LMFDB - Embedded newform 16.8.e.a.5.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,8,Mod(5,16)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("16.5");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	16.e (of order $4$, degree $2$, minimal)

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:	no
Analytic conductor:	$4.99816040775$
Analytic rank:	$0$
Dimension:	$26$
Relative dimension:	$13$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			5.7
Character	$\chi$	$=$	16.5
Dual form			16.8.e.a.13.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.35505 + 11.0659i) q^{2} +(50.5872 - 50.5872i) q^{3} +(-116.907 - 52.1215i) q^{4} +(-364.370 - 364.370i) q^{5} +(440.657 + 678.928i) q^{6} -182.346i q^{7} +(852.094 - 1170.93i) q^{8} -2931.14i q^{9} +O(q^{10})$	\(q+(-2.35505 + 11.0659i) q^{2} +(50.5872 - 50.5872i) q^{3} +(-116.907 - 52.1215i) q^{4} +(-364.370 - 364.370i) q^{5} +(440.657 + 678.928i) q^{6} -182.346i q^{7} +(852.094 - 1170.93i) q^{8} -2931.14i q^{9} +(4890.18 - 3173.96i) q^{10} +(3098.82 + 3098.82i) q^{11} +(-8550.71 + 3277.34i) q^{12} +(551.331 - 551.331i) q^{13} +(2017.82 + 429.435i) q^{14} -36864.9 q^{15} +(10950.7 + 12186.8i) q^{16} -5052.14 q^{17} +(32435.6 + 6902.99i) q^{18} +(16262.6 - 16262.6i) q^{19} +(23606.0 + 61589.0i) q^{20} +(-9224.39 - 9224.39i) q^{21} +(-41589.1 + 26993.3i) q^{22} -85254.9i q^{23} +(-16129.3 - 102339. i) q^{24} +187406. i q^{25} +(4802.55 + 7399.38i) q^{26} +(-37644.0 - 37644.0i) q^{27} +(-9504.15 + 21317.6i) q^{28} +(84428.5 - 84428.5i) q^{29} +(86818.9 - 407943. i) q^{30} -89901.8 q^{31} +(-160647. + 92478.6i) q^{32} +313522. q^{33} +(11898.1 - 55906.4i) q^{34} +(-66441.4 + 66441.4i) q^{35} +(-152775. + 342672. i) q^{36} +(288342. + 288342. i) q^{37} +(141661. + 218259. i) q^{38} -55780.6i q^{39} +(-737130. + 116176. i) q^{40} -614965. i q^{41} +(123800. - 80352.0i) q^{42} +(250103. + 250103. i) q^{43} +(-200760. - 523791. i) q^{44} +(-1.06802e6 + 1.06802e6i) q^{45} +(943421. + 200780. i) q^{46} -233960. q^{47} +(1.17046e6 + 62530.2i) q^{48} +790293. q^{49} +(-2.07381e6 - 441350. i) q^{50} +(-255574. + 255574. i) q^{51} +(-93190.9 + 35718.5i) q^{52} +(76228.4 + 76228.4i) q^{53} +(505217. - 327910. i) q^{54} -2.25824e6i q^{55} +(-213515. - 155376. i) q^{56} -1.64536e6i q^{57} +(735442. + 1.13311e6i) q^{58} +(-237487. - 237487. i) q^{59} +(4.30978e6 + 1.92146e6i) q^{60} +(-693245. + 693245. i) q^{61} +(211724. - 994842. i) q^{62} -534482. q^{63} +(-645025. - 1.99549e6i) q^{64} -401777. q^{65} +(-738361. + 3.46940e6i) q^{66} +(-154050. + 154050. i) q^{67} +(590633. + 263325. i) q^{68} +(-4.31281e6 - 4.31281e6i) q^{69} +(-578759. - 891706. i) q^{70} +3.04501e6i q^{71} +(-3.43217e6 - 2.49761e6i) q^{72} +1.83395e6i q^{73} +(-3.86982e6 + 2.51170e6i) q^{74} +(9.48033e6 + 9.48033e6i) q^{75} +(-2.74885e6 + 1.05359e6i) q^{76} +(565058. - 565058. i) q^{77} +(617262. + 131366. i) q^{78} -715721. q^{79} +(450392. - 8.43060e6i) q^{80} +2.60179e6 q^{81} +(6.80513e6 + 1.44828e6i) q^{82} +(-343278. + 343278. i) q^{83} +(597610. + 1.55919e6i) q^{84} +(1.84085e6 + 1.84085e6i) q^{85} +(-3.35662e6 + 2.17861e6i) q^{86} -8.54201e6i q^{87} +(6.26901e6 - 988032. i) q^{88} -7.36969e6i q^{89} +(-9.30332e6 - 1.43338e7i) q^{90} +(-100533. - 100533. i) q^{91} +(-4.44361e6 + 9.96693e6i) q^{92} +(-4.54788e6 + 4.54788e6i) q^{93} +(550988. - 2.58897e6i) q^{94} -1.18512e7 q^{95} +(-3.44845e6 + 1.28049e7i) q^{96} +8.74152e6 q^{97} +(-1.86118e6 + 8.74529e6i) q^{98} +(9.08308e6 - 9.08308e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 2 q^{2} - 2 q^{3} - 184 q^{4} - 2 q^{5} - 176 q^{6} - 1004 q^{8}+O(q^{10}) $ 26 * q - 2 * q^2 - 2 * q^3 - 184 * q^4 - 2 * q^5 - 176 * q^6 - 1004 * q^8	\( 26 q - 2 q^{2} - 2 q^{3} - 184 q^{4} - 2 q^{5} - 176 q^{6} - 1004 q^{8} + 12972 q^{10} + 1202 q^{11} - 27356 q^{12} - 2 q^{13} + 22268 q^{14} - 27004 q^{15} + 13336 q^{16} - 4 q^{17} - 29346 q^{18} + 60582 q^{19} + 46204 q^{20} + 4372 q^{21} - 44348 q^{22} - 59216 q^{24} - 35960 q^{26} - 233672 q^{27} + 220312 q^{28} - 51690 q^{29} + 27636 q^{30} + 357488 q^{31} - 248632 q^{32} - 4 q^{33} + 924660 q^{34} - 252004 q^{35} - 1015508 q^{36} + 415574 q^{37} - 5472 q^{38} - 1121976 q^{40} + 124600 q^{42} + 569754 q^{43} - 758620 q^{44} + 151874 q^{45} + 2335660 q^{46} - 2076464 q^{47} + 4141288 q^{48} - 1647090 q^{49} - 787194 q^{50} + 2609508 q^{51} + 410324 q^{52} + 907814 q^{53} - 7404512 q^{54} - 4093160 q^{56} - 1860712 q^{58} - 4865142 q^{59} + 5147328 q^{60} + 2279886 q^{61} + 6274096 q^{62} + 8295108 q^{63} + 10452224 q^{64} - 1426892 q^{65} + 10937812 q^{66} - 5564458 q^{67} - 7403760 q^{68} - 4786076 q^{69} - 22140800 q^{70} - 25293948 q^{72} - 13177044 q^{74} + 6212566 q^{75} + 17814260 q^{76} + 7604308 q^{77} + 37993916 q^{78} - 9598912 q^{79} + 40047272 q^{80} - 5314414 q^{81} + 22858240 q^{82} + 4531198 q^{83} - 30159704 q^{84} + 7377748 q^{85} - 54129468 q^{86} - 59216392 q^{88} - 33515304 q^{90} + 2587652 q^{91} + 21810936 q^{92} - 14504144 q^{93} + 77196112 q^{94} - 4900620 q^{95} + 116940464 q^{96} - 4 q^{97} + 21823866 q^{98} + 18815006 q^{99}+O(q^{100}) \) 26 * q - 2 * q^2 - 2 * q^3 - 184 * q^4 - 2 * q^5 - 176 * q^6 - 1004 * q^8 + 12972 * q^10 + 1202 * q^11 - 27356 * q^12 - 2 * q^13 + 22268 * q^14 - 27004 * q^15 + 13336 * q^16 - 4 * q^17 - 29346 * q^18 + 60582 * q^19 + 46204 * q^20 + 4372 * q^21 - 44348 * q^22 - 59216 * q^24 - 35960 * q^26 - 233672 * q^27 + 220312 * q^28 - 51690 * q^29 + 27636 * q^30 + 357488 * q^31 - 248632 * q^32 - 4 * q^33 + 924660 * q^34 - 252004 * q^35 - 1015508 * q^36 + 415574 * q^37 - 5472 * q^38 - 1121976 * q^40 + 124600 * q^42 + 569754 * q^43 - 758620 * q^44 + 151874 * q^45 + 2335660 * q^46 - 2076464 * q^47 + 4141288 * q^48 - 1647090 * q^49 - 787194 * q^50 + 2609508 * q^51 + 410324 * q^52 + 907814 * q^53 - 7404512 * q^54 - 4093160 * q^56 - 1860712 * q^58 - 4865142 * q^59 + 5147328 * q^60 + 2279886 * q^61 + 6274096 * q^62 + 8295108 * q^63 + 10452224 * q^64 - 1426892 * q^65 + 10937812 * q^66 - 5564458 * q^67 - 7403760 * q^68 - 4786076 * q^69 - 22140800 * q^70 - 25293948 * q^72 - 13177044 * q^74 + 6212566 * q^75 + 17814260 * q^76 + 7604308 * q^77 + 37993916 * q^78 - 9598912 * q^79 + 40047272 * q^80 - 5314414 * q^81 + 22858240 * q^82 + 4531198 * q^83 - 30159704 * q^84 + 7377748 * q^85 - 54129468 * q^86 - 59216392 * q^88 - 33515304 * q^90 + 2587652 * q^91 + 21810936 * q^92 - 14504144 * q^93 + 77196112 * q^94 - 4900620 * q^95 + 116940464 * q^96 - 4 * q^97 + 21823866 * q^98 + 18815006 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−2.35505	+	11.0659i	−0.208159	+	0.978095i
$2$	−2.35505	+	11.0659i	−0.208159	+	0.978095i
$3$	50.5872	−	50.5872i	1.08172	−	1.08172i	0.0853756	−	0.996349i	$-0.472791\pi$
$3$	50.5872	−	50.5872i	1.08172	−	1.08172i	0.996349	−	0.0853756i	$-0.0272090\pi$
$4$	−116.907	−	52.1215i	−0.913339	−	0.407199i
$5$	−364.370	−	364.370i	−1.30361	−	1.30361i	−0.925941	−	0.377668i	$-0.876726\pi$
$5$	−364.370	−	364.370i	−1.30361	−	1.30361i	−0.377668	−	0.925941i	$-0.623274\pi$
$6$	440.657	+	678.928i	0.832858	+	1.28320i
$7$		−	182.346i		−	0.200934i	−0.994940	−	0.100467i	$-0.967966\pi$
$7$		−	182.346i		−	0.200934i	0.994940	−	0.100467i	$-0.0320337\pi$
$8$	852.094	−	1170.93i	0.588400	−	0.808570i
$9$		−	2931.14i		−	1.34026i
$10$	4890.18	−	3173.96i	1.54641	−	1.00369i
$11$	3098.82	+	3098.82i	0.701976	+	0.701976i	0.964834	−	0.262858i	$-0.0846651\pi$
$11$	3098.82	+	3098.82i	0.701976	+	0.701976i	−0.262858	+	0.964834i	$0.584665\pi$
$12$	−8550.71	+	3277.34i	−1.42846	+	0.547504i
$13$	551.331	−	551.331i	0.0696002	−	0.0696002i	−0.671450	−	0.741050i	$-0.734328\pi$
$13$	551.331	−	551.331i	0.0696002	−	0.0696002i	0.741050	+	0.671450i	$0.234328\pi$
$14$	2017.82	+	429.435i	0.196532	+	0.0418263i
$15$	−36864.9			−2.82029
$16$	10950.7	+	12186.8i	0.668378	+	0.743822i
$17$	−5052.14			−0.249404			−0.124702	−	0.992194i	$-0.539798\pi$
$17$	−5052.14			−0.249404			−0.124702	+	0.992194i	$0.539798\pi$
$18$	32435.6	+	6902.99i	1.31090	+	0.278987i
$19$	16262.6	−	16262.6i	0.543942	−	0.543942i	−0.380740	−	0.924682i	$-0.624331\pi$
$19$	16262.6	−	16262.6i	0.543942	−	0.543942i	0.924682	+	0.380740i	$0.124331\pi$
$20$	23606.0	+	61589.0i	0.659809	+	1.72147i
$21$	−9224.39	−	9224.39i	−0.217355	−	0.217355i
$22$	−41589.1	+	26993.3i	−0.832722	+	0.540477i
$23$		−	85254.9i		−	1.46107i	−0.682874	−	0.730537i	$-0.739270\pi$
$23$		−	85254.9i		−	1.46107i	0.682874	−	0.730537i	$-0.260730\pi$
$24$	−16129.3	−	102339.i	−0.238164	−	1.51114i
$25$			187406.i			2.39879i
$26$	4802.55	+	7399.38i	0.0535877	+	0.0825636i
$27$	−37644.0	−	37644.0i	−0.368063	−	0.368063i
$28$	−9504.15	+	21317.6i	−0.0818201	+	0.183521i
$29$	84428.5	−	84428.5i	0.642830	−	0.642830i	−0.308420	−	0.951250i	$-0.599800\pi$
$29$	84428.5	−	84428.5i	0.642830	−	0.642830i	0.951250	+	0.308420i	$0.0998003\pi$
$30$	86818.9	−	407943.i	0.587070	−	2.75851i
$31$	−89901.8			−0.542004			−0.271002	−	0.962579i	$-0.587355\pi$
$31$	−89901.8			−0.542004			−0.271002	+	0.962579i	$0.587355\pi$
$32$	−160647.	+	92478.6i	−0.866658	+	0.498903i
$33$	313522.			1.51869
$34$	11898.1	−	55906.4i	0.0519159	−	0.243941i
$35$	−66441.4	+	66441.4i	−0.261939	+	0.261939i
$36$	−152775.	+	342672.i	−0.545751	+	1.22411i
$37$	288342.	+	288342.i	0.935841	+	0.935841i	0.998062	−	0.0622215i	$-0.0198185\pi$
$37$	288342.	+	288342.i	0.935841	+	0.935841i	−0.0622215	+	0.998062i	$0.519819\pi$
$38$	141661.	+	218259.i	0.418800	+	0.645253i
$39$		−	55780.6i		−	0.150577i
$40$	−737130.	+	116176.i	−1.82110	+	0.287016i
$41$		−	614965.i		−	1.39350i	−0.717314	−	0.696750i	$-0.754629\pi$
$41$		−	614965.i		−	1.39350i	0.717314	−	0.696750i	$-0.245371\pi$
$42$	123800.	−	80352.0i	0.257838	−	0.167349i
$43$	250103.	+	250103.i	0.479711	+	0.479711i	0.905039	−	0.425328i	$-0.139841\pi$
$43$	250103.	+	250103.i	0.479711	+	0.479711i	−0.425328	+	0.905039i	$0.639841\pi$
$44$	−200760.	−	523791.i	−0.355298	−	0.926987i
$45$	−1.06802e6	+	1.06802e6i	−1.74717	+	1.74717i
$46$	943421.	+	200780.i	1.42907	+	0.304136i
$47$	−233960.			−0.328699			−0.164350	−	0.986402i	$-0.552553\pi$
$47$	−233960.			−0.328699			−0.164350	+	0.986402i	$0.552553\pi$
$48$	1.17046e6	+	62530.2i	1.52761	+	0.0816103i
$49$	790293.			0.959626
$50$	−2.07381e6	−	441350.i	−2.34625	−	0.499331i
$51$	−255574.	+	255574.i	−0.269787	+	0.269787i
$52$	−93190.9	+	35718.5i	−0.0919098	+	0.0352275i
$53$	76228.4	+	76228.4i	0.0703317	+	0.0703317i	0.741398	−	0.671066i	$-0.234163\pi$
$53$	76228.4	+	76228.4i	0.0703317	+	0.0703317i	−0.671066	+	0.741398i	$0.734163\pi$
$54$	505217.	−	327910.i	0.436616	−	0.283385i
$55$		−	2.25824e6i		−	1.83021i
$56$	−213515.	−	155376.i	−0.162469	−	0.118229i
$57$		−	1.64536e6i		−	1.17679i
$58$	735442.	+	1.13311e6i	0.494938	+	0.762560i
$59$	−237487.	−	237487.i	−0.150542	−	0.150542i	0.627818	−	0.778360i	$-0.283948\pi$
$59$	−237487.	−	237487.i	−0.150542	−	0.150542i	−0.778360	+	0.627818i	$0.783948\pi$
$60$	4.30978e6	+	1.92146e6i	2.57588	+	1.14842i
$61$	−693245.	+	693245.i	−0.391050	+	0.391050i	−0.875062	−	0.484011i	$-0.839179\pi$
$61$	−693245.	+	693245.i	−0.391050	+	0.391050i	0.484011	+	0.875062i	$0.339179\pi$
$62$	211724.	−	994842.i	0.112823	−	0.530131i
$63$	−534482.			−0.269303
$64$	−645025.	−	1.99549e6i	−0.307572	−	0.951525i
$65$	−401777.			−0.181463
$66$	−738361.	+	3.46940e6i	−0.316130	+	1.48542i
$67$	−154050.	+	154050.i	−0.0625748	+	0.0625748i	−0.737702	−	0.675127i	$-0.764089\pi$
$67$	−154050.	+	154050.i	−0.0625748	+	0.0625748i	0.675127	+	0.737702i	$0.264089\pi$
$68$	590633.	+	263325.i	0.227791	+	0.101557i
$69$	−4.31281e6	−	4.31281e6i	−1.58048	−	1.58048i
$70$	−578759.	−	891706.i	−0.201676	−	0.310727i
$71$			3.04501e6i			1.00968i	0.863212	+	0.504841i	$0.168449\pi$
$71$			3.04501e6i			1.00968i	−0.863212	+	0.504841i	$0.831551\pi$
$72$	−3.43217e6	−	2.49761e6i	−1.08369	−	0.788606i
$73$			1.83395e6i			0.551770i	0.961191	+	0.275885i	$0.0889710\pi$
$73$			1.83395e6i			0.551770i	−0.961191	+	0.275885i	$0.911029\pi$
$74$	−3.86982e6	+	2.51170e6i	−1.11015	+	0.720537i
$75$	9.48033e6	+	9.48033e6i	2.59483	+	2.59483i
$76$	−2.74885e6	+	1.05359e6i	−0.718296	+	0.275311i
$77$	565058.	−	565058.i	0.141051	−	0.141051i
$78$	617262.	+	131366.i	0.147278	+	0.0313439i
$79$	−715721.			−0.163324			−0.0816619	−	0.996660i	$-0.526023\pi$
$79$	−715721.			−0.163324			−0.0816619	+	0.996660i	$0.526023\pi$
$80$	450392.	−	8.43060e6i	0.0983503	−	1.84096i
$81$	2.60179e6			0.543970
$82$	6.80513e6	+	1.44828e6i	1.36298	+	0.290070i
$83$	−343278.	+	343278.i	−0.0658982	+	0.0658982i	−0.739288	−	0.673390i	$-0.764838\pi$
$83$	−343278.	+	343278.i	−0.0658982	+	0.0658982i	0.673390	+	0.739288i	$0.264838\pi$
$84$	597610.	+	1.55919e6i	0.110012	+	0.287026i
$85$	1.84085e6	+	1.84085e6i	0.325126	+	0.325126i
$86$	−3.35662e6	+	2.17861e6i	−0.569059	+	0.369347i
$87$		−	8.54201e6i		−	1.39073i
$88$	6.26901e6	−	988032.i	0.980640	−	0.154555i
$89$		−	7.36969e6i		−	1.10811i	−0.832479	−	0.554057i	$-0.813079\pi$
$89$		−	7.36969e6i		−	1.10811i	0.832479	−	0.554057i	$-0.186921\pi$
$90$	−9.30332e6	−	1.43338e7i	−1.34521	−	2.07259i
$91$	−100533.	−	100533.i	−0.0139850	−	0.0139850i
$92$	−4.44361e6	+	9.96693e6i	−0.594948	+	1.33446i
$93$	−4.54788e6	+	4.54788e6i	−0.586299	+	0.586299i
$94$	550988.	−	2.58897e6i	0.0684218	−	0.321499i
$95$	−1.18512e7			−1.41817
$96$	−3.44845e6	+	1.28049e7i	−0.397809	+	1.47716i
$97$	8.74152e6			0.972492			0.486246	−	0.873822i	$-0.338366\pi$
$97$	8.74152e6			0.972492			0.486246	+	0.873822i	$0.338366\pi$
$98$	−1.86118e6	+	8.74529e6i	−0.199755	+	0.938605i
$99$	9.08308e6	−	9.08308e6i	0.940828	−	0.940828i
$100$	9.76786e6	−	2.19091e7i	0.976786	−	2.19091i
$101$	7.43990e6	+	7.43990e6i	0.718526	+	0.718526i	0.968303	−	0.249777i	$-0.0803574\pi$
$101$	7.43990e6	+	7.43990e6i	0.718526	+	0.718526i	−0.249777	+	0.968303i	$0.580357\pi$
$102$	−2.22626e6	−	3.43004e6i	−0.207718	−	0.320036i
$103$			2.45578e6i			0.221442i	0.993852	+	0.110721i	$0.0353160\pi$
$103$			2.45578e6i			0.221442i	−0.993852	+	0.110721i	$0.964684\pi$
$104$	−175787.	−	1.11536e6i	−0.0153239	−	0.0972294i
$105$			6.72217e6i			0.566692i
$106$	−1.02306e6	+	664012.i	−0.0834313	+	0.0541509i
$107$	−1.61877e7	−	1.61877e7i	−1.27744	−	1.27744i	−0.942095	−	0.335346i	$-0.891147\pi$
$107$	−1.61877e7	−	1.61877e7i	−1.27744	−	1.27744i	−0.335346	−	0.942095i	$-0.608853\pi$
$108$	2.43880e6	+	6.36292e6i	0.186291	+	0.486041i
$109$	−9.10305e6	+	9.10305e6i	−0.673278	+	0.673278i	−0.958470	−	0.285193i	$-0.907942\pi$
$109$	−9.10305e6	+	9.10305e6i	−0.673278	+	0.673278i	0.285193	+	0.958470i	$0.407942\pi$
$110$	2.49894e7	+	5.31827e6i	1.79011	+	0.380974i
$111$	2.91729e7			2.02464
$112$	2.22221e6	−	1.99682e6i	0.149459	−	0.134300i
$113$	−2.09244e7			−1.36420			−0.682100	−	0.731259i	$-0.738933\pi$
$113$	−2.09244e7			−1.36420			−0.682100	+	0.731259i	$0.738933\pi$
$114$	1.82074e7	+	3.87491e6i	1.15101	+	0.244960i
$115$	−3.10643e7	+	3.10643e7i	−1.90467	+	1.90467i
$116$	−1.42709e7	+	5.46978e6i	−0.848882	+	0.325362i
$117$	−1.61603e6	−	1.61603e6i	−0.0932821	−	0.0932821i
$118$	3.18729e6	−	2.06871e6i	0.178581	−	0.115908i
$119$			921238.i			0.0501138i
$120$	−3.14124e7	+	4.31664e7i	−1.65946	+	2.28040i
$121$		−	281755.i		−	0.0144585i
$122$	−6.03874e6	−	9.30400e6i	−0.301083	−	0.463885i
$123$	−3.11094e7	−	3.11094e7i	−1.50738	−	1.50738i
$124$	1.05102e7	+	4.68582e6i	0.495033	+	0.220704i
$125$	3.98186e7	−	3.98186e7i	1.82348	−	1.82348i
$126$	1.25873e6	−	5.91451e6i	0.0560579	−	0.263404i
$127$	−1.57776e7			−0.683485			−0.341742	−	0.939794i	$-0.611017\pi$
$127$	−1.57776e7			−0.683485			−0.341742	+	0.939794i	$0.611017\pi$
$128$	2.36009e7	−	2.43827e6i	0.994706	−	0.102765i
$129$	2.53041e7			1.03783
$130$	946206.	−	4.44601e6i	0.0377732	−	0.177488i
$131$	2.36854e7	−	2.36854e7i	0.920514	−	0.920514i	−0.0765517	−	0.997066i	$-0.524391\pi$
$131$	2.36854e7	−	2.36854e7i	0.920514	−	0.920514i	0.997066	+	0.0765517i	$0.0243910\pi$
$132$	−3.66530e7	−	1.63412e7i	−1.38708	−	0.618409i
$133$	−2.96542e6	−	2.96542e6i	−0.109296	−	0.109296i
$134$	−1.34190e6	−	2.06749e6i	−0.0481786	−	0.0742296i
$135$			2.74326e7i			0.959620i
$136$	−4.30490e6	+	5.91573e6i	−0.146749	+	0.201661i
$137$			2.83060e7i			0.940495i	0.882535	+	0.470248i	$0.155835\pi$
$137$			2.83060e7i			0.940495i	−0.882535	+	0.470248i	$0.844165\pi$
$138$	5.78820e7	−	3.75681e7i	1.87485	−	1.21687i
$139$	2.43457e7	+	2.43457e7i	0.768902	+	0.768902i	0.977913	−	0.209011i	$-0.0670246\pi$
$139$	2.43457e7	+	2.43457e7i	0.768902	+	0.768902i	−0.209011	+	0.977913i	$0.567025\pi$
$140$	1.12305e7	−	4.30447e6i	0.345901	−	0.132578i
$141$	−1.18354e7	+	1.18354e7i	−0.355562	+	0.355562i
$142$	−3.36957e7	−	7.17117e6i	−0.987565	−	0.210175i
$143$	3.41696e6			0.0977154
$144$	3.57212e7	−	3.20980e7i	0.996912	−	0.895797i
$145$	−6.15264e7			−1.67600
$146$	−2.02943e7	−	4.31906e6i	−0.539684	−	0.114856i
$147$	3.99787e7	−	3.99787e7i	1.03805	−	1.03805i
$148$	−1.86805e7	−	4.87382e7i	−0.473667	−	1.23581i
$149$	5.10801e7	+	5.10801e7i	1.26503	+	1.26503i	0.948625	+	0.316401i	$0.102475\pi$
$149$	5.10801e7	+	5.10801e7i	1.26503	+	1.26503i	0.316401	+	0.948625i	$0.397525\pi$
$150$	−1.27235e8	+	8.25816e7i	−3.07813	+	1.99785i
$151$			3.63413e6i			0.0858976i	0.999077	+	0.0429488i	$0.0136752\pi$
$151$			3.63413e6i			0.0858976i	−0.999077	+	0.0429488i	$0.986325\pi$
$152$	−5.18518e6	−	3.28997e7i	−0.119760	−	0.759870i
$153$			1.48085e7i			0.334266i
$154$	4.92212e6	+	7.58361e6i	0.108600	+	0.167322i
$155$	3.27575e7	+	3.27575e7i	0.706561	+	0.706561i
$156$	−2.90737e6	+	6.52117e6i	−0.0613147	+	0.137527i
$157$	2.98429e7	−	2.98429e7i	0.615449	−	0.615449i	−0.328912	−	0.944361i	$-0.606682\pi$
$157$	2.98429e7	−	2.98429e7i	0.615449	−	0.615449i	0.944361	+	0.328912i	$0.106682\pi$
$158$	1.68556e6	−	7.92009e6i	0.0339974	−	0.159746i
$159$	7.71237e6			0.152159
$160$	9.22313e7	+	2.48385e7i	1.78016	+	0.479408i
$161$	−1.55459e7			−0.293579
$162$	−6.12737e6	+	2.87911e7i	−0.113233	+	0.532055i
$163$	−1.50978e7	+	1.50978e7i	−0.273058	+	0.273058i	−0.830330	−	0.557272i	$-0.811848\pi$
$163$	−1.50978e7	+	1.50978e7i	−0.273058	+	0.273058i	0.557272	+	0.830330i	$0.311848\pi$
$164$	−3.20529e7	+	7.18940e7i	−0.567432	+	1.27274i
$165$	−1.14238e8	−	1.14238e8i	−1.97978	−	1.97978i
$166$	−2.99024e6	−	4.60712e6i	−0.0507373	−	0.0781720i
$167$			4.42359e7i			0.734966i	0.930030	+	0.367483i	$0.119780\pi$
$167$			4.42359e7i			0.734966i	−0.930030	+	0.367483i	$0.880220\pi$
$168$	−1.86612e7	+	2.94111e6i	−0.303639	+	0.0478552i
$169$			6.21406e7i			0.990312i
$170$	−2.47059e7	+	1.60353e7i	−0.385682	+	0.250326i
$171$	−4.76679e7	−	4.76679e7i	−0.729021	−	0.729021i
$172$	−1.62032e7	−	4.22747e7i	−0.242801	−	0.633477i
$173$	3.79117e7	−	3.79117e7i	0.556688	−	0.556688i	−0.371675	−	0.928363i	$-0.621217\pi$
$173$	3.79117e7	−	3.79117e7i	0.556688	−	0.556688i	0.928363	+	0.371675i	$0.121217\pi$
$174$	9.45249e7	+	2.01169e7i	1.36027	+	0.289493i
$175$	3.41727e7			0.481999
$176$	−3.83041e6	+	7.16990e7i	−0.0529604	+	0.991331i
$177$	−2.40276e7			−0.325690
$178$	8.15521e7	+	1.73560e7i	1.08384	+	0.230664i
$179$	−5.67952e7	+	5.67952e7i	−0.740161	+	0.740161i	−0.972609	−	0.232448i	$-0.925326\pi$
$179$	−5.67952e7	+	5.67952e7i	−0.740161	+	0.740161i	0.232448	+	0.972609i	$0.425326\pi$
$180$	1.80526e8	−	6.91926e7i	2.30720	−	0.884312i
$181$	2.17934e7	+	2.17934e7i	0.273180	+	0.273180i	0.830379	−	0.557199i	$-0.188124\pi$
$181$	2.17934e7	+	2.17934e7i	0.273180	+	0.273180i	−0.557199	+	0.830379i	$0.688124\pi$
$182$	1.34925e6	−	875726.i	0.0165898	−	0.0107676i
$183$			7.01387e7i			0.846017i
$184$	−9.98279e7	−	7.26452e7i	−1.18138	−	0.859695i
$185$		−	2.10126e8i		−	2.43994i
$186$	−3.96158e7	−	6.10368e7i	−0.451412	−	0.695499i
$187$	−1.56557e7	−	1.56557e7i	−0.175076	−	0.175076i
$188$	2.73516e7	+	1.21943e7i	0.300214	+	0.133846i
$189$	−6.86423e6	+	6.86423e6i	−0.0739563	+	0.0739563i
$190$	2.79102e7	−	1.31144e8i	0.295206	−	1.38711i
$191$	1.55665e8			1.61649			0.808247	−	0.588843i	$-0.200416\pi$
$191$	1.55665e8			1.61649			0.808247	+	0.588843i	$0.200416\pi$
$192$	−1.33576e8	−	6.83165e7i	−1.36200	−	0.696580i
$193$	−3.76346e7			−0.376823			−0.188411	−	0.982090i	$-0.560334\pi$
$193$	−3.76346e7			−0.376823			−0.188411	+	0.982090i	$0.560334\pi$
$194$	−2.05868e7	+	9.67327e7i	−0.202433	+	0.951190i
$195$	−2.03248e7	+	2.03248e7i	−0.196293	+	0.196293i
$196$	−9.23911e7	−	4.11913e7i	−0.876464	−	0.390759i
$197$	−1.83891e7	−	1.83891e7i	−0.171368	−	0.171368i	0.616212	−	0.787580i	$-0.288666\pi$
$197$	−1.83891e7	−	1.83891e7i	−0.171368	−	0.171368i	−0.787580	+	0.616212i	$0.788666\pi$
$198$	7.91212e7	+	1.21903e8i	0.724377	+	1.11606i
$199$		−	1.25278e8i		−	1.12691i	−0.826148	−	0.563453i	$-0.809473\pi$
$199$		−	1.25278e8i		−	1.12691i	0.826148	−	0.563453i	$-0.190527\pi$
$200$	2.19440e8	+	1.59687e8i	1.93959	+	1.41145i
$201$			1.55859e7i			0.135377i
$202$	−9.98505e7	+	6.48077e7i	−0.852355	+	0.553219i
$203$	−1.53952e7	−	1.53952e7i	−0.129166	−	0.129166i
$204$	4.31994e7	−	1.65576e7i	0.356264	−	0.136550i
$205$	−2.24075e8	+	2.24075e8i	−1.81658	+	1.81658i
$206$	−2.71754e7	−	5.78350e6i	−0.216591	−	0.0460952i
$207$	−2.49894e8			−1.95821
$208$	1.27564e7	+	681492.i	0.0982894	+	0.00525097i
$209$	1.00790e8			0.763668
$210$	−7.43868e7	−	1.58311e7i	−0.554279	−	0.117962i
$211$	1.14943e8	−	1.14943e8i	0.842350	−	0.842350i	−0.146814	−	0.989164i	$-0.546902\pi$
$211$	1.14943e8	−	1.14943e8i	0.842350	−	0.842350i	0.989164	+	0.146814i	$0.0469019\pi$
$212$	−4.93853e6	−	1.28848e7i	−0.0355977	−	0.0928757i
$213$	1.54039e8	+	1.54039e8i	1.09220	+	1.09220i
$214$	2.17254e8	−	1.41008e8i	1.51537	−	0.983547i
$215$		−	1.82260e8i		−	1.25071i
$216$	−7.61548e7	+	1.20024e7i	−0.514173	+	0.0810366i
$217$			1.63932e7i			0.108907i
$218$	−7.92951e7	−	1.22171e8i	−0.518380	−	0.798678i
$219$	9.27747e7	+	9.27747e7i	0.596864	+	0.596864i
$220$	−1.17703e8	+	2.64004e8i	−0.745258	+	1.67160i
$221$	−2.78540e6	+	2.78540e6i	−0.0173586	+	0.0173586i
$222$	−6.87037e7	+	3.22823e8i	−0.421449	+	1.98029i
$223$	−1.42305e7			−0.0859316			−0.0429658	−	0.999077i	$-0.513681\pi$
$223$	−1.42305e7			−0.0859316			−0.0429658	+	0.999077i	$0.513681\pi$
$224$	1.68631e7	+	2.92933e7i	0.100247	+	0.174141i
$225$	5.49312e8			3.21499
$226$	4.92780e7	−	2.31547e8i	0.283971	−	1.33432i
$227$	−1.83197e8	+	1.83197e8i	−1.03951	+	1.03951i	−0.0403185	+	0.999187i	$0.512837\pi$
$227$	−1.83197e8	+	1.83197e8i	−1.03951	+	1.03951i	−0.999187	+	0.0403185i	$0.987163\pi$
$228$	−8.57587e7	+	1.92355e8i	−0.479188	+	1.07481i
$229$	1.55425e8	+	1.55425e8i	0.855260	+	0.855260i	0.990775	−	0.135516i	$-0.0432691\pi$
$229$	1.55425e8	+	1.55425e8i	0.855260	+	0.855260i	−0.135516	+	0.990775i	$0.543269\pi$
$230$	−2.70596e8	−	4.16912e8i	−1.46647	−	2.25942i
$231$		−	5.71695e7i		−	0.305156i
$232$	−2.69193e7	−	1.70801e8i	−0.141532	−	0.898014i
$233$			1.10056e8i			0.569993i	0.958529	+	0.284996i	$0.0919924\pi$
$233$			1.10056e8i			0.569993i	−0.958529	+	0.284996i	$0.908008\pi$
$234$	2.16886e7	−	1.40769e7i	0.110656	−	0.0718212i
$235$	8.52479e7	+	8.52479e7i	0.428495	+	0.428495i
$236$	1.53858e7	+	4.01421e7i	0.0761953	+	0.198796i
$237$	−3.62064e7	+	3.62064e7i	−0.176671	+	0.176671i
$238$	−1.01943e7	−	2.16956e6i	−0.0490161	−	0.0104317i
$239$	−3.88486e8			−1.84070			−0.920349	−	0.391099i	$-0.872095\pi$
$239$	−3.88486e8			−1.84070			−0.920349	+	0.391099i	$0.872095\pi$
$240$	−4.03697e8	−	4.49265e8i	−1.88502	−	2.09780i
$241$	−3.32345e8			−1.52943			−0.764715	−	0.644368i	$-0.777120\pi$
$241$	−3.32345e8			−1.52943			−0.764715	+	0.644368i	$0.777120\pi$
$242$	3.11786e6	+	663548.i	0.0141418	+	0.00300967i
$243$	2.13945e8	−	2.13945e8i	0.956489	−	0.956489i
$244$	1.17179e8	−	4.49125e7i	0.516397	−	0.197926i
$245$	−2.87959e8	−	2.87959e8i	−1.25098	−	1.25098i
$246$	4.17517e8	−	2.70989e8i	1.78814	−	1.16059i
$247$		−	1.79322e7i		−	0.0757169i
$248$	−7.66047e7	+	1.05269e8i	−0.318915	+	0.438248i
$249$			3.47310e7i			0.142567i
$250$	3.46853e8	+	5.34402e8i	1.40396	+	2.16311i
$251$	2.96661e8	+	2.96661e8i	1.18414	+	1.18414i	0.978662	+	0.205477i	$0.0658747\pi$
$251$	2.96661e8	+	2.96661e8i	1.18414	+	1.18414i	0.205477	+	0.978662i	$0.434125\pi$
$252$	6.24849e7	+	2.78580e7i	0.245965	+	0.109660i
$253$	2.64190e8	−	2.64190e8i	1.02564	−	1.02564i
$254$	3.71572e7	−	1.74593e8i	0.142274	−	0.668513i
$255$	1.86247e8			0.703393
$256$	−2.85999e7	+	2.66908e8i	−0.106543	+	0.994308i
$257$	3.18636e7			0.117092			0.0585462	−	0.998285i	$-0.481353\pi$
$257$	3.18636e7			0.117092			0.0585462	+	0.998285i	$0.481353\pi$
$258$	−5.95925e7	+	2.80012e8i	−0.216034	+	1.01510i
$259$	5.25780e7	−	5.25780e7i	0.188042	−	0.188042i
$260$	4.69707e7	+	2.09412e7i	0.165737	+	0.0738916i
$261$	−2.47472e8	−	2.47472e8i	−0.861556	−	0.861556i
$262$	2.06319e8	+	3.17880e8i	0.708736	+	1.09196i
$263$		−	2.06508e8i		−	0.699990i	−0.936752	−	0.349995i	$-0.886183\pi$
$263$		−	2.06508e8i		−	0.699990i	0.936752	−	0.349995i	$-0.113817\pi$
$264$	2.67150e8	−	3.67114e8i	0.893597	−	1.22797i
$265$		−	5.55506e7i		−	0.183370i
$266$	3.97987e7	−	2.58313e7i	0.129653	−	0.0841511i
$267$	−3.72812e8	−	3.72812e8i	−1.19867	−	1.19867i
$268$	2.60389e7	−	9.98027e6i	0.0826325	−	0.0316716i
$269$	2.81668e7	−	2.81668e7i	0.0882276	−	0.0882276i	−0.661616	−	0.749843i	$-0.730129\pi$
$269$	2.81668e7	−	2.81668e7i	0.0882276	−	0.0882276i	0.749843	+	0.661616i	$0.230129\pi$
$270$	−3.03566e8	−	6.46053e7i	−0.938599	−	0.199754i
$271$	5.21818e7			0.159267			0.0796336	−	0.996824i	$-0.474625\pi$
$271$	5.21818e7			0.159267			0.0796336	+	0.996824i	$0.474625\pi$
$272$	−5.53244e7	−	6.15693e7i	−0.166696	−	0.185513i
$273$	−1.01714e7			−0.0302559
$274$	−3.13231e8	−	6.66622e7i	−0.919893	−	0.195773i
$275$	−5.80737e8	+	5.80737e8i	−1.68390	+	1.68390i
$276$	2.79409e8	+	7.28990e8i	0.799944	+	2.08708i
$277$	1.06576e8	+	1.06576e8i	0.301287	+	0.301287i	0.841517	−	0.540230i	$-0.181663\pi$
$277$	1.06576e8	+	1.06576e8i	0.301287	+	0.301287i	−0.540230	+	0.841517i	$0.681663\pi$
$278$	−3.26742e8	+	2.12071e8i	−0.912113	+	0.592005i
$279$			2.63515e8i			0.726424i
$280$	2.11842e7	+	1.34413e8i	0.0576713	+	0.365921i
$281$		−	3.05257e7i		−	0.0820717i	−0.999158	−	0.0410358i	$-0.986934\pi$
$281$		−	3.05257e7i		−	0.0820717i	0.999158	−	0.0410358i	$-0.0130658\pi$
$282$	−1.03096e8	−	1.58842e8i	−0.273760	−	0.421787i
$283$	6.35872e7	+	6.35872e7i	0.166770	+	0.166770i	0.785558	−	0.618788i	$-0.212376\pi$
$283$	6.35872e7	+	6.35872e7i	0.166770	+	0.166770i	−0.618788	+	0.785558i	$0.712376\pi$
$284$	1.58711e8	−	3.55985e8i	0.411142	−	0.922183i
$285$	−5.99520e8	+	5.99520e8i	−1.53407	+	1.53407i
$286$	−8.04712e6	+	3.78116e7i	−0.0203404	+	0.0955750i
$287$	−1.12137e8			−0.280002
$288$	2.71068e8	+	4.70879e8i	0.668658	+	1.16154i
$289$	−3.84815e8			−0.937797
$290$	1.44898e8	−	6.80844e8i	0.348875	−	1.63928i
$291$	4.42210e8	−	4.42210e8i	1.05197	−	1.05197i
$292$	9.55884e7	−	2.14403e8i	0.224680	−	0.503954i
$293$	1.37480e8	+	1.37480e8i	0.319304	+	0.319304i	0.848500	−	0.529196i	$-0.177506\pi$
$293$	1.37480e8	+	1.37480e8i	0.319304	+	0.319304i	−0.529196	+	0.848500i	$0.677506\pi$
$294$	3.48248e8	+	5.36552e8i	0.799232	+	1.23139i
$295$			1.73066e8i			0.392495i
$296$	5.83324e8	−	9.19353e7i	1.30734	−	0.206045i
$297$		−	2.33304e8i		−	0.516743i
$298$	−6.85543e8	+	4.44950e8i	−1.50064	+	0.973989i
$299$	−4.70037e7	−	4.70037e7i	−0.101691	−	0.101691i
$300$	−6.14192e8	−	1.60245e9i	−1.31335	−	3.42658i
$301$	4.56053e7	−	4.56053e7i	0.0963902	−	0.0963902i
$302$	−4.02148e7	−	8.55857e6i	−0.0840160	−	0.0178804i
$303$	7.52728e8			1.55449
$304$	3.76276e8	+	2.01020e7i	0.768154	+	0.0410375i
$305$	5.05195e8			1.01955
$306$	−1.63869e8	−	3.48749e7i	−0.326944	−	0.0695805i
$307$	3.02669e8	−	3.02669e8i	0.597013	−	0.597013i	−0.342503	−	0.939517i	$-0.611275\pi$
$307$	3.02669e8	−	3.02669e8i	0.597013	−	0.597013i	0.939517	+	0.342503i	$0.111275\pi$
$308$	−9.55112e7	+	3.66078e7i	−0.186263	+	0.0713915i
$309$	1.24231e8	+	1.24231e8i	0.239539	+	0.239539i
$310$	−4.39636e8	+	2.85345e8i	−0.838161	+	0.544006i
$311$			2.02990e8i			0.382659i	0.981526	+	0.191330i	$0.0612800\pi$
$311$			2.02990e8i			0.382659i	−0.981526	+	0.191330i	$0.938720\pi$
$312$	−6.53155e7	−	4.75303e7i	−0.121752	−	0.0885992i
$313$		−	9.59531e8i		−	1.76870i	−0.466827	−	0.884349i	$-0.654603\pi$
$313$		−	9.59531e8i		−	1.76870i	0.466827	−	0.884349i	$-0.345397\pi$
$314$	2.59956e8	+	4.00519e8i	0.473856	+	0.730079i
$315$	1.94749e8	+	1.94749e8i	0.351066	+	0.351066i
$316$	8.36732e7	+	3.73045e7i	0.149170	+	0.0665053i
$317$	3.13149e8	−	3.13149e8i	0.552132	−	0.552132i	−0.374924	−	0.927056i	$-0.622331\pi$
$317$	3.13149e8	−	3.13149e8i	0.552132	−	0.552132i	0.927056	+	0.374924i	$0.122331\pi$
$318$	−1.81630e7	+	8.53441e7i	−0.0316733	+	0.148826i
$319$	5.23258e8			0.902503
$320$	−4.92070e8	+	9.62124e8i	−0.839463	+	1.64137i
$321$	−1.63778e9			−2.76368
$322$	3.66114e7	−	1.72029e8i	0.0611113	−	0.287148i
$323$	−8.21609e7	+	8.21609e7i	−0.135661	+	0.135661i
$324$	−3.04169e8	−	1.35609e8i	−0.496830	−	0.221504i
$325$	1.03323e8	+	1.03323e8i	0.166956	+	0.166956i
$326$	−1.31514e8	−	2.02626e8i	−0.210237	−	0.323917i
$327$			9.20996e8i			1.45660i
$328$	−7.20084e8	−	5.24008e8i	−1.12674	−	0.819935i
$329$			4.26616e7i			0.0660468i
$330$	1.53318e9	−	9.95107e8i	2.34852	−	1.52430i
$331$	−2.89090e8	−	2.89090e8i	−0.438163	−	0.438163i	0.453230	−	0.891393i	$-0.350272\pi$
$331$	−2.89090e8	−	2.89090e8i	−0.438163	−	0.438163i	−0.891393	+	0.453230i	$0.850272\pi$
$332$	5.80240e7	−	2.22396e7i	0.0870211	−	0.0333537i
$333$	8.45171e8	−	8.45171e8i	1.25427	−	1.25427i
$334$	−4.89509e8	−	1.04178e8i	−0.718866	−	0.152990i
$335$	1.12262e8			0.163146
$336$	1.14021e7	−	2.13429e8i	0.0163983	−	0.306949i
$337$	1.01278e9			1.44148			0.720742	−	0.693204i	$-0.243801\pi$
$337$	1.01278e9			1.44148			0.720742	+	0.693204i	$0.243801\pi$
$338$	−6.87640e8	−	1.46344e8i	−0.968619	−	0.206143i
$339$	−1.05851e9	+	1.05851e9i	−1.47569	+	1.47569i
$340$	−1.19261e8	−	3.11156e8i	−0.164559	−	0.429341i
$341$	−2.78590e8	−	2.78590e8i	−0.380474	−	0.380474i
$342$	6.39748e8	−	4.15227e8i	0.864804	−	0.561299i
$343$		−	2.94277e8i		−	0.393755i
$344$	5.05966e8	−	7.97432e7i	0.670142	−	0.105618i
$345$			3.14292e9i			4.12065i
$346$	3.30242e8	+	5.08810e8i	0.428614	+	0.660373i
$347$	−9.02390e8	−	9.02390e8i	−1.15942	−	1.15942i	−0.984600	−	0.174821i	$-0.944065\pi$
$347$	−9.02390e8	−	9.02390e8i	−1.15942	−	1.15942i	−0.174821	−	0.984600i	$-0.555935\pi$
$348$	−4.45222e8	+	9.98625e8i	−0.566304	+	1.27021i
$349$	2.77719e8	−	2.77719e8i	0.349716	−	0.349716i	−0.510288	−	0.860004i	$-0.670461\pi$
$349$	2.77719e8	−	2.77719e8i	0.349716	−	0.349716i	0.860004	+	0.510288i	$0.170461\pi$
$350$	−8.04785e7	+	3.78151e8i	−0.100333	+	0.471440i
$351$	−4.15086e7			−0.0512345
$352$	−7.84391e8	−	2.11242e8i	−0.958591	−	0.258155i
$353$	5.54112e8			0.670480			0.335240	−	0.942133i	$-0.391183\pi$
$353$	5.54112e8			0.670480			0.335240	+	0.942133i	$0.391183\pi$
$354$	5.65863e7	−	2.65887e8i	0.0677954	−	0.318555i
$355$	1.10951e9	−	1.10951e9i	1.31623	−	1.31623i
$356$	−3.84119e8	+	8.61571e8i	−0.451223	+	1.01208i
$357$	4.66029e7	+	4.66029e7i	0.0542093	+	0.0542093i
$358$	−4.94733e8	−	7.62245e8i	−0.569876	−	0.878019i
$359$			1.54442e9i			1.76171i	0.473384	+	0.880856i	$0.343032\pi$
$359$			1.54442e9i			1.76171i	−0.473384	+	0.880856i	$0.656968\pi$
$360$	3.40528e8	+	2.16063e9i	0.384675	+	2.44074i
$361$			3.64927e8i			0.408255i
$362$	−2.92487e8	+	1.89838e8i	−0.324061	+	0.210331i
$363$	−1.42532e7	−	1.42532e7i	−0.0156401	−	0.0156401i
$364$	6.51313e6	+	1.69930e7i	0.00707839	+	0.0184678i
$365$	6.68237e8	−	6.68237e8i	0.719293	−	0.719293i
$366$	−7.76147e8	−	1.65181e8i	−0.827485	−	0.176106i
$367$	−1.49540e9			−1.57916			−0.789579	−	0.613650i	$-0.789701\pi$
$367$	−1.49540e9			−1.57916			−0.789579	+	0.613650i	$0.789701\pi$
$368$	1.03898e9	−	9.33601e8i	1.08678	−	0.976548i
$369$	−1.80255e9			−1.86765
$370$	2.32523e9	+	4.94859e8i	2.38649	+	0.507897i
$371$	1.38999e7	−	1.38999e7i	0.0141320	−	0.0141320i
$372$	7.68724e8	−	2.94639e8i	0.774230	−	0.296749i
$373$	−1.25005e8	−	1.25005e8i	−0.124723	−	0.124723i	0.641990	−	0.766713i	$-0.278109\pi$
$373$	−1.25005e8	−	1.25005e8i	−0.124723	−	0.124723i	−0.766713	+	0.641990i	$0.778109\pi$
$374$	2.10114e8	−	1.36374e8i	0.207685	−	0.134797i
$375$		−	4.02862e9i		−	3.94500i
$376$	−1.99356e8	+	2.73952e8i	−0.193407	+	0.265776i
$377$		−	9.30961e7i		−	0.0894822i
$378$	−5.97931e7	−	9.21243e7i	−0.0569416	−	0.0877310i
$379$	−5.45383e8	−	5.45383e8i	−0.514594	−	0.514594i	0.401337	−	0.915930i	$-0.368546\pi$
$379$	−5.45383e8	−	5.45383e8i	−0.514594	−	0.514594i	−0.915930	+	0.401337i	$0.868546\pi$
$380$	1.38549e9	+	6.17702e8i	1.29527	+	0.577480i
$381$	−7.98147e8	+	7.98147e8i	−0.739342	+	0.739342i
$382$	−3.66600e8	+	1.72257e9i	−0.336488	+	1.58109i
$383$	−7.37797e8			−0.671029			−0.335514	−	0.942035i	$-0.608910\pi$
$383$	−7.37797e8			−0.671029			−0.335514	+	0.942035i	$0.608910\pi$
$384$	1.07056e9	−	1.31725e9i	0.964833	−	1.18716i
$385$	−4.11780e8			−0.367750
$386$	8.86316e7	−	4.16460e8i	0.0784391	−	0.368568i
$387$	7.33087e8	−	7.33087e8i	0.642935	−	0.642935i
$388$	−1.02195e9	−	4.55621e8i	−0.888215	−	0.395998i
$389$	1.33031e9	+	1.33031e9i	1.14586	+	1.14586i	0.987360	+	0.158496i	$0.0506644\pi$
$389$	1.33031e9	+	1.33031e9i	1.14586	+	1.14586i	0.158496	+	0.987360i	$0.449336\pi$
$390$	−1.77046e8	−	2.72778e8i	−0.151133	−	0.232853i
$391$			4.30720e8i			0.364398i
$392$	6.73404e8	−	9.25381e8i	0.564643	−	0.775925i
$393$		−	2.39635e9i		−	1.99148i
$394$	2.46799e8	−	1.60185e8i	0.203286	−	0.131942i
$395$	2.60787e8	+	2.60787e8i	0.212910	+	0.212910i
$396$	−1.53530e9	+	5.88456e8i	−1.24240	+	0.476191i
$397$	−8.07909e8	+	8.07909e8i	−0.648031	+	0.648031i	−0.952517	−	0.304486i	$-0.901515\pi$
$397$	−8.07909e8	+	8.07909e8i	−0.648031	+	0.648031i	0.304486	+	0.952517i	$0.401515\pi$
$398$	1.38631e9	+	2.95035e8i	1.10222	+	0.234576i
$399$	−3.00025e8			−0.236457
$400$	−2.28387e9	+	2.05222e9i	−1.78427	+	1.60330i
$401$	1.70090e9			1.31727			0.658634	−	0.752464i	$-0.271135\pi$
$401$	1.70090e9			1.31727			0.658634	+	0.752464i	$0.271135\pi$
$402$	−1.72472e8	−	3.67057e7i	−0.132412	−	0.0281801i
$403$	−4.95656e7	+	4.95656e7i	−0.0377236	+	0.0377236i
$404$	−4.82001e8	−	1.25756e9i	−0.363675	−	0.948841i
$405$	−9.48015e8	−	9.48015e8i	−0.709125	−	0.709125i
$406$	2.06618e8	−	1.34105e8i	0.153224	−	0.0994497i
$407$			1.78704e9i			1.31388i
$408$	8.14874e7	+	5.17033e8i	0.0593991	+	0.376884i
$409$			4.89976e8i			0.354114i	0.984201	+	0.177057i	$0.0566578\pi$
$409$			4.89976e8i			0.354114i	−0.984201	+	0.177057i	$0.943342\pi$
$410$	−1.95188e9	−	3.00729e9i	−1.39865	−	2.15493i
$411$	1.43192e9	+	1.43192e9i	1.01736	+	1.01736i
$412$	1.27999e8	−	2.87099e8i	0.0901710	−	0.202252i
$413$	−4.33048e7	+	4.33048e7i	−0.0302490	+	0.0302490i
$414$	5.88514e8	−	2.76530e9i	0.407620	−	1.91532i
$415$	2.50161e8			0.171811
$416$	−3.75834e7	+	1.39556e8i	−0.0255958	+	0.0950434i
$417$	2.46317e9			1.66348
$418$	−2.37366e8	+	1.11533e9i	−0.158965	+	0.746940i
$419$	−9.43370e8	+	9.43370e8i	−0.626517	+	0.626517i	−0.947190	−	0.320673i	$-0.896091\pi$
$419$	−9.43370e8	+	9.43370e8i	−0.626517	+	0.626517i	0.320673	+	0.947190i	$0.396091\pi$
$420$	3.50370e8	−	7.85872e8i	0.230757	−	0.517582i
$421$	7.48084e8	+	7.48084e8i	0.488611	+	0.488611i	0.907868	−	0.419257i	$-0.137709\pi$
$421$	7.48084e8	+	7.48084e8i	0.488611	+	0.488611i	−0.419257	+	0.907868i	$0.637709\pi$
$422$	1.00125e9	+	1.54264e9i	0.648555	+	0.999241i
$423$			6.85769e8i			0.440541i
$424$	1.54212e8	−	2.43047e7i	0.0982513	−	0.0154850i
$425$		−	9.46799e8i		−	0.598269i
$426$	−2.06734e9	+	1.34180e9i	−1.29562	+	0.840922i
$427$	1.26411e8	+	1.26411e8i	0.0785752	+	0.0785752i
$428$	1.04873e9	+	2.73618e9i	0.646564	+	1.68691i
$429$	1.72854e8	−	1.72854e8i	0.105701	−	0.105701i
$430$	2.01687e9	+	4.29232e8i	1.22331	+	0.260347i
$431$	1.69202e9			1.01797			0.508986	−	0.860775i	$-0.330021\pi$
$431$	1.69202e9			1.01797			0.508986	+	0.860775i	$0.330021\pi$
$432$	4.65311e7	−	8.70986e8i	0.0277684	−	0.519778i
$433$	−9.65526e7			−0.0571553			−0.0285776	−	0.999592i	$-0.509098\pi$
$433$	−9.65526e7			−0.0571553			−0.0285776	+	0.999592i	$0.509098\pi$
$434$	−1.81406e8	−	3.86070e7i	−0.106521	−	0.0226700i
$435$	−3.11245e9	+	3.11245e9i	−1.81297	+	1.81297i
$436$	1.53868e9	−	5.89749e8i	0.889089	−	0.340773i
$437$	−1.38647e9	−	1.38647e9i	−0.794739	−	0.794739i
$438$	−1.24512e9	+	8.08144e8i	−0.708032	+	0.459546i
$439$		−	1.15106e9i		−	0.649340i	−0.945827	−	0.324670i	$-0.894747\pi$
$439$		−	1.15106e9i		−	0.649340i	0.945827	−	0.324670i	$-0.105253\pi$
$440$	−2.64425e9	−	1.92423e9i	−1.47985	−	1.07689i
$441$		−	2.31646e9i		−	1.28614i
$442$	−2.42631e7	−	3.73827e7i	−0.0133650	−	0.0205917i
$443$	4.29638e8	+	4.29638e8i	0.234796	+	0.234796i	0.814691	−	0.579895i	$-0.196907\pi$
$443$	4.29638e8	+	4.29638e8i	0.234796	+	0.234796i	−0.579895	+	0.814691i	$0.696907\pi$
$444$	−3.41052e9	−	1.52053e9i	−1.84919	−	0.824433i
$445$	−2.68529e9	+	2.68529e9i	−1.44455	+	1.44455i
$446$	3.35136e7	−	1.57473e8i	0.0178875	−	0.0840493i
$447$	5.16800e9			2.73682
$448$	−3.63870e8	+	1.17618e8i	−0.191194	+	0.0618016i
$449$	−3.75101e9			−1.95562			−0.977812	−	0.209482i	$-0.932822\pi$
$449$	−3.75101e9			−1.95562			−0.977812	+	0.209482i	$0.932822\pi$
$450$	−1.29366e9	+	6.07862e9i	−0.669231	+	3.14457i
$451$	1.90567e9	−	1.90567e9i	0.978204	−	0.978204i
$452$	2.44621e9	+	1.09061e9i	1.24598	+	0.555501i
$453$	1.83841e8	+	1.83841e8i	0.0929175	+	0.0929175i
$454$	−1.59579e9	−	2.45867e9i	−0.800352	−	1.23312i
$455$			7.32624e7i			0.0364621i
$456$	−1.92661e9	−	1.40200e9i	−0.951518	−	0.692423i
$457$			1.33004e8i			0.0651866i	0.999469	+	0.0325933i	$0.0103766\pi$
$457$			1.33004e8i			0.0651866i	−0.999469	+	0.0325933i	$0.989623\pi$
$458$	−2.08596e9	+	1.35388e9i	−1.01456	+	0.658495i
$459$	1.90182e8	+	1.90182e8i	0.0917965	+	0.0917965i
$460$	5.25077e9	−	2.01253e9i	2.51519	−	0.964029i
$461$	5.45820e8	−	5.45820e8i	0.259475	−	0.259475i	−0.565365	−	0.824841i	$-0.691265\pi$
$461$	5.45820e8	−	5.45820e8i	0.259475	−	0.259475i	0.824841	+	0.565365i	$0.191265\pi$
$462$	6.32631e8	+	1.34637e8i	0.298472	+	0.0635211i
$463$	−3.34593e9			−1.56669			−0.783346	−	0.621585i	$-0.786489\pi$
$463$	−3.34593e9			−1.56669			−0.783346	+	0.621585i	$0.786489\pi$
$464$	1.95346e9	+	1.04361e8i	0.907804	+	0.0484981i
$465$	3.31422e9			1.52861
$466$	−1.21787e9	−	2.59189e8i	−0.557507	−	0.118649i
$467$	2.54684e9	−	2.54684e9i	1.15716	−	1.15716i	0.172072	−	0.985084i	$-0.444954\pi$
$467$	2.54684e9	−	2.54684e9i	1.15716	−	1.15716i	0.985084	−	0.172072i	$-0.0550461\pi$
$468$	1.04696e8	+	2.73155e8i	0.0472138	+	0.123183i
$469$	2.80904e7	+	2.80904e7i	0.0125734	+	0.0125734i
$470$	−1.14411e9	+	7.42579e8i	−0.508304	+	0.329914i
$471$		−	3.01934e9i		−	1.33149i
$472$	−4.80442e8	+	7.57205e7i	−0.210302	+	0.0331449i
$473$			1.55005e9i			0.673492i
$474$	−3.15387e8	−	4.85923e8i	−0.136025	−	0.209577i
$475$	3.04770e9	+	3.04770e9i	1.30480	+	1.30480i
$476$	4.80163e7	−	1.07700e8i	0.0204063	−	0.0457709i
$477$	2.23436e8	−	2.23436e8i	0.0942625	−	0.0942625i
$478$	9.14905e8	−	4.29894e9i	0.383158	−	1.80038i
$479$	−2.17828e9			−0.905607			−0.452804	−	0.891610i	$-0.649576\pi$
$479$	−2.17828e9			−0.905607			−0.452804	+	0.891610i	$0.649576\pi$
$480$	5.92224e9	−	3.40922e9i	2.44423	−	1.40705i
$481$	3.17944e8			0.130269
$482$	7.82691e8	−	3.67769e9i	0.318365	−	1.49593i
$483$	−7.86424e8	+	7.86424e8i	−0.317572	+	0.317572i
$484$	−1.46855e7	+	3.29392e7i	−0.00588748	+	0.0132055i
$485$	−3.18515e9	−	3.18515e9i	−1.26775	−	1.26775i
$486$	1.86364e9	+	2.87134e9i	0.736435	+	1.13464i
$487$			2.53398e9i			0.994150i	0.867707	+	0.497075i	$0.165593\pi$
$487$			2.53398e9i			0.994150i	−0.867707	+	0.497075i	$0.834407\pi$
$488$	2.21035e8	+	1.40246e9i	0.0860977	+	0.546285i
$489$			1.52751e9i			0.590748i
$490$	3.86468e9	−	2.50836e9i	1.48398	−	0.963171i
$491$	−2.32715e9	−	2.32715e9i	−0.887237	−	0.887237i	0.107020	−	0.994257i	$-0.465869\pi$
$491$	−2.32715e9	−	2.32715e9i	−0.887237	−	0.887237i	−0.994257	+	0.107020i	$0.965869\pi$
$492$	2.01545e9	+	5.25839e9i	0.762947	+	1.99056i
$493$	−4.26545e8	+	4.26545e8i	−0.160325	+	0.160325i
$494$	1.98435e8	+	4.22312e7i	0.0740584	+	0.0157612i
$495$	−6.61920e9			−2.45294
$496$	−9.84487e8	−	1.09561e9i	−0.362263	−	0.403154i
$497$	5.55246e8			0.202879
$498$	−3.84329e8	−	8.17935e7i	−0.139444	−	0.0296767i
$499$	−1.37717e9	+	1.37717e9i	−0.496177	+	0.496177i	−0.910246	−	0.414069i	$-0.864107\pi$
$499$	−1.37717e9	+	1.37717e9i	−0.496177	+	0.496177i	0.414069	+	0.910246i	$0.364107\pi$
$500$	−6.73049e9	+	2.57968e9i	−2.40797	+	0.922935i
$501$	2.23777e9	+	2.23777e9i	0.795030	+	0.795030i
$502$	−3.98147e9	+	2.58416e9i	−1.40469	+	0.911711i
$503$		−	4.15787e9i		−	1.45674i	−0.685182	−	0.728372i	$-0.740277\pi$
$503$		−	4.15787e9i		−	1.45674i	0.685182	−	0.728372i	$-0.259723\pi$
$504$	−4.55428e8	+	6.25843e8i	−0.158458	+	0.217750i
$505$		−	5.42175e9i		−	1.87335i
$506$	2.30131e9	+	3.54568e9i	0.789676	+	1.21667i
$507$	3.14352e9	+	3.14352e9i	1.07124	+	1.07124i
$508$	1.84452e9	+	8.22354e8i	0.624253	+	0.278314i
$509$	−5.02429e8	+	5.02429e8i	−0.168874	+	0.168874i	−0.786484	−	0.617610i	$-0.788101\pi$
$509$	−5.02429e8	+	5.02429e8i	−0.168874	+	0.168874i	0.617610	+	0.786484i	$0.288101\pi$
$510$	−4.38621e8	+	2.06098e9i	−0.146418	+	0.687985i
$511$	3.34414e8			0.110869
$512$	−2.88621e9	−	9.45065e8i	−0.950350	−	0.311184i
$513$	−1.22438e9			−0.400410
$514$	−7.50405e7	+	3.52599e8i	−0.0243739	+	0.114528i
$515$	8.94813e8	−	8.94813e8i	0.288674	−	0.288674i
$516$	−2.95823e9	−	1.31889e9i	−0.947891	−	0.422604i
$517$	−7.25000e8	−	7.25000e8i	−0.230739	−	0.230739i
$518$	4.57998e8	+	7.05646e8i	0.144780	+	0.223066i
$519$		−	3.83569e9i		−	1.20437i
$520$	−3.42351e8	+	4.70454e8i	−0.106773	+	0.146726i
$521$			1.87264e9i			0.580125i	0.957008	+	0.290063i	$0.0936761\pi$
$521$			1.87264e9i			0.580125i	−0.957008	+	0.290063i	$0.906324\pi$
$522$	3.32130e9	−	2.15568e9i	1.02202	−	0.663343i
$523$	−1.15423e9	−	1.15423e9i	−0.352806	−	0.352806i	0.508346	−	0.861153i	$-0.330257\pi$
$523$	−1.15423e9	−	1.15423e9i	−0.352806	−	0.352806i	−0.861153	+	0.508346i	$0.830257\pi$
$524$	−4.00351e9	+	1.53448e9i	−1.21557	+	0.465909i
$525$	1.72870e9	−	1.72870e9i	0.521390	−	0.521390i
$526$	2.28519e9	+	4.86338e8i	0.684656	+	0.145709i
$527$	4.54196e8			0.135178
$528$	3.43328e9	+	3.82082e9i	1.01506	+	1.12964i
$529$	−3.86357e9			−1.13473
$530$	6.14717e8	+	1.30825e8i	0.179353	+	0.0381702i
$531$	−6.96107e8	+	6.96107e8i	−0.201765	+	0.201765i
$532$	1.92118e8	+	5.01242e8i	0.0553193	+	0.144330i
$533$	−3.39049e8	−	3.39049e8i	−0.0969880	−	0.0969880i
$534$	5.00349e9	−	3.24750e9i	1.42193	−	0.922901i
$535$			1.17966e10i			3.33057i
$536$	4.91174e7	+	3.11647e8i	0.0137771	+	0.0874151i
$537$			5.74622e9i			1.60130i
$538$	2.45356e8	+	3.78025e8i	0.0679296	+	0.104660i
$539$	2.44898e9	+	2.44898e9i	0.673634	+	0.673634i
$540$	1.42983e9	−	3.20708e9i	0.390757	−	0.876459i
$541$	3.31651e9	−	3.31651e9i	0.900515	−	0.900515i	−0.0949657	−	0.995481i	$-0.530274\pi$
$541$	3.31651e9	−	3.31651e9i	0.900515	−	0.900515i	0.995481	+	0.0949657i	$0.0302741\pi$
$542$	−1.22891e8	+	5.77437e8i	−0.0331530	+	0.155778i
$543$	2.20493e9			0.591011
$544$	8.11611e8	−	4.67215e8i	0.216148	−	0.124429i
$545$	6.63375e9			1.75538
$546$	2.39542e7	−	1.12555e8i	0.00629806	−	0.0295932i
$547$	3.57793e9	−	3.57793e9i	0.934709	−	0.934709i	−0.0632867	−	0.997995i	$-0.520158\pi$
$547$	3.57793e9	−	3.57793e9i	0.934709	−	0.934709i	0.997995	+	0.0632867i	$0.0201583\pi$
$548$	1.47535e9	−	3.30918e9i	0.382969	−	0.858991i
$549$	2.03200e9	+	2.03200e9i	0.524107	+	0.524107i
$550$	−5.05870e9	−	7.79403e9i	−1.29649	−	1.99753i
$551$		−	2.74605e9i		−	0.699324i
$552$	−8.72494e9	+	1.37510e9i	−2.20788	+	0.347975i
$553$			1.30509e8i			0.0328173i
$554$	−1.43035e9	+	9.28364e8i	−0.357403	+	0.231971i
$555$	−1.06297e10	−	1.06297e10i	−2.63934	−	2.63934i
$556$	−1.57726e9	−	4.11513e9i	−0.389172	−	1.01536i
$557$	−5.33119e9	+	5.33119e9i	−1.30717	+	1.30717i	−0.383716	+	0.923451i	$0.625356\pi$
$557$	−5.33119e9	+	5.33119e9i	−1.30717	+	1.30717i	−0.923451	+	0.383716i	$0.874644\pi$
$558$	−2.91602e9	−	6.20591e8i	−0.710511	−	0.151212i
$559$	2.75779e8			0.0667760
$560$	−1.53729e9	−	8.21272e7i	−0.369911	−	0.0197619i
$561$	−1.58396e9			−0.378768
$562$	3.37794e8	+	7.18896e7i	0.0802739	+	0.0170840i
$563$	−3.25048e9	+	3.25048e9i	−0.767660	+	0.767660i	−0.977694	−	0.210034i	$-0.932642\pi$
$563$	−3.25048e9	+	3.25048e9i	−0.767660	+	0.767660i	0.210034	+	0.977694i	$0.432642\pi$
$564$	2.00052e9	−	7.66766e8i	0.469533	−	0.179964i
$565$	7.62421e9	+	7.62421e9i	1.77838	+	1.77838i
$566$	−8.53400e8	+	5.53897e8i	−0.197831	+	0.128402i
$567$		−	4.74427e8i		−	0.109302i
$568$	3.56551e9	+	2.59464e9i	0.816399	+	0.594097i
$569$			3.21428e9i			0.731461i	0.930721	+	0.365730i	$0.119181\pi$
$569$			3.21428e9i			0.731461i	−0.930721	+	0.365730i	$0.880819\pi$
$570$	−5.22231e9	−	8.04611e9i	−1.18114	−	1.81980i
$571$	−2.82906e9	−	2.82906e9i	−0.635939	−	0.635939i	0.313612	−	0.949551i	$-0.398461\pi$
$571$	−2.82906e9	−	2.82906e9i	−0.635939	−	0.635939i	−0.949551	+	0.313612i	$0.898461\pi$
$572$	−3.99467e8	−	1.78097e8i	−0.0892473	−	0.0397897i
$573$	7.87466e9	−	7.87466e9i	1.74860	−	1.74860i
$574$	2.64088e8	−	1.24089e9i	0.0582849	−	0.273868i
$575$	1.59772e10			3.50481
$576$	−5.84907e9	+	1.89066e9i	−1.27529	+	0.412225i
$577$	4.87408e8			0.105628			0.0528138	−	0.998604i	$-0.483181\pi$
$577$	4.87408e8			0.105628			0.0528138	+	0.998604i	$0.483181\pi$
$578$	9.06259e8	−	4.25831e9i	0.195211	−	0.917255i
$579$	−1.90383e9	+	1.90383e9i	−0.407618	+	0.407618i
$580$	7.19289e9	+	3.20685e9i	1.53075	+	0.682465i
$581$	6.25955e7	+	6.25955e7i	0.0132412	+	0.0132412i
$582$	3.85201e9	+	5.93487e9i	0.809948	+	1.24790i
$583$			4.72437e8i			0.0987424i
$584$	2.14744e9	+	1.56270e9i	0.446145	+	0.324662i
$585$			1.17766e9i			0.243207i
$586$	−1.84512e9	+	1.19757e9i	−0.378776	+	0.245843i
$587$	−4.27968e9	−	4.27968e9i	−0.873329	−	0.873329i	0.119505	−	0.992834i	$-0.461869\pi$
$587$	−4.27968e9	−	4.27968e9i	−0.873329	−	0.873329i	−0.992834	+	0.119505i	$0.961869\pi$
$588$	−6.75756e9	+	2.59006e9i	−1.37079	+	0.525399i
$589$	−1.46204e9	+	1.46204e9i	−0.294818	+	0.294818i
$590$	−1.91513e9	−	4.07580e8i	−0.383898	−	0.0817016i
$591$	−1.86051e9			−0.370746
$592$	−3.56415e8	+	6.67151e9i	−0.0706042	+	1.32159i
$593$	−2.87074e9			−0.565331			−0.282665	−	0.959219i	$-0.591219\pi$
$593$	−2.87074e9			−0.565331			−0.282665	+	0.959219i	$0.591219\pi$
$594$	2.58171e9	+	5.49443e8i	0.505424	+	0.107565i
$595$	3.35671e8	−	3.35671e8i	0.0653288	−	0.0653288i
$596$	−3.30927e9	−	8.63401e9i	−0.640281	−	1.67052i
$597$	−6.33744e9	−	6.33744e9i	−1.21900	−	1.21900i
$598$	6.30833e8	−	4.09441e8i	0.120631	−	0.0782955i
$599$		−	7.56451e9i		−	1.43809i	−0.694962	−	0.719047i	$-0.744579\pi$
$599$		−	7.56451e9i		−	1.43809i	0.694962	−	0.719047i	$-0.255421\pi$
$600$	1.91790e10	−	3.02272e9i	3.62490	−	0.571306i
$601$		−	5.12673e9i		−	0.963341i	−0.876352	−	0.481670i	$-0.840030\pi$
$601$		−	5.12673e9i		−	0.963341i	0.876352	−	0.481670i	$-0.159970\pi$
$602$	3.97260e8	+	6.12066e8i	0.0742142	+	0.114343i
$603$	4.51542e8	+	4.51542e8i	0.0838663	+	0.0838663i
$604$	1.89416e8	−	4.24857e8i	0.0349774	−	0.0784536i
$605$	−1.02663e8	+	1.02663e8i	−0.0188482	+	0.0188482i
$606$	−1.77272e9	+	8.32960e9i	−0.323583	+	1.52044i
$607$	−7.68230e9			−1.39422			−0.697109	−	0.716965i	$-0.745531\pi$
$607$	−7.68230e9			−1.39422			−0.697109	+	0.716965i	$0.745531\pi$
$608$	−1.10860e9	+	4.11648e9i	−0.200037	+	0.742786i
$609$	−1.55760e9			−0.279445
$610$	−1.18976e9	+	5.59043e9i	−0.212230	+	0.997220i
$611$	−1.28989e8	+	1.28989e8i	−0.0228775	+	0.0228775i
$612$	7.71843e8	−	1.73123e9i	0.136113	−	0.305298i
$613$	2.07134e9	+	2.07134e9i	0.363194	+	0.363194i	0.864988	−	0.501793i	$-0.167326\pi$
$613$	2.07134e9	+	2.07134e9i	0.363194	+	0.363194i	−0.501793	+	0.864988i	$0.667326\pi$
$614$	2.63650e9	+	4.06211e9i	0.459662	+	0.708210i
$615$			2.26707e10i			3.93008i
$616$	−1.80164e8	−	1.14313e9i	−0.0310552	−	0.197044i
$617$			3.13478e9i			0.537290i	0.963239	+	0.268645i	$0.0865759\pi$
$617$			3.13478e9i			0.537290i	−0.963239	+	0.268645i	$0.913424\pi$
$618$	−1.66730e9	+	1.08216e9i	−0.284154	+	0.184430i
$619$	7.43909e9	+	7.43909e9i	1.26067	+	1.26067i	0.950767	+	0.309907i	$0.100298\pi$
$619$	7.43909e9	+	7.43909e9i	1.26067	+	1.26067i	0.309907	+	0.950767i	$0.399702\pi$
$620$	−2.12222e9	−	5.53696e9i	−0.357619	−	0.933041i
$621$	−3.20933e9	+	3.20933e9i	−0.537767	+	0.537767i
$622$	−2.24626e9	−	4.78052e8i	−0.374277	−	0.0796541i
$623$	−1.34383e9			−0.222658
$624$	6.79787e8	−	6.10837e8i	0.112002	−	0.100642i
$625$	−1.43763e10			−2.35541
$626$	1.06181e10	+	2.25975e9i	1.72995	+	0.368171i
$627$	5.09868e9	−	5.09868e9i	0.826079	−	0.826079i
$628$	−5.04431e9	+	1.93340e9i	−0.812724	+	0.311503i
$629$	−1.45674e9	−	1.45674e9i	−0.233403	−	0.233403i
$630$	−2.61371e9	+	1.69642e9i	−0.416453	+	0.270298i
$631$		−	4.52146e9i		−	0.716433i	−0.933639	−	0.358216i	$-0.883385\pi$
$631$		−	4.52146e9i		−	0.716433i	0.933639	−	0.358216i	$-0.116615\pi$
$632$	−6.09862e8	+	8.38063e8i	−0.0960996	+	0.132059i
$633$		−	1.16293e10i		−	1.82238i
$634$	2.72778e9	+	4.20275e9i	0.425106	+	0.654969i
$635$	5.74889e9	+	5.74889e9i	0.890996	+	0.890996i
$636$	−9.01633e8	−	4.01980e8i	−0.138973	−	0.0619590i
$637$	4.35713e8	−	4.35713e8i	0.0667902	−	0.0667902i
$638$	−1.23230e9	+	5.79031e9i	−0.187864	+	0.882733i
$639$	8.92535e9			1.35323
$640$	−9.48790e9	−	7.71104e9i	−1.43067	−	1.16274i
$641$	2.12980e8			0.0319401			0.0159700	−	0.999872i	$-0.494916\pi$
$641$	2.12980e8			0.0319401			0.0159700	+	0.999872i	$0.494916\pi$
$642$	3.85706e9	−	1.81235e10i	0.575286	−	2.70314i
$643$	1.46716e9	−	1.46716e9i	0.217641	−	0.217641i	−0.589863	−	0.807503i	$-0.700818\pi$
$643$	1.46716e9	−	1.46716e9i	0.217641	−	0.217641i	0.807503	+	0.589863i	$0.200818\pi$
$644$	1.81743e9	+	8.10275e8i	0.268137	+	0.119545i
$645$	−9.22004e9	−	9.22004e9i	−1.35292	−	1.35292i
$646$	−7.15690e8	−	1.10268e9i	−0.104451	−	0.160929i
$647$		−	1.13883e9i		−	0.165308i	−0.996578	−	0.0826540i	$-0.973660\pi$
$647$		−	1.13883e9i		−	0.165308i	0.996578	−	0.0826540i	$-0.0263396\pi$
$648$	2.21697e9	−	3.04653e9i	0.320072	−	0.439838i
$649$		−	1.47186e9i		−	0.211354i
$650$	−1.38669e9	+	9.00025e8i	−0.198053	+	0.128546i
$651$	8.29289e8	+	8.29289e8i	0.117807	+	0.117807i
$652$	2.55196e9	−	9.78122e8i	0.360584	−	0.138206i
$653$	7.14734e9	−	7.14734e9i	1.00450	−	1.00450i	0.00450598	−	0.999990i	$-0.498566\pi$
$653$	7.14734e9	−	7.14734e9i	1.00450	−	1.00450i	0.999990	−	0.00450598i	$-0.00143430\pi$
$654$	−1.01916e10	−	2.16900e9i	−1.42469	−	0.303205i
$655$	−1.72605e10			−2.39998
$656$	7.49445e9	−	6.73430e9i	1.03652	−	0.931384i
$657$	5.37557e9			0.739513
$658$	−4.72089e8	−	1.00470e8i	−0.0646001	−	0.0137483i
$659$	−6.87655e9	+	6.87655e9i	−0.935991	+	0.935991i	−0.998071	−	0.0620805i	$-0.980226\pi$
$659$	−6.87655e9	+	6.87655e9i	−0.935991	+	0.935991i	0.0620805	+	0.998071i	$0.480226\pi$
$660$	7.40101e9	+	1.93095e10i	1.00204	+	2.61437i
$661$	6.51600e9	+	6.51600e9i	0.877558	+	0.877558i	0.993281	−	0.115724i	$-0.0369187\pi$
$661$	6.51600e9	+	6.51600e9i	0.877558	+	0.877558i	−0.115724	+	0.993281i	$0.536919\pi$
$662$	3.87986e9	−	2.51822e9i	0.519773	−	0.337357i
$663$			2.81812e8i			0.0375545i
$664$	1.09451e8	+	6.94462e8i	0.0145088	+	0.0920577i
$665$			2.16102e9i			0.284959i
$666$	7.36214e9	+	1.13430e10i	0.965704	+	1.48788i
$667$	−7.19794e9	−	7.19794e9i	−0.939221	−	0.939221i
$668$	2.30564e9	−	5.17150e9i	0.299277	−	0.671273i
$669$	−7.19882e8	+	7.19882e8i	−0.0929543	+	0.0929543i
$670$	−2.64384e8	+	1.24228e9i	−0.0339604	+	0.159572i
$671$	−4.29649e9			−0.549016
$672$	2.33493e9	+	6.28812e8i	0.296812	+	0.0799334i
$673$	2.89013e9			0.365481			0.182740	−	0.983161i	$-0.441503\pi$
$673$	2.89013e9			0.365481			0.182740	+	0.983161i	$0.441503\pi$
$674$	−2.38515e9	+	1.12073e10i	−0.300058	+	1.40991i
$675$	7.05469e9	−	7.05469e9i	0.882906	−	0.882906i
$676$	3.23886e9	−	7.26470e9i	0.403254	−	0.904491i
$677$	−9.86110e9	−	9.86110e9i	−1.22142	−	1.22142i	−0.967127	−	0.254292i	$-0.918158\pi$
$677$	−9.86110e9	−	9.86110e9i	−1.22142	−	1.22142i	−0.254292	−	0.967127i	$-0.581842\pi$
$678$	−9.22046e9	−	1.42061e10i	−1.13618	−	1.75054i
$679$		−	1.59398e9i		−	0.195407i
$680$	3.72409e9	−	5.86938e8i	0.454191	−	0.0715831i
$681$			1.85348e10i			2.24892i
$682$	3.73893e9	−	2.42675e9i	0.451339	−	0.292940i
$683$	5.80910e9	+	5.80910e9i	0.697649	+	0.697649i	0.963903	−	0.266254i	$-0.0857861\pi$
$683$	5.80910e9	+	5.80910e9i	0.697649	+	0.697649i	−0.266254	+	0.963903i	$0.585786\pi$
$684$	3.08821e9	+	8.05726e9i	0.368987	+	0.962700i
$685$	1.03139e10	−	1.03139e10i	1.22604	−	1.22604i
$686$	3.25643e9	+	6.93037e8i	0.385130	+	0.0819638i
$687$	1.57251e10			1.85031
$688$	−3.09149e8	+	5.78676e9i	−0.0361916	+	0.677448i
$689$	8.40541e7			0.00979020
$690$	−3.47791e10	−	7.40174e9i	−4.03039	−	0.857752i
$691$	−4.82018e7	+	4.82018e7i	−0.00555763	+	0.00555763i	−0.709880	−	0.704323i	$-0.751251\pi$
$691$	−4.82018e7	+	4.82018e7i	−0.00555763	+	0.00555763i	0.704323	+	0.709880i	$0.251251\pi$
$692$	−6.40817e9	+	2.45614e9i	−0.735127	+	0.281762i
$693$	−1.65626e9	−	1.65626e9i	−0.189044	−	0.189044i
$694$	1.21109e10	−	7.86056e9i	1.37537	−	0.892680i
$695$		−	1.77417e10i		−	2.00469i
$696$	−1.00021e10	−	7.27859e9i	−1.12450	−	0.818305i
$697$			3.10689e9i			0.347545i
$698$	2.41916e9	+	3.72724e9i	0.269259	+	0.414852i
$699$	5.56745e9	+	5.56745e9i	0.616575	+	0.616575i
$700$	−3.99504e9	−	1.78113e9i	−0.440228	−	0.196269i
$701$	−7.99473e9	+	7.99473e9i	−0.876578	+	0.876578i	−0.993179	−	0.116601i	$-0.962800\pi$
$701$	−7.99473e9	+	7.99473e9i	−0.876578	+	0.876578i	0.116601	+	0.993179i	$0.462800\pi$
$702$	9.77549e7	−	4.59329e8i	0.0106649	−	0.0501122i
$703$	9.37838e9			1.01809
$704$	4.18486e9	−	8.18250e9i	0.452040	−	0.883856i
$705$	8.62491e9			0.927028
$706$	−1.30496e9	+	6.13174e9i	−0.139567	+	0.655794i
$707$	1.35664e9	−	1.35664e9i	0.144376	−	0.144376i
$708$	2.80901e9	+	1.25235e9i	0.297465	+	0.132621i
$709$	8.19875e9	+	8.19875e9i	0.863944	+	0.863944i	0.991794	−	0.127849i	$-0.0408073\pi$
$709$	8.19875e9	+	8.19875e9i	0.863944	+	0.863944i	−0.127849	+	0.991794i	$0.540807\pi$
$710$	9.66475e9	+	1.48907e10i	1.01341	+	1.56138i
$711$			2.09788e9i			0.218896i
$712$	−8.62943e9	−	6.27967e9i	−0.895987	−	0.652013i
$713$			7.66457e9i			0.791907i
$714$	−6.25454e8	+	4.05950e8i	−0.0643060	+	0.0417377i
$715$	−1.24504e9	−	1.24504e9i	−0.127383	−	0.127383i
$716$	9.60003e9	−	3.67953e9i	0.977411	−	0.374625i
$717$	−1.96524e10	+	1.96524e10i	−1.99113	+	1.99113i
$718$	−1.70904e10	−	3.63719e9i	−1.72312	−	0.366717i
$719$	5.02344e9			0.504023			0.252011	−	0.967724i	$-0.418908\pi$
$719$	5.02344e9			0.504023			0.252011	+	0.967724i	$0.418908\pi$
$720$	−2.47113e10	−	1.32016e9i	−2.46735	−	0.131815i
$721$	4.47802e8			0.0444952
$722$	−4.03824e9	−	8.59424e8i	−0.399312	−	0.0849820i
$723$	−1.68124e10	+	1.68124e10i	−1.65442	+	1.65442i
$724$	−1.41190e9	−	3.68371e9i	−0.138267	−	0.360745i
$725$	1.58224e10	+	1.58224e10i	1.54202	+	1.54202i
$726$	1.91291e8	−	1.24157e8i	0.0185531	−	0.0120419i
$727$			4.15849e9i			0.401389i	0.979654	+	0.200694i	$0.0643198\pi$
$727$			4.15849e9i			0.401389i	−0.979654	+	0.200694i	$0.935680\pi$
$728$	−2.03381e8	+	3.20541e7i	−0.0195367	+	0.00307910i
$729$		−	1.59556e10i		−	1.52534i
$730$	5.82090e9	+	8.96837e9i	0.553809	+	0.853264i
$731$	−1.26356e9	−	1.26356e9i	−0.119642	−	0.119642i
$732$	3.65574e9	−	8.19974e9i	0.344498	−	0.772701i
$733$	−2.56443e9	+	2.56443e9i	−0.240507	+	0.240507i	−0.817060	−	0.576553i	$-0.804397\pi$
$733$	−2.56443e9	+	2.56443e9i	−0.240507	+	0.240507i	0.576553	+	0.817060i	$0.304397\pi$
$734$	3.52174e9	−	1.65479e10i	0.328716	−	1.54457i
$735$	−2.91341e10			−2.70642
$736$	7.88425e9	+	1.36959e10i	0.728934	+	1.26625i
$737$	−9.54747e8			−0.0878521
$738$	4.24510e9	−	1.99468e10i	0.388768	−	1.82674i
$739$	7.39235e9	−	7.39235e9i	0.673793	−	0.673793i	−0.284795	−	0.958588i	$-0.591926\pi$
$739$	7.39235e9	−	7.39235e9i	0.673793	−	0.673793i	0.958588	+	0.284795i	$0.0919255\pi$
$740$	−1.09521e10	+	2.45653e10i	−0.993542	+	2.22849i
$741$	−9.07138e8	−	9.07138e8i	−0.0819049	−	0.0819049i
$742$	1.21080e8	+	1.86550e8i	0.0108807	+	0.0167642i
$743$			1.35467e10i			1.21164i	0.795603	+	0.605818i	$0.207154\pi$
$743$			1.35467e10i			1.21164i	−0.795603	+	0.605818i	$0.792846\pi$
$744$	1.45005e9	+	9.20050e9i	0.129086	+	0.819042i
$745$		−	3.72241e10i		−	3.29820i
$746$	1.67769e9	−	1.08890e9i	0.147953	−	0.0960288i
$747$	1.00620e9	+	1.00620e9i	0.0883204	+	0.0883204i
$748$	1.01427e9	+	2.64626e9i	0.0886130	+	0.231195i
$749$	−2.95176e9	+	2.95176e9i	−0.256681	+	0.256681i
$750$	4.45803e10	+	9.48762e9i	3.85859	+	0.821189i
$751$	−6.20538e9			−0.534599			−0.267300	−	0.963613i	$-0.586131\pi$
$751$	−6.20538e9			−0.534599			−0.267300	+	0.963613i	$0.586131\pi$
$752$	−2.56202e9	−	2.85122e9i	−0.219695	−	0.244494i
$753$	3.00146e10			2.56182
$754$	1.03019e9	+	2.19246e8i	0.0875221	+	0.0186266i
$755$	1.32417e9	−	1.32417e9i	0.111977	−	0.111977i
$756$	1.16025e9	−	4.44705e8i	0.0976622	−	0.0374323i
$757$	−7.86627e9	−	7.86627e9i	−0.659073	−	0.659073i	0.296088	−	0.955161i	$-0.404318\pi$
$757$	−7.86627e9	−	7.86627e9i	−0.659073	−	0.659073i	−0.955161	+	0.296088i	$0.904318\pi$
$758$	7.31955e9	−	4.75074e9i	0.610439	−	0.396204i
$759$		−	2.67293e10i		−	2.21892i
$760$	−1.00983e10	+	1.38770e10i	−0.834453	+	1.14669i
$761$			3.24057e9i			0.266548i	0.991079	+	0.133274i	$0.0425490\pi$
$761$			3.24057e9i			0.266548i	−0.991079	+	0.133274i	$0.957451\pi$
$762$	−6.95252e9	−	1.07119e10i	−0.569246	−	0.877048i
$763$	1.65991e9	+	1.65991e9i	0.135284	+	0.135284i
$764$	−1.81984e10	−	8.11349e9i	−1.47641	−	0.658235i
$765$	5.39578e9	−	5.39578e9i	0.435752	−	0.435752i
$766$	1.73755e9	−	8.16437e9i	0.139681	−	0.656330i
$767$	−2.61868e8			−0.0209555
$768$	1.20553e10	+	1.49489e10i	0.960317	+	1.19082i
$769$	1.47209e10			1.16732			0.583661	−	0.811997i	$-0.301620\pi$
$769$	1.47209e10			1.16732			0.583661	+	0.811997i	$0.301620\pi$
$770$	9.69765e8	−	4.55671e9i	0.0765507	−	0.359695i
$771$	1.61189e9	−	1.61189e9i	0.126662	−	0.126662i
$772$	4.39977e9	+	1.96157e9i	0.344167	+	0.153442i
$773$	8.59506e9	+	8.59506e9i	0.669300	+	0.669300i	0.957554	−	0.288254i	$-0.0930747\pi$
$773$	8.59506e9	+	8.59506e9i	0.669300	+	0.669300i	−0.288254	+	0.957554i	$0.593075\pi$
$774$	6.38580e9	+	9.83872e9i	0.495019	+	0.762685i
$775$		−	1.68481e10i		−	1.30015i
$776$	7.44860e9	−	1.02358e10i	0.572214	−	0.786328i
$777$		−	5.31956e9i		−	0.406820i
$778$	−1.78540e10	+	1.15881e10i	−1.35928	+	0.882235i
$779$	−1.00009e10	−	1.00009e10i	−0.757983	−	0.757983i
$780$	3.43548e9	−	1.31676e9i	0.259212	−	0.0993517i
$781$	−9.43595e9	+	9.43595e9i	−0.708773	+	0.708773i
$782$	−4.76629e9	−	1.01437e9i	−0.356416	−	0.0758529i
$783$	−6.35644e9			−0.473204
$784$	8.65426e9	+	9.63113e9i	0.641392	+	0.713791i
$785$	−2.17477e10			−1.60461
$786$	2.65178e10	+	5.64354e9i	1.94786	+	0.414546i
$787$	−6.15063e9	+	6.15063e9i	−0.449788	+	0.449788i	−0.895284	−	0.445496i	$-0.853027\pi$
$787$	−6.15063e9	+	6.15063e9i	−0.449788	+	0.449788i	0.445496	+	0.895284i	$0.353027\pi$
$788$	1.19136e9	+	3.10830e9i	0.0867362	+	0.226298i
$789$	−1.04467e10	−	1.04467e10i	−0.757196	−	0.757196i
$790$	−3.50001e9	+	2.27167e9i	−0.252566	+	0.163927i
$791$			3.81548e9i			0.274114i
$792$	−2.89606e9	−	1.83753e10i	−0.207143	−	1.31431i
$793$			7.64415e8i			0.0544344i
$794$	−7.03756e9	−	1.08429e10i	−0.498942	−	0.768730i
$795$	−2.81015e9	−	2.81015e9i	−0.198356	−	0.198356i
$796$	−6.52965e9	+	1.46459e10i	−0.458875	+	1.02925i
$797$	−5.77333e9	+	5.77333e9i	−0.403945	+	0.403945i	−0.879621	−	0.475676i	$-0.842204\pi$
$797$	−5.77333e9	+	5.77333e9i	−0.403945	+	0.403945i	0.475676	+	0.879621i	$0.342204\pi$
$798$	7.06575e8	−	3.32004e9i	0.0492208	−	0.231277i
$799$	1.18200e9			0.0819790
$800$	−1.73310e10	−	3.01061e10i	−1.19676	−	2.07893i
$801$	−2.16016e10			−1.48516
$802$	−4.00572e9	+	1.88220e10i	−0.274202	+	1.28841i
$803$	−5.68310e9	+	5.68310e9i	−0.387330	+	0.387330i
$804$	8.12362e8	−	1.82211e9i	0.0551256	−	0.123646i
$805$	5.66445e9	+	5.66445e9i	0.382712	+	0.382712i
$806$	−4.31758e8	−	6.65217e8i	−0.0290447	−	0.0447498i
$807$		−	2.84976e9i		−	0.190876i
$808$	1.50511e10	−	2.37215e9i	1.00376	−	0.158198i
$809$			8.41810e9i			0.558977i	0.960149	+	0.279489i	$0.0901650\pi$
$809$			8.41810e9i			0.558977i	−0.960149	+	0.279489i	$0.909835\pi$
$810$	1.27232e10	−	8.25799e9i	0.841202	−	0.545980i
$811$	1.44170e10	+	1.44170e10i	0.949081	+	0.949081i	0.998765	−	0.0496839i	$-0.0158214\pi$
$811$	1.44170e10	+	1.44170e10i	0.949081	+	0.949081i	−0.0496839	+	0.998765i	$0.515821\pi$
$812$	9.97393e8	+	2.60223e9i	0.0653763	+	0.170569i
$813$	2.63973e9	−	2.63973e9i	0.172283	−	0.172283i
$814$	−1.97752e10	−	4.20858e9i	−1.28510	−	0.273496i
$815$	1.10023e10			0.711923
$816$	−5.91333e9	−	3.15911e8i	−0.380993	−	0.0203540i
$817$	8.13466e9			0.521870
$818$	−5.42202e9	−	1.15392e9i	−0.346358	−	0.0737122i
$819$	−2.94676e8	+	2.94676e8i	−0.0187435	+	0.0187435i
$820$	3.78751e10	−	1.45169e10i	2.39886	−	0.919444i
$821$	−1.26793e10	−	1.26793e10i	−0.799641	−	0.799641i	0.183398	−	0.983039i	$-0.441290\pi$
$821$	−1.26793e10	−	1.26793e10i	−0.799641	−	0.799641i	−0.983039	+	0.183398i	$0.941290\pi$
$822$	−1.92177e10	+	1.24732e10i	−1.20684	+	0.783299i
$823$			1.08290e10i			0.677156i	0.940938	+	0.338578i	$0.109946\pi$
$823$			1.08290e10i			0.677156i	−0.940938	+	0.338578i	$0.890054\pi$
$824$	2.87556e9	+	2.09256e9i	0.179051	+	0.130296i
$825$			5.87558e10i			3.64302i
$826$	−3.77220e8	−	5.81191e8i	−0.0232898	−	0.0358830i
$827$	−3.11527e9	−	3.11527e9i	−0.191526	−	0.191526i	0.604829	−	0.796355i	$-0.293241\pi$
$827$	−3.11527e9	−	3.11527e9i	−0.191526	−	0.191526i	−0.796355	+	0.604829i	$0.793241\pi$
$828$	2.92145e10	+	1.30249e10i	1.78851	+	0.797382i
$829$	1.42216e10	−	1.42216e10i	0.866980	−	0.866980i	−0.125157	−	0.992137i	$-0.539944\pi$
$829$	1.42216e10	−	1.42216e10i	0.866980	−	0.866980i	0.992137	+	0.125157i	$0.0399435\pi$
$830$	−5.89142e8	+	2.76825e9i	−0.0357640	+	0.168047i
$831$	1.07828e10			0.651818
$832$	−1.45580e9	−	7.44555e8i	−0.0876334	−	0.0448193i
$833$	−3.99267e9			−0.239335
$834$	−5.80089e9	+	2.72571e10i	−0.346269	+	1.62704i
$835$	1.61182e10	−	1.61182e10i	0.958108	−	0.958108i
$836$	−1.17831e10	−	5.25332e9i	−0.697488	−	0.310965i
$837$	3.38426e9	+	3.38426e9i	0.199491	+	0.199491i
$838$	−8.21753e9	−	1.26609e10i	−0.482378	−	0.743209i
$839$			2.77633e9i			0.162295i	0.996702	+	0.0811473i	$0.0258584\pi$
$839$			2.77633e9i			0.162295i	−0.996702	+	0.0811473i	$0.974142\pi$
$840$	7.87123e9	+	5.72792e9i	0.458210	+	0.333441i
$841$			2.99354e9i			0.173540i
$842$	−1.00400e10	+	6.51643e9i	−0.579617	+	0.376199i
$843$	−1.54421e9	−	1.54421e9i	−0.0887789	−	0.0887789i
$844$	−1.94286e10	+	7.44667e9i	−1.11236	+	0.426347i
$845$	2.26421e10	−	2.26421e10i	1.29098	−	1.29098i
$846$	−7.58863e9	−	1.61502e9i	−0.430891	−	0.0917027i
$847$	−5.13769e7			−0.00290520
$848$	−9.42248e7	+	1.76373e9i	−0.00530615	+	0.0993224i
$849$	6.43341e9			0.360798
$850$	1.04772e10	+	2.22976e9i	0.585164	+	0.124535i
$851$	2.45826e10	−	2.45826e10i	1.36733	−	1.36733i
$852$	−9.97954e9	−	2.60370e10i	−0.552805	−	1.44229i
$853$	−1.05781e10	−	1.05781e10i	−0.583560	−	0.583560i	0.352319	−	0.935880i	$-0.385393\pi$
$853$	−1.05781e10	−	1.05781e10i	−0.583560	−	0.583560i	−0.935880	+	0.352319i	$0.885393\pi$
$854$	−1.69655e9	+	1.10114e9i	−0.0932102	+	0.0604979i
$855$			3.47375e10i			1.90072i
$856$	−3.27481e10	+	5.16129e9i	−1.78455	+	0.281255i
$857$		−	1.27645e10i		−	0.692744i	−0.938097	−	0.346372i	$-0.887414\pi$
$857$		−	1.27645e10i		−	0.692744i	0.938097	−	0.346372i	$-0.112586\pi$
$858$	1.50570e9	+	2.31987e9i	0.0813831	+	0.125388i
$859$	1.27116e10	+	1.27116e10i	0.684264	+	0.684264i	0.960958	−	0.276694i	$-0.0892388\pi$
$859$	1.27116e10	+	1.27116e10i	0.684264	+	0.684264i	−0.276694	+	0.960958i	$0.589239\pi$
$860$	−9.49967e9	+	2.13076e10i	−0.509289	+	1.14232i
$861$	−5.67268e9	+	5.67268e9i	−0.302884	+	0.302884i
$862$	−3.98481e9	+	1.87237e10i	−0.211900	+	0.995673i
$863$	−2.35352e10			−1.24647			−0.623234	−	0.782036i	$-0.714181\pi$
$863$	−2.35352e10			−1.24647			−0.623234	+	0.782036i	$0.714181\pi$
$864$	9.52865e9	+	2.56613e9i	0.502612	+	0.135357i
$865$	−2.76277e10			−1.45141
$866$	2.27387e8	−	1.06844e9i	0.0118974	−	0.0559033i
$867$	−1.94667e10	+	1.94667e10i	−1.01444	+	1.01444i
$868$	8.54440e8	−	1.91649e9i	0.0443468	−	0.0994690i
$869$	−2.21789e9	−	2.21789e9i	−0.114649	−	0.114649i
$870$	−2.71120e10	−	4.17720e10i	−1.39587	−	2.15064i
$871$			1.69865e8i			0.00871044i
$872$	2.90243e9	+	1.84157e10i	0.148236	+	0.940548i
$873$		−	2.56226e10i		−	1.30339i
$874$	1.86077e10	−	1.20773e10i	0.942762	−	0.611898i
$875$	−7.26076e9	−	7.26076e9i	−0.366399	−	0.366399i
$876$	−6.01049e9	−	1.56816e10i	−0.302097	−	0.788181i
$877$	1.81165e10	−	1.81165e10i	0.906936	−	0.906936i	−0.0890875	−	0.996024i	$-0.528395\pi$
$877$	1.81165e10	−	1.81165e10i	0.906936	−	0.906936i	0.996024	+	0.0890875i	$0.0283951\pi$
$878$	1.27375e10	+	2.71081e9i	0.635116	+	0.135166i
$879$	1.39095e10			0.690798
$880$	2.75206e10	−	2.47293e10i	1.36135	−	1.22327i
$881$	−1.09285e9			−0.0538450			−0.0269225	−	0.999638i	$-0.508571\pi$
$881$	−1.09285e9			−0.0538450			−0.0269225	+	0.999638i	$0.508571\pi$
$882$	2.56337e10	+	5.45539e9i	1.25797	+	0.267723i
$883$	−1.64794e10	+	1.64794e10i	−0.805523	+	0.805523i	−0.983953	−	0.178429i	$-0.942898\pi$
$883$	−1.64794e10	+	1.64794e10i	−0.805523	+	0.805523i	0.178429	+	0.983953i	$0.442898\pi$
$884$	4.70813e8	−	1.80455e8i	0.0229227	−	0.00878589i
$885$	8.75493e9	+	8.75493e9i	0.424572	+	0.424572i
$886$	−5.76615e9	+	3.74251e9i	−0.278527	+	0.180778i
$887$			5.92682e9i			0.285160i	0.989783	+	0.142580i	$0.0455398\pi$
$887$			5.92682e9i			0.285160i	−0.989783	+	0.142580i	$0.954460\pi$
$888$	2.48580e10	−	3.41595e10i	1.19130	−	1.63707i
$889$			2.87699e9i			0.137335i
$890$	−2.33911e10	−	3.60391e10i	−1.11221	−	1.71360i
$891$	8.06250e9	+	8.06250e9i	0.381854	+	0.381854i
$892$	1.66365e9	+	7.41715e8i	0.0784847	+	0.0349913i
$893$	−3.80479e9	+	3.80479e9i	−0.178793	+	0.178793i
$894$	−1.21709e10	+	5.71885e10i	−0.569695	+	2.67687i
$895$	4.13889e10			1.92976
$896$	−4.44609e8	−	4.30354e9i	−0.0206491	−	0.199870i
$897$	−4.75557e9			−0.220003
$898$	8.83382e9	−	4.15082e10i	0.407082	−	1.91279i
$899$	−7.59027e9	+	7.59027e9i	−0.348416	+	0.348416i
$900$	−6.42187e10	−	2.86310e10i	−2.93638	−	1.30914i
$901$	−3.85116e8	−	3.85116e8i	−0.0175410	−	0.0175410i
$902$	1.66000e10	+	2.55759e10i	0.753154	+	1.16040i
$903$		−	4.61410e9i		−	0.208535i
$904$	−1.78295e10	+	2.45011e10i	−0.802694	+	1.10305i
$905$		−	1.58817e10i		−	0.712240i
$906$	−2.46731e9	+	1.60140e9i	−0.110224	+	0.0715405i
$907$	6.25118e9	+	6.25118e9i	0.278187	+	0.278187i	0.832385	−	0.554198i	$-0.186975\pi$
$907$	6.25118e9	+	6.25118e9i	0.278187	+	0.278187i	−0.554198	+	0.832385i	$0.686975\pi$
$908$	3.09655e10	−	1.18686e10i	1.37271	−	0.526135i
$909$	2.18074e10	−	2.18074e10i	0.963009	−	0.963009i
$910$	−8.10713e8	−	1.72537e8i	−0.0356634	−	0.00758992i
$911$	1.53944e10			0.674604			0.337302	−	0.941396i	$-0.390486\pi$
$911$	1.53944e10			0.674604			0.337302	+	0.941396i	$0.390486\pi$
$912$	2.00517e10	−	1.80178e10i	0.875323	−	0.786540i
$913$	−2.12752e9			−0.0925179
$914$	−1.47181e9	−	3.13232e8i	−0.0637587	−	0.0135692i
$915$	2.55564e10	−	2.55564e10i	1.10288	−	1.10288i
$916$	−1.00694e10	−	2.62714e10i	−0.432881	−	1.12940i
$917$	−4.31893e9	−	4.31893e9i	−0.184962	−	0.184962i
$918$	−2.55243e9	+	1.65665e9i	−0.108894	+	0.0706774i
$919$			3.63682e10i			1.54567i	0.634606	+	0.772836i	$0.281162\pi$
$919$			3.63682e10i			1.54567i	−0.634606	+	0.772836i	$0.718838\pi$
$920$	9.90458e9	+	6.28440e10i	0.419352	+	2.66076i
$921$		−	3.06224e10i		−	1.29161i
$922$	4.75454e9	+	7.32541e9i	0.199779	+	0.307804i
$923$	1.67881e9	+	1.67881e9i	0.0702741	+	0.0702741i
$924$	−2.97976e9	+	6.68354e9i	−0.124259	+	0.278711i
$925$	−5.40369e10	+	5.40369e10i	−2.24489	+	2.24489i
$926$	7.87986e9	−	3.70257e10i	0.326122	−	1.53237i
$927$	7.19824e9			0.296789
$928$	−5.75536e9	+	2.13710e10i	−0.236404	+	0.877823i
$929$	−1.62239e10			−0.663896			−0.331948	−	0.943298i	$-0.607706\pi$
$929$	−1.62239e10			−0.663896			−0.331948	+	0.943298i	$0.607706\pi$
$930$	−7.80517e9	+	3.66748e10i	−0.318194	+	1.49512i
$931$	1.28522e10	−	1.28522e10i	0.521980	−	0.521980i
$932$	5.73630e9	−	1.28664e10i	0.232101	−	0.520597i
$933$	1.02687e10	+	1.02687e10i	0.413932	+	0.413932i
$934$	2.21851e10	+	3.41809e10i	0.890936	+	1.37268i
$935$			1.14089e10i			0.456461i
$936$	−3.26927e9	+	5.15256e8i	−0.130312	+	0.0205380i
$937$			4.30630e10i			1.71008i	0.518565	+	0.855038i	$0.326467\pi$
$937$			4.30630e10i			1.71008i	−0.518565	+	0.855038i	$0.673533\pi$
$938$	−3.76999e8	+	2.44691e8i	−0.0149153	+	0.00968071i
$939$	−4.85400e10	−	4.85400e10i	−1.91324	−	1.91324i
$940$	−5.52286e9	−	1.44094e10i	−0.216879	−	0.565844i
$941$	−9.56307e9	+	9.56307e9i	−0.374140	+	0.374140i	−0.868983	−	0.494843i	$-0.835226\pi$
$941$	−9.56307e9	+	9.56307e9i	−0.374140	+	0.374140i	0.494843	+	0.868983i	$0.335226\pi$
$942$	3.34116e10	+	7.11071e9i	1.30233	+	0.277163i
$943$	−5.24288e10			−2.03601
$944$	2.93554e8	−	5.49484e9i	0.0113576	−	0.212595i
$945$	5.00223e9			0.192820
$946$	−1.71527e10	−	3.65046e9i	−0.658739	−	0.140194i
$947$	7.32127e8	−	7.32127e8i	0.0280131	−	0.0280131i	−0.692961	−	0.720975i	$-0.743694\pi$
$947$	7.32127e8	−	7.32127e8i	0.0280131	−	0.0280131i	0.720975	+	0.692961i	$0.243694\pi$
$948$	6.11993e9	−	2.34566e9i	0.233301	−	0.0894204i
$949$	1.01112e9	+	1.01112e9i	0.0384033	+	0.0384033i
$950$	−4.09030e10	+	2.65480e10i	−1.54783	+	1.00461i
$951$		−	3.16826e10i		−	1.19451i
$952$	1.07871e9	+	7.84981e8i	0.0405205	+	0.0294869i
$953$			1.38654e7i			0.000518927i	1.00000		0.000259464i	$8.25898e-5\pi$
$953$			1.38654e7i			0.000518927i	−1.00000		0.000259464i	$0.999917\pi$
$954$	1.94631e9	+	2.99872e9i	0.0725760	+	0.111819i
$955$	−5.67196e10	−	5.67196e10i	−2.10728	−	2.10728i
$956$	4.54169e10	+	2.02485e10i	1.68118	+	0.749531i
$957$	2.64702e10	−	2.64702e10i	0.976259	−	0.976259i
$958$	5.12997e9	−	2.41046e10i	0.188511	−	0.885770i
$959$	5.16149e9			0.188977
$960$	2.37788e10	+	7.35637e10i	0.867442	+	2.68358i
$961$	−1.94303e10			−0.706232
$962$	−7.48775e8	+	3.51833e9i	−0.0271168	+	0.127416i
$963$	−4.74483e10	+	4.74483e10i	−1.71210	+	1.71210i
$964$	3.88536e10	+	1.73223e10i	1.39689	+	0.622783i
$965$	1.37129e10	+	1.37129e10i	0.491229	+	0.491229i
$966$	−6.85040e9	−	1.05545e10i	−0.244510	−	0.376721i
$967$		−	4.68187e10i		−	1.66505i	−0.553989	−	0.832524i	$-0.686895\pi$
$967$		−	4.68187e10i		−	1.66505i	0.553989	−	0.832524i	$-0.313105\pi$
$968$	−3.29916e8	−	2.40081e8i	−0.0116907	−	0.00850736i
$969$			8.31259e9i			0.293497i
$970$	4.27477e10	−	2.77453e10i	1.50387	−	0.976085i
$971$	4.50787e9	+	4.50787e9i	0.158017	+	0.158017i	0.781687	−	0.623670i	$-0.214359\pi$
$971$	4.50787e9	+	4.50787e9i	0.158017	+	0.158017i	−0.623670	+	0.781687i	$0.714359\pi$
$972$	−3.61629e10	+	1.38606e10i	−1.26308	+	0.484117i
$973$	4.43935e9	−	4.43935e9i	0.154498	−	0.154498i
$974$	−2.80407e10	−	5.96767e9i	−0.972374	−	0.206942i
$975$	1.04536e10			0.361202
$976$	−1.60400e10	−	8.56910e8i	−0.552241	−	0.0295026i
$977$	2.95679e10			1.01435			0.507176	−	0.861842i	$-0.330689\pi$
$977$	2.95679e10			1.01435			0.507176	+	0.861842i	$0.330689\pi$
$978$	−1.69032e10	−	3.59736e9i	−0.577808	−	0.122970i
$979$	2.28374e10	−	2.28374e10i	0.777869	−	0.777869i
$980$	1.86557e10	+	4.86734e10i	0.633169	+	1.65196i
$981$	2.66823e10	+	2.66823e10i	0.902364	+	0.902364i
$982$	3.12326e10	−	2.02714e10i	1.05249	−	0.683115i
$983$			3.22911e10i			1.08429i	0.840285	+	0.542146i	$0.182388\pi$
$983$			3.22911e10i			1.08429i	−0.840285	+	0.542146i	$0.817612\pi$
$984$	−6.29352e10	+	9.91896e9i	−2.10577	+	0.331882i
$985$			1.34009e10i			0.446794i
$986$	−3.71556e9	−	5.72463e9i	−0.123440	−	0.190186i
$987$	2.15813e9	+	2.15813e9i	0.0714445	+	0.0714445i
$988$	−9.34651e8	+	2.09640e9i	−0.0308319	+	0.0691553i
$989$	2.13225e10	−	2.13225e10i	0.700893	−	0.700893i
$990$	1.55886e10	−	7.32473e10i	0.510603	−	2.39921i
$991$	2.68078e10			0.874989			0.437495	−	0.899221i	$-0.355866\pi$
$991$	2.68078e10			0.874989			0.437495	+	0.899221i	$0.355866\pi$
$992$	1.44424e10	−	8.31399e9i	0.469732	−	0.270407i
$993$	−2.92486e10			−0.947943
$994$	−1.30763e9	+	6.14428e9i	−0.0422313	+	0.198435i
$995$	−4.56473e10	+	4.56473e10i	−1.46904	+	1.46904i
$996$	1.81023e9	−	4.06032e9i	0.0580533	−	0.130212i
$997$	1.12341e10	+	1.12341e10i	0.359010	+	0.359010i	0.863448	−	0.504438i	$-0.168300\pi$
$997$	1.12341e10	+	1.12341e10i	0.359010	+	0.359010i	−0.504438	+	0.863448i	$0.668300\pi$
$998$	−1.19963e10	−	1.84829e10i	−0.382024	−	0.588592i
$999$		−	2.17087e10i		−	0.688897i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.8.e.a.5.7	✓	26
4.3	odd	2		64.8.e.a.49.2		26
8.3	odd	2		128.8.e.a.97.12		26
8.5	even	2		128.8.e.b.97.2		26
16.3	odd	4		64.8.e.a.17.2		26
16.5	even	4		128.8.e.b.33.2		26
16.11	odd	4		128.8.e.a.33.12		26
16.13	even	4	inner	16.8.e.a.13.7	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.8.e.a.5.7	✓	26	1.1	even	1	trivial
16.8.e.a.13.7	yes	26	16.13	even	4	inner
64.8.e.a.17.2		26	16.3	odd	4
64.8.e.a.49.2		26	4.3	odd	2
128.8.e.a.33.12		26	16.11	odd	4
128.8.e.a.97.12		26	8.3	odd	2
128.8.e.b.33.2		26	16.5	even	4
128.8.e.b.97.2		26	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	16.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.35505 + 11.0659i) q^{2} +(50.5872 - 50.5872i) q^{3} +(-116.907 - 52.1215i) q^{4} +(-364.370 - 364.370i) q^{5} +(440.657 + 678.928i) q^{6} -182.346i q^{7} +(852.094 - 1170.93i) q^{8} -2931.14i q^{9} +O(q^{10})\)	\(q+(-2.35505 + 11.0659i) q^{2} +(50.5872 - 50.5872i) q^{3} +(-116.907 - 52.1215i) q^{4} +(-364.370 - 364.370i) q^{5} +(440.657 + 678.928i) q^{6} -182.346i q^{7} +(852.094 - 1170.93i) q^{8} -2931.14i q^{9} +(4890.18 - 3173.96i) q^{10} +(3098.82 + 3098.82i) q^{11} +(-8550.71 + 3277.34i) q^{12} +(551.331 - 551.331i) q^{13} +(2017.82 + 429.435i) q^{14} -36864.9 q^{15} +(10950.7 + 12186.8i) q^{16} -5052.14 q^{17} +(32435.6 + 6902.99i) q^{18} +(16262.6 - 16262.6i) q^{19} +(23606.0 + 61589.0i) q^{20} +(-9224.39 - 9224.39i) q^{21} +(-41589.1 + 26993.3i) q^{22} -85254.9i q^{23} +(-16129.3 - 102339. i) q^{24} +187406. i q^{25} +(4802.55 + 7399.38i) q^{26} +(-37644.0 - 37644.0i) q^{27} +(-9504.15 + 21317.6i) q^{28} +(84428.5 - 84428.5i) q^{29} +(86818.9 - 407943. i) q^{30} -89901.8 q^{31} +(-160647. + 92478.6i) q^{32} +313522. q^{33} +(11898.1 - 55906.4i) q^{34} +(-66441.4 + 66441.4i) q^{35} +(-152775. + 342672. i) q^{36} +(288342. + 288342. i) q^{37} +(141661. + 218259. i) q^{38} -55780.6i q^{39} +(-737130. + 116176. i) q^{40} -614965. i q^{41} +(123800. - 80352.0i) q^{42} +(250103. + 250103. i) q^{43} +(-200760. - 523791. i) q^{44} +(-1.06802e6 + 1.06802e6i) q^{45} +(943421. + 200780. i) q^{46} -233960. q^{47} +(1.17046e6 + 62530.2i) q^{48} +790293. q^{49} +(-2.07381e6 - 441350. i) q^{50} +(-255574. + 255574. i) q^{51} +(-93190.9 + 35718.5i) q^{52} +(76228.4 + 76228.4i) q^{53} +(505217. - 327910. i) q^{54} -2.25824e6i q^{55} +(-213515. - 155376. i) q^{56} -1.64536e6i q^{57} +(735442. + 1.13311e6i) q^{58} +(-237487. - 237487. i) q^{59} +(4.30978e6 + 1.92146e6i) q^{60} +(-693245. + 693245. i) q^{61} +(211724. - 994842. i) q^{62} -534482. q^{63} +(-645025. - 1.99549e6i) q^{64} -401777. q^{65} +(-738361. + 3.46940e6i) q^{66} +(-154050. + 154050. i) q^{67} +(590633. + 263325. i) q^{68} +(-4.31281e6 - 4.31281e6i) q^{69} +(-578759. - 891706. i) q^{70} +3.04501e6i q^{71} +(-3.43217e6 - 2.49761e6i) q^{72} +1.83395e6i q^{73} +(-3.86982e6 + 2.51170e6i) q^{74} +(9.48033e6 + 9.48033e6i) q^{75} +(-2.74885e6 + 1.05359e6i) q^{76} +(565058. - 565058. i) q^{77} +(617262. + 131366. i) q^{78} -715721. q^{79} +(450392. - 8.43060e6i) q^{80} +2.60179e6 q^{81} +(6.80513e6 + 1.44828e6i) q^{82} +(-343278. + 343278. i) q^{83} +(597610. + 1.55919e6i) q^{84} +(1.84085e6 + 1.84085e6i) q^{85} +(-3.35662e6 + 2.17861e6i) q^{86} -8.54201e6i q^{87} +(6.26901e6 - 988032. i) q^{88} -7.36969e6i q^{89} +(-9.30332e6 - 1.43338e7i) q^{90} +(-100533. - 100533. i) q^{91} +(-4.44361e6 + 9.96693e6i) q^{92} +(-4.54788e6 + 4.54788e6i) q^{93} +(550988. - 2.58897e6i) q^{94} -1.18512e7 q^{95} +(-3.44845e6 + 1.28049e7i) q^{96} +8.74152e6 q^{97} +(-1.86118e6 + 8.74529e6i) q^{98} +(9.08308e6 - 9.08308e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 2 q^{2} - 2 q^{3} - 184 q^{4} - 2 q^{5} - 176 q^{6} - 1004 q^{8}+O(q^{10}) \) 26 * q - 2 * q^2 - 2 * q^3 - 184 * q^4 - 2 * q^5 - 176 * q^6 - 1004 * q^8	\( 26 q - 2 q^{2} - 2 q^{3} - 184 q^{4} - 2 q^{5} - 176 q^{6} - 1004 q^{8} + 12972 q^{10} + 1202 q^{11} - 27356 q^{12} - 2 q^{13} + 22268 q^{14} - 27004 q^{15} + 13336 q^{16} - 4 q^{17} - 29346 q^{18} + 60582 q^{19} + 46204 q^{20} + 4372 q^{21} - 44348 q^{22} - 59216 q^{24} - 35960 q^{26} - 233672 q^{27} + 220312 q^{28} - 51690 q^{29} + 27636 q^{30} + 357488 q^{31} - 248632 q^{32} - 4 q^{33} + 924660 q^{34} - 252004 q^{35} - 1015508 q^{36} + 415574 q^{37} - 5472 q^{38} - 1121976 q^{40} + 124600 q^{42} + 569754 q^{43} - 758620 q^{44} + 151874 q^{45} + 2335660 q^{46} - 2076464 q^{47} + 4141288 q^{48} - 1647090 q^{49} - 787194 q^{50} + 2609508 q^{51} + 410324 q^{52} + 907814 q^{53} - 7404512 q^{54} - 4093160 q^{56} - 1860712 q^{58} - 4865142 q^{59} + 5147328 q^{60} + 2279886 q^{61} + 6274096 q^{62} + 8295108 q^{63} + 10452224 q^{64} - 1426892 q^{65} + 10937812 q^{66} - 5564458 q^{67} - 7403760 q^{68} - 4786076 q^{69} - 22140800 q^{70} - 25293948 q^{72} - 13177044 q^{74} + 6212566 q^{75} + 17814260 q^{76} + 7604308 q^{77} + 37993916 q^{78} - 9598912 q^{79} + 40047272 q^{80} - 5314414 q^{81} + 22858240 q^{82} + 4531198 q^{83} - 30159704 q^{84} + 7377748 q^{85} - 54129468 q^{86} - 59216392 q^{88} - 33515304 q^{90} + 2587652 q^{91} + 21810936 q^{92} - 14504144 q^{93} + 77196112 q^{94} - 4900620 q^{95} + 116940464 q^{96} - 4 q^{97} + 21823866 q^{98} + 18815006 q^{99}+O(q^{100}) \) 26 * q - 2 * q^2 - 2 * q^3 - 184 * q^4 - 2 * q^5 - 176 * q^6 - 1004 * q^8 + 12972 * q^10 + 1202 * q^11 - 27356 * q^12 - 2 * q^13 + 22268 * q^14 - 27004 * q^15 + 13336 * q^16 - 4 * q^17 - 29346 * q^18 + 60582 * q^19 + 46204 * q^20 + 4372 * q^21 - 44348 * q^22 - 59216 * q^24 - 35960 * q^26 - 233672 * q^27 + 220312 * q^28 - 51690 * q^29 + 27636 * q^30 + 357488 * q^31 - 248632 * q^32 - 4 * q^33 + 924660 * q^34 - 252004 * q^35 - 1015508 * q^36 + 415574 * q^37 - 5472 * q^38 - 1121976 * q^40 + 124600 * q^42 + 569754 * q^43 - 758620 * q^44 + 151874 * q^45 + 2335660 * q^46 - 2076464 * q^47 + 4141288 * q^48 - 1647090 * q^49 - 787194 * q^50 + 2609508 * q^51 + 410324 * q^52 + 907814 * q^53 - 7404512 * q^54 - 4093160 * q^56 - 1860712 * q^58 - 4865142 * q^59 + 5147328 * q^60 + 2279886 * q^61 + 6274096 * q^62 + 8295108 * q^63 + 10452224 * q^64 - 1426892 * q^65 + 10937812 * q^66 - 5564458 * q^67 - 7403760 * q^68 - 4786076 * q^69 - 22140800 * q^70 - 25293948 * q^72 - 13177044 * q^74 + 6212566 * q^75 + 17814260 * q^76 + 7604308 * q^77 + 37993916 * q^78 - 9598912 * q^79 + 40047272 * q^80 - 5314414 * q^81 + 22858240 * q^82 + 4531198 * q^83 - 30159704 * q^84 + 7377748 * q^85 - 54129468 * q^86 - 59216392 * q^88 - 33515304 * q^90 + 2587652 * q^91 + 21810936 * q^92 - 14504144 * q^93 + 77196112 * q^94 - 4900620 * q^95 + 116940464 * q^96 - 4 * q^97 + 21823866 * q^98 + 18815006 * q^99

Introduction

L-functions

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