LMFDB - Embedded newform 20.7.b.a.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,7,Mod(11,20)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(20, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("20.11");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	20.b (of order $2$, degree $1$, 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:	$4.60108167240$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 18 x^{10} - 30 x^{9} + 174 x^{8} + 1853 x^{7} + 10388 x^{6} - 17262 x^{5} + \cdots + 7603655 $ x^12 - x^11 - 18x^10 - 30x^9 + 174x^8 + 1853x^7 + 10388x^6 - 17262x^5 - 88626x^4 - 240665x^3 - 173034x^2 + 3703420x + 7603655
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{33}\cdot 5^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.5
Root			$-0.552397 + 3.35995i$ of defining polynomial
Character	$\chi$	$=$	20.11
Dual form			20.7.b.a.11.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.34086 - 6.71989i) q^{2} +5.31460i q^{3} +(-26.3138 + 58.3402i) q^{4} -55.9017 q^{5} +(35.7136 - 23.0700i) q^{6} +502.023i q^{7} +(506.265 - 76.4207i) q^{8} +700.755 q^{9} +O(q^{10})$	\(q+(-4.34086 - 6.71989i) q^{2} +5.31460i q^{3} +(-26.3138 + 58.3402i) q^{4} -55.9017 q^{5} +(35.7136 - 23.0700i) q^{6} +502.023i q^{7} +(506.265 - 76.4207i) q^{8} +700.755 q^{9} +(242.662 + 375.653i) q^{10} +1429.16i q^{11} +(-310.055 - 139.848i) q^{12} -3407.04 q^{13} +(3373.54 - 2179.21i) q^{14} -297.095i q^{15} +(-2711.16 - 3070.31i) q^{16} -2248.72 q^{17} +(-3041.88 - 4709.00i) q^{18} +5860.18i q^{19} +(1470.99 - 3261.32i) q^{20} -2668.06 q^{21} +(9603.77 - 6203.77i) q^{22} -5940.46i q^{23} +(406.146 + 2690.60i) q^{24} +3125.00 q^{25} +(14789.5 + 22894.9i) q^{26} +7598.58i q^{27} +(-29288.2 - 13210.2i) q^{28} +14695.2 q^{29} +(-1996.45 + 1289.65i) q^{30} +5777.03i q^{31} +(-8863.37 + 31546.5i) q^{32} -7595.40 q^{33} +(9761.40 + 15111.2i) q^{34} -28064.0i q^{35} +(-18439.6 + 40882.2i) q^{36} -1199.24 q^{37} +(39379.8 - 25438.2i) q^{38} -18107.1i q^{39} +(-28301.1 + 4272.05i) q^{40} +123534. q^{41} +(11581.7 + 17929.0i) q^{42} -144934. i q^{43} +(-83377.3 - 37606.6i) q^{44} -39173.4 q^{45} +(-39919.2 + 25786.7i) q^{46} +110535. i q^{47} +(16317.5 - 14408.8i) q^{48} -134378. q^{49} +(-13565.2 - 20999.7i) q^{50} -11951.1i q^{51} +(89652.3 - 198767. i) q^{52} -31900.5 q^{53} +(51061.6 - 32984.4i) q^{54} -79892.3i q^{55} +(38365.0 + 254157. i) q^{56} -31144.5 q^{57} +(-63789.8 - 98750.1i) q^{58} +263692. i q^{59} +(17332.6 + 7817.72i) q^{60} -26885.8 q^{61} +(38821.0 - 25077.3i) q^{62} +351795. i q^{63} +(250464. - 77378.2i) q^{64} +190459. q^{65} +(32970.6 + 51040.2i) q^{66} +388481. i q^{67} +(59172.6 - 131191. i) q^{68} +31571.2 q^{69} +(-188587. + 121822. i) q^{70} -545782. i q^{71} +(354767. - 53552.2i) q^{72} -88774.1 q^{73} +(5205.74 + 8058.76i) q^{74} +16608.1i q^{75} +(-341884. - 154204. i) q^{76} -717470. q^{77} +(-121677. + 78600.2i) q^{78} -260741. i q^{79} +(151559. + 171636. i) q^{80} +470467. q^{81} +(-536245. - 830136. i) q^{82} -220472. i q^{83} +(70206.8 - 155655. i) q^{84} +125708. q^{85} +(-973943. + 629140. i) q^{86} +78099.2i q^{87} +(109217. + 723531. i) q^{88} +371922. q^{89} +(170046. + 263241. i) q^{90} -1.71041e6i q^{91} +(346568. + 156316. i) q^{92} -30702.6 q^{93} +(742784. - 479818. i) q^{94} -327594. i q^{95} +(-167657. - 47105.3i) q^{96} +676250. q^{97} +(583318. + 903008. i) q^{98} +1.00149e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 10 q^{2} + 156 q^{4} - 672 q^{6} + 440 q^{8} - 1996 q^{9}+O(q^{10}) $ 12 * q - 10 * q^2 + 156 * q^4 - 672 * q^6 + 440 * q^8 - 1996 * q^9	\( 12 q - 10 q^{2} + 156 q^{4} - 672 q^{6} + 440 q^{8} - 1996 q^{9} + 750 q^{10} - 440 q^{12} - 5040 q^{13} + 6248 q^{14} + 3312 q^{16} + 6840 q^{17} + 15790 q^{18} - 3500 q^{20} - 27464 q^{21} - 26160 q^{22} + 28528 q^{24} + 37500 q^{25} - 18684 q^{26} + 19320 q^{28} - 74968 q^{29} - 13000 q^{30} - 60800 q^{32} + 112880 q^{33} + 48204 q^{34} - 128580 q^{36} + 62640 q^{37} + 74800 q^{38} + 57000 q^{40} - 16976 q^{41} - 138360 q^{42} - 222160 q^{44} + 77000 q^{45} - 144792 q^{46} + 297600 q^{48} + 72564 q^{49} - 31250 q^{50} + 548280 q^{52} + 322160 q^{53} + 150416 q^{54} - 246512 q^{56} - 1213440 q^{57} + 350700 q^{58} + 157000 q^{60} + 46464 q^{61} - 7120 q^{62} - 542784 q^{64} - 133000 q^{65} - 65200 q^{66} - 1678280 q^{68} + 41256 q^{69} - 360000 q^{70} + 2317560 q^{72} - 415080 q^{73} + 1581924 q^{74} + 208320 q^{76} + 75600 q^{77} + 473200 q^{78} + 734000 q^{80} + 2287428 q^{81} - 3169500 q^{82} - 2256224 q^{84} + 372000 q^{85} - 62512 q^{86} - 278880 q^{88} + 278392 q^{89} - 2162250 q^{90} + 4095720 q^{92} - 3646000 q^{93} + 4706568 q^{94} - 2641152 q^{96} + 2344680 q^{97} + 1050270 q^{98}+O(q^{100}) \) 12 * q - 10 * q^2 + 156 * q^4 - 672 * q^6 + 440 * q^8 - 1996 * q^9 + 750 * q^10 - 440 * q^12 - 5040 * q^13 + 6248 * q^14 + 3312 * q^16 + 6840 * q^17 + 15790 * q^18 - 3500 * q^20 - 27464 * q^21 - 26160 * q^22 + 28528 * q^24 + 37500 * q^25 - 18684 * q^26 + 19320 * q^28 - 74968 * q^29 - 13000 * q^30 - 60800 * q^32 + 112880 * q^33 + 48204 * q^34 - 128580 * q^36 + 62640 * q^37 + 74800 * q^38 + 57000 * q^40 - 16976 * q^41 - 138360 * q^42 - 222160 * q^44 + 77000 * q^45 - 144792 * q^46 + 297600 * q^48 + 72564 * q^49 - 31250 * q^50 + 548280 * q^52 + 322160 * q^53 + 150416 * q^54 - 246512 * q^56 - 1213440 * q^57 + 350700 * q^58 + 157000 * q^60 + 46464 * q^61 - 7120 * q^62 - 542784 * q^64 - 133000 * q^65 - 65200 * q^66 - 1678280 * q^68 + 41256 * q^69 - 360000 * q^70 + 2317560 * q^72 - 415080 * q^73 + 1581924 * q^74 + 208320 * q^76 + 75600 * q^77 + 473200 * q^78 + 734000 * q^80 + 2287428 * q^81 - 3169500 * q^82 - 2256224 * q^84 + 372000 * q^85 - 62512 * q^86 - 278880 * q^88 + 278392 * q^89 - 2162250 * q^90 + 4095720 * q^92 - 3646000 * q^93 + 4706568 * q^94 - 2641152 * q^96 + 2344680 * q^97 + 1050270 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$-1$	$1$

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 $

$2$	−4.34086	−	6.71989i	−0.542608	−	0.839986i
$2$	−4.34086	−	6.71989i	−0.542608	−	0.839986i
$3$			5.31460i			0.196837i	0.995145	+	0.0984186i	$0.0313784\pi$
$3$			5.31460i			0.196837i	−0.995145	+	0.0984186i	$0.968622\pi$
$4$	−26.3138	+	58.3402i	−0.411154	+	0.911566i
$5$	−55.9017			−0.447214
$5$	−55.9017			−0.447214
$6$	35.7136	−	23.0700i	0.165341	−	0.106805i
$7$			502.023i			1.46362i	0.681506	+	0.731812i	$0.261325\pi$
$7$			502.023i			1.46362i	−0.681506	+	0.731812i	$0.738675\pi$
$8$	506.265	−	76.4207i	0.988798	−	0.149259i
$9$	700.755			0.961255
$10$	242.662	+	375.653i	0.242662	+	0.375653i
$11$			1429.16i			1.07375i	0.843663	+	0.536873i	$0.180395\pi$
$11$			1429.16i			1.07375i	−0.843663	+	0.536873i	$0.819605\pi$
$12$	−310.055	−	139.848i	−0.179430	−	0.0809304i
$13$	−3407.04			−1.55077			−0.775384	−	0.631490i	$-0.782444\pi$
$13$	−3407.04			−1.55077			−0.775384	+	0.631490i	$0.782444\pi$
$14$	3373.54	−	2179.21i	1.22942	−	0.794174i
$15$		−	297.095i		−	0.0880283i
$16$	−2711.16	−	3070.31i	−0.661905	−	0.749588i
$17$	−2248.72			−0.457709			−0.228855	−	0.973461i	$-0.573498\pi$
$17$	−2248.72			−0.457709			−0.228855	+	0.973461i	$0.573498\pi$
$18$	−3041.88	−	4709.00i	−0.521584	−	0.807441i
$19$			5860.18i			0.854378i	0.904162	+	0.427189i	$0.140496\pi$
$19$			5860.18i			0.854378i	−0.904162	+	0.427189i	$0.859504\pi$
$20$	1470.99	−	3261.32i	0.183874	−	0.407665i
$21$	−2668.06			−0.288096
$22$	9603.77	−	6203.77i	0.901932	−	0.582623i
$23$		−	5940.46i		−	0.488244i	−0.969745	−	0.244122i	$-0.921500\pi$
$23$		−	5940.46i		−	0.488244i	0.969745	−	0.244122i	$-0.0784997\pi$
$24$	406.146	+	2690.60i	0.0293798	+	0.194632i
$25$	3125.00			0.200000
$26$	14789.5	+	22894.9i	0.841459	+	1.30262i
$27$			7598.58i			0.386048i
$28$	−29288.2	−	13210.2i	−1.33419	−	0.601775i
$29$	14695.2			0.602534			0.301267	−	0.953540i	$-0.402590\pi$
$29$	14695.2			0.602534			0.301267	+	0.953540i	$0.402590\pi$
$30$	−1996.45	+	1289.65i	−0.0739425	+	0.0477648i
$31$			5777.03i			0.193919i	0.995288	+	0.0969593i	$0.0309117\pi$
$31$			5777.03i			0.193919i	−0.995288	+	0.0969593i	$0.969088\pi$
$32$	−8863.37	+	31546.5i	−0.270489	+	0.962723i
$33$	−7595.40			−0.211353
$34$	9761.40	+	15111.2i	0.248356	+	0.384469i
$35$		−	28064.0i		−	0.654553i
$36$	−18439.6	+	40882.2i	−0.395224	+	0.876247i
$37$	−1199.24			−0.0236756			−0.0118378	−	0.999930i	$-0.503768\pi$
$37$	−1199.24			−0.0236756			−0.0118378	+	0.999930i	$0.503768\pi$
$38$	39379.8	−	25438.2i	0.717666	−	0.463592i
$39$		−	18107.1i		−	0.305249i
$40$	−28301.1	+	4272.05i	−0.442204	+	0.0667507i
$41$	123534.			1.79240			0.896201	−	0.443648i	$-0.146316\pi$
$41$	123534.			1.79240			0.896201	+	0.443648i	$0.146316\pi$
$42$	11581.7	+	17929.0i	0.156323	+	0.241997i
$43$		−	144934.i		−	1.82291i	−0.411396	−	0.911457i	$-0.634958\pi$
$43$		−	144934.i		−	1.82291i	0.411396	−	0.911457i	$-0.365042\pi$
$44$	−83377.3	−	37606.6i	−0.978790	−	0.441475i
$45$	−39173.4			−0.429886
$46$	−39919.2	+	25786.7i	−0.410118	+	0.264925i
$47$			110535.i			1.06465i	0.846540	+	0.532325i	$0.178682\pi$
$47$			110535.i			1.06465i	−0.846540	+	0.532325i	$0.821318\pi$
$48$	16317.5	−	14408.8i	0.147547	−	0.130288i
$49$	−134378.			−1.14220
$50$	−13565.2	−	20999.7i	−0.108522	−	0.167997i
$51$		−	11951.1i		−	0.0900942i
$52$	89652.3	−	198767.i	0.637604	−	1.41363i
$53$	−31900.5			−0.214274			−0.107137	−	0.994244i	$-0.534168\pi$
$53$	−31900.5			−0.214274			−0.107137	+	0.994244i	$0.534168\pi$
$54$	51061.6	−	32984.4i	0.324275	−	0.209473i
$55$		−	79892.3i		−	0.480194i
$56$	38365.0	+	254157.i	0.218459	+	1.44723i
$57$	−31144.5			−0.168173
$58$	−63789.8	−	98750.1i	−0.326939	−	0.506120i
$59$			263692.i			1.28393i	0.766735	+	0.641963i	$0.221880\pi$
$59$			263692.i			1.28393i	−0.766735	+	0.641963i	$0.778120\pi$
$60$	17332.6	+	7817.72i	0.0802436	+	0.0361932i
$61$	−26885.8			−0.118450			−0.0592249	−	0.998245i	$-0.518863\pi$
$61$	−26885.8			−0.118450			−0.0592249	+	0.998245i	$0.518863\pi$
$62$	38821.0	−	25077.3i	0.162889	−	0.105222i
$63$			351795.i			1.40692i
$64$	250464.	−	77378.2i	0.955443	−	0.295174i
$65$	190459.			0.693525
$66$	32970.6	+	51040.2i	0.114682	+	0.177534i
$67$			388481.i			1.29165i	0.763484	+	0.645827i	$0.223487\pi$
$67$			388481.i			1.29165i	−0.763484	+	0.645827i	$0.776513\pi$
$68$	59172.6	−	131191.i	0.188189	−	0.417232i
$69$	31571.2			0.0961045
$70$	−188587.	+	121822.i	−0.549815	+	0.355165i
$71$		−	545782.i		−	1.52491i	−0.647041	−	0.762456i	$-0.723994\pi$
$71$		−	545782.i		−	1.52491i	0.647041	−	0.762456i	$-0.276006\pi$
$72$	354767.	−	53552.2i	0.950487	−	0.143476i
$73$	−88774.1			−0.228201			−0.114101	−	0.993469i	$-0.536399\pi$
$73$	−88774.1			−0.228201			−0.114101	+	0.993469i	$0.536399\pi$
$74$	5205.74	+	8058.76i	0.0128466	+	0.0198872i
$75$			16608.1i			0.0393674i
$76$	−341884.	−	154204.i	−0.778822	−	0.351281i
$77$	−717470.			−1.57156
$78$	−121677.	+	78600.2i	−0.256405	+	0.165630i
$79$		−	260741.i		−	0.528844i	−0.964407	−	0.264422i	$-0.914819\pi$
$79$		−	260741.i		−	0.528844i	0.964407	−	0.264422i	$-0.0851811\pi$
$80$	151559.	+	171636.i	0.296013	+	0.335226i
$81$	470467.			0.885267
$82$	−536245.	−	830136.i	−0.972571	−	1.50559i
$83$		−	220472.i		−	0.385583i	−0.981240	−	0.192792i	$-0.938246\pi$
$83$		−	220472.i		−	0.385583i	0.981240	−	0.192792i	$-0.0617542\pi$
$84$	70206.8	−	155655.i	0.118452	−	0.262618i
$85$	125708.			0.204694
$86$	−973943.	+	629140.i	−1.53122	+	0.989127i
$87$			78099.2i			0.118601i
$88$	109217.	+	723531.i	0.160266	+	1.06172i
$89$	371922.			0.527572			0.263786	−	0.964581i	$-0.415029\pi$
$89$	371922.			0.527572			0.263786	+	0.964581i	$0.415029\pi$
$90$	170046.	+	263241.i	0.233260	+	0.361099i
$91$		−	1.71041e6i		−	2.26974i
$92$	346568.	+	156316.i	0.445066	+	0.200743i
$93$	−30702.6			−0.0381704
$94$	742784.	−	479818.i	0.894291	−	0.577687i
$95$		−	327594.i		−	0.382090i
$96$	−167657.	−	47105.3i	−0.189500	−	0.0532422i
$97$	676250.			0.740956			0.370478	−	0.928841i	$-0.379194\pi$
$97$	676250.			0.740956			0.370478	+	0.928841i	$0.379194\pi$
$98$	583318.	+	903008.i	0.619765	+	0.959430i
$99$			1.00149e6i			1.03214i
$100$	−82230.8	+	182313.i	−0.0822308	+	0.182313i
$101$	399219.			0.387478			0.193739	−	0.981053i	$-0.437939\pi$
$101$	399219.			0.387478			0.193739	+	0.981053i	$0.437939\pi$
$102$	−80309.9	+	51878.0i	−0.0756779	+	0.0488858i
$103$			1.45632e6i			1.33274i	0.745622	+	0.666369i	$0.232152\pi$
$103$			1.45632e6i			1.33274i	−0.745622	+	0.666369i	$0.767848\pi$
$104$	−1.72486e6	+	260368.i	−1.53340	+	0.231466i
$105$	149149.			0.128840
$106$	138476.	+	214368.i	0.116267	+	0.179988i
$107$		−	15889.5i		−	0.0129706i	−0.999979	−	0.00648528i	$-0.997936\pi$
$107$		−	15889.5i		−	0.0129706i	0.999979	−	0.00648528i	$-0.00206434\pi$
$108$	−443303.	−	199948.i	−0.351908	−	0.158725i
$109$	−1.79984e6			−1.38981			−0.694904	−	0.719103i	$-0.744553\pi$
$109$	−1.79984e6			−1.38981			−0.694904	+	0.719103i	$0.744553\pi$
$110$	−536867.	+	346801.i	−0.403356	+	0.260557i
$111$		−	6373.49i		−	0.00466024i
$112$	1.54137e6	−	1.36107e6i	1.09712	−	0.968781i
$113$	2.12678e6			1.47397			0.736983	−	0.675912i	$-0.236250\pi$
$113$	2.12678e6			1.47397			0.736983	+	0.675912i	$0.236250\pi$
$114$	135194.	+	209288.i	0.0912522	+	0.141263i
$115$			332082.i			0.218349i
$116$	−386687.	+	857321.i	−0.247734	+	0.549249i
$117$	−2.38750e6			−1.49068
$118$	1.77198e6	−	1.14465e6i	1.07848	−	0.696668i
$119$		−	1.12891e6i		−	0.669914i
$120$	−22704.2	−	150409.i	−0.0131390	−	0.0870422i
$121$	−270926.			−0.152931
$122$	116708.	+	180670.i	0.0642718	+	0.0994962i
$123$			656535.i			0.352811i
$124$	−337033.	−	152016.i	−0.176770	−	0.0797304i
$125$	−174693.			−0.0894427
$126$	2.36403e6	−	1.52709e6i	1.18179	−	0.763404i
$127$			1.68543e6i			0.822812i	0.911452	+	0.411406i	$0.134962\pi$
$127$			1.68543e6i			0.822812i	−0.911452	+	0.411406i	$0.865038\pi$
$128$	−1.60720e6	−	1.34720e6i	−0.766373	−	0.642395i
$129$	770269.			0.358817
$130$	−826757.	−	1.27987e6i	−0.376312	−	0.582551i
$131$			496195.i			0.220718i	0.993892	+	0.110359i	$0.0352001\pi$
$131$			496195.i			0.220718i	−0.993892	+	0.110359i	$0.964800\pi$
$132$	199864.	−	443117.i	0.0868987	−	0.192662i
$133$	−2.94195e6			−1.25049
$134$	2.61055e6	−	1.68634e6i	1.08497	−	0.700861i
$135$		−	424774.i		−	0.172646i
$136$	−1.13845e6	+	171849.i	−0.452582	+	0.0683173i
$137$	1.64598e6			0.640120			0.320060	−	0.947397i	$-0.396297\pi$
$137$	1.64598e6			0.640120			0.320060	+	0.947397i	$0.396297\pi$
$138$	−137046.	−	212155.i	−0.0521470	−	0.0807265i
$139$			1.53472e6i			0.571457i	0.958311	+	0.285729i	$0.0922356\pi$
$139$			1.53472e6i			0.571457i	−0.958311	+	0.285729i	$0.907764\pi$
$140$	1.63726e6	+	738471.i	0.596668	+	0.269122i
$141$	−587451.			−0.209563
$142$	−3.66760e6	+	2.36917e6i	−1.28090	+	0.827428i
$143$		−	4.86919e6i		−	1.66513i
$144$	−1.89986e6	−	2.15154e6i	−0.636260	−	0.720545i
$145$	−821487.			−0.269461
$146$	385356.	+	596552.i	0.123824	+	0.191686i
$147$		−	714168.i		−	0.224827i
$148$	31556.6	−	69964.0i	0.00973432	−	0.0215819i
$149$	387060.			0.117009			0.0585045	−	0.998287i	$-0.481367\pi$
$149$	387060.			0.117009			0.0585045	+	0.998287i	$0.481367\pi$
$150$	111605.	−	72093.6i	0.0330681	−	0.0213611i
$151$			5.66925e6i			1.64662i	0.567589	+	0.823312i	$0.307876\pi$
$151$			5.66925e6i			1.64662i	−0.567589	+	0.823312i	$0.692124\pi$
$152$	447839.	+	2.96680e6i	0.127524	+	0.844808i
$153$	−1.57580e6			−0.439975
$154$	3.11444e6	+	4.82132e6i	0.852741	+	1.32009i
$155$		−	322946.i		−	0.0867231i
$156$	1.05637e6	+	476466.i	0.278255	+	0.125504i
$157$	5.26666e6			1.36093			0.680466	−	0.732779i	$-0.261777\pi$
$157$	5.26666e6			1.36093			0.680466	+	0.732779i	$0.261777\pi$
$158$	−1.75215e6	+	1.13184e6i	−0.444221	+	0.286955i
$159$		−	169539.i		−	0.0421772i
$160$	495477.	−	1.76350e6i	0.120966	−	0.430543i
$161$	2.98225e6			0.714605
$162$	−2.04223e6	−	3.16149e6i	−0.480352	−	0.743612i
$163$		−	2.86208e6i		−	0.660875i	−0.943828	−	0.330437i	$-0.892804\pi$
$163$		−	2.86208e6i		−	0.660875i	0.943828	−	0.330437i	$-0.107196\pi$
$164$	−3.25066e6	+	7.20701e6i	−0.736953	+	1.63389i
$165$	424596.			0.0945200
$166$	−1.48155e6	+	957037.i	−0.323885	+	0.209221i
$167$		−	5.21981e6i		−	1.12074i	−0.828242	−	0.560371i	$-0.810659\pi$
$167$		−	5.21981e6i		−	1.12074i	0.828242	−	0.560371i	$-0.189341\pi$
$168$	−1.35074e6	+	203895.i	−0.284869	+	0.0430009i
$169$	6.78110e6			1.40488
$170$	−545679.	−	844741.i	−0.111068	−	0.171940i
$171$			4.10655e6i			0.821275i
$172$	8.45551e6	+	3.81378e6i	1.66171	+	0.749498i
$173$	−2.22314e6			−0.429366			−0.214683	−	0.976684i	$-0.568872\pi$
$173$	−2.22314e6			−0.429366			−0.214683	+	0.976684i	$0.568872\pi$
$174$	524818.	−	339018.i	0.0996233	−	0.0643538i
$175$			1.56882e6i			0.292725i
$176$	4.38795e6	−	3.87468e6i	0.804867	−	0.710718i
$177$	−1.40142e6			−0.252724
$178$	−1.61446e6	−	2.49927e6i	−0.286264	−	0.443153i
$179$		−	1.02612e7i		−	1.78911i	−0.446953	−	0.894557i	$-0.647491\pi$
$179$		−	1.02612e7i		−	1.78911i	0.446953	−	0.894557i	$-0.352509\pi$
$180$	1.03080e6	−	2.28538e6i	0.176749	−	0.391870i
$181$	−1.09916e7			−1.85365			−0.926823	−	0.375500i	$-0.877471\pi$
$181$	−1.09916e7			−1.85365			−0.926823	+	0.375500i	$0.877471\pi$
$182$	−1.14938e7	+	7.42467e6i	−1.90655	+	1.23158i
$183$		−	142888.i		−	0.0233153i
$184$	−453974.	−	3.00744e6i	−0.0728748	−	0.482774i
$185$	67039.6			0.0105881
$186$	133276.	+	206318.i	0.0207116	+	0.0320626i
$187$		−	3.21378e6i		−	0.491463i
$188$	−6.44865e6	−	2.90860e6i	−0.970499	−	0.437735i
$189$	−3.81467e6			−0.565029
$190$	−2.20140e6	+	1.42204e6i	−0.320950	+	0.207325i
$191$			201591.i			0.0289316i	0.999895	+	0.0144658i	$0.00460476\pi$
$191$			201591.i			0.0289316i	−0.999895	+	0.0144658i	$0.995395\pi$
$192$	411234.	+	1.33112e6i	0.0581013	+	0.188067i
$193$	1.00133e7			1.39286			0.696430	−	0.717625i	$-0.254771\pi$
$193$	1.00133e7			1.39286			0.696430	+	0.717625i	$0.254771\pi$
$194$	−2.93551e6	−	4.54433e6i	−0.402048	−	0.622393i
$195$			1.01222e6i			0.136511i
$196$	3.53601e6	−	7.83967e6i	0.469619	−	1.04119i
$197$	3.29004e6			0.430331			0.215166	−	0.976578i	$-0.430971\pi$
$197$	3.29004e6			0.430331			0.215166	+	0.976578i	$0.430971\pi$
$198$	6.72989e6	−	4.34732e6i	0.866987	−	0.560049i
$199$			8.71965e6i			1.10647i	0.833025	+	0.553235i	$0.186607\pi$
$199$			8.71965e6i			1.10647i	−0.833025	+	0.553235i	$0.813393\pi$
$200$	1.58208e6	−	238815.i	0.197760	−	0.0298518i
$201$	−2.06463e6			−0.254245
$202$	−1.73295e6	−	2.68270e6i	−0.210248	−	0.325476i
$203$			7.37733e6i			0.881883i
$204$	697229.	+	314479.i	0.0821268	+	0.0370426i
$205$	−6.90577e6			−0.801587
$206$	9.78630e6	−	6.32167e6i	1.11948	−	0.723153i
$207$		−	4.16281e6i		−	0.469327i
$208$	9.23704e6	+	1.04607e7i	1.02646	+	1.16244i
$209$	−8.37511e6			−0.917385
$210$	−647434.	−	1.00226e6i	−0.0699098	−	0.108224i
$211$			9.16995e6i			0.976157i	0.872800	+	0.488079i	$0.162302\pi$
$211$			9.16995e6i			0.976157i	−0.872800	+	0.488079i	$0.837698\pi$
$212$	839425.	−	1.86108e6i	0.0880997	−	0.195325i
$213$	2.90062e6			0.300159
$214$	−106776.	+	68974.1i	−0.0108951	+	0.00703792i
$215$			8.10208e6i			0.815232i
$216$	580689.	+	3.84689e6i	0.0576212	+	0.381723i
$217$	−2.90020e6			−0.283824
$218$	7.81286e6	+	1.20947e7i	0.754120	+	1.16742i
$219$		−	471799.i		−	0.0449185i
$220$	4.66093e6	+	2.10227e6i	0.437728	+	0.197434i
$221$	7.66149e6			0.709801
$222$	−42829.1	+	27666.4i	−0.00391454	+	0.00252868i
$223$			5.55433e6i			0.500861i	0.968135	+	0.250430i	$0.0805721\pi$
$223$			5.55433e6i			0.500861i	−0.968135	+	0.250430i	$0.919428\pi$
$224$	−1.58371e7	−	4.44962e6i	−1.40907	−	0.395894i
$225$	2.18986e6			0.192251
$226$	−9.23206e6	−	1.42917e7i	−0.799785	−	1.23811i
$227$			5.31906e6i			0.454734i	0.973809	+	0.227367i	$0.0730117\pi$
$227$			5.31906e6i			0.454734i	−0.973809	+	0.227367i	$0.926988\pi$
$228$	819532.	−	1.81698e6i	0.0691451	−	0.153301i
$229$	7.25741e6			0.604331			0.302166	−	0.953255i	$-0.402290\pi$
$229$	7.25741e6			0.604331			0.302166	+	0.953255i	$0.402290\pi$
$230$	2.23155e6	−	1.44152e6i	0.183410	−	0.118478i
$231$		−	3.81307e6i		−	0.309342i
$232$	7.43966e6	−	1.12302e6i	0.595784	−	0.0899337i
$233$	−1.11670e7			−0.882813			−0.441407	−	0.897307i	$-0.645520\pi$
$233$	−1.11670e7			−0.882813			−0.441407	+	0.897307i	$0.645520\pi$
$234$	1.03638e7	+	1.60437e7i	0.808857	+	1.25215i
$235$		−	6.17910e6i		−	0.476126i
$236$	−1.53838e7	−	6.93874e6i	−1.17038	−	0.527891i
$237$	1.38573e6			0.104096
$238$	−7.58617e6	+	4.90045e6i	−0.562719	+	0.363501i
$239$		−	7.94996e6i		−	0.582333i	−0.956672	−	0.291166i	$-0.905957\pi$
$239$		−	7.94996e6i		−	0.582333i	0.956672	−	0.291166i	$-0.0940433\pi$
$240$	−912175.	+	805474.i	−0.0659849	+	0.0582664i
$241$	−1.48608e7			−1.06168			−0.530839	−	0.847473i	$-0.678123\pi$
$241$	−1.48608e7			−1.06168			−0.530839	+	0.847473i	$0.678123\pi$
$242$	1.17605e6	+	1.82059e6i	0.0829814	+	0.128460i
$243$			8.03971e6i			0.560301i
$244$	707470.	−	1.56853e6i	0.0487011	−	0.107975i
$245$	7.51198e6			0.510806
$246$	4.41184e6	−	2.84993e6i	0.296357	−	0.191438i
$247$		−	1.99659e7i		−	1.32494i
$248$	441485.	+	2.92471e6i	0.0289441	+	0.191746i
$249$	1.17172e6			0.0758972
$250$	758317.	+	1.17392e6i	0.0485323	+	0.0751307i
$251$		−	1.69142e7i		−	1.06962i	−0.844972	−	0.534811i	$-0.820383\pi$
$251$		−	1.69142e7i		−	1.06962i	0.844972	−	0.534811i	$-0.179617\pi$
$252$	−2.05238e7	−	9.25709e6i	−1.28250	−	0.578459i
$253$	8.48984e6			0.524250
$254$	1.13259e7	−	7.31624e6i	0.691151	−	0.446464i
$255$			668086.i			0.0402913i
$256$	−2.07640e6	+	1.66482e7i	−0.123763	+	0.992312i
$257$	4.52047e6			0.266308			0.133154	−	0.991095i	$-0.457490\pi$
$257$	4.52047e6			0.266308			0.133154	+	0.991095i	$0.457490\pi$
$258$	−3.34363e6	−	5.17612e6i	−0.194697	−	0.301402i
$259$		−	602047.i		−	0.0346522i
$260$	−5.01172e6	+	1.11114e7i	−0.285145	+	0.632194i
$261$	1.02977e7			0.579189
$262$	3.33437e6	−	2.15391e6i	0.185400	−	0.119763i
$263$		−	8.53093e6i		−	0.468953i	−0.972122	−	0.234476i	$-0.924662\pi$
$263$		−	8.53093e6i		−	0.468953i	0.972122	−	0.234476i	$-0.0753376\pi$
$264$	−3.84528e6	+	580446.i	−0.208986	+	0.0315464i
$265$	1.78329e6			0.0958264
$266$	1.27706e7	+	1.97696e7i	0.678525	+	1.05039i
$267$			1.97662e6i			0.103846i
$268$	−2.26641e7	−	1.02224e7i	−1.17743	−	0.531068i
$269$	1.69223e7			0.869365			0.434683	−	0.900584i	$-0.356861\pi$
$269$	1.69223e7			0.869365			0.434683	+	0.900584i	$0.356861\pi$
$270$	−2.85443e6	+	1.84388e6i	−0.145020	+	0.0936790i
$271$		−	2.73224e7i		−	1.37281i	−0.727219	−	0.686405i	$-0.759188\pi$
$271$		−	2.73224e7i		−	1.37281i	0.727219	−	0.686405i	$-0.240812\pi$
$272$	6.09666e6	+	6.90428e6i	0.302960	+	0.343093i
$273$	9.09017e6			0.446770
$274$	−7.14495e6	−	1.10608e7i	−0.347334	−	0.537692i
$275$			4.46611e6i			0.214749i
$276$	−830759.	+	1.84187e6i	−0.0395137	+	0.0876056i
$277$	−1.71484e7			−0.806832			−0.403416	−	0.915017i	$-0.632177\pi$
$277$	−1.71484e7			−0.806832			−0.403416	+	0.915017i	$0.632177\pi$
$278$	1.03131e7	−	6.66199e6i	0.480016	−	0.310077i
$279$			4.04828e6i			0.186405i
$280$	−2.14467e6	−	1.42078e7i	−0.0976980	−	0.647221i
$281$	−1.51245e7			−0.681653			−0.340826	−	0.940126i	$-0.610707\pi$
$281$	−1.51245e7			−0.681653			−0.340826	+	0.940126i	$0.610707\pi$
$282$	2.55004e6	+	3.94760e6i	0.113710	+	0.176030i
$283$		−	1.20906e7i		−	0.533445i	−0.963773	−	0.266722i	$-0.914059\pi$
$283$		−	1.20906e7i		−	0.533445i	0.963773	−	0.266722i	$-0.0859407\pi$
$284$	3.18411e7	+	1.43616e7i	1.39006	+	0.626973i
$285$	1.74103e6			0.0752094
$286$	−3.27204e7	+	2.11365e7i	−1.39869	+	0.903513i
$287$			6.20170e7i			2.62340i
$288$	−6.21105e6	+	2.21064e7i	−0.260008	+	0.925423i
$289$	−1.90808e7			−0.790502
$290$	3.56596e6	+	5.52030e6i	0.146212	+	0.226344i
$291$			3.59400e6i			0.145848i
$292$	2.33599e6	−	5.17910e6i	0.0938257	−	0.208020i
$293$	−2.05333e7			−0.816312			−0.408156	−	0.912912i	$-0.633828\pi$
$293$	−2.05333e7			−0.816312			−0.408156	+	0.912912i	$0.633828\pi$
$294$	−4.79913e6	+	3.10010e6i	−0.188852	+	0.121993i
$295$		−	1.47408e7i		−	0.574189i
$296$	−607133.	+	91646.8i	−0.0234104	+	0.00353380i
$297$	−1.08596e7			−0.414517
$298$	−1.68017e6	−	2.60100e6i	−0.0634900	−	0.0982859i
$299$			2.02394e7i			0.757153i
$300$	−968922.	−	437024.i	−0.0358860	−	0.0161861i
$301$	7.27605e7			2.66806
$302$	3.80967e7	−	2.46094e7i	1.38314	−	0.893471i
$303$			2.12169e6i			0.0762700i
$304$	1.79926e7	−	1.58879e7i	0.640431	−	0.565517i
$305$	1.50296e6			0.0529723
$306$	6.84035e6	+	1.05892e7i	0.238734	+	0.369573i
$307$			4.56041e6i			0.157612i	0.996890	+	0.0788059i	$0.0251107\pi$
$307$			4.56041e6i			0.157612i	−0.996890	+	0.0788059i	$0.974889\pi$
$308$	1.88794e7	−	4.18573e7i	0.646154	−	1.43258i
$309$	−7.73975e6			−0.262332
$310$	−2.17016e6	+	1.40186e6i	−0.0728462	+	0.0470566i
$311$			4.90702e7i			1.63131i	0.578539	+	0.815654i	$0.303623\pi$
$311$			4.90702e7i			1.63131i	−0.578539	+	0.815654i	$0.696377\pi$
$312$	−1.38375e6	−	9.16697e6i	−0.0455612	−	0.301830i
$313$	−2.81641e7			−0.918467			−0.459233	−	0.888316i	$-0.651876\pi$
$313$	−2.81641e7			−0.918467			−0.459233	+	0.888316i	$0.651876\pi$
$314$	−2.28619e7	−	3.53914e7i	−0.738453	−	1.14316i
$315$		−	1.96660e7i		−	0.629192i
$316$	1.52117e7	+	6.86109e6i	0.482076	+	0.217436i
$317$	1.51561e7			0.475784			0.237892	−	0.971292i	$-0.423544\pi$
$317$	1.51561e7			0.475784			0.237892	+	0.971292i	$0.423544\pi$
$318$	−1.13928e6	+	735944.i	−0.0354282	+	0.0228857i
$319$			2.10017e7i			0.646968i
$320$	−1.40013e7	+	4.32557e6i	−0.427287	+	0.132006i
$321$	84446.3			0.00255309
$322$	−1.29455e7	−	2.00404e7i	−0.387750	−	0.600259i
$323$		−	1.31779e7i		−	0.391057i
$324$	−1.23798e7	+	2.74471e7i	−0.363981	+	0.806979i
$325$	−1.06470e7			−0.310154
$326$	−1.92329e7	+	1.24239e7i	−0.555126	+	0.358596i
$327$		−	9.56544e6i		−	0.273566i
$328$	6.25410e7	−	9.44056e6i	1.77232	−	0.267532i
$329$	−5.54912e7			−1.55825
$330$	−1.84311e6	−	2.85324e6i	−0.0512873	−	0.0793955i
$331$		−	4.80370e7i		−	1.32462i	−0.749229	−	0.662311i	$-0.769576\pi$
$331$		−	4.80370e7i		−	1.32462i	0.749229	−	0.662311i	$-0.230424\pi$
$332$	1.28624e7	+	5.80146e6i	0.351485	+	0.158534i
$333$	−840374.			−0.0227583
$334$	−3.50766e7	+	2.26585e7i	−0.941408	+	0.608123i
$335$		−	2.17168e7i		−	0.577645i
$336$	7.23353e6	+	8.19176e6i	0.190692	+	0.215953i
$337$	−2.86285e7			−0.748012			−0.374006	−	0.927426i	$-0.622016\pi$
$337$	−2.86285e7			−0.748012			−0.374006	+	0.927426i	$0.622016\pi$
$338$	−2.94358e7	−	4.55683e7i	−0.762301	−	1.18008i
$339$			1.13030e7i			0.290131i
$340$	−3.30785e6	+	7.33380e6i	−0.0841606	+	0.186592i
$341$	−8.25628e6			−0.208219
$342$	2.75956e7	−	1.78260e7i	0.689860	−	0.445630i
$343$		−	8.39856e6i		−	0.208124i
$344$	−1.10760e7	−	7.33752e7i	−0.272087	−	1.80249i
$345$	−1.76488e6			−0.0429792
$346$	9.65033e6	+	1.49392e7i	0.232978	+	0.360662i
$347$			6.31778e7i			1.51208i	0.654523	+	0.756042i	$0.272870\pi$
$347$			6.31778e7i			1.51208i	−0.654523	+	0.756042i	$0.727130\pi$
$348$	−4.55632e6	−	2.05509e6i	−0.108113	−	0.0487633i
$349$	1.71181e7			0.402699			0.201349	−	0.979520i	$-0.435467\pi$
$349$	1.71181e7			0.402699			0.201349	+	0.979520i	$0.435467\pi$
$350$	1.05423e7	−	6.81004e6i	0.245885	−	0.158835i
$351$		−	2.58887e7i		−	0.598671i
$352$	−4.50849e7	−	1.26671e7i	−1.03372	−	0.290436i
$353$	5.48327e7			1.24657			0.623283	−	0.781997i	$-0.285799\pi$
$353$	5.48327e7			1.24657			0.623283	+	0.781997i	$0.285799\pi$
$354$	6.08335e6	+	9.41736e6i	0.137130	+	0.212285i
$355$			3.05102e7i			0.681961i
$356$	−9.78669e6	+	2.16980e7i	−0.216913	+	0.480916i
$357$	5.99972e6			0.131864
$358$	−6.89540e7	+	4.45424e7i	−1.50283	+	0.970788i
$359$		−	6.51539e7i		−	1.40818i	−0.710113	−	0.704088i	$-0.751356\pi$
$359$		−	6.51539e7i		−	1.40818i	0.710113	−	0.704088i	$-0.248644\pi$
$360$	−1.98321e7	+	2.99366e6i	−0.425071	+	0.0641645i
$361$	1.27042e7			0.270038
$362$	4.77132e7	+	7.38626e7i	1.00580	+	1.55704i
$363$		−	1.43987e6i		−	0.0301025i
$364$	9.97859e7	+	4.50075e7i	2.06902	+	0.933214i
$365$	4.96262e6			0.102055
$366$	−960189.	+	620255.i	−0.0195845	+	0.0126511i
$367$		−	1.94852e7i		−	0.394191i	−0.980384	−	0.197096i	$-0.936849\pi$
$367$		−	1.94852e7i		−	0.394191i	0.980384	−	0.197096i	$-0.0631509\pi$
$368$	−1.82391e7	+	1.61056e7i	−0.365981	+	0.323171i
$369$	8.65672e7			1.72296
$370$	−291010.	−	450499.i	−0.00574516	−	0.00889382i
$371$		−	1.60148e7i		−	0.313617i
$372$	807904.	−	1.79120e6i	0.0156939	−	0.0347948i
$373$	1.04195e7			0.200779			0.100390	−	0.994948i	$-0.467991\pi$
$373$	1.04195e7			0.200779			0.100390	+	0.994948i	$0.467991\pi$
$374$	−2.15962e7	+	1.39506e7i	−0.412822	+	0.266672i
$375$		−	928423.i		−	0.0176057i
$376$	8.44717e6	+	5.59600e7i	0.158909	+	1.05272i
$377$	−5.00671e7			−0.934391
$378$	1.65589e7	+	2.56341e7i	0.306589	+	0.474617i
$379$			5.69455e7i			1.04602i	0.852325	+	0.523012i	$0.175192\pi$
$379$			5.69455e7i			1.04602i	−0.852325	+	0.523012i	$0.824808\pi$
$380$	1.91119e7	+	8.62026e6i	0.348300	+	0.157098i
$381$	−8.95742e6			−0.161960
$382$	1.35467e6	−	875081.i	0.0243021	−	0.0156985i
$383$			3.76033e7i			0.669313i	0.942340	+	0.334657i	$0.108620\pi$
$383$			3.76033e7i			0.669313i	−0.942340	+	0.334657i	$0.891380\pi$
$384$	7.15984e6	−	8.54164e6i	0.126447	−	0.150851i
$385$	4.01078e7			0.702824
$386$	−4.34665e7	−	6.72886e7i	−0.755776	−	1.16998i
$387$		−	1.01564e8i		−	1.75229i
$388$	−1.77947e7	+	3.94526e7i	−0.304647	+	0.675430i
$389$	−8.88855e6			−0.151002			−0.0755009	−	0.997146i	$-0.524056\pi$
$389$	−8.88855e6			−0.151002			−0.0755009	+	0.997146i	$0.524056\pi$
$390$	6.80198e6	−	4.39389e6i	0.114668	−	0.0740722i
$391$			1.33585e7i			0.223473i
$392$	−6.80310e7	+	1.02693e7i	−1.12940	+	0.170483i
$393$	−2.63708e6			−0.0434456
$394$	−1.42816e7	−	2.21087e7i	−0.233501	−	0.361472i
$395$			1.45758e7i			0.236506i
$396$	−5.84270e7	−	2.63530e7i	−0.940867	−	0.424370i
$397$	9.22516e7			1.47436			0.737178	−	0.675699i	$-0.236158\pi$
$397$	9.22516e7			1.47436			0.737178	+	0.675699i	$0.236158\pi$
$398$	5.85951e7	−	3.78508e7i	0.929420	−	0.600380i
$399$		−	1.56353e7i		−	0.246143i
$400$	−8.47239e6	−	9.59472e6i	−0.132381	−	0.149918i
$401$	−4.81067e7			−0.746058			−0.373029	−	0.927820i	$-0.621681\pi$
$401$	−4.81067e7			−0.746058			−0.373029	+	0.927820i	$0.621681\pi$
$402$	8.96225e6	+	1.38741e7i	0.137955	+	0.213563i
$403$		−	1.96826e7i		−	0.300723i
$404$	−1.05050e7	+	2.32905e7i	−0.159313	+	0.353211i
$405$	−2.62999e7			−0.395903
$406$	4.95749e7	−	3.20240e7i	0.740770	−	0.478517i
$407$		−	1.71390e6i		−	0.0254216i
$408$	−913310.	−	6.05041e6i	−0.0134474	−	0.0890849i
$409$	−3.88101e7			−0.567250			−0.283625	−	0.958935i	$-0.591537\pi$
$409$	−3.88101e7			−0.567250			−0.283625	+	0.958935i	$0.591537\pi$
$410$	2.99770e7	+	4.64060e7i	0.434947	+	0.673322i
$411$			8.74771e6i			0.125999i
$412$	−8.49619e7	−	3.83213e7i	−1.21488	−	0.547960i
$413$	−1.32379e8			−1.87919
$414$	−2.79736e7	+	1.80702e7i	−0.394228	+	0.254660i
$415$			1.23247e7i			0.172438i
$416$	3.01978e7	−	1.07480e8i	0.419465	−	1.49296i
$417$	−8.15641e6			−0.112484
$418$	3.63552e7	+	5.62798e7i	0.497780	+	0.770591i
$419$		−	7.36223e7i		−	1.00085i	−0.865781	−	0.500423i	$-0.833178\pi$
$419$		−	7.36223e7i		−	1.00085i	0.865781	−	0.500423i	$-0.166822\pi$
$420$	−3.92468e6	+	8.70138e6i	−0.0529732	+	0.117446i
$421$	−2.26299e7			−0.303275			−0.151638	−	0.988436i	$-0.548455\pi$
$421$	−2.26299e7			−0.303275			−0.151638	+	0.988436i	$0.548455\pi$
$422$	6.16211e7	−	3.98055e7i	0.819959	−	0.529670i
$423$			7.74581e7i			1.02340i
$424$	−1.61501e7	+	2.43786e6i	−0.211874	+	0.0319824i
$425$	−7.02726e6			−0.0915418
$426$	−1.25912e7	−	1.94918e7i	−0.162869	−	0.252130i
$427$		−	1.34973e7i		−	0.173366i
$428$	926996.	+	418113.i	0.0118235	+	0.00533289i
$429$	2.58778e7			0.327760
$430$	5.44451e7	−	3.51700e7i	0.684784	−	0.442351i
$431$		−	1.43189e7i		−	0.178846i	−0.995994	−	0.0894229i	$-0.971498\pi$
$431$		−	1.43189e7i		−	0.178846i	0.995994	−	0.0894229i	$-0.0285023\pi$
$432$	2.33300e7	−	2.06010e7i	0.289377	−	0.255527i
$433$	1.16527e8			1.43537			0.717686	−	0.696367i	$-0.245201\pi$
$433$	1.16527e8			1.43537			0.717686	+	0.696367i	$0.245201\pi$
$434$	1.25894e7	+	1.94891e7i	0.154005	+	0.238408i
$435$		−	4.36588e6i		−	0.0530400i
$436$	4.73607e7	−	1.05003e8i	0.571425	−	1.26690i
$437$	3.48122e7			0.417145
$438$	−3.17044e6	+	2.04801e6i	−0.0377309	+	0.0243731i
$439$			4.30408e7i			0.508730i	0.967108	+	0.254365i	$0.0818664\pi$
$439$			4.30408e7i			0.508730i	−0.967108	+	0.254365i	$0.918134\pi$
$440$	−6.10542e6	−	4.04466e7i	−0.0716733	−	0.474815i
$441$	−9.41663e7			−1.09794
$442$	−3.32575e7	−	5.14844e7i	−0.385143	−	0.596223i
$443$			4.15286e7i			0.477679i	0.971059	+	0.238839i	$0.0767669\pi$
$443$			4.15286e7i			0.477679i	−0.971059	+	0.238839i	$0.923233\pi$
$444$	371831.	+	167711.i	0.00424812	+	0.00191608i
$445$	−2.07911e7			−0.235937
$446$	3.73245e7	−	2.41106e7i	0.420716	−	0.271771i
$447$			2.05707e6i			0.0230317i
$448$	3.88457e7	+	1.25739e8i	0.432025	+	1.39841i
$449$	5.58210e7			0.616678			0.308339	−	0.951277i	$-0.400227\pi$
$449$	5.58210e7			0.616678			0.308339	+	0.951277i	$0.400227\pi$
$450$	−9.50588e6	−	1.47156e7i	−0.104317	−	0.161488i
$451$			1.76550e8i			1.92458i
$452$	−5.59638e7	+	1.24077e8i	−0.606026	+	1.34362i
$453$	−3.01298e7			−0.324117
$454$	3.57435e7	−	2.30893e7i	0.381971	−	0.246742i
$455$			9.56150e7i			1.01506i
$456$	−1.57674e7	+	2.38009e6i	−0.166290	+	0.0251014i
$457$	−3.55787e7			−0.372771			−0.186385	−	0.982477i	$-0.559677\pi$
$457$	−3.55787e7			−0.372771			−0.186385	+	0.982477i	$0.559677\pi$
$458$	−3.15034e7	−	4.87690e7i	−0.327915	−	0.507630i
$459$		−	1.70871e7i		−	0.176698i
$460$	−1.93737e7	−	8.73835e6i	−0.199040	−	0.0897751i
$461$	4.59892e6			0.0469411			0.0234705	−	0.999725i	$-0.492528\pi$
$461$	4.59892e6			0.0469411			0.0234705	+	0.999725i	$0.492528\pi$
$462$	−2.56234e7	+	1.65520e7i	−0.259843	+	0.167851i
$463$		−	3.59469e7i		−	0.362175i	−0.983467	−	0.181087i	$-0.942038\pi$
$463$		−	3.59469e7i		−	0.362175i	0.983467	−	0.181087i	$-0.0579617\pi$
$464$	−3.98411e7	−	4.51188e7i	−0.398820	−	0.451652i
$465$	1.71633e6			0.0170703
$466$	4.84744e7	+	7.50410e7i	0.479021	+	0.741551i
$467$		−	4.76144e7i		−	0.467506i	−0.972296	−	0.233753i	$-0.924899\pi$
$467$		−	4.76144e7i		−	0.467506i	0.972296	−	0.233753i	$-0.0751008\pi$
$468$	6.28243e7	−	1.39287e8i	0.612901	−	1.35886i
$469$	−1.95027e8			−1.89050
$470$	−4.15229e7	+	2.68226e7i	−0.399939	+	0.258350i
$471$			2.79902e7i			0.267882i
$472$	2.01515e7	+	1.33498e8i	0.191638	+	1.26954i
$473$	2.07134e8			1.95735
$474$	−6.01527e6	−	9.31197e6i	−0.0564833	−	0.0874393i
$475$			1.83131e7i			0.170876i
$476$	6.58610e7	+	2.97060e7i	0.610671	+	0.275438i
$477$	−2.23544e7			−0.205972
$478$	−5.34229e7	+	3.45097e7i	−0.489152	+	0.315978i
$479$		−	3.87884e7i		−	0.352936i	−0.984306	−	0.176468i	$-0.943533\pi$
$479$		−	3.87884e7i		−	0.352936i	0.984306	−	0.176468i	$-0.0564671\pi$
$480$	9.37232e6	+	2.63327e6i	0.0847469	+	0.0238106i
$481$	4.08586e6			0.0367154
$482$	6.45089e7	+	9.98633e7i	0.576074	+	0.891794i
$483$			1.58495e7i			0.140661i
$484$	7.12911e6	−	1.58059e7i	0.0628781	−	0.139407i
$485$	−3.78035e7			−0.331366
$486$	5.40260e7	−	3.48993e7i	0.470645	−	0.304024i
$487$		−	1.30693e8i		−	1.13153i	−0.824566	−	0.565765i	$-0.808581\pi$
$487$		−	1.30693e8i		−	1.13153i	0.824566	−	0.565765i	$-0.191419\pi$
$488$	−1.36114e7	+	2.05464e6i	−0.117123	+	0.0176797i
$489$	1.52108e7			0.130085
$490$	−3.26085e7	−	5.04797e7i	−0.277167	−	0.429070i
$491$			2.72341e7i			0.230075i	0.993361	+	0.115037i	$0.0366988\pi$
$491$			2.72341e7i			0.230075i	−0.993361	+	0.115037i	$0.963301\pi$
$492$	−3.83024e7	−	1.72760e7i	−0.321611	−	0.145060i
$493$	−3.30455e7			−0.275785
$494$	−1.34168e8	+	8.66690e7i	−1.11293	+	0.718924i
$495$		−	5.59849e7i		−	0.461589i
$496$	1.77373e7	−	1.56625e7i	0.145359	−	0.128356i
$497$	2.73996e8			2.23190
$498$	−5.08627e6	−	7.87383e6i	−0.0411824	−	0.0637526i
$499$		−	3.61384e7i		−	0.290849i	−0.989369	−	0.145424i	$-0.953545\pi$
$499$		−	3.61384e7i		−	0.290849i	0.989369	−	0.145424i	$-0.0464547\pi$
$500$	4.59684e6	−	1.01916e7i	0.0367747	−	0.0815329i
$501$	2.77412e7			0.220604
$502$	−1.13661e8	+	7.34221e7i	−0.898467	+	0.580385i
$503$		−	1.70857e8i		−	1.34255i	−0.741210	−	0.671274i	$-0.765748\pi$
$503$		−	1.70857e8i		−	1.34255i	0.741210	−	0.671274i	$-0.234252\pi$
$504$	2.68844e7	+	1.78102e8i	0.209995	+	1.39116i
$505$	−2.23170e7			−0.173285
$506$	−3.68532e7	−	5.70508e7i	−0.284462	−	0.440362i
$507$			3.60389e7i			0.276533i
$508$	−9.83287e7	−	4.43503e7i	−0.750048	−	0.338302i
$509$	2.02403e8			1.53484			0.767421	−	0.641144i	$-0.221540\pi$
$509$	2.02403e8			1.53484			0.767421	+	0.641144i	$0.221540\pi$
$510$	4.48946e6	−	2.90007e6i	0.0338442	−	0.0218624i
$511$		−	4.45667e7i		−	0.334001i
$512$	1.20888e8	−	5.83145e7i	0.900683	−	0.434477i
$513$	−4.45291e7			−0.329831
$514$	−1.96227e7	−	3.03771e7i	−0.144501	−	0.223695i
$515$		−	8.14106e7i		−	0.596018i
$516$	−2.02687e7	+	4.49377e7i	−0.147529	+	0.327086i
$517$	−1.57972e8			−1.14316
$518$	−4.04569e6	+	2.61340e6i	−0.0291074	+	0.0188026i
$519$		−	1.18151e7i		−	0.0845153i
$520$	9.64228e7	−	1.45550e7i	0.685756	−	0.103515i
$521$	−1.22836e8			−0.868587			−0.434294	−	0.900771i	$-0.643002\pi$
$521$	−1.22836e8			−0.868587			−0.434294	+	0.900771i	$0.643002\pi$
$522$	−4.47010e7	−	6.91996e7i	−0.314272	−	0.486511i
$523$		−	1.41912e8i		−	0.992009i	−0.868320	−	0.496004i	$-0.834800\pi$
$523$		−	1.41912e8i		−	0.992009i	0.868320	−	0.496004i	$-0.165200\pi$
$524$	−2.89481e7	−	1.30568e7i	−0.201199	−	0.0907491i
$525$	−8.33767e6			−0.0576192
$526$	−5.73269e7	+	3.70316e7i	−0.393914	+	0.254457i
$527$		−	1.29910e7i		−	0.0887583i
$528$	2.05924e7	+	2.33202e7i	0.139896	+	0.158428i
$529$	1.12747e8			0.761618
$530$	−7.74103e6	−	1.19835e7i	−0.0519961	−	0.0804929i
$531$			1.84783e8i			1.23418i
$532$	7.74139e7	−	1.71634e8i	0.514143	−	1.13990i
$533$	−4.20886e8			−2.77960
$534$	1.32826e7	−	8.58022e6i	0.0872290	−	0.0563475i
$535$			888249.i			0.00580061i
$536$	2.96880e7	+	1.96674e8i	0.192791	+	1.27718i
$537$	5.45341e7			0.352164
$538$	−7.34573e7	−	1.13716e8i	−0.471724	−	0.730255i
$539$		−	1.92048e8i		−	1.22643i
$540$	2.47814e7	+	1.11774e7i	0.157378	+	0.0709840i
$541$	2.41291e8			1.52388			0.761938	−	0.647650i	$-0.224248\pi$
$541$	2.41291e8			1.52388			0.761938	+	0.647650i	$0.224248\pi$
$542$	−1.83603e8	+	1.18603e8i	−1.15314	+	0.744897i
$543$		−	5.84162e7i		−	0.364866i
$544$	1.99313e7	−	7.09394e7i	0.123805	−	0.440647i
$545$	1.00614e8			0.621541
$546$	−3.94592e7	−	6.10849e7i	−0.242421	−	0.375281i
$547$			1.38352e7i			0.0845322i	0.999106	+	0.0422661i	$0.0134577\pi$
$547$			1.38352e7i			0.0845322i	−0.999106	+	0.0422661i	$0.986542\pi$
$548$	−4.33119e7	+	9.60266e7i	−0.263188	+	0.583512i
$549$	−1.88404e7			−0.113860
$550$	3.00118e7	−	1.93868e7i	0.180386	−	0.116525i
$551$			8.61165e7i			0.514792i
$552$	1.59834e7	−	2.41269e6i	0.0950279	−	0.0143445i
$553$	1.30898e8			0.774029
$554$	7.44386e7	+	1.15235e8i	0.437793	+	0.677728i
$555$			356289.i			0.00208412i
$556$	−8.95357e7	−	4.03843e7i	−0.520921	−	0.234957i
$557$	7.83223e6			0.0453231			0.0226616	−	0.999743i	$-0.492786\pi$
$557$	7.83223e6			0.0453231			0.0226616	+	0.999743i	$0.492786\pi$
$558$	2.72040e7	−	1.75730e7i	0.156578	−	0.101145i
$559$			4.93797e8i			2.82692i
$560$	−8.61651e7	+	7.60860e7i	−0.490645	+	0.433252i
$561$	1.70800e7			0.0967383
$562$	6.56535e7	+	1.01635e8i	0.369870	+	0.572579i
$563$			1.26861e8i			0.710894i	0.934696	+	0.355447i	$0.115671\pi$
$563$			1.26861e8i			0.710894i	−0.934696	+	0.355447i	$0.884329\pi$
$564$	1.54581e7	−	3.42720e7i	0.0861625	−	0.191030i
$565$	−1.18891e8			−0.659177
$566$	−8.12477e7	+	5.24837e7i	−0.448086	+	0.289451i
$567$			2.36185e8i			1.29570i
$568$	−4.17091e7	−	2.76310e8i	−0.227607	−	1.50783i
$569$	−1.56881e8			−0.851598			−0.425799	−	0.904818i	$-0.640007\pi$
$569$	−1.56881e8			−0.851598			−0.425799	+	0.904818i	$0.640007\pi$
$570$	−7.55758e6	−	1.16995e7i	−0.0408092	−	0.0631749i
$571$		−	2.12179e8i		−	1.13971i	−0.821746	−	0.569854i	$-0.807000\pi$
$571$		−	2.12179e8i		−	1.13971i	0.821746	−	0.569854i	$-0.193000\pi$
$572$	2.84070e8	+	1.28127e8i	1.51788	+	0.684625i
$573$	−1.07138e6			−0.00569481
$574$	4.16748e8	−	2.69207e8i	2.20362	−	1.42348i
$575$		−	1.85639e7i		−	0.0976487i
$576$	1.75514e8	−	5.42232e7i	0.918425	−	0.283738i
$577$	−2.26242e8			−1.17773			−0.588865	−	0.808231i	$-0.700425\pi$
$577$	−2.26242e8			−1.17773			−0.588865	+	0.808231i	$0.700425\pi$
$578$	8.28271e7	+	1.28221e8i	0.428933	+	0.664011i
$579$			5.32170e7i			0.274166i
$580$	2.16165e7	−	4.79257e7i	0.110790	−	0.245632i
$581$	1.10682e8			0.564350
$582$	2.41513e7	−	1.56011e7i	0.122510	−	0.0791381i
$583$		−	4.55908e7i		−	0.230076i
$584$	−4.49432e7	+	6.78418e6i	−0.225645	+	0.0340611i
$585$	1.33465e8			0.666654
$586$	8.91323e7	+	1.37982e8i	0.442937	+	0.685691i
$587$			1.31180e8i			0.648567i	0.945960	+	0.324284i	$0.105123\pi$
$587$			1.31180e8i			0.648567i	−0.945960	+	0.324284i	$0.894877\pi$
$588$	4.16647e7	+	1.87925e7i	0.204945	+	0.0924385i
$589$	−3.38544e7			−0.165680
$590$	−9.90566e7	+	6.39878e7i	−0.482311	+	0.311560i
$591$			1.74853e7i			0.0847052i
$592$	3.25134e6	+	3.68204e6i	0.0156710	+	0.0177469i
$593$	2.50657e8			1.20203			0.601016	−	0.799237i	$-0.294763\pi$
$593$	2.50657e8			1.20203			0.601016	+	0.799237i	$0.294763\pi$
$594$	4.71398e7	+	7.29750e7i	0.224920	+	0.348189i
$595$			6.31081e7i			0.299595i
$596$	−1.01850e7	+	2.25811e7i	−0.0481087	+	0.106661i
$597$	−4.63415e7			−0.217795
$598$	1.36006e8	−	8.78563e7i	0.635998	−	0.410837i
$599$		−	1.80944e8i		−	0.841904i	−0.907083	−	0.420952i	$-0.861696\pi$
$599$		−	1.80944e8i		−	0.841904i	0.907083	−	0.420952i	$-0.138304\pi$
$600$	1.26921e6	+	8.40811e6i	0.00587595	+	0.0389264i
$601$	−3.43181e8			−1.58088			−0.790441	−	0.612538i	$-0.790149\pi$
$601$	−3.43181e8			−1.58088			−0.790441	+	0.612538i	$0.790149\pi$
$602$	−3.15843e8	−	4.88942e8i	−1.44771	−	2.24114i
$603$			2.72230e8i			1.24161i
$604$	−3.30745e8	−	1.49180e8i	−1.50101	−	0.677016i
$605$	1.51452e7			0.0683927
$606$	1.42575e7	−	9.20996e6i	0.0640658	−	0.0413847i
$607$			9.14325e7i			0.408822i	0.978885	+	0.204411i	$0.0655279\pi$
$607$			9.14325e7i			0.408822i	−0.978885	+	0.204411i	$0.934472\pi$
$608$	−1.84868e8	−	5.19409e7i	−0.822530	−	0.231099i
$609$	−3.92076e7			−0.173587
$610$	−6.52416e6	−	1.00998e7i	−0.0287432	−	0.0444960i
$611$		−	3.76598e8i		−	1.65103i
$612$	4.14655e7	−	9.19328e7i	0.180897	−	0.401066i
$613$	−4.70613e7			−0.204307			−0.102153	−	0.994769i	$-0.532573\pi$
$613$	−4.70613e7			−0.204307			−0.102153	+	0.994769i	$0.532573\pi$
$614$	3.06454e7	−	1.97961e7i	0.132392	−	0.0855214i
$615$		−	3.67014e7i		−	0.157782i
$616$	−3.63230e8	+	5.48295e7i	−1.55396	+	0.234570i
$617$	−3.14231e8			−1.33781			−0.668905	−	0.743348i	$-0.733237\pi$
$617$	−3.14231e8			−1.33781			−0.668905	+	0.743348i	$0.733237\pi$
$618$	3.35972e7	+	5.20103e7i	0.142343	+	0.220355i
$619$			5.43914e7i			0.229329i	0.993404	+	0.114664i	$0.0365793\pi$
$619$			5.43914e7i			0.229329i	−0.993404	+	0.114664i	$0.963421\pi$
$620$	1.88407e7	+	8.49795e6i	0.0790538	+	0.0356565i
$621$	4.51391e7			0.188485
$622$	3.29746e8	−	2.13007e8i	1.37028	−	0.885161i
$623$			1.86713e8i			0.772167i
$624$	−5.55943e7	+	4.90912e7i	−0.228811	+	0.202046i
$625$	9.76562e6			0.0400000
$626$	1.22257e8	+	1.89260e8i	0.498367	+	0.771499i
$627$		−	4.45104e7i		−	0.180576i
$628$	−1.38586e8	+	3.07258e8i	−0.559553	+	1.24058i
$629$	2.69676e6			0.0108365
$630$	−1.32153e8	+	8.53672e7i	−0.528513	+	0.341405i
$631$		−	4.17792e8i		−	1.66292i	−0.555582	−	0.831462i	$-0.687505\pi$
$631$		−	4.17792e8i		−	1.66292i	0.555582	−	0.831462i	$-0.312495\pi$
$632$	−1.99260e7	−	1.32004e8i	−0.0789348	−	0.522920i
$633$	−4.87347e7			−0.192144
$634$	−6.57905e7	−	1.01847e8i	−0.258164	−	0.399652i
$635$		−	9.42187e7i		−	0.367973i
$636$	9.89092e6	+	4.46121e6i	0.0384473	+	0.0173413i
$637$	4.57832e8			1.77128
$638$	1.41129e8	−	9.11656e7i	0.543445	−	0.351050i
$639$		−	3.82460e8i		−	1.46583i
$640$	8.98453e7	+	7.53108e7i	0.342733	+	0.287288i
$641$	3.47108e8			1.31792			0.658962	−	0.752177i	$-0.270996\pi$
$641$	3.47108e8			1.31792			0.658962	+	0.752177i	$0.270996\pi$
$642$	−366570.	−	567470.i	−0.00138532	−	0.00214456i
$643$		−	2.85548e7i		−	0.107410i	−0.998557	−	0.0537051i	$-0.982897\pi$
$643$		−	2.85548e7i		−	0.107410i	0.998557	−	0.0537051i	$-0.0171031\pi$
$644$	−7.84744e7	+	1.73985e8i	−0.293813	+	0.651410i
$645$	−4.30593e7			−0.160468
$646$	−8.85542e7	+	5.72036e7i	−0.328482	+	0.212190i
$647$		−	3.48845e7i		−	0.128801i	−0.997924	−	0.0644006i	$-0.979486\pi$
$647$		−	3.48845e7i		−	0.128801i	0.997924	−	0.0644006i	$-0.0205136\pi$
$648$	2.38181e8	−	3.59534e7i	0.875350	−	0.132134i
$649$	−3.76856e8			−1.37861
$650$	4.62171e7	+	7.15466e7i	0.168292	+	0.260525i
$651$		−	1.54134e7i		−	0.0558672i
$652$	1.66974e8	+	7.53124e7i	0.602431	+	0.271721i
$653$	1.27679e8			0.458545			0.229272	−	0.973362i	$-0.426365\pi$
$653$	1.27679e8			0.458545			0.229272	+	0.973362i	$0.426365\pi$
$654$	−6.42787e7	+	4.15223e7i	−0.229791	+	0.148439i
$655$		−	2.77381e7i		−	0.0987082i
$656$	−3.34921e8	−	3.79288e8i	−1.18640	−	1.34356i
$657$	−6.22089e7			−0.219359
$658$	2.40880e8	+	3.72895e8i	0.845517	+	1.30891i
$659$			3.30561e8i			1.15503i	0.816378	+	0.577517i	$0.195978\pi$
$659$			3.30561e8i			1.15503i	−0.816378	+	0.577517i	$0.804022\pi$
$660$	−1.11727e7	+	2.47710e7i	−0.0388623	+	0.0861612i
$661$	3.14273e8			1.08819			0.544093	−	0.839025i	$-0.316874\pi$
$661$	3.14273e8			1.08819			0.544093	+	0.839025i	$0.316874\pi$
$662$	−3.22803e8	+	2.08522e8i	−1.11266	+	0.718750i
$663$			4.07178e7i			0.139715i
$664$	−1.68486e7	−	1.11617e8i	−0.0575519	−	0.381264i
$665$	1.64460e8			0.559236
$666$	3.64795e6	+	5.64722e6i	0.0123488	+	0.0191167i
$667$		−	8.72962e7i		−	0.294183i
$668$	3.04525e8	+	1.37353e8i	1.02163	+	0.460797i
$669$	−2.95190e7			−0.0985880
$670$	−1.45934e8	+	9.42695e7i	−0.485214	+	0.313435i
$671$		−	3.84241e7i		−	0.127185i
$672$	2.36480e7	−	8.41678e7i	0.0779266	−	0.277357i
$673$	3.85226e8			1.26378			0.631888	−	0.775060i	$-0.282280\pi$
$673$	3.85226e8			1.26378			0.631888	+	0.775060i	$0.282280\pi$
$674$	1.24272e8	+	1.92380e8i	0.405877	+	0.628320i
$675$			2.37456e7i			0.0772096i
$676$	−1.78437e8	+	3.95611e8i	−0.577623	+	1.28064i
$677$	−6.99468e7			−0.225425			−0.112712	−	0.993628i	$-0.535954\pi$
$677$	−6.99468e7			−0.225425			−0.112712	+	0.993628i	$0.535954\pi$
$678$	7.59549e7	−	4.90647e7i	0.243706	−	0.157427i
$679$			3.39493e8i			1.08448i
$680$	6.36413e7	−	9.60666e6i	0.202401	−	0.0305524i
$681$	−2.82687e7			−0.0895086
$682$	3.58394e7	+	5.54813e7i	0.112981	+	0.174901i
$683$		−	6.56603e7i		−	0.206082i	−0.994677	−	0.103041i	$-0.967143\pi$
$683$		−	6.56603e7i		−	0.206082i	0.994677	−	0.103041i	$-0.0328573\pi$
$684$	−2.39577e8	−	1.08059e8i	−0.748647	−	0.337670i
$685$	−9.20128e7			−0.286271
$686$	−5.64374e7	+	3.64570e7i	−0.174821	+	0.112930i
$687$			3.85703e7i			0.118955i
$688$	−4.44994e8	+	3.92941e8i	−1.36643	+	1.20660i
$689$	1.08686e8			0.332290
$690$	7.66111e6	+	1.18598e7i	0.0233209	+	0.0361020i
$691$		−	2.17976e8i		−	0.660653i	−0.943867	−	0.330327i	$-0.892841\pi$
$691$		−	2.17976e8i		−	0.660653i	0.943867	−	0.330327i	$-0.107159\pi$
$692$	5.84993e7	−	1.29698e8i	0.176536	−	0.391396i
$693$	−5.02770e8			−1.51067
$694$	4.24548e8	−	2.74246e8i	1.27013	−	0.820469i
$695$		−	8.57932e7i		−	0.255563i
$696$	5.96839e6	+	3.95388e7i	0.0177023	+	0.117273i
$697$	−2.77794e8			−0.820399
$698$	−7.43074e7	−	1.15032e8i	−0.218507	−	0.338261i
$699$		−	5.93482e7i		−	0.173770i
$700$	−9.15255e7	−	4.12818e7i	−0.266838	−	0.120355i
$701$	1.81653e8			0.527337			0.263668	−	0.964613i	$-0.415068\pi$
$701$	1.81653e8			0.527337			0.263668	+	0.964613i	$0.415068\pi$
$702$	−1.73969e8	+	1.12379e8i	−0.502875	+	0.324844i
$703$		−	7.02777e6i		−	0.0202279i
$704$	1.10586e8	+	3.57952e8i	0.316942	+	1.02590i
$705$	3.28395e7			0.0937193
$706$	−2.38021e8	−	3.68469e8i	−0.676396	−	1.04710i
$707$			2.00417e8i			0.567122i
$708$	3.68766e7	−	8.17589e7i	0.103909	−	0.230375i
$709$	4.11862e8			1.15562			0.577808	−	0.816173i	$-0.303908\pi$
$709$	4.11862e8			1.15562			0.577808	+	0.816173i	$0.303908\pi$
$710$	2.05025e8	−	1.32440e8i	0.572838	−	0.370037i
$711$		−	1.82715e8i		−	0.508354i
$712$	1.88291e8	−	2.84225e7i	0.521662	−	0.0787449i
$713$	3.43182e7			0.0946795
$714$	−2.60440e7	−	4.03175e7i	−0.0715505	−	0.110764i
$715$			2.72196e8i			0.744670i
$716$	5.98640e8	+	2.70011e8i	1.63090	+	0.735601i
$717$	4.22509e7			0.114625
$718$	−4.37827e8	+	2.82824e8i	−1.18285	+	0.764087i
$719$		−	5.34296e8i		−	1.43746i	−0.695290	−	0.718730i	$-0.744724\pi$
$719$		−	5.34296e8i		−	1.43746i	0.695290	−	0.718730i	$-0.255276\pi$
$720$	1.06205e8	+	1.20275e8i	0.284544	+	0.322238i
$721$	−7.31106e8			−1.95063
$722$	−5.51471e7	−	8.53706e7i	−0.146525	−	0.226828i
$723$		−	7.89795e7i		−	0.208978i
$724$	2.89232e8	−	6.41254e8i	0.762133	−	1.68972i
$725$	4.59225e7			0.120507
$726$	−9.67574e6	+	6.25026e6i	−0.0252857	+	0.0163338i
$727$			3.34950e8i			0.871720i	0.900015	+	0.435860i	$0.143556\pi$
$727$			3.34950e8i			0.871720i	−0.900015	+	0.435860i	$0.856444\pi$
$728$	−1.30711e8	−	8.65922e8i	−0.338780	−	2.24432i
$729$	3.00243e8			0.774978
$730$	−2.15421e7	−	3.33483e7i	−0.0553756	−	0.0857245i
$731$			3.25918e8i			0.834364i
$732$	8.33610e6	+	3.75992e6i	0.0212535	+	0.00958618i
$733$	−2.65703e7			−0.0674659			−0.0337329	−	0.999431i	$-0.510740\pi$
$733$	−2.65703e7			−0.0674659			−0.0337329	+	0.999431i	$0.510740\pi$
$734$	−1.30938e8	+	8.45826e7i	−0.331115	+	0.213891i
$735$			3.99232e7i			0.100546i
$736$	1.87401e8	+	5.26525e7i	0.470043	+	0.132064i
$737$	−5.55201e8			−1.38691
$738$	−3.75776e8	−	5.81722e8i	−0.934889	−	1.44726i
$739$			2.04250e8i			0.506091i	0.967454	+	0.253045i	$0.0814322\pi$
$739$			2.04250e8i			0.506091i	−0.967454	+	0.253045i	$0.918568\pi$
$740$	−1.76407e6	+	3.91110e6i	−0.00435332	+	0.00965171i
$741$	1.06111e8			0.260798
$742$	−1.07618e8	+	6.95181e7i	−0.263434	+	0.170171i
$743$			6.10775e8i			1.48907i	0.667584	+	0.744535i	$0.267329\pi$
$743$			6.10775e8i			1.48907i	−0.667584	+	0.744535i	$0.732671\pi$
$744$	−1.55437e7	+	2.34632e6i	−0.0377428	+	0.00569728i
$745$	−2.16373e7			−0.0523280
$746$	−4.52295e7	−	7.00177e7i	−0.108944	−	0.168652i
$747$		−	1.54497e8i		−	0.370644i
$748$	1.87493e8	+	8.45669e7i	0.448001	+	0.202067i
$749$	7.97689e6			0.0189840
$750$	−6.23890e6	+	4.03016e6i	−0.0147885	+	0.00955296i
$751$			5.53487e8i			1.30674i	0.757041	+	0.653368i	$0.226644\pi$
$751$			5.53487e8i			1.30674i	−0.757041	+	0.653368i	$0.773356\pi$
$752$	3.39377e8	−	2.99679e8i	0.798049	−	0.704697i
$753$	8.98922e7			0.210541
$754$	2.17334e8	+	3.36445e8i	0.507008	+	0.784875i
$755$		−	3.16920e8i		−	0.736393i
$756$	1.00379e8	−	2.22548e8i	0.232314	−	0.515062i
$757$	7.94693e8			1.83194			0.915971	−	0.401244i	$-0.131422\pi$
$757$	7.94693e8			1.83194			0.915971	+	0.401244i	$0.131422\pi$
$758$	3.82667e8	−	2.47192e8i	0.878646	−	0.567581i
$759$			4.51202e7i			0.103192i
$760$	−2.50350e7	−	1.65849e8i	−0.0570304	−	0.377809i
$761$	−8.56540e8			−1.94354			−0.971771	−	0.235928i	$-0.924187\pi$
$761$	−8.56540e8			−1.94354			−0.971771	+	0.235928i	$0.924187\pi$
$762$	3.88829e7	+	6.01929e7i	0.0878808	+	0.136044i
$763$		−	9.03562e8i		−	2.03416i
$764$	−1.17609e7	−	5.30465e6i	−0.0263730	−	0.0118953i
$765$	8.80902e7			0.196763
$766$	2.52690e8	−	1.63231e8i	0.562214	−	0.363174i
$767$		−	8.98407e8i		−	1.99107i
$768$	−8.84787e7	−	1.10353e7i	−0.195324	−	0.0243612i
$769$	−6.32938e8			−1.39182			−0.695909	−	0.718130i	$-0.744998\pi$
$769$	−6.32938e8			−1.39182			−0.695909	+	0.718130i	$0.744998\pi$
$770$	−1.74102e8	−	2.69520e8i	−0.381358	−	0.590362i
$771$			2.40245e7i			0.0524193i
$772$	−2.63490e8	+	5.84181e8i	−0.572679	+	1.26968i
$773$	−6.52834e8			−1.41340			−0.706698	−	0.707515i	$-0.749816\pi$
$773$	−6.52834e8			−1.41340			−0.706698	+	0.707515i	$0.749816\pi$
$774$	−6.82496e8	+	4.40873e8i	−1.47190	+	0.950803i
$775$			1.80532e7i			0.0387837i
$776$	3.42362e8	−	5.16795e7i	0.732656	−	0.110594i
$777$	3.19964e6			0.00682084
$778$	3.85840e7	+	5.97301e7i	0.0819348	+	0.126839i
$779$			7.23932e8i			1.53139i
$780$	−5.90529e7	−	2.66353e7i	−0.124439	−	0.0561272i
$781$	7.80008e8			1.63737
$782$	8.97674e7	−	5.79872e7i	0.187715	−	0.121258i
$783$			1.11663e8i			0.232607i
$784$	3.64322e8	+	4.12584e8i	0.756027	+	0.856177i
$785$	−2.94415e8			−0.608628
$786$	1.14472e7	+	1.77209e7i	0.0235739	+	0.0364937i
$787$			3.46939e8i			0.711752i	0.934533	+	0.355876i	$0.115817\pi$
$787$			3.46939e8i			0.711752i	−0.934533	+	0.355876i	$0.884183\pi$
$788$	−8.65736e7	+	1.91942e8i	−0.176932	+	0.392275i
$789$	4.53385e7			0.0923074
$790$	9.79480e7	−	6.32717e7i	0.198662	−	0.128330i
$791$			1.06769e9i			2.15733i
$792$	7.65344e7	+	5.07018e8i	0.154057	+	1.02058i
$793$	9.16011e7			0.183688
$794$	−4.00451e8	−	6.19920e8i	−0.799997	−	1.23844i
$795$			9.47750e6i			0.0188622i
$796$	−5.08707e8	−	2.29448e8i	−1.00862	−	0.454930i
$797$	1.39554e8			0.275656			0.137828	−	0.990456i	$-0.455988\pi$
$797$	1.39554e8			0.275656			0.137828	+	0.990456i	$0.455988\pi$
$798$	−1.05067e8	+	6.78706e7i	−0.206757	+	0.133559i
$799$		−	2.48563e8i		−	0.487300i
$800$	−2.76980e7	+	9.85829e7i	−0.0540977	+	0.192545i
$801$	2.60626e8			0.507131
$802$	2.08825e8	+	3.23272e8i	0.404817	+	0.626679i
$803$		−	1.26872e8i		−	0.245030i
$804$	5.43282e7	−	1.20451e8i	0.104534	−	0.231761i
$805$	−1.66713e8			−0.319581
$806$	−1.32265e8	+	8.54393e7i	−0.252603	+	0.163175i
$807$			8.99353e7i			0.171123i
$808$	2.02110e8	−	3.05086e7i	0.383137	−	0.0578346i
$809$	5.69038e8			1.07472			0.537360	−	0.843353i	$-0.319421\pi$
$809$	5.69038e8			1.07472			0.537360	+	0.843353i	$0.319421\pi$
$810$	1.14164e8	+	1.76732e8i	0.214820	+	0.332553i
$811$			6.02741e8i			1.12997i	0.825100	+	0.564987i	$0.191119\pi$
$811$			6.02741e8i			1.12997i	−0.825100	+	0.564987i	$0.808881\pi$
$812$	−4.30395e8	−	1.94126e8i	−0.803895	−	0.362590i
$813$	1.45208e8			0.270220
$814$	−1.15172e7	+	7.43981e6i	−0.0213538	+	0.0137940i
$815$			1.59995e8i			0.295552i
$816$	−3.66935e7	+	3.24013e7i	−0.0675335	+	0.0596338i
$817$	8.49342e8			1.55746
$818$	1.68469e8	+	2.60800e8i	0.307794	+	0.476483i
$819$		−	1.19858e9i		−	2.18180i
$820$	1.81717e8	−	4.02884e8i	0.329575	−	0.730699i
$821$	2.66963e8			0.482415			0.241208	−	0.970474i	$-0.422457\pi$
$821$	2.66963e8			0.482415			0.241208	+	0.970474i	$0.422457\pi$
$822$	5.87836e7	−	3.79726e7i	0.105838	−	0.0683683i
$823$		−	1.01295e9i		−	1.81713i	−0.417741	−	0.908566i	$-0.637178\pi$
$823$		−	1.01295e9i		−	1.81713i	0.417741	−	0.908566i	$-0.362822\pi$
$824$	1.11293e8	+	7.37282e8i	0.198923	+	1.31781i
$825$	−2.37356e7			−0.0422706
$826$	5.74640e8	+	8.89574e8i	1.01966	+	1.57849i
$827$		−	3.69724e8i		−	0.653675i	−0.945081	−	0.326837i	$-0.894017\pi$
$827$		−	3.69724e8i		−	0.653675i	0.945081	−	0.326837i	$-0.105983\pi$
$828$	2.42859e8	+	1.09539e8i	0.427822	+	0.192965i
$829$	−3.89705e8			−0.684025			−0.342012	−	0.939695i	$-0.611109\pi$
$829$	−3.89705e8			−0.684025			−0.342012	+	0.939695i	$0.611109\pi$
$830$	8.28209e7	−	5.35000e7i	0.144846	−	0.0935663i
$831$		−	9.11367e7i		−	0.158815i
$832$	−8.53340e8	+	2.63630e8i	−1.48167	+	0.457747i
$833$	3.02180e8			0.522794
$834$	3.54058e7	+	5.48102e7i	0.0610347	+	0.0944850i
$835$			2.91796e8i			0.501211i
$836$	2.20381e8	−	4.88606e8i	0.377186	−	0.836257i
$837$	−4.38972e7			−0.0748619
$838$	−4.94734e8	+	3.19584e8i	−0.840697	+	0.543067i
$839$			1.45047e8i			0.245596i	0.992432	+	0.122798i	$0.0391867\pi$
$839$			1.45047e8i			0.245596i	−0.992432	+	0.122798i	$0.960813\pi$
$840$	7.55088e7	−	1.13981e7i	0.127397	−	0.0192306i
$841$	−3.78874e8			−0.636953
$842$	9.82334e7	+	1.52071e8i	0.164559	+	0.254747i
$843$		−	8.03809e7i		−	0.134175i
$844$	−5.34977e8	−	2.41297e8i	−0.889832	−	0.401351i
$845$	−3.79075e8			−0.628283
$846$	5.20510e8	−	3.36235e8i	0.859642	−	0.555305i
$847$		−	1.36011e8i		−	0.223833i
$848$	8.64875e7	+	9.79445e7i	0.141829	+	0.160617i
$849$	6.42569e7			0.105002
$850$	3.05044e7	+	4.72224e7i	0.0496713	+	0.0768939i
$851$			7.12404e6i			0.0115595i
$852$	−7.63264e7	+	1.69223e8i	−0.123412	+	0.273615i
$853$	3.16634e8			0.510164			0.255082	−	0.966919i	$-0.417897\pi$
$853$	3.16634e8			0.510164			0.255082	+	0.966919i	$0.417897\pi$
$854$	−9.07005e7	+	5.85900e7i	−0.145625	+	0.0940697i
$855$		−	2.29563e8i		−	0.367286i
$856$	−1.21429e6	−	8.04428e6i	−0.00193597	−	0.0128253i
$857$	−6.72143e7			−0.106787			−0.0533936	−	0.998574i	$-0.517004\pi$
$857$	−6.72143e7			−0.106787			−0.0533936	+	0.998574i	$0.517004\pi$
$858$	−1.12332e8	−	1.73896e8i	−0.177845	−	0.275314i
$859$		−	2.67276e8i		−	0.421677i	−0.977521	−	0.210839i	$-0.932381\pi$
$859$		−	2.67276e8i		−	0.421677i	0.977521	−	0.210839i	$-0.0676194\pi$
$860$	−4.72677e8	−	2.13197e8i	−0.743138	−	0.335186i
$861$	−3.29596e8			−0.516384
$862$	−9.62216e7	+	6.21565e7i	−0.150228	+	0.0970431i
$863$			9.04298e7i			0.140695i	0.997523	+	0.0703476i	$0.0224108\pi$
$863$			9.04298e7i			0.140695i	−0.997523	+	0.0703476i	$0.977589\pi$
$864$	−2.39709e8	−	6.73490e7i	−0.371657	−	0.104422i
$865$	1.24277e8			0.192019
$866$	−5.05829e8	−	7.83051e8i	−0.778844	−	1.20569i
$867$		−	1.01407e8i		−	0.155600i
$868$	7.63155e7	−	1.69199e8i	0.116695	−	0.258724i
$869$	3.72639e8			0.567844
$870$	−2.93382e7	+	1.89517e7i	−0.0445529	+	0.0287799i
$871$		−	1.32357e9i		−	2.00306i
$872$	−9.11196e8	+	1.37545e8i	−1.37424	+	0.207442i
$873$	4.73886e8			0.712248
$874$	−1.51115e8	−	2.33934e8i	−0.226346	−	0.350396i
$875$		−	8.76999e7i		−	0.130911i
$876$	2.75249e7	+	1.24148e7i	0.0409461	+	0.0184684i
$877$	−1.59956e7			−0.0237138			−0.0118569	−	0.999930i	$-0.503774\pi$
$877$	−1.59956e7			−0.0237138			−0.0118569	+	0.999930i	$0.503774\pi$
$878$	2.89230e8	−	1.86834e8i	0.427326	−	0.276041i
$879$		−	1.09126e8i		−	0.160681i
$880$	−2.45294e8	+	2.16601e8i	−0.359947	+	0.317843i
$881$	−9.17384e8			−1.34160			−0.670800	−	0.741638i	$-0.734049\pi$
$881$	−9.17384e8			−1.34160			−0.670800	+	0.741638i	$0.734049\pi$
$882$	4.08763e8	+	6.32788e8i	0.595753	+	0.922257i
$883$			7.24207e8i			1.05192i	0.850511	+	0.525958i	$0.176293\pi$
$883$			7.24207e8i			1.05192i	−0.850511	+	0.525958i	$0.823707\pi$
$884$	−2.01603e8	+	4.46973e8i	−0.291837	+	0.647030i
$885$	7.83415e7			0.113022
$886$	2.79067e8	−	1.80270e8i	0.401243	−	0.259192i
$887$		−	6.82509e8i		−	0.977997i	−0.872285	−	0.488999i	$-0.837362\pi$
$887$		−	6.82509e8i		−	0.977997i	0.872285	−	0.488999i	$-0.162638\pi$
$888$	−487066.	−	3.22667e6i	−0.000695584	−	0.00460804i
$889$	−8.46128e8			−1.20429
$890$	9.02511e7	+	1.39714e8i	0.128021	+	0.198184i
$891$			6.72371e8i			0.950552i
$892$	−3.24041e8	−	1.46156e8i	−0.456567	−	0.205931i
$893$	−6.47756e8			−0.909614
$894$	1.38233e7	−	8.92945e6i	0.0193463	−	0.0124972i
$895$			5.73617e8i			0.800117i
$896$	6.76326e8	−	8.06853e8i	0.940226	−	1.12168i
$897$	−1.07564e8			−0.149036
$898$	−2.42311e8	−	3.75111e8i	−0.334614	−	0.518001i
$899$			8.48946e7i			0.116843i
$900$	−5.76236e7	+	1.27757e8i	−0.0790447	+	0.175249i
$901$	7.17355e7			0.0980753
$902$	1.18639e9	−	7.66377e8i	1.61662	−	1.04429i
$903$			3.86693e8i			0.525174i
$904$	1.07671e9	−	1.62530e8i	1.45745	−	0.220003i
$905$	6.14451e8			0.828975
$906$	1.30789e8	+	2.02469e8i	0.175868	+	0.272254i
$907$		−	9.16111e8i		−	1.22780i	−0.789385	−	0.613898i	$-0.789601\pi$
$907$		−	9.16111e8i		−	1.22780i	0.789385	−	0.613898i	$-0.210399\pi$
$908$	−3.10315e8	−	1.39965e8i	−0.414520	−	0.186966i
$909$	2.79754e8			0.372465
$910$	6.42522e8	−	4.15051e8i	0.852637	−	0.550779i
$911$			1.10245e9i			1.45815i	0.684433	+	0.729076i	$0.260050\pi$
$911$			1.10245e9i			1.45815i	−0.684433	+	0.729076i	$0.739950\pi$
$912$	8.44379e7	+	9.56234e7i	0.111315	+	0.126061i
$913$	3.15088e8			0.414019
$914$	1.54442e8	+	2.39085e8i	0.202268	+	0.313122i
$915$			7.98766e6i			0.0104269i
$916$	−1.90970e8	+	4.23399e8i	−0.248473	+	0.550888i
$917$	−2.49101e8			−0.323049
$918$	−1.14824e8	+	7.41728e7i	−0.148424	+	0.0958775i
$919$			5.02290e8i			0.647154i	0.946202	+	0.323577i	$0.104885\pi$
$919$			5.02290e8i			0.647154i	−0.946202	+	0.323577i	$0.895115\pi$
$920$	2.53779e7	+	1.68121e8i	0.0325906	+	0.215903i
$921$	−2.42368e7			−0.0310239
$922$	−1.99633e7	−	3.09042e7i	−0.0254706	−	0.0394299i
$923$			1.85950e9i			2.36478i
$924$	2.22455e8	+	1.00336e8i	0.281985	+	0.127187i
$925$	−3.74763e6			−0.00473512
$926$	−2.41559e8	+	1.56041e8i	−0.304222	+	0.196519i
$927$			1.02052e9i			1.28110i
$928$	−1.30249e8	+	4.63582e8i	−0.162978	+	0.580073i
$929$	8.08879e8			1.00887			0.504436	−	0.863449i	$-0.331700\pi$
$929$	8.08879e8			1.00887			0.504436	+	0.863449i	$0.331700\pi$
$930$	−7.45035e6	−	1.15335e7i	−0.00926249	−	0.0143388i
$931$		−	7.87482e8i		−	0.975869i
$932$	2.93847e8	−	6.51485e8i	0.362972	−	0.804743i
$933$	−2.60788e8			−0.321102
$934$	−3.19963e8	+	2.06687e8i	−0.392699	+	0.253673i
$935$			1.79656e8i			0.219789i
$936$	−1.20871e9	+	1.82454e8i	−1.47399	+	0.222498i
$937$	−6.59940e7			−0.0802205			−0.0401103	−	0.999195i	$-0.512771\pi$
$937$	−6.59940e7			−0.0802205			−0.0401103	+	0.999195i	$0.512771\pi$
$938$	8.46584e8	+	1.31056e9i	1.02580	+	1.58799i
$939$		−	1.49681e8i		−	0.180788i
$940$	3.60490e8	+	1.62596e8i	0.434020	+	0.195761i
$941$	−5.26043e8			−0.631325			−0.315662	−	0.948872i	$-0.602227\pi$
$941$	−5.26043e8			−0.631325			−0.315662	+	0.948872i	$0.602227\pi$
$942$	1.88091e8	−	1.21502e8i	0.225017	−	0.145355i
$943$		−	7.33850e8i		−	0.875129i
$944$	8.09615e8	−	7.14911e8i	0.962415	−	0.849837i
$945$	2.13246e8			0.252689
$946$	−8.99140e8	−	1.39192e9i	−1.06207	−	1.64414i
$947$			8.24336e8i			0.970631i	0.874339	+	0.485316i	$0.161295\pi$
$947$			8.24336e8i			0.970631i	−0.874339	+	0.485316i	$0.838705\pi$
$948$	−3.64640e7	+	8.08440e7i	−0.0427995	+	0.0948905i
$949$	3.02457e8			0.353887
$950$	1.23062e8	−	7.94945e7i	0.143533	−	0.0927184i
$951$			8.05487e7i			0.0936520i
$952$	−8.62723e7	−	5.71528e8i	−0.0999909	−	0.662410i
$953$	−3.56949e8			−0.412409			−0.206204	−	0.978509i	$-0.566111\pi$
$953$	−3.56949e8			−0.412409			−0.206204	+	0.978509i	$0.566111\pi$
$954$	9.70376e7	+	1.50219e8i	0.111762	+	0.173014i
$955$		−	1.12693e7i		−	0.0129386i
$956$	4.63802e8	+	2.09194e8i	0.530835	+	0.239428i
$957$	−1.11616e8			−0.127347
$958$	−2.60654e8	+	1.68375e8i	−0.296461	+	0.191506i
$959$			8.26318e8i			0.936896i
$960$	−2.29887e7	−	7.44116e7i	−0.0259837	−	0.0841060i
$961$	8.54130e8			0.962396
$962$	−1.77361e7	−	2.74565e7i	−0.0199221	−	0.0308404i
$963$		−	1.11346e7i		−	0.0124680i
$964$	3.91046e8	−	8.66985e8i	0.436513	−	0.967789i
$965$	−5.59763e8			−0.622905
$966$	1.06507e8	−	6.88004e7i	0.118153	−	0.0763237i
$967$			8.18526e7i			0.0905217i	0.998975	+	0.0452609i	$0.0144119\pi$
$967$			8.18526e7i			0.0905217i	−0.998975	+	0.0452609i	$0.985588\pi$
$968$	−1.37160e8	+	2.07044e7i	−0.151218	+	0.0228263i
$969$	7.00355e7			0.0769745
$970$	1.64100e8	+	2.54036e8i	0.179801	+	0.278342i
$971$		−	1.63787e9i		−	1.78904i	−0.447025	−	0.894522i	$-0.647516\pi$
$971$		−	1.63787e9i		−	1.78904i	0.447025	−	0.894522i	$-0.352484\pi$
$972$	−4.69039e8	−	2.11556e8i	−0.510752	−	0.230370i
$973$	−7.70463e8			−0.836399
$974$	−8.78244e8	+	5.67321e8i	−0.950470	+	0.613977i
$975$		−	5.65846e7i		−	0.0610498i
$976$	7.28919e7	+	8.25479e7i	0.0784025	+	0.0887885i
$977$	−1.12151e8			−0.120260			−0.0601299	−	0.998191i	$-0.519152\pi$
$977$	−1.12151e8			−0.120260			−0.0601299	+	0.998191i	$0.519152\pi$
$978$	−6.60281e7	−	1.02215e8i	−0.0705850	−	0.109269i
$979$			5.31534e8i			0.566478i
$980$	−1.97669e8	+	4.38251e8i	−0.210020	+	0.465634i
$981$	−1.26125e9			−1.33596
$982$	1.83010e8	−	1.18219e8i	0.193259	−	0.124840i
$983$		−	2.47054e8i		−	0.260095i	−0.991508	−	0.130048i	$-0.958487\pi$
$983$		−	2.47054e8i		−	0.260095i	0.991508	−	0.130048i	$-0.0415130\pi$
$984$	5.01729e7	+	3.32380e8i	0.0526603	+	0.348859i
$985$	−1.83919e8			−0.192450
$986$	1.43446e8	+	2.22062e8i	0.149643	+	0.231656i
$987$		−	2.94914e8i		−	0.306721i
$988$	1.16481e9	+	5.25379e8i	1.20777	+	0.544755i
$989$	−8.60977e8			−0.890026
$990$	−3.76212e8	+	2.43023e8i	−0.387728	+	0.250462i
$991$		−	3.67287e8i		−	0.377385i	−0.982036	−	0.188693i	$-0.939575\pi$
$991$		−	3.67287e8i		−	0.377385i	0.982036	−	0.188693i	$-0.0604250\pi$
$992$	−1.82245e8	−	5.12040e7i	−0.186690	−	0.0524528i
$993$	2.55298e8			0.260735
$994$	−1.18938e9	−	1.84122e9i	−1.21104	−	1.87476i
$995$		−	4.87443e8i		−	0.494829i
$996$	−3.08324e7	+	6.83584e7i	−0.0312054	+	0.0691853i
$997$	−1.29622e9			−1.30796			−0.653980	−	0.756512i	$-0.726902\pi$
$997$	−1.29622e9			−1.30796			−0.653980	+	0.756512i	$0.726902\pi$
$998$	−2.42846e8	+	1.56872e8i	−0.244309	+	0.157817i
$999$		−	9.11253e6i		−	0.00913992i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.7.b.a.11.5	✓	12
3.2	odd	2		180.7.c.a.91.8		12
4.3	odd	2	inner	20.7.b.a.11.6	yes	12
5.2	odd	4		100.7.d.b.99.21		24
5.3	odd	4		100.7.d.b.99.4		24
5.4	even	2		100.7.b.h.51.8		12
8.3	odd	2		320.7.b.d.191.7		12
8.5	even	2		320.7.b.d.191.6		12
12.11	even	2		180.7.c.a.91.7		12
20.3	even	4		100.7.d.b.99.22		24
20.7	even	4		100.7.d.b.99.3		24
20.19	odd	2		100.7.b.h.51.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.7.b.a.11.5	✓	12	1.1	even	1	trivial
20.7.b.a.11.6	yes	12	4.3	odd	2	inner
100.7.b.h.51.7		12	20.19	odd	2
100.7.b.h.51.8		12	5.4	even	2
100.7.d.b.99.3		24	20.7	even	4
100.7.d.b.99.4		24	5.3	odd	4
100.7.d.b.99.21		24	5.2	odd	4
100.7.d.b.99.22		24	20.3	even	4
180.7.c.a.91.7		12	12.11	even	2
180.7.c.a.91.8		12	3.2	odd	2
320.7.b.d.191.6		12	8.5	even	2
320.7.b.d.191.7		12	8.3	odd	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:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	20.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.34086 - 6.71989i) q^{2} +5.31460i q^{3} +(-26.3138 + 58.3402i) q^{4} -55.9017 q^{5} +(35.7136 - 23.0700i) q^{6} +502.023i q^{7} +(506.265 - 76.4207i) q^{8} +700.755 q^{9} +O(q^{10})\)	\(q+(-4.34086 - 6.71989i) q^{2} +5.31460i q^{3} +(-26.3138 + 58.3402i) q^{4} -55.9017 q^{5} +(35.7136 - 23.0700i) q^{6} +502.023i q^{7} +(506.265 - 76.4207i) q^{8} +700.755 q^{9} +(242.662 + 375.653i) q^{10} +1429.16i q^{11} +(-310.055 - 139.848i) q^{12} -3407.04 q^{13} +(3373.54 - 2179.21i) q^{14} -297.095i q^{15} +(-2711.16 - 3070.31i) q^{16} -2248.72 q^{17} +(-3041.88 - 4709.00i) q^{18} +5860.18i q^{19} +(1470.99 - 3261.32i) q^{20} -2668.06 q^{21} +(9603.77 - 6203.77i) q^{22} -5940.46i q^{23} +(406.146 + 2690.60i) q^{24} +3125.00 q^{25} +(14789.5 + 22894.9i) q^{26} +7598.58i q^{27} +(-29288.2 - 13210.2i) q^{28} +14695.2 q^{29} +(-1996.45 + 1289.65i) q^{30} +5777.03i q^{31} +(-8863.37 + 31546.5i) q^{32} -7595.40 q^{33} +(9761.40 + 15111.2i) q^{34} -28064.0i q^{35} +(-18439.6 + 40882.2i) q^{36} -1199.24 q^{37} +(39379.8 - 25438.2i) q^{38} -18107.1i q^{39} +(-28301.1 + 4272.05i) q^{40} +123534. q^{41} +(11581.7 + 17929.0i) q^{42} -144934. i q^{43} +(-83377.3 - 37606.6i) q^{44} -39173.4 q^{45} +(-39919.2 + 25786.7i) q^{46} +110535. i q^{47} +(16317.5 - 14408.8i) q^{48} -134378. q^{49} +(-13565.2 - 20999.7i) q^{50} -11951.1i q^{51} +(89652.3 - 198767. i) q^{52} -31900.5 q^{53} +(51061.6 - 32984.4i) q^{54} -79892.3i q^{55} +(38365.0 + 254157. i) q^{56} -31144.5 q^{57} +(-63789.8 - 98750.1i) q^{58} +263692. i q^{59} +(17332.6 + 7817.72i) q^{60} -26885.8 q^{61} +(38821.0 - 25077.3i) q^{62} +351795. i q^{63} +(250464. - 77378.2i) q^{64} +190459. q^{65} +(32970.6 + 51040.2i) q^{66} +388481. i q^{67} +(59172.6 - 131191. i) q^{68} +31571.2 q^{69} +(-188587. + 121822. i) q^{70} -545782. i q^{71} +(354767. - 53552.2i) q^{72} -88774.1 q^{73} +(5205.74 + 8058.76i) q^{74} +16608.1i q^{75} +(-341884. - 154204. i) q^{76} -717470. q^{77} +(-121677. + 78600.2i) q^{78} -260741. i q^{79} +(151559. + 171636. i) q^{80} +470467. q^{81} +(-536245. - 830136. i) q^{82} -220472. i q^{83} +(70206.8 - 155655. i) q^{84} +125708. q^{85} +(-973943. + 629140. i) q^{86} +78099.2i q^{87} +(109217. + 723531. i) q^{88} +371922. q^{89} +(170046. + 263241. i) q^{90} -1.71041e6i q^{91} +(346568. + 156316. i) q^{92} -30702.6 q^{93} +(742784. - 479818. i) q^{94} -327594. i q^{95} +(-167657. - 47105.3i) q^{96} +676250. q^{97} +(583318. + 903008. i) q^{98} +1.00149e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 10 q^{2} + 156 q^{4} - 672 q^{6} + 440 q^{8} - 1996 q^{9}+O(q^{10}) \) 12 * q - 10 * q^2 + 156 * q^4 - 672 * q^6 + 440 * q^8 - 1996 * q^9	\( 12 q - 10 q^{2} + 156 q^{4} - 672 q^{6} + 440 q^{8} - 1996 q^{9} + 750 q^{10} - 440 q^{12} - 5040 q^{13} + 6248 q^{14} + 3312 q^{16} + 6840 q^{17} + 15790 q^{18} - 3500 q^{20} - 27464 q^{21} - 26160 q^{22} + 28528 q^{24} + 37500 q^{25} - 18684 q^{26} + 19320 q^{28} - 74968 q^{29} - 13000 q^{30} - 60800 q^{32} + 112880 q^{33} + 48204 q^{34} - 128580 q^{36} + 62640 q^{37} + 74800 q^{38} + 57000 q^{40} - 16976 q^{41} - 138360 q^{42} - 222160 q^{44} + 77000 q^{45} - 144792 q^{46} + 297600 q^{48} + 72564 q^{49} - 31250 q^{50} + 548280 q^{52} + 322160 q^{53} + 150416 q^{54} - 246512 q^{56} - 1213440 q^{57} + 350700 q^{58} + 157000 q^{60} + 46464 q^{61} - 7120 q^{62} - 542784 q^{64} - 133000 q^{65} - 65200 q^{66} - 1678280 q^{68} + 41256 q^{69} - 360000 q^{70} + 2317560 q^{72} - 415080 q^{73} + 1581924 q^{74} + 208320 q^{76} + 75600 q^{77} + 473200 q^{78} + 734000 q^{80} + 2287428 q^{81} - 3169500 q^{82} - 2256224 q^{84} + 372000 q^{85} - 62512 q^{86} - 278880 q^{88} + 278392 q^{89} - 2162250 q^{90} + 4095720 q^{92} - 3646000 q^{93} + 4706568 q^{94} - 2641152 q^{96} + 2344680 q^{97} + 1050270 q^{98}+O(q^{100}) \) 12 * q - 10 * q^2 + 156 * q^4 - 672 * q^6 + 440 * q^8 - 1996 * q^9 + 750 * q^10 - 440 * q^12 - 5040 * q^13 + 6248 * q^14 + 3312 * q^16 + 6840 * q^17 + 15790 * q^18 - 3500 * q^20 - 27464 * q^21 - 26160 * q^22 + 28528 * q^24 + 37500 * q^25 - 18684 * q^26 + 19320 * q^28 - 74968 * q^29 - 13000 * q^30 - 60800 * q^32 + 112880 * q^33 + 48204 * q^34 - 128580 * q^36 + 62640 * q^37 + 74800 * q^38 + 57000 * q^40 - 16976 * q^41 - 138360 * q^42 - 222160 * q^44 + 77000 * q^45 - 144792 * q^46 + 297600 * q^48 + 72564 * q^49 - 31250 * q^50 + 548280 * q^52 + 322160 * q^53 + 150416 * q^54 - 246512 * q^56 - 1213440 * q^57 + 350700 * q^58 + 157000 * q^60 + 46464 * q^61 - 7120 * q^62 - 542784 * q^64 - 133000 * q^65 - 65200 * q^66 - 1678280 * q^68 + 41256 * q^69 - 360000 * q^70 + 2317560 * q^72 - 415080 * q^73 + 1581924 * q^74 + 208320 * q^76 + 75600 * q^77 + 473200 * q^78 + 734000 * q^80 + 2287428 * q^81 - 3169500 * q^82 - 2256224 * q^84 + 372000 * q^85 - 62512 * q^86 - 278880 * q^88 + 278392 * q^89 - 2162250 * q^90 + 4095720 * q^92 - 3646000 * q^93 + 4706568 * q^94 - 2641152 * q^96 + 2344680 * q^97 + 1050270 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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