026 q^{5} + 309 q^{6} + 4116 q^{7} + 228 q^{8} + 10902 q^{9} + 6668 q^{10} + 12168 q^{11} - 183 q^{12} + 26364 q^{13} + 2058 q^{14} - 28790 q^{15} + 85914 q^{16} + 82710 q^{17} - 44965 q^{18} - 10302 q^{19} + 141318 q^{20} + 28126 q^{21} - 97457 q^{22} + 98376 q^{23} - 519981 q^{24} + 272736 q^{25} + 13182 q^{26} + 306652 q^{27} + 338198 q^{28} + 350592 q^{29} + 231528 q^{30} + 55092 q^{31} + 114420 q^{32} + 609912 q^{33} + 812002 q^{34} + 351918 q^{35} + 1472143 q^{36} + 376310 q^{37} + 2825424 q^{38} + 180154 q^{39} + 2169290 q^{40} + 1387272 q^{41} + 105987 q^{42} + 568708 q^{43} + 3392031 q^{44} + 3556226 q^{45} - 1736829 q^{46} + 1359444 q^{47} + 4151249 q^{48} + 1411788 q^{49} + 3983712 q^{50} + 2709260 q^{51} + 2166242 q^{52} + 2061780 q^{53} + 2196651 q^{54} - 2112846 q^{55} + 78204 q^{56} + 2359902 q^{57} + 670268 q^{58} + 395964 q^{59} - 1052376 q^{60} + 444006 q^{61} + 2854353 q^{62} + 3739386 q^{63} + 12026858 q^{64} + 2254122 q^{65} - 4605681 q^{66} - 3094010 q^{67} + 4668954 q^{68} + 3839892 q^{69} + 2287124 q^{70} + 5694366 q^{71} - 9780585 q^{72} + 7052346 q^{73} - 4436259 q^{74} - 16288696 q^{75} - 3051830 q^{76} + 4173624 q^{77} + 678873 q^{78} + 4304160 q^{79} + 3807018 q^{80} - 6689556 q^{81} - 4733665 q^{82} + 2704554 q^{83} - 62769 q^{84} + 9301878 q^{85} + 1510998 q^{86} + 16231802 q^{87} - 70453923 q^{88} - 10986042 q^{89} - 12851300 q^{90} + 9042852 q^{91} - 16505451 q^{92} - 47230934 q^{93} - 24306151 q^{94} - 21839424 q^{95} - 86512741 q^{96} - 24462382 q^{97} + 705894 q^{98} + 11555078 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 + 82 * q^3 + 986 * q^4 + 1026 * q^5 + 309 * q^6 + 4116 * q^7 + 228 * q^8 + 10902 * q^9 + 6668 * q^10 + 12168 * q^11 - 183 * q^12 + 26364 * q^13 + 2058 * q^14 - 28790 * q^15 + 85914 * q^16 + 82710 * q^17 - 44965 * q^18 - 10302 * q^19 + 141318 * q^20 + 28126 * q^21 - 97457 * q^22 + 98376 * q^23 - 519981 * q^24 + 272736 * q^25 + 13182 * q^26 + 306652 * q^27 + 338198 * q^28 + 350592 * q^29 + 231528 * q^30 + 55092 * q^31 + 114420 * q^32 + 609912 * q^33 + 812002 * q^34 + 351918 * q^35 + 1472143 * q^36 + 376310 * q^37 + 2825424 * q^38 + 180154 * q^39 + 2169290 * q^40 + 1387272 * q^41 + 105987 * q^42 + 568708 * q^43 + 3392031 * q^44 + 3556226 * q^45 - 1736829 * q^46 + 1359444 * q^47 + 4151249 * q^48 + 1411788 * q^49 + 3983712 * q^50 + 2709260 * q^51 + 2166242 * q^52 + 2061780 * q^53 + 2196651 * q^54 - 2112846 * q^55 + 78204 * q^56 + 2359902 * q^57 + 670268 * q^58 + 395964 * q^59 - 1052376 * q^60 + 444006 * q^61 + 2854353 * q^62 + 3739386 * q^63 + 12026858 * q^64 + 2254122 * q^65 - 4605681 * q^66 - 3094010 * q^67 + 4668954 * q^68 + 3839892 * q^69 + 2287124 * q^70 + 5694366 * q^71 - 9780585 * q^72 + 7052346 * q^73 - 4436259 * q^74 - 16288696 * q^75 - 3051830 * q^76 + 4173624 * q^77 + 678873 * q^78 + 4304160 * q^79 + 3807018 * q^80 - 6689556 * q^81 - 4733665 * q^82 + 2704554 * q^83 - 62769 * q^84 + 9301878 * q^85 + 1510998 * q^86 + 16231802 * q^87 - 70453923 * q^88 - 10986042 * q^89 - 12851300 * q^90 + 9042852 * q^91 - 16505451 * q^92 - 47230934 * q^93 - 24306151 * q^94 - 21839424 * q^95 - 86512741 * q^96 - 24462382 * q^97 + 705894 * q^98 + 11555078 * 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 $

$2$	0.930860	0.0822771	0.0411386	−	0.999153i	$-0.486901\pi$
$2$	0.930860	0.0822771	0.0411386	+	0.999153i	$0.486901\pi$
$3$	23.4478	0.501392	0.250696	−	0.968066i	$-0.419340\pi$
$3$	23.4478	0.501392	0.250696	+	0.968066i	$0.419340\pi$
$4$	−127.134	−0.993230
$5$	−494.625	−1.76963	−0.884813	−	0.465946i	$-0.845714\pi$
$5$	−494.625	−1.76963	−0.884813	+	0.465946i	$0.845714\pi$
$6$	21.8266	0.0412531
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	−237.493	−0.163997
$9$	−1637.20	−0.748606
$10$	−460.427	−0.145600
$11$	−2424.00	−0.549109	−0.274554	−	0.961572i	$-0.588530\pi$
$11$	−2424.00	−0.549109	−0.274554	+	0.961572i	$0.588530\pi$
$12$	−2981.00	−0.497998
$13$	2197.00	0.277350
$13$	2197.00	0.277350
$14$	319.285	0.0310978
$15$	−11597.9	−0.887277
$16$	16052.0	0.979737
$17$	3893.57	0.192210	0.0961052	−	0.995371i	$-0.469361\pi$
$17$	3893.57	0.192210	0.0961052	+	0.995371i	$0.469361\pi$
$18$	−1524.00	−0.0615931
$19$	−4518.07	−0.151118	−0.0755588	−	0.997141i	$-0.524074\pi$
$19$	−4518.07	−0.151118	−0.0755588	+	0.997141i	$0.524074\pi$
$20$	62883.5	1.75765
$21$	8042.60	0.189509
$22$	−2256.40	−0.0451791
$23$	66046.1	1.13188	0.565939	−	0.824447i	$-0.308514\pi$
$23$	66046.1	1.13188	0.565939	+	0.824447i	$0.308514\pi$
$24$	−5568.70	−0.0822270
$25$	166529.	2.13158
$26$	2045.10	0.0228196
$27$	−89669.1	−0.876738
$28$	−43606.8	−0.375406
$29$	6156.48	0.0468748	0.0234374	−	0.999725i	$-0.492539\pi$
$29$	6156.48	0.0468748	0.0234374	+	0.999725i	$0.492539\pi$
$30$	−10796.0	−0.0730026
$31$	17664.1	0.106494	0.0532470	−	0.998581i	$-0.483043\pi$
$31$	17664.1	0.106494	0.0532470	+	0.998581i	$0.483043\pi$
$32$	45341.3	0.244607
$33$	−56837.5	−0.275319
$34$	3624.37	0.0158145
$35$	−169657.	−0.668856
$36$	208143.	0.743538
$37$	−516218.	−1.67543	−0.837717	−	0.546104i	$-0.816110\pi$
$37$	−516218.	−1.67543	−0.837717	+	0.546104i	$0.816110\pi$
$38$	−4205.69	−0.0124335
$39$	51514.8	0.139061
$40$	117470.	0.290214
$41$	470707.	1.06661	0.533307	−	0.845922i	$-0.320949\pi$
$41$	470707.	1.06661	0.533307	+	0.845922i	$0.320949\pi$
$42$	7486.53	0.0155922
$43$	−10789.1	−0.0206940	−0.0103470	−	0.999946i	$-0.503294\pi$
$43$	−10789.1	−0.0206940	−0.0103470	+	0.999946i	$0.503294\pi$
$44$	308172.	0.545391
$45$	809801.	1.32475
$46$	61479.6	0.0931277
$47$	326569.	0.458809	0.229405	−	0.973331i	$-0.426322\pi$
$47$	326569.	0.458809	0.229405	+	0.973331i	$0.426322\pi$
$48$	376385.	0.491233
$49$	117649.	0.142857
$50$	155015.	0.175380
$51$	91295.7	0.0963729
$52$	−279312.	−0.275473
$53$	1.91089e6	1.76307	0.881536	−	0.472117i	$-0.156510\pi$
$53$	1.91089e6	1.76307	0.881536	+	0.472117i	$0.156510\pi$
$54$	−83469.3	−0.0721355
$55$	1.19897e6	0.971717
$56$	−81460.3	−0.0619852
$57$	−105939.	−0.0757692
$58$	5730.82	0.00385673
$59$	558449.	0.353999	0.176999	−	0.984211i	$-0.443361\pi$
$59$	558449.	0.353999	0.176999	+	0.984211i	$0.443361\pi$
$60$	1.47448e6	0.881271
$61$	−1.32987e6	−0.750162	−0.375081	−	0.926992i	$-0.622385\pi$
$61$	−1.32987e6	−0.750162	−0.375081	+	0.926992i	$0.622385\pi$
$62$	16442.8	0.00876203
$63$	−561560.	−0.282946
$64$	−2.01245e6	−0.959612
$65$	−1.08669e6	−0.490806
$66$	−52907.7	−0.0226524
$67$	2.71304e6	1.10203	0.551017	−	0.834494i	$-0.314240\pi$
$67$	2.71304e6	1.10203	0.551017	+	0.834494i	$0.314240\pi$
$68$	−495004.	−0.190909
$69$	1.54864e6	0.567515
$70$	−157926.	−0.0550315
$71$	−2.18693e6	−0.725153	−0.362577	−	0.931954i	$-0.618103\pi$
$71$	−2.18693e6	−0.725153	−0.362577	+	0.931954i	$0.618103\pi$
$72$	388824.	0.122769
$73$	−2.12208e6	−0.638458	−0.319229	−	0.947678i	$-0.603424\pi$
$73$	−2.12208e6	−0.638458	−0.319229	+	0.947678i	$0.603424\pi$
$74$	−480527.	−0.137850
$75$	3.90475e6	1.06876
$76$	574398.	0.150095
$77$	−831432.	−0.207544
$78$	47953.1	0.0114416
$79$	−3.62059e6	−0.826200	−0.413100	−	0.910686i	$-0.635554\pi$
$79$	−3.62059e6	−0.826200	−0.413100	+	0.910686i	$0.635554\pi$
$80$	−7.93974e6	−1.73377
$81$	1.47801e6	0.309016
$82$	438162.	0.0877580
$83$	8.69991e6	1.67010	0.835048	−	0.550177i	$-0.185440\pi$
$83$	8.69991e6	1.67010	0.835048	+	0.550177i	$0.185440\pi$
$84$	−1.02248e6	−0.188226
$85$	−1.92586e6	−0.340141
$86$	−10043.1	−0.00170265
$87$	144356.	0.0235027
$88$	575684.	0.0900523
$89$	−2.94631e6	−0.443010	−0.221505	−	0.975159i	$-0.571097\pi$
$89$	−2.94631e6	−0.443010	−0.221505	+	0.975159i	$0.571097\pi$
$90$	753811.	0.108997
$91$	753571.	0.104828
$92$	−8.39667e6	−1.12422
$93$	414184.	0.0533953
$94$	303990.	0.0377495
$95$	2.23475e6	0.267422
$96$	1.06315e6	0.122644
$97$	−1.35540e7	−1.50788	−0.753940	−	0.656944i	$-0.771849\pi$
$97$	−1.35540e7	−1.50788	−0.753940	+	0.656944i	$0.771849\pi$
$98$	109515.	0.0117539
$99$	3.96857e6	0.411066
$100$	−2.11715e7	−2.11715
$101$	−877418.	−0.0847387	−0.0423694	−	0.999102i	$-0.513491\pi$
$101$	−877418.	−0.0847387	−0.0423694	+	0.999102i	$0.513491\pi$
$102$	84983.5	0.00792929
$103$	−4.70617e6	−0.424363	−0.212182	−	0.977230i	$-0.568057\pi$
$103$	−4.70617e6	−0.424363	−0.212182	+	0.977230i	$0.568057\pi$
$104$	−521773.	−0.0454847
$105$	−3.97807e6	−0.335359
$106$	1.77877e6	0.145061
$107$	1.75215e7	1.38270	0.691348	−	0.722522i	$-0.257017\pi$
$107$	1.75215e7	1.38270	0.691348	+	0.722522i	$0.257017\pi$
$108$	1.13999e7	0.870803
$109$	2.32662e7	1.72081	0.860405	−	0.509610i	$-0.170210\pi$
$109$	2.32662e7	1.72081	0.860405	+	0.509610i	$0.170210\pi$
$110$	1.11607e6	0.0799501
$111$	−1.21042e7	−0.840050
$112$	5.50584e6	0.370306
$113$	−1.35712e7	−0.884798	−0.442399	−	0.896818i	$-0.645872\pi$
$113$	−1.35712e7	−0.884798	−0.442399	+	0.896818i	$0.645872\pi$
$114$	−98614.1	−0.00623407
$115$	−3.26681e7	−2.00300
$116$	−782695.	−0.0465575
$117$	−3.59693e6	−0.207626
$118$	519838.	0.0291260
$119$	1.33550e6	0.0726487
$120$	2.75442e6	0.145511
$121$	−1.36114e7	−0.698480
$122$	−1.23792e6	−0.0617212
$123$	1.10371e7	0.534792
$124$	−2.24570e6	−0.105773
$125$	−4.37271e7	−2.00247
$126$	−522733.	−0.0232800
$127$	3.70642e7	1.60562	0.802808	−	0.596238i	$-0.203338\pi$
$127$	3.70642e7	1.60562	0.802808	+	0.596238i	$0.203338\pi$
$128$	−7.67700e6	−0.323561
$129$	−252981.	−0.0103758
$130$	−1.01156e6	−0.0403821
$131$	2.90039e7	1.12722	0.563608	−	0.826042i	$-0.309413\pi$
$131$	2.90039e7	1.12722	0.563608	+	0.826042i	$0.309413\pi$
$132$	7.22595e6	0.273455
$133$	−1.54970e6	−0.0571171
$134$	2.52546e6	0.0906722
$135$	4.43526e7	1.55150
$136$	−924698.	−0.0315220
$137$	−5.47775e7	−1.82004	−0.910018	−	0.414568i	$-0.863933\pi$
$137$	−5.47775e7	−1.82004	−0.910018	+	0.414568i	$0.863933\pi$
$138$	1.44156e6	0.0466935
$139$	5.17133e6	0.163324	0.0816620	−	0.996660i	$-0.473977\pi$
$139$	5.17133e6	0.163324	0.0816620	+	0.996660i	$0.473977\pi$
$140$	2.15690e7	0.664328
$141$	7.65732e6	0.230044
$142$	−2.03572e6	−0.0596635
$143$	−5.32553e6	−0.152295
$144$	−2.62804e7	−0.733437
$145$	−3.04515e6	−0.0829509
$146$	−1.97536e6	−0.0525305
$147$	2.75861e6	0.0716275
$148$	6.56287e7	1.66409
$149$	−4.51810e7	−1.11893	−0.559467	−	0.828853i	$-0.688994\pi$
$149$	−4.51810e7	−1.11893	−0.559467	+	0.828853i	$0.688994\pi$
$150$	3.63477e6	0.0879342
$151$	−4.62761e7	−1.09380	−0.546899	−	0.837199i	$-0.684192\pi$
$151$	−4.62761e7	−1.09380	−0.546899	+	0.837199i	$0.684192\pi$
$152$	1.07301e6	0.0247829
$153$	−6.37456e6	−0.143890
$154$	−773946.	−0.0170761
$155$	−8.73711e6	−0.188455
$156$	−6.54926e6	−0.138120
$157$	6.09778e7	1.25754	0.628771	−	0.777590i	$-0.283558\pi$
$157$	6.09778e7	1.25754	0.628771	+	0.777590i	$0.283558\pi$
$158$	−3.37027e6	−0.0679774
$159$	4.48062e7	0.883991
$160$	−2.24270e7	−0.432863
$161$	2.26538e7	0.427810
$162$	1.37582e6	0.0254249
$163$	9.57829e7	1.73233	0.866166	−	0.499756i	$-0.166577\pi$
$163$	9.57829e7	1.73233	0.866166	+	0.499756i	$0.166577\pi$
$164$	−5.98427e7	−1.05939
$165$	2.81133e7	0.487211
$166$	8.09840e6	0.137411
$167$	9.10292e7	1.51242	0.756211	−	0.654328i	$-0.227048\pi$
$167$	9.10292e7	1.51242	0.756211	+	0.654328i	$0.227048\pi$
$168$	−1.91006e6	−0.0310789
$169$	4.82681e6	0.0769231
$170$	−1.79271e6	−0.0279858
$171$	7.39698e6	0.113127
$172$	1.37166e6	0.0205540
$173$	5.65303e7	0.830080	0.415040	−	0.909803i	$-0.363768\pi$
$173$	5.65303e7	0.830080	0.415040	+	0.909803i	$0.363768\pi$
$174$	134375.	0.00193373
$175$	5.71196e7	0.805660
$176$	−3.89101e7	−0.537982
$177$	1.30944e7	0.177492
$178$	−2.74260e6	−0.0364496
$179$	1.07498e8	1.40092	0.700462	−	0.713690i	$-0.252977\pi$
$179$	1.07498e8	1.40092	0.700462	+	0.713690i	$0.252977\pi$
$180$	−1.02953e8	−1.31578
$181$	360328.	0.00451672	0.00225836	−	0.999997i	$-0.499281\pi$
$181$	360328.	0.00451672	0.00225836	+	0.999997i	$0.499281\pi$
$182$	701469.	0.00862499
$183$	−3.11826e7	−0.376126
$184$	−1.56855e7	−0.185625
$185$	2.55335e8	2.96489
$186$	385547.	0.00439321
$187$	−9.43802e6	−0.105544
$188$	−4.15178e7	−0.455703
$189$	−3.07565e7	−0.331376
$190$	2.08024e6	0.0220027
$191$	−9.36138e7	−0.972127	−0.486063	−	0.873924i	$-0.661568\pi$
$191$	−9.36138e7	−0.972127	−0.486063	+	0.873924i	$0.661568\pi$
$192$	−4.71876e7	−0.481142
$193$	2.52440e7	0.252759	0.126380	−	0.991982i	$-0.459664\pi$
$193$	2.52440e7	0.252759	0.126380	+	0.991982i	$0.459664\pi$
$194$	−1.26169e7	−0.124064
$195$	−2.54805e7	−0.246086
$196$	−1.49571e7	−0.141890
$197$	2.48755e7	0.231814	0.115907	−	0.993260i	$-0.463023\pi$
$197$	2.48755e7	0.231814	0.115907	+	0.993260i	$0.463023\pi$
$198$	3.69418e6	0.0338213
$199$	9.49592e7	0.854184	0.427092	−	0.904208i	$-0.359538\pi$
$199$	9.49592e7	0.854184	0.427092	+	0.904208i	$0.359538\pi$
$200$	−3.95496e7	−0.349573
$201$	6.36149e7	0.552552
$202$	−816753.	−0.00697206
$203$	2.11167e6	0.0177170
$204$	−1.16067e7	−0.0957205
$205$	−2.32824e8	−1.88751
$206$	−4.38079e6	−0.0349154
$207$	−1.08131e8	−0.847330
$208$	3.52663e7	0.271730
$209$	1.09518e7	0.0829799
$210$	−3.70303e6	−0.0275924
$211$	−1.66589e8	−1.22084	−0.610419	−	0.792079i	$-0.708999\pi$
$211$	−1.66589e8	−1.22084	−0.610419	+	0.792079i	$0.708999\pi$
$212$	−2.42938e8	−1.75114
$213$	−5.12786e7	−0.363586
$214$	1.63100e7	0.113764
$215$	5.33656e6	0.0366207
$216$	2.12958e7	0.143783
$217$	6.05878e6	0.0402510
$218$	2.16576e7	0.141583
$219$	−4.97582e7	−0.320118
$220$	−1.52430e8	−0.965139
$221$	8.55418e6	0.0533096
$222$	−1.12673e7	−0.0691169
$223$	2.41515e8	1.45840	0.729202	−	0.684299i	$-0.239892\pi$
$223$	2.41515e8	1.45840	0.729202	+	0.684299i	$0.239892\pi$
$224$	1.55521e7	0.0924529
$225$	−2.72642e8	−1.59571
$226$	−1.26329e7	−0.0727986
$227$	2.97079e8	1.68571	0.842853	−	0.538143i	$-0.180874\pi$
$227$	2.97079e8	1.68571	0.842853	+	0.538143i	$0.180874\pi$
$228$	1.34684e7	0.0752563
$229$	4.88538e7	0.268828	0.134414	−	0.990925i	$-0.457085\pi$
$229$	4.88538e7	0.268828	0.134414	+	0.990925i	$0.457085\pi$
$230$	−3.04094e7	−0.164801
$231$	−1.94953e7	−0.104061
$232$	−1.46212e6	−0.00768735
$233$	1.21240e8	0.627915	0.313957	−	0.949437i	$-0.398345\pi$
$233$	1.21240e8	0.627915	0.313957	+	0.949437i	$0.398345\pi$
$234$	−3.34824e6	−0.0170829
$235$	−1.61529e8	−0.811921
$236$	−7.09976e7	−0.351602
$237$	−8.48950e7	−0.414250
$238$	1.24316e6	0.00597733
$239$	−1.38404e8	−0.655779	−0.327889	−	0.944716i	$-0.606337\pi$
$239$	−1.38404e8	−0.655779	−0.327889	+	0.944716i	$0.606337\pi$
$240$	−1.86169e8	−0.869298
$241$	1.27947e8	0.588805	0.294402	−	0.955682i	$-0.404879\pi$
$241$	1.27947e8	0.588805	0.294402	+	0.955682i	$0.404879\pi$
$242$	−1.26703e7	−0.0574689
$243$	2.30763e8	1.03168
$244$	1.69071e8	0.745084
$245$	−5.81922e7	−0.252804
$246$	1.02739e7	0.0440012
$247$	−9.92619e6	−0.0419125
$248$	−4.19511e6	−0.0174647
$249$	2.03994e8	0.837374
$250$	−4.07038e7	−0.164757
$251$	−1.07601e8	−0.429495	−0.214748	−	0.976670i	$-0.568893\pi$
$251$	−1.07601e8	−0.429495	−0.214748	+	0.976670i	$0.568893\pi$
$252$	7.13931e7	0.281031
$253$	−1.60096e8	−0.621524
$254$	3.45016e7	0.132105
$255$	−4.51572e7	−0.170544
$256$	2.50448e8	0.932990
$257$	−4.81773e7	−0.177042	−0.0885210	−	0.996074i	$-0.528214\pi$
$257$	−4.81773e7	−0.177042	−0.0885210	+	0.996074i	$0.528214\pi$
$258$	−235489.	−0.000853694 0
$259$	−1.77063e8	−0.633255
$260$	1.38155e8	0.487483
$261$	−1.00794e7	−0.0350908
$262$	2.69986e7	0.0927441
$263$	4.31418e8	1.46236	0.731178	−	0.682187i	$-0.238971\pi$
$263$	4.31418e8	1.46236	0.731178	+	0.682187i	$0.238971\pi$
$264$	1.34985e7	0.0451516
$265$	−9.45175e8	−3.11998
$266$	−1.44255e6	−0.00469943
$267$	−6.90845e7	−0.222122
$268$	−3.44919e8	−1.09457
$269$	4.66698e8	1.46185	0.730925	−	0.682458i	$-0.239089\pi$
$269$	4.66698e8	1.46185	0.730925	+	0.682458i	$0.239089\pi$
$270$	4.12861e7	0.127653
$271$	−2.20036e8	−0.671587	−0.335793	−	0.941936i	$-0.609004\pi$
$271$	−2.20036e8	−0.671587	−0.335793	+	0.941936i	$0.609004\pi$
$272$	6.24997e7	0.188316
$273$	1.76696e7	0.0525602
$274$	−5.09901e7	−0.149747
$275$	−4.03667e8	−1.17047
$276$	−1.96883e8	−0.563673
$277$	−1.79201e8	−0.506596	−0.253298	−	0.967388i	$-0.581515\pi$
$277$	−1.79201e8	−0.506596	−0.253298	+	0.967388i	$0.581515\pi$
$278$	4.81378e6	0.0134378
$279$	−2.89197e7	−0.0797221
$280$	4.02923e7	0.109691
$281$	2.85279e8	0.767003	0.383501	−	0.923540i	$-0.374718\pi$
$281$	2.85279e8	0.767003	0.383501	+	0.923540i	$0.374718\pi$
$282$	7.12789e6	0.0189273
$283$	2.09994e8	0.550750	0.275375	−	0.961337i	$-0.411198\pi$
$283$	2.09994e8	0.550750	0.275375	+	0.961337i	$0.411198\pi$
$284$	2.78031e8	0.720244
$285$	5.24000e7	0.134083
$286$	−4.95732e6	−0.0125304
$287$	1.61453e8	0.403142
$288$	−7.42329e7	−0.183114
$289$	−3.95179e8	−0.963055
$290$	−2.83461e6	−0.00682497
$291$	−3.17812e8	−0.756039
$292$	2.69788e8	0.634136
$293$	1.67817e8	0.389762	0.194881	−	0.980827i	$-0.437568\pi$
$293$	1.67817e8	0.389762	0.194881	+	0.980827i	$0.437568\pi$
$294$	2.56788e6	0.00589331
$295$	−2.76223e8	−0.626445
$296$	1.22599e8	0.274767
$297$	2.17358e8	0.481424
$298$	−4.20572e7	−0.0920626
$299$	1.45103e8	0.313926
$300$	−4.96424e8	−1.06152
$301$	−3.70066e6	−0.00782161
$302$	−4.30765e7	−0.0899945
$303$	−2.05735e7	−0.0424874
$304$	−7.25241e7	−0.148056
$305$	6.57788e8	1.32751
$306$	−5.93382e6	−0.0118388
$307$	−1.67749e8	−0.330885	−0.165442	−	0.986219i	$-0.552905\pi$
$307$	−1.67749e8	−0.330885	−0.165442	+	0.986219i	$0.552905\pi$
$308$	1.05703e8	0.206139
$309$	−1.10349e8	−0.212772
$310$	−8.13302e6	−0.0155055
$311$	4.39640e8	0.828774	0.414387	−	0.910101i	$-0.363996\pi$
$311$	4.39640e8	0.828774	0.414387	+	0.910101i	$0.363996\pi$
$312$	−1.22344e7	−0.0228057
$313$	1.04202e9	1.92075	0.960375	−	0.278712i	$-0.0899074\pi$
$313$	1.04202e9	1.92075	0.960375	+	0.278712i	$0.0899074\pi$
$314$	5.67618e7	0.103467
$315$	2.77762e8	0.500709
$316$	4.60299e8	0.820607
$317$	3.08564e8	0.544049	0.272024	−	0.962290i	$-0.412307\pi$
$317$	3.08564e8	0.544049	0.272024	+	0.962290i	$0.412307\pi$
$318$	4.17082e7	0.0727322
$319$	−1.49233e7	−0.0257394
$320$	9.95410e8	1.69815
$321$	4.10840e8	0.693274
$322$	2.10875e7	0.0351990
$323$	−1.75914e7	−0.0290464
$324$	−1.87905e8	−0.306924
$325$	3.65865e8	0.591193
$326$	8.91604e7	0.142531
$327$	5.45542e8	0.862801
$328$	−1.11790e8	−0.174922
$329$	1.12013e8	0.173414
$330$	2.61695e7	0.0400864
$331$	3.23910e8	0.490938	0.245469	−	0.969404i	$-0.421058\pi$
$331$	3.23910e8	0.490938	0.245469	+	0.969404i	$0.421058\pi$
$332$	−1.10605e9	−1.65879
$333$	8.45153e8	1.25424
$334$	8.47354e7	0.124438
$335$	−1.34194e9	−1.95019
$336$	1.29100e8	0.185669
$337$	−1.01210e8	−0.144051	−0.0720256	−	0.997403i	$-0.522946\pi$
$337$	−1.01210e8	−0.144051	−0.0720256	+	0.997403i	$0.522946\pi$
$338$	4.49308e6	0.00632901
$339$	−3.18215e8	−0.443631
$340$	2.44841e8	0.337838
$341$	−4.28178e7	−0.0584768
$342$	6.88555e6	0.00930780
$343$	4.03536e7	0.0539949
$344$	2.56234e6	0.00339377
$345$	−7.65995e8	−1.00429
$346$	5.26217e7	0.0682966
$347$	−3.55081e8	−0.456220	−0.228110	−	0.973635i	$-0.573255\pi$
$347$	−3.55081e8	−0.456220	−0.228110	+	0.973635i	$0.573255\pi$
$348$	−1.83525e7	−0.0233436
$349$	−1.43782e9	−1.81057	−0.905284	−	0.424806i	$-0.860342\pi$
$349$	−1.43782e9	−1.81057	−0.905284	+	0.424806i	$0.860342\pi$
$350$	5.31703e7	0.0662874
$351$	−1.97003e8	−0.243163
$352$	−1.09907e8	−0.134316
$353$	3.80937e8	0.460937	0.230469	−	0.973080i	$-0.425974\pi$
$353$	3.80937e8	0.460937	0.230469	+	0.973080i	$0.425974\pi$
$354$	1.21891e7	0.0146036
$355$	1.08171e9	1.28325
$356$	3.74574e8	0.440011
$357$	3.13144e7	0.0364255
$358$	1.00066e8	0.115264
$359$	−2.87741e8	−0.328225	−0.164112	−	0.986442i	$-0.552476\pi$
$359$	−2.87741e8	−0.328225	−0.164112	+	0.986442i	$0.552476\pi$
$360$	−1.92322e8	−0.217256
$361$	−8.73459e8	−0.977163
$362$	335415.	0.000371623 0
$363$	−3.19157e8	−0.350213
$364$	−9.58041e7	−0.104119
$365$	1.04964e9	1.12983
$366$	−2.90266e7	−0.0309465
$367$	−2.01071e8	−0.212334	−0.106167	−	0.994348i	$-0.533858\pi$
$367$	−2.01071e8	−0.212334	−0.106167	+	0.994348i	$0.533858\pi$
$368$	1.06017e9	1.10894
$369$	−7.70642e8	−0.798473
$370$	2.37681e8	0.243943
$371$	6.55435e8	0.666378
$372$	−5.26567e7	−0.0530339
$373$	−3.59090e8	−0.358280	−0.179140	−	0.983824i	$-0.557331\pi$
$373$	−3.59090e8	−0.358280	−0.179140	+	0.983824i	$0.557331\pi$
$374$	−8.78547e6	−0.00868389
$375$	−1.02530e9	−1.00402
$376$	−7.75580e7	−0.0752435
$377$	1.35258e7	0.0130007
$378$	−2.86300e7	−0.0272646
$379$	−1.48278e9	−1.39907	−0.699537	−	0.714597i	$-0.746610\pi$
$379$	−1.48278e9	−1.39907	−0.699537	+	0.714597i	$0.746610\pi$
$380$	−2.84112e8	−0.265611
$381$	8.69074e8	0.805044
$382$	−8.71413e7	−0.0799838
$383$	−1.60399e9	−1.45883	−0.729417	−	0.684069i	$-0.760209\pi$
$383$	−1.60399e9	−1.45883	−0.729417	+	0.684069i	$0.760209\pi$
$384$	−1.80009e8	−0.162231
$385$	4.11247e8	0.367274
$386$	2.34986e7	0.0207963
$387$	1.76639e7	0.0154917
$388$	1.72317e9	1.49767
$389$	7.26145e8	0.625460	0.312730	−	0.949842i	$-0.398756\pi$
$389$	7.26145e8	0.625460	0.312730	+	0.949842i	$0.398756\pi$
$390$	−2.37188e7	−0.0202473
$391$	2.57155e8	0.217559
$392$	−2.79409e7	−0.0234282
$393$	6.80078e8	0.565178
$394$	2.31556e7	0.0190730
$395$	1.79084e9	1.46206
$396$	−5.04539e8	−0.408283
$397$	−6.04307e7	−0.0484720	−0.0242360	−	0.999706i	$-0.507715\pi$
$397$	−6.04307e7	−0.0484720	−0.0242360	+	0.999706i	$0.507715\pi$
$398$	8.83937e7	0.0702798
$399$	−3.63370e7	−0.0286381
$400$	2.67313e9	2.08838
$401$	−1.70581e9	−1.32107	−0.660534	−	0.750796i	$-0.729670\pi$
$401$	−1.70581e9	−1.32107	−0.660534	+	0.750796i	$0.729670\pi$
$402$	5.92166e7	0.0454624
$403$	3.88080e7	0.0295361
$404$	1.11549e8	0.0841651
$405$	−7.31063e8	−0.546843
$406$	1.96567e6	0.00145771
$407$	1.25131e9	0.919995
$408$	−2.16821e7	−0.0158049
$409$	−9.81645e8	−0.709452	−0.354726	−	0.934970i	$-0.615426\pi$
$409$	−9.81645e8	−0.709452	−0.354726	+	0.934970i	$0.615426\pi$
$410$	−2.16726e8	−0.155299
$411$	−1.28441e9	−0.912553
$412$	5.98312e8	0.421490
$413$	1.91548e8	0.133799
$414$	−1.00654e8	−0.0697159
$415$	−4.30320e9	−2.95545
$416$	9.96149e7	0.0678419
$417$	1.21256e8	0.0818895
$418$	1.01946e7	0.00682735
$419$	7.44824e8	0.494657	0.247329	−	0.968932i	$-0.420447\pi$
$419$	7.44824e8	0.494657	0.247329	+	0.968932i	$0.420447\pi$
$420$	5.05746e8	0.333089
$421$	−2.00261e9	−1.30800	−0.654001	−	0.756494i	$-0.726911\pi$
$421$	−2.00261e9	−1.30800	−0.654001	+	0.756494i	$0.726911\pi$
$422$	−1.55071e8	−0.100447
$423$	−5.34659e8	−0.343467
$424$	−4.53824e8	−0.289139
$425$	6.48394e8	0.409711
$426$	−4.77332e7	−0.0299148
$427$	−4.56146e8	−0.283535
$428$	−2.22756e9	−1.37334
$429$	−1.24872e8	−0.0763597
$430$	4.96759e6	0.00301305
$431$	−1.33664e9	−0.804162	−0.402081	−	0.915604i	$-0.631713\pi$
$431$	−1.33664e9	−0.804162	−0.402081	+	0.915604i	$0.631713\pi$
$432$	−1.43937e9	−0.858973
$433$	1.70086e9	1.00684	0.503421	−	0.864042i	$-0.332075\pi$
$433$	1.70086e9	1.00684	0.503421	+	0.864042i	$0.332075\pi$
$434$	5.63988e6	0.00331174
$435$	−7.14022e7	−0.0415910
$436$	−2.95792e9	−1.70916
$437$	−2.98401e8	−0.171047
$438$	−4.63179e7	−0.0263384
$439$	9.42702e8	0.531800	0.265900	−	0.964001i	$-0.414331\pi$
$439$	9.42702e8	0.531800	0.265900	+	0.964001i	$0.414331\pi$
$440$	−2.84748e8	−0.159359
$441$	−1.92615e8	−0.106944
$442$	7.96274e6	0.00438616
$443$	−6.17406e8	−0.337410	−0.168705	−	0.985667i	$-0.553958\pi$
$443$	−6.17406e8	−0.337410	−0.168705	+	0.985667i	$0.553958\pi$
$444$	1.53885e9	0.834364
$445$	1.45732e9	0.783961
$446$	2.24817e8	0.119993
$447$	−1.05940e9	−0.561025
$448$	−6.90271e8	−0.362699
$449$	−2.97982e9	−1.55356	−0.776780	−	0.629772i	$-0.783148\pi$
$449$	−2.97982e9	−1.55356	−0.776780	+	0.629772i	$0.783148\pi$
$450$	−2.53791e8	−0.131290
$451$	−1.14099e9	−0.585687
$452$	1.72536e9	0.878808
$453$	−1.08507e9	−0.548422
$454$	2.76539e8	0.138695
$455$	−3.72735e8	−0.185507
$456$	2.51598e7	0.0124259
$457$	−1.82029e9	−0.892141	−0.446070	−	0.894998i	$-0.647177\pi$
$457$	−1.82029e9	−0.892141	−0.446070	+	0.894998i	$0.647177\pi$
$458$	4.54760e7	0.0221184
$459$	−3.49133e8	−0.168518
$460$	4.15321e9	1.98944
$461$	3.33514e9	1.58548	0.792740	−	0.609560i	$-0.208654\pi$
$461$	3.33514e9	1.58548	0.792740	+	0.609560i	$0.208654\pi$
$462$	−1.81473e7	−0.00856182
$463$	4.70190e8	0.220161	0.110080	−	0.993923i	$-0.464889\pi$
$463$	4.70190e8	0.220161	0.110080	+	0.993923i	$0.464889\pi$
$464$	9.88240e7	0.0459250
$465$	−2.04866e8	−0.0944897
$466$	1.12858e8	0.0516630
$467$	−1.86051e9	−0.845325	−0.422663	−	0.906287i	$-0.638904\pi$
$467$	−1.86051e9	−0.845325	−0.422663	+	0.906287i	$0.638904\pi$
$468$	4.57290e8	0.206220
$469$	9.30574e8	0.416530
$470$	−1.50361e8	−0.0668025
$471$	1.42980e9	0.630523
$472$	−1.32628e8	−0.0580548
$473$	2.61528e7	0.0113633
$474$	−7.90253e7	−0.0340833
$475$	−7.52391e8	−0.322119
$476$	−1.69786e8	−0.0721569
$477$	−3.12851e9	−1.31985
$478$	−1.28835e8	−0.0539556
$479$	−1.06883e8	−0.0444358	−0.0222179	−	0.999753i	$-0.507073\pi$
$479$	−1.06883e8	−0.0444358	−0.0222179	+	0.999753i	$0.507073\pi$
$480$	−5.25863e8	−0.217034
$481$	−1.13413e9	−0.464682
$482$	1.19101e8	0.0484452
$483$	5.31182e8	0.214501
$484$	1.73046e9	0.693751
$485$	6.70416e9	2.66838
$486$	2.14807e8	0.0848833
$487$	2.49058e9	0.977121	0.488560	−	0.872530i	$-0.337522\pi$
$487$	2.49058e9	0.977121	0.488560	+	0.872530i	$0.337522\pi$
$488$	3.15836e8	0.123025
$489$	2.24590e9	0.868578
$490$	−5.41688e7	−0.0208000
$491$	8.23614e8	0.314006	0.157003	−	0.987598i	$-0.449817\pi$
$491$	8.23614e8	0.314006	0.157003	+	0.987598i	$0.449817\pi$
$492$	−1.40318e9	−0.531172
$493$	2.39707e7	0.00900984
$494$	−9.23989e6	−0.00344844
$495$	−1.96296e9	−0.727433
$496$	2.83544e8	0.104336
$497$	−7.50115e8	−0.274082
$498$	1.89890e8	0.0688967
$499$	−2.73013e8	−0.0983629	−0.0491814	−	0.998790i	$-0.515661\pi$
$499$	−2.73013e8	−0.0983629	−0.0491814	+	0.998790i	$0.515661\pi$
$500$	5.55917e9	1.98891
$501$	2.13443e9	0.758317
$502$	−1.00161e8	−0.0353376
$503$	3.81756e9	1.33751	0.668756	−	0.743482i	$-0.266827\pi$
$503$	3.81756e9	1.33751	0.668756	+	0.743482i	$0.266827\pi$
$504$	1.33367e8	0.0464024
$505$	4.33993e8	0.149956
$506$	−1.49027e8	−0.0511372
$507$	1.13178e8	0.0385687
$508$	−4.71210e9	−1.59475
$509$	2.03749e9	0.684830	0.342415	−	0.939549i	$-0.388755\pi$
$509$	2.03749e9	0.684830	0.342415	+	0.939549i	$0.388755\pi$
$510$	−4.20350e7	−0.0140319
$511$	−7.27875e8	−0.241315
$512$	1.21579e9	0.400325
$513$	4.05131e8	0.132490
$514$	−4.48463e7	−0.0145665
$515$	2.32779e9	0.750964
$516$	3.21623e7	0.0103056
$517$	−7.91603e8	−0.251936
$518$	−1.64821e8	−0.0521024
$519$	1.32551e9	0.416196
$520$	2.58082e8	0.0804908
$521$	2.57357e9	0.797269	0.398634	−	0.917110i	$-0.369484\pi$
$521$	2.57357e9	0.797269	0.398634	+	0.917110i	$0.369484\pi$
$522$	−9.38250e6	−0.00288717
$523$	3.57873e9	1.09389	0.546944	−	0.837169i	$-0.315791\pi$
$523$	3.57873e9	1.09389	0.546944	+	0.837169i	$0.315791\pi$
$524$	−3.68737e9	−1.11959
$525$	1.33933e9	0.403952
$526$	4.01590e8	0.120319
$527$	6.87764e7	0.0204693
$528$	−9.12356e8	−0.269740
$529$	9.57259e8	0.281148
$530$	−8.79825e8	−0.256703
$531$	−9.14293e8	−0.265005
$532$	1.97018e8	0.0567304
$533$	1.03414e9	0.295826
$534$	−6.43079e7	−0.0182755
$535$	−8.66656e9	−2.44686
$536$	−6.44330e8	−0.180731
$537$	2.52059e9	0.702413
$538$	4.34430e8	0.120277
$539$	−2.85181e8	−0.0784441
$540$	−5.63870e9	−1.54099
$541$	−2.56998e8	−0.0697812	−0.0348906	−	0.999391i	$-0.511108\pi$
$541$	−2.56998e8	−0.0697812	−0.0348906	+	0.999391i	$0.511108\pi$
$542$	−2.04823e8	−0.0552562
$543$	8.44890e6	0.00226465
$544$	1.76540e8	0.0470161
$545$	−1.15081e10	−3.04519
$546$	1.64479e7	0.00432450
$547$	−3.40405e9	−0.889283	−0.444641	−	0.895709i	$-0.646669\pi$
$547$	−3.40405e9	−0.889283	−0.444641	+	0.895709i	$0.646669\pi$
$548$	6.96405e9	1.80772
$549$	2.17727e9	0.561576
$550$	−3.75757e8	−0.0963026
$551$	−2.78154e7	−0.00708361
$552$	−3.67791e8	−0.0930709
$553$	−1.24186e9	−0.312274
$554$	−1.66811e8	−0.0416813
$555$	5.98704e9	1.48657
$556$	−6.57449e8	−0.162218
$557$	4.01934e9	0.985511	0.492756	−	0.870168i	$-0.335990\pi$
$557$	4.01934e9	0.985511	0.492756	+	0.870168i	$0.335990\pi$
$558$	−2.69201e7	−0.00655930
$559$	−2.37036e7	−0.00573949
$560$	−2.72333e9	−0.655303
$561$	−2.21301e8	−0.0529192
$562$	2.65554e8	0.0631068
$563$	2.08931e9	0.493428	0.246714	−	0.969088i	$-0.420649\pi$
$563$	2.08931e9	0.493428	0.246714	+	0.969088i	$0.420649\pi$
$564$	−9.73502e8	−0.228486
$565$	6.71267e9	1.56576
$566$	1.95475e8	0.0453141
$567$	5.06959e8	0.116797
$568$	5.19381e8	0.118923
$569$	−3.02694e9	−0.688829	−0.344415	−	0.938818i	$-0.611923\pi$
$569$	−3.02694e9	−0.688829	−0.344415	+	0.938818i	$0.611923\pi$
$570$	4.87770e7	0.0110320
$571$	−4.05575e9	−0.911684	−0.455842	−	0.890061i	$-0.650662\pi$
$571$	−4.05575e9	−0.911684	−0.455842	+	0.890061i	$0.650662\pi$
$572$	6.77053e8	0.151264
$573$	−2.19504e9	−0.487417
$574$	1.50290e8	0.0331694
$575$	1.09986e10	2.41268
$576$	3.29479e9	0.718371
$577$	−7.14490e9	−1.54839	−0.774196	−	0.632946i	$-0.781846\pi$
$577$	−7.14490e9	−1.54839	−0.774196	+	0.632946i	$0.781846\pi$
$578$	−3.67856e8	−0.0792374
$579$	5.91915e8	0.126731
$580$	3.87141e8	0.0823894
$581$	2.98407e9	0.631237
$582$	−2.95838e8	−0.0622047
$583$	−4.63200e9	−0.968118
$584$	5.03981e8	0.104705
$585$	1.77913e9	0.367420
$586$	1.56214e8	0.0320685
$587$	2.15170e9	0.439085	0.219543	−	0.975603i	$-0.429544\pi$
$587$	2.15170e9	0.439085	0.219543	+	0.975603i	$0.429544\pi$
$588$	−3.50712e8	−0.0711426
$589$	−7.98075e7	−0.0160931
$590$	−2.57125e8	−0.0515421
$591$	5.83275e8	0.116230
$592$	−8.28635e9	−1.64149
$593$	−5.66161e9	−1.11493	−0.557466	−	0.830200i	$-0.688226\pi$
$593$	−5.66161e9	−1.11493	−0.557466	+	0.830200i	$0.688226\pi$
$594$	2.02330e8	0.0396102
$595$	−6.60570e8	−0.128561
$596$	5.74402e9	1.11136
$597$	2.22659e9	0.428281
$598$	1.35071e8	0.0258290
$599$	5.97313e9	1.13556	0.567778	−	0.823182i	$-0.307803\pi$
$599$	5.97313e9	1.13556	0.567778	+	0.823182i	$0.307803\pi$
$600$	−9.27352e8	−0.175273
$601$	−1.48842e8	−0.0279681	−0.0139841	−	0.999902i	$-0.504451\pi$
$601$	−1.48842e8	−0.0279681	−0.0139841	+	0.999902i	$0.504451\pi$
$602$	−3.44479e6	−0.000643540 0
$603$	−4.44180e9	−0.824989
$604$	5.88324e9	1.08639
$605$	6.73254e9	1.23605
$606$	−1.91511e7	−0.00349574
$607$	8.30448e9	1.50714	0.753568	−	0.657370i	$-0.228331\pi$
$607$	8.30448e9	1.50714	0.753568	+	0.657370i	$0.228331\pi$
$608$	−2.04855e8	−0.0369645
$609$	4.95141e7	0.00888318
$610$	6.12308e8	0.109223
$611$	7.17472e8	0.127251
$612$	8.10420e8	0.142916
$613$	−3.33245e9	−0.584321	−0.292160	−	0.956369i	$-0.594374\pi$
$613$	−3.33245e9	−0.584321	−0.292160	+	0.956369i	$0.594374\pi$
$614$	−1.56151e8	−0.0272243
$615$	−5.45921e9	−0.946382
$616$	1.97460e8	0.0340366
$617$	5.78863e9	0.992152	0.496076	−	0.868279i	$-0.334774\pi$
$617$	5.78863e9	0.992152	0.496076	+	0.868279i	$0.334774\pi$
$618$	−1.02720e8	−0.0175063
$619$	−8.22318e9	−1.39355	−0.696775	−	0.717290i	$-0.745382\pi$
$619$	−8.22318e9	−1.39355	−0.696775	+	0.717290i	$0.745382\pi$
$620$	1.11078e9	0.187179
$621$	−5.92229e9	−0.992360
$622$	4.09243e8	0.0681891
$623$	−1.01058e9	−0.167442
$624$	8.26917e8	0.136243
$625$	8.61841e9	1.41204
$626$	9.69974e8	0.158034
$627$	2.56795e8	0.0416055
$628$	−7.75232e9	−1.24903
$629$	−2.00993e9	−0.322036
$630$	2.58557e8	0.0411969
$631$	−5.56524e9	−0.881823	−0.440911	−	0.897551i	$-0.645345\pi$
$631$	−5.56524e9	−0.881823	−0.440911	+	0.897551i	$0.645345\pi$
$632$	8.59868e8	0.135495
$633$	−3.90615e9	−0.612119
$634$	2.87230e8	0.0447628
$635$	−1.83329e10	−2.84134
$636$	−5.69636e9	−0.878007
$637$	2.58475e8	0.0396214
$638$	−1.38915e7	−0.00211776
$639$	3.58044e9	0.542854
$640$	3.79724e9	0.572583
$641$	−2.29706e9	−0.344484	−0.172242	−	0.985055i	$-0.555101\pi$
$641$	−2.29706e9	−0.344484	−0.172242	+	0.985055i	$0.555101\pi$
$642$	3.82434e8	0.0570406
$643$	5.78591e9	0.858289	0.429145	−	0.903236i	$-0.358815\pi$
$643$	5.78591e9	0.858289	0.429145	+	0.903236i	$0.358815\pi$
$644$	−2.88006e9	−0.424914
$645$	1.25131e8	0.0183614
$646$	−1.63751e7	−0.00238985
$647$	−1.34228e9	−0.194840	−0.0974201	−	0.995243i	$-0.531059\pi$
$647$	−1.34228e9	−0.194840	−0.0974201	+	0.995243i	$0.531059\pi$
$648$	−3.51019e8	−0.0506778
$649$	−1.35368e9	−0.194384
$650$	3.40569e8	0.0486417
$651$	1.42065e8	0.0201815
$652$	−1.21772e10	−1.72061
$653$	7.74737e8	0.108883	0.0544413	−	0.998517i	$-0.482662\pi$
$653$	7.74737e8	0.108883	0.0544413	+	0.998517i	$0.482662\pi$
$654$	5.07823e8	0.0709888
$655$	−1.43461e10	−1.99475
$656$	7.55580e9	1.04500
$657$	3.47428e9	0.477953
$658$	1.04268e8	0.0142680
$659$	−1.02191e10	−1.39095	−0.695477	−	0.718549i	$-0.744807\pi$
$659$	−1.02191e10	−1.39095	−0.695477	+	0.718549i	$0.744807\pi$
$660$	−3.57414e9	−0.483913
$661$	−7.88600e9	−1.06207	−0.531033	−	0.847351i	$-0.678196\pi$
$661$	−7.88600e9	−1.06207	−0.531033	+	0.847351i	$0.678196\pi$
$662$	3.01515e8	0.0403930
$663$	2.00577e8	0.0267290
$664$	−2.06617e9	−0.273891
$665$	7.66519e8	0.101076
$666$	7.86719e8	0.103195
$667$	4.06612e8	0.0530566
$668$	−1.15729e10	−1.50218
$669$	5.66301e9	0.731233
$670$	−1.24916e9	−0.160456
$671$	3.22361e9	0.411920
$672$	3.64662e8	0.0463552
$673$	9.48355e9	1.19927	0.599637	−	0.800272i	$-0.295312\pi$
$673$	9.48355e9	1.19927	0.599637	+	0.800272i	$0.295312\pi$
$674$	−9.42119e7	−0.0118521
$675$	−1.49325e10	−1.86883
$676$	−6.13649e8	−0.0764023
$677$	−1.15389e10	−1.42924	−0.714621	−	0.699512i	$-0.753401\pi$
$677$	−1.15389e10	−1.42924	−0.714621	+	0.699512i	$0.753401\pi$
$678$	−2.96214e8	−0.0365007
$679$	−4.64902e9	−0.569925
$680$	4.57379e8	0.0557822
$681$	6.96586e9	0.845201
$682$	−3.98573e7	−0.00481130
$683$	−1.07688e10	−1.29328	−0.646641	−	0.762795i	$-0.723827\pi$
$683$	−1.07688e10	−1.29328	−0.646641	+	0.762795i	$0.723827\pi$
$684$	−9.40404e8	−0.112362
$685$	2.70943e10	3.22078
$686$	3.75635e7	0.00444255
$687$	1.14551e9	0.134788
$688$	−1.73187e8	−0.0202747
$689$	4.19822e9	0.488988
$690$	−7.13033e8	−0.0826301
$691$	1.58123e10	1.82315	0.911576	−	0.411132i	$-0.134866\pi$
$691$	1.58123e10	1.82315	0.911576	+	0.411132i	$0.134866\pi$
$692$	−7.18689e9	−0.824460
$693$	1.36122e9	0.155368
$694$	−3.30530e8	−0.0375364
$695$	−2.55787e9	−0.289022
$696$	−3.42836e7	−0.00385438
$697$	1.83273e9	0.205014
$698$	−1.33841e9	−0.148968
$699$	2.84282e9	0.314832
$700$	−7.26181e9	−0.800206
$701$	1.58969e10	1.74301	0.871506	−	0.490385i	$-0.163144\pi$
$701$	1.58969e10	1.74301	0.871506	+	0.490385i	$0.163144\pi$
$702$	−1.83382e8	−0.0200068
$703$	2.33231e9	0.253188
$704$	4.87818e9	0.526931
$705$	−3.78751e9	−0.407091
$706$	3.54599e8	0.0379246
$707$	−3.00954e8	−0.0320282
$708$	−1.66474e9	−0.176291
$709$	1.17268e10	1.23571	0.617856	−	0.786291i	$-0.288001\pi$
$709$	1.17268e10	1.23571	0.617856	+	0.786291i	$0.288001\pi$
$710$	1.00692e9	0.105582
$711$	5.92764e9	0.618498
$712$	6.99729e8	0.0726524
$713$	1.16664e9	0.120538
$714$	2.91493e7	0.00299699
$715$	2.63414e9	0.269506
$716$	−1.36666e10	−1.39144
$717$	−3.24528e9	−0.328802
$718$	−2.67846e8	−0.0270054
$719$	1.50068e10	1.50570	0.752849	−	0.658194i	$-0.228679\pi$
$719$	1.50068e10	1.50570	0.752849	+	0.658194i	$0.228679\pi$
$720$	1.29989e10	1.29791
$721$	−1.61422e9	−0.160394
$722$	−8.13068e8	−0.0803982
$723$	3.00008e9	0.295222
$724$	−4.58098e7	−0.00448614
$725$	1.02524e9	0.0999173
$726$	−2.97091e8	−0.0288145
$727$	8.31455e9	0.802543	0.401271	−	0.915959i	$-0.368568\pi$
$727$	8.31455e9	0.802543	0.401271	+	0.915959i	$0.368568\pi$
$728$	−1.78968e8	−0.0171916
$729$	2.17846e9	0.208259
$730$	9.77064e8	0.0929594
$731$	−4.20081e7	−0.00397761
$732$	3.96435e9	0.373579
$733$	−2.20982e8	−0.0207249	−0.0103625	−	0.999946i	$-0.503299\pi$
$733$	−2.20982e8	−0.0207249	−0.0103625	+	0.999946i	$0.503299\pi$
$734$	−1.87169e8	−0.0174702
$735$	−1.36448e9	−0.126754
$736$	2.99462e9	0.276866
$737$	−6.57642e9	−0.605136
$738$	−7.17360e8	−0.0656961
$739$	−1.17435e10	−1.07039	−0.535196	−	0.844728i	$-0.679762\pi$
$739$	−1.17435e10	−1.07039	−0.535196	+	0.844728i	$0.679762\pi$
$740$	−3.24616e10	−2.94482
$741$	−2.32747e8	−0.0210146
$742$	6.10118e8	0.0548277
$743$	−1.70101e10	−1.52141	−0.760703	−	0.649100i	$-0.775146\pi$
$743$	−1.70101e10	−1.52141	−0.760703	+	0.649100i	$0.775146\pi$
$744$	−9.83660e7	−0.00875669
$745$	2.23477e10	1.98009
$746$	−3.34262e8	−0.0294782
$747$	−1.42435e10	−1.25024
$748$	1.19989e9	0.104830
$749$	6.00986e9	0.522610
$750$	−9.54414e8	−0.0826080
$751$	1.69564e10	1.46081	0.730406	−	0.683013i	$-0.239331\pi$
$751$	1.69564e10	1.46081	0.730406	+	0.683013i	$0.239331\pi$
$752$	5.24209e9	0.449513
$753$	−2.52301e9	−0.215346
$754$	1.25906e7	0.00106966
$755$	2.28893e10	1.93561
$756$	3.91018e9	0.329132
$757$	2.09466e10	1.75500	0.877502	−	0.479573i	$-0.159208\pi$
$757$	2.09466e10	1.75500	0.877502	+	0.479573i	$0.159208\pi$
$758$	−1.38026e9	−0.115112
$759$	−3.75389e9	−0.311627
$760$	−5.30739e8	−0.0438564
$761$	−1.82678e10	−1.50259	−0.751293	−	0.659969i	$-0.770569\pi$
$761$	−1.82678e10	−1.50259	−0.751293	+	0.659969i	$0.770569\pi$
$762$	8.08986e8	0.0662367
$763$	7.98031e9	0.650405
$764$	1.19014e10	0.965546
$765$	3.15302e9	0.254631
$766$	−1.49309e9	−0.120029
$767$	1.22691e9	0.0981815
$768$	5.87245e9	0.467794
$769$	1.33445e10	1.05818	0.529090	−	0.848566i	$-0.322533\pi$
$769$	1.33445e10	1.05818	0.529090	+	0.848566i	$0.322533\pi$
$770$	3.82814e8	0.0302183
$771$	−1.12965e9	−0.0887676
$772$	−3.20935e9	−0.251048
$773$	7.46551e9	0.581342	0.290671	−	0.956823i	$-0.406122\pi$
$773$	7.46551e9	0.581342	0.290671	+	0.956823i	$0.406122\pi$
$774$	1.64426e7	0.00127461
$775$	2.94159e9	0.227000
$776$	3.21899e9	0.247288
$777$	−4.15174e9	−0.317509
$778$	6.75939e8	0.0514611
$779$	−2.12669e9	−0.161184
$780$	3.23943e9	0.244421
$781$	5.30111e9	0.398188
$782$	2.39375e8	0.0179001
$783$	−5.52046e8	−0.0410969
$784$	1.88850e9	0.139962
$785$	−3.01612e10	−2.22538
$786$	6.33057e8	0.0465012
$787$	−1.97846e10	−1.44682	−0.723412	−	0.690417i	$-0.757427\pi$
$787$	−1.97846e10	−1.44682	−0.723412	+	0.690417i	$0.757427\pi$
$788$	−3.16250e9	−0.230245
$789$	1.01158e10	0.733214
$790$	1.66702e9	0.120294
$791$	−4.65493e9	−0.334422
$792$	−9.42510e8	−0.0674137
$793$	−2.92173e9	−0.208058
$794$	−5.62525e7	−0.00398813
$795$	−2.21623e10	−1.56433
$796$	−1.20725e10	−0.848401
$797$	9.89344e9	0.692218	0.346109	−	0.938194i	$-0.387503\pi$
$797$	9.89344e9	0.692218	0.346109	+	0.938194i	$0.387503\pi$
$798$	−3.38246e7	−0.00235626
$799$	1.27152e9	0.0881880
$800$	7.55066e9	0.521399
$801$	4.82370e9	0.331639
$802$	−1.58787e9	−0.108694
$803$	5.14393e9	0.350583
$804$	−8.08759e9	−0.548811
$805$	−1.12051e10	−0.757063
$806$	3.61248e7	0.00243015
$807$	1.09430e10	0.732960
$808$	2.08381e8	0.0138969
$809$	2.41288e10	1.60219	0.801097	−	0.598534i	$-0.204250\pi$
$809$	2.41288e10	1.60219	0.801097	+	0.598534i	$0.204250\pi$
$810$	−6.80517e8	−0.0449927
$811$	1.84984e10	1.21776	0.608881	−	0.793262i	$-0.291619\pi$
$811$	1.84984e10	1.21776	0.608881	+	0.793262i	$0.291619\pi$
$812$	−2.68465e8	−0.0175971
$813$	−5.15937e9	−0.336728
$814$	1.16480e9	0.0756946
$815$	−4.73767e10	−3.06558
$816$	1.46548e9	0.0944201
$817$	4.87458e7	0.00312723
$818$	−9.13773e8	−0.0583716
$819$	−1.23375e9	−0.0784752
$820$	2.95997e10	1.87473
$821$	2.81863e10	1.77761	0.888807	−	0.458283i	$-0.151535\pi$
$821$	2.81863e10	1.77761	0.888807	+	0.458283i	$0.151535\pi$
$822$	−1.19561e9	−0.0750822
$823$	2.04648e10	1.27970	0.639851	−	0.768499i	$-0.278996\pi$
$823$	2.04648e10	1.27970	0.639851	+	0.768499i	$0.278996\pi$
$824$	1.11769e9	0.0695944
$825$	−9.46511e9	−0.586863
$826$	1.78304e8	0.0110086
$827$	7.73565e9	0.475584	0.237792	−	0.971316i	$-0.423576\pi$
$827$	7.73565e9	0.475584	0.237792	+	0.971316i	$0.423576\pi$
$828$	1.37470e10	0.841594
$829$	2.90659e10	1.77192	0.885959	−	0.463763i	$-0.153501\pi$
$829$	2.90659e10	1.77192	0.885959	+	0.463763i	$0.153501\pi$
$830$	−4.00567e9	−0.243166
$831$	−4.20187e9	−0.254003
$832$	−4.42136e9	−0.266148
$833$	4.58075e8	0.0274586
$834$	1.12873e8	0.00673763
$835$	−4.50253e10	−2.67642
$836$	−1.39234e9	−0.0824182
$837$	−1.58392e9	−0.0933674
$838$	6.93326e8	0.0406990
$839$	−2.26036e10	−1.32133	−0.660666	−	0.750680i	$-0.729726\pi$
$839$	−2.26036e10	−1.32133	−0.660666	+	0.750680i	$0.729726\pi$
$840$	9.44766e8	0.0549980
$841$	−1.72120e10	−0.997803
$842$	−1.86415e9	−0.107619
$843$	6.68915e9	0.384569
$844$	2.11790e10	1.21257
$845$	−2.38746e9	−0.136125
$846$	−4.97692e8	−0.0282595
$847$	−4.66871e9	−0.264001
$848$	3.06736e10	1.72735
$849$	4.92390e9	0.276142
$850$	6.03564e8	0.0337099
$851$	−3.40942e10	−1.89639
$852$	6.51923e9	0.361125
$853$	−2.79034e9	−0.153934	−0.0769671	−	0.997034i	$-0.524524\pi$
$853$	−2.79034e9	−0.153934	−0.0769671	+	0.997034i	$0.524524\pi$
$854$	−4.24608e8	−0.0233284
$855$	−3.65873e9	−0.200193
$856$	−4.16123e9	−0.226759
$857$	−1.71802e10	−0.932387	−0.466194	−	0.884683i	$-0.654375\pi$
$857$	−1.71802e10	−0.932387	−0.466194	+	0.884683i	$0.654375\pi$
$858$	−1.16238e8	−0.00628266
$859$	3.72890e9	0.200726	0.100363	−	0.994951i	$-0.468000\pi$
$859$	3.72890e9	0.200726	0.100363	+	0.994951i	$0.468000\pi$
$860$	−6.78456e8	−0.0363728
$861$	3.78571e9	0.202132
$862$	−1.24422e9	−0.0661641
$863$	1.86053e10	0.985369	0.492685	−	0.870208i	$-0.336016\pi$
$863$	1.86053e10	0.985369	0.492685	+	0.870208i	$0.336016\pi$
$864$	−4.06572e9	−0.214456
$865$	−2.79613e10	−1.46893
$866$	1.58326e9	0.0828400
$867$	−9.26607e9	−0.482869
$868$	−7.70274e8	−0.0399785
$869$	8.77632e9	0.453673
$870$	−6.64654e7	−0.00342199
$871$	5.96056e9	0.305649
$872$	−5.52557e9	−0.282208
$873$	2.21906e10	1.12881
$874$	−2.77769e8	−0.0140732
$875$	−1.49984e10	−0.756861
$876$	6.32593e9	0.317951
$877$	1.56029e10	0.781098	0.390549	−	0.920582i	$-0.372285\pi$
$877$	1.56029e10	0.781098	0.390549	+	0.920582i	$0.372285\pi$
$878$	8.77523e8	0.0437550
$879$	3.93494e9	0.195424
$880$	1.92459e10	0.952027
$881$	−2.33038e10	−1.14818	−0.574092	−	0.818791i	$-0.694645\pi$
$881$	−2.33038e10	−1.14818	−0.574092	+	0.818791i	$0.694645\pi$
$882$	−1.79298e8	−0.00879902
$883$	1.37344e10	0.671349	0.335675	−	0.941978i	$-0.391036\pi$
$883$	1.37344e10	0.671349	0.335675	+	0.941978i	$0.391036\pi$
$884$	−1.08752e9	−0.0529487
$885$	−6.47683e9	−0.314095
$886$	−5.74718e8	−0.0277611
$887$	−3.05740e10	−1.47102	−0.735511	−	0.677512i	$-0.763058\pi$
$887$	−3.05740e10	−1.47102	−0.735511	+	0.677512i	$0.763058\pi$
$888$	2.87467e9	0.137766
$889$	1.27130e10	0.606866
$890$	1.35656e9	0.0645021
$891$	−3.58270e9	−0.169683
$892$	−3.07047e10	−1.44853
$893$	−1.47546e9	−0.0693342
$894$	−9.86149e8	−0.0461595
$895$	−5.31712e10	−2.47911
$896$	−2.63321e9	−0.122295
$897$	3.40235e9	0.157400
$898$	−2.77380e9	−0.127823
$899$	1.08749e8	0.00499189
$900$	3.46619e10	1.58491
$901$	7.44019e9	0.338881
$902$	−1.06211e9	−0.0481886
$903$	−8.67723e7	−0.00392170
$904$	3.22307e9	0.145104
$905$	−1.78227e8	−0.00799290
$906$	−1.01005e9	−0.0451226
$907$	−8.11332e9	−0.361055	−0.180527	−	0.983570i	$-0.557780\pi$
$907$	−8.11332e9	−0.361055	−0.180527	+	0.983570i	$0.557780\pi$
$908$	−3.77687e10	−1.67430
$909$	1.43651e9	0.0634359
$910$	−3.46964e8	−0.0152630
$911$	9.37494e9	0.410823	0.205411	−	0.978676i	$-0.434147\pi$
$911$	9.37494e9	0.410823	0.205411	+	0.978676i	$0.434147\pi$
$912$	−1.70053e9	−0.0742339
$913$	−2.10886e10	−0.917064
$914$	−1.69443e9	−0.0734028
$915$	1.54237e10	0.665602
$916$	−6.21095e9	−0.267008
$917$	9.94835e9	0.426048
$918$	−3.24994e8	−0.0138652
$919$	1.42577e10	0.605962	0.302981	−	0.952997i	$-0.402018\pi$
$919$	1.42577e10	0.605962	0.302981	+	0.952997i	$0.402018\pi$
$920$	7.75845e9	0.328487
$921$	−3.93336e9	−0.165903
$922$	3.10455e9	0.130449
$923$	−4.80468e9	−0.201121
$924$	2.47850e9	0.103356
$925$	−8.59655e10	−3.57132
$926$	4.37681e8	0.0181142
$927$	7.70495e9	0.317681
$928$	2.79143e8	0.0114659
$929$	7.88274e9	0.322569	0.161284	−	0.986908i	$-0.448436\pi$
$929$	7.88274e9	0.322569	0.161284	+	0.986908i	$0.448436\pi$
$930$	−1.90702e8	−0.00777435
$931$	−5.31546e8	−0.0215882
$932$	−1.54137e10	−0.623664
$933$	1.03086e10	0.415541
$934$	−1.73188e9	−0.0695509
$935$	4.66829e9	0.186774
$936$	8.54247e8	0.0340501
$937$	−4.64928e10	−1.84628	−0.923139	−	0.384466i	$-0.874386\pi$
$937$	−4.64928e10	−1.84628	−0.923139	+	0.384466i	$0.874386\pi$
$938$	8.66234e8	0.0342709
$939$	2.44331e10	0.963049
$940$	2.05358e10	0.806425
$941$	1.45357e10	0.568685	0.284342	−	0.958723i	$-0.408225\pi$
$941$	1.45357e10	0.568685	0.284342	+	0.958723i	$0.408225\pi$
$942$	1.33094e9	0.0518776
$943$	3.10884e10	1.20728
$944$	8.96423e9	0.346826
$945$	1.52130e10	0.586411
$946$	2.43445e7	0.000934938 0
$947$	2.94544e9	0.112700	0.0563502	−	0.998411i	$-0.482054\pi$
$947$	2.94544e9	0.112700	0.0563502	+	0.998411i	$0.482054\pi$
$948$	1.07930e10	0.411446
$949$	−4.66222e9	−0.177076
$950$	−7.00370e8	−0.0265030
$951$	7.23515e9	0.272782
$952$	−3.17171e8	−0.0119142
$953$	3.44178e9	0.128812	0.0644062	−	0.997924i	$-0.479485\pi$
$953$	3.44178e9	0.128812	0.0644062	+	0.997924i	$0.479485\pi$
$954$	−2.91220e9	−0.108593
$955$	4.63037e10	1.72030
$956$	1.75958e10	0.651339
$957$	−3.49919e8	−0.0129055
$958$	−9.94928e7	−0.00365605
$959$	−1.87887e10	−0.687909
$960$	2.33402e10	0.851441
$961$	−2.72006e10	−0.988659
$962$	−1.05572e9	−0.0382327
$963$	−2.86861e10	−1.03509
$964$	−1.62664e10	−0.584819
$965$	−1.24863e10	−0.447289
$966$	4.94456e8	0.0176485
$967$	−3.90155e10	−1.38754	−0.693768	−	0.720198i	$-0.744051\pi$
$967$	−3.90155e10	−1.38754	−0.693768	+	0.720198i	$0.744051\pi$
$968$	3.23262e9	0.114549
$969$	−4.12480e8	−0.0145636
$970$	6.24063e9	0.219547
$971$	2.36083e10	0.827556	0.413778	−	0.910378i	$-0.364209\pi$
$971$	2.36083e10	0.827556	0.413778	+	0.910378i	$0.364209\pi$
$972$	−2.93376e10	−1.02469
$973$	1.77377e9	0.0617307
$974$	2.31838e9	0.0803947
$975$	8.57873e9	0.296420
$976$	−2.13471e10	−0.734962
$977$	1.53065e10	0.525105	0.262552	−	0.964918i	$-0.415436\pi$
$977$	1.53065e10	0.525105	0.262552	+	0.964918i	$0.415436\pi$
$978$	2.09062e9	0.0714642
$979$	7.14185e9	0.243260
$980$	7.39818e9	0.251092
$981$	−3.80915e10	−1.28821
$982$	7.66669e8	0.0258356
$983$	−1.63433e10	−0.548785	−0.274393	−	0.961618i	$-0.588477\pi$
$983$	−1.63433e10	−0.548785	−0.274393	+	0.961618i	$0.588477\pi$
$984$	−2.62123e9	−0.0877045
$985$	−1.23040e10	−0.410224
$986$	2.23134e7	0.000741304 0
$987$	2.62646e9	0.0869483
$988$	1.26195e9	0.0416287
$989$	−7.12577e8	−0.0234231
$990$	−1.82724e9	−0.0598511
$991$	1.13554e10	0.370633	0.185316	−	0.982679i	$-0.440669\pi$
$991$	1.13554e10	0.370633	0.185316	+	0.982679i	$0.440669\pi$
$992$	8.00914e8	0.0260492
$993$	7.59498e9	0.246153
$994$	−6.98252e8	−0.0225507
$995$	−4.69693e10	−1.51159
$996$	−2.59345e10	−0.831705
$997$	−6.06817e10	−1.93921	−0.969605	−	0.244674i	$-0.921319\pi$
$997$	−6.06817e10	−1.93921	−0.969605	+	0.244674i	$0.921319\pi$
$998$	−2.54137e8	−0.00809302
$999$	4.62888e10	1.46892

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.a.e.1.6	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.a.e.1.6	✓	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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	91.a (trivial)

\(f(q)\)	\(=\)	\(q+0.930860 q^{2} +23.4478 q^{3} -127.134 q^{4} -494.625 q^{5} +21.8266 q^{6} +343.000 q^{7} -237.493 q^{8} -1637.20 q^{9} +O(q^{10})\)	\(q+0.930860 q^{2} +23.4478 q^{3} -127.134 q^{4} -494.625 q^{5} +21.8266 q^{6} +343.000 q^{7} -237.493 q^{8} -1637.20 q^{9} -460.427 q^{10} -2424.00 q^{11} -2981.00 q^{12} +2197.00 q^{13} +319.285 q^{14} -11597.9 q^{15} +16052.0 q^{16} +3893.57 q^{17} -1524.00 q^{18} -4518.07 q^{19} +62883.5 q^{20} +8042.60 q^{21} -2256.40 q^{22} +66046.1 q^{23} -5568.70 q^{24} +166529. q^{25} +2045.10 q^{26} -89669.1 q^{27} -43606.8 q^{28} +6156.48 q^{29} -10796.0 q^{30} +17664.1 q^{31} +45341.3 q^{32} -56837.5 q^{33} +3624.37 q^{34} -169657. q^{35} +208143. q^{36} -516218. q^{37} -4205.69 q^{38} +51514.8 q^{39} +117470. q^{40} +470707. q^{41} +7486.53 q^{42} -10789.1 q^{43} +308172. q^{44} +809801. q^{45} +61479.6 q^{46} +326569. q^{47} +376385. q^{48} +117649. q^{49} +155015. q^{50} +91295.7 q^{51} -279312. q^{52} +1.91089e6 q^{53} -83469.3 q^{54} +1.19897e6 q^{55} -81460.3 q^{56} -105939. q^{57} +5730.82 q^{58} +558449. q^{59} +1.47448e6 q^{60} -1.32987e6 q^{61} +16442.8 q^{62} -561560. q^{63} -2.01245e6 q^{64} -1.08669e6 q^{65} -52907.7 q^{66} +2.71304e6 q^{67} -495004. q^{68} +1.54864e6 q^{69} -157926. q^{70} -2.18693e6 q^{71} +388824. q^{72} -2.12208e6 q^{73} -480527. q^{74} +3.90475e6 q^{75} +574398. q^{76} -831432. q^{77} +47953.1 q^{78} -3.62059e6 q^{79} -7.93974e6 q^{80} +1.47801e6 q^{81} +438162. q^{82} +8.69991e6 q^{83} -1.02248e6 q^{84} -1.92586e6 q^{85} -10043.1 q^{86} +144356. q^{87} +575684. q^{88} -2.94631e6 q^{89} +753811. q^{90} +753571. q^{91} -8.39667e6 q^{92} +414184. q^{93} +303990. q^{94} +2.23475e6 q^{95} +1.06315e6 q^{96} -1.35540e7 q^{97} +109515. q^{98} +3.96857e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 82 q^{3} + 986 q^{4} + 1026 q^{5} + 309 q^{6} + 4116 q^{7} + 228 q^{8} + 10902 q^{9}+O(q^{10}) \) 12 * q + 6 * q^2 + 82 * q^3 + 986 * q^4 + 1026 * q^5 + 309 * q^6 + 4116 * q^7 + 228 * q^8 + 10902 * q^9	\( 12 q + 6 q^{2} + 82 q^{3} + 986 q^{4} + 1026 q^{5} + 309 q^{6} + 4116 q^{7} + 228 q^{8} + 10902 q^{9} + 6668 q^{10} + 12168 q^{11} - 183 q^{12} + 26364 q^{13} + 2058 q^{14} - 28790 q^{15} + 85914 q^{16} + 82710 q^{17} - 44965 q^{18} - 10302 q^{19} + 141318 q^{20} + 28126 q^{21} - 97457 q^{22} + 98376 q^{23} - 519981 q^{24} + 272736 q^{25} + 13182 q^{26} + 306652 q^{27} + 338198 q^{28} + 350592 q^{29} + 231528 q^{30} + 55092 q^{31} + 114420 q^{32} + 609912 q^{33} + 812002 q^{34} + 351918 q^{35} + 1472143 q^{36} + 376310 q^{37} + 2825424 q^{38} + 180154 q^{39} + 2169290 q^{40} + 1387272 q^{41} + 105987 q^{42} + 568708 q^{43} + 3392031 q^{44} + 3556226 q^{45} - 1736829 q^{46} + 1359444 q^{47} + 4151249 q^{48} + 1411788 q^{49} + 3983712 q^{50} + 2709260 q^{51} + 2166242 q^{52} + 2061780 q^{53} + 2196651 q^{54} - 2112846 q^{55} + 78204 q^{56} + 2359902 q^{57} + 670268 q^{58} + 395964 q^{59} - 1052376 q^{60} + 444006 q^{61} + 2854353 q^{62} + 3739386 q^{63} + 12026858 q^{64} + 2254122 q^{65} - 4605681 q^{66} - 3094010 q^{67} + 4668954 q^{68} + 3839892 q^{69} + 2287124 q^{70} + 5694366 q^{71} - 9780585 q^{72} + 7052346 q^{73} - 4436259 q^{74} - 16288696 q^{75} - 3051830 q^{76} + 4173624 q^{77} + 678873 q^{78} + 4304160 q^{79} + 3807018 q^{80} - 6689556 q^{81} - 4733665 q^{82} + 2704554 q^{83} - 62769 q^{84} + 9301878 q^{85} + 1510998 q^{86} + 16231802 q^{87} - 70453923 q^{88} - 10986042 q^{89} - 12851300 q^{90} + 9042852 q^{91} - 16505451 q^{92} - 47230934 q^{93} - 24306151 q^{94} - 21839424 q^{95} - 86512741 q^{96} - 24462382 q^{97} + 705894 q^{98} + 11555078 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 + 82 * q^3 + 986 * q^4 + 1026 * q^5 + 309 * q^6 + 4116 * q^7 + 228 * q^8 + 10902 * q^9 + 6668 * q^10 + 12168 * q^11 - 183 * q^12 + 26364 * q^13 + 2058 * q^14 - 28790 * q^15 + 85914 * q^16 + 82710 * q^17 - 44965 * q^18 - 10302 * q^19 + 141318 * q^20 + 28126 * q^21 - 97457 * q^22 + 98376 * q^23 - 519981 * q^24 + 272736 * q^25 + 13182 * q^26 + 306652 * q^27 + 338198 * q^28 + 350592 * q^29 + 231528 * q^30 + 55092 * q^31 + 114420 * q^32 + 609912 * q^33 + 812002 * q^34 + 351918 * q^35 + 1472143 * q^36 + 376310 * q^37 + 2825424 * q^38 + 180154 * q^39 + 2169290 * q^40 + 1387272 * q^41 + 105987 * q^42 + 568708 * q^43 + 3392031 * q^44 + 3556226 * q^45 - 1736829 * q^46 + 1359444 * q^47 + 4151249 * q^48 + 1411788 * q^49 + 3983712 * q^50 + 2709260 * q^51 + 2166242 * q^52 + 2061780 * q^53 + 2196651 * q^54 - 2112846 * q^55 + 78204 * q^56 + 2359902 * q^57 + 670268 * q^58 + 395964 * q^59 - 1052376 * q^60 + 444006 * q^61 + 2854353 * q^62 + 3739386 * q^63 + 12026858 * q^64 + 2254122 * q^65 - 4605681 * q^66 - 3094010 * q^67 + 4668954 * q^68 + 3839892 * q^69 + 2287124 * q^70 + 5694366 * q^71 - 9780585 * q^72 + 7052346 * q^73 - 4436259 * q^74 - 16288696 * q^75 - 3051830 * q^76 + 4173624 * q^77 + 678873 * q^78 + 4304160 * q^79 + 3807018 * q^80 - 6689556 * q^81 - 4733665 * q^82 + 2704554 * q^83 - 62769 * q^84 + 9301878 * q^85 + 1510998 * q^86 + 16231802 * q^87 - 70453923 * q^88 - 10986042 * q^89 - 12851300 * q^90 + 9042852 * q^91 - 16505451 * q^92 - 47230934 * q^93 - 24306151 * q^94 - 21839424 * q^95 - 86512741 * q^96 - 24462382 * q^97 + 705894 * q^98 + 11555078 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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