LMFDB - Embedded newform 16.7.f.a.3.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,7,Mod(3,16)]

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([2, 3]))

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

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

chi := DirichletCharacter("16.3");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	16.f (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:	$3.68086533792$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.8
Character	$\chi$	$=$	16.3
Dual form			16.7.f.a.11.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.82644 - 5.48203i) q^{2} +(-6.79913 + 6.79913i) q^{3} +(3.89476 - 63.8814i) q^{4} +(158.437 - 158.437i) q^{5} +(-2.34170 + 76.8878i) q^{6} -213.507 q^{7} +(-327.507 - 393.552i) q^{8} +636.544i q^{9} +O(q^{10})$	\(q+(5.82644 - 5.48203i) q^{2} +(-6.79913 + 6.79913i) q^{3} +(3.89476 - 63.8814i) q^{4} +(158.437 - 158.437i) q^{5} +(-2.34170 + 76.8878i) q^{6} -213.507 q^{7} +(-327.507 - 393.552i) q^{8} +636.544i q^{9} +(54.5675 - 1791.68i) q^{10} +(1309.41 + 1309.41i) q^{11} +(407.857 + 460.819i) q^{12} +(11.6360 + 11.6360i) q^{13} +(-1243.99 + 1170.45i) q^{14} +2154.47i q^{15} +(-4065.66 - 497.605i) q^{16} +2834.10 q^{17} +(3489.55 + 3708.78i) q^{18} +(-7194.40 + 7194.40i) q^{19} +(-9504.10 - 10738.3i) q^{20} +(1451.67 - 1451.67i) q^{21} +(14807.4 + 450.974i) q^{22} +7839.29 q^{23} +(4902.58 + 449.050i) q^{24} -34579.6i q^{25} +(131.585 + 4.00756i) q^{26} +(-9284.51 - 9284.51i) q^{27} +(-831.561 + 13639.2i) q^{28} +(-112.081 - 112.081i) q^{29} +(11810.9 + 12552.9i) q^{30} +7877.51i q^{31} +(-26416.2 + 19388.8i) q^{32} -17805.7 q^{33} +(16512.7 - 15536.6i) q^{34} +(-33827.5 + 33827.5i) q^{35} +(40663.3 + 2479.19i) q^{36} +(22766.4 - 22766.4i) q^{37} +(-2477.83 + 81357.6i) q^{38} -158.229 q^{39} +(-114242. - 10464.0i) q^{40} -20200.8i q^{41} +(499.970 - 16416.1i) q^{42} +(29632.7 + 29632.7i) q^{43} +(88746.6 - 78546.9i) q^{44} +(100852. + 100852. i) q^{45} +(45675.2 - 42975.2i) q^{46} -79640.8i q^{47} +(31026.3 - 24259.7i) q^{48} -72063.5 q^{49} +(-189566. - 201476. i) q^{50} +(-19269.4 + 19269.4i) q^{51} +(788.641 - 698.002i) q^{52} +(-189013. + 189013. i) q^{53} +(-104994. - 3197.69i) q^{54} +414917. q^{55} +(69925.2 + 84026.3i) q^{56} -97831.3i q^{57} +(-1267.46 - 38.6018i) q^{58} +(-251413. - 251413. i) q^{59} +(137630. + 8391.14i) q^{60} +(197272. + 197272. i) q^{61} +(43184.7 + 45897.8i) q^{62} -135907. i q^{63} +(-47622.5 + 257782. i) q^{64} +3687.14 q^{65} +(-103744. + 97611.1i) q^{66} +(-214576. + 214576. i) q^{67} +(11038.1 - 181046. i) q^{68} +(-53300.4 + 53300.4i) q^{69} +(-11650.6 + 382537. i) q^{70} -275257. q^{71} +(250513. - 208472. i) q^{72} -106038. i q^{73} +(7840.99 - 257453. i) q^{74} +(235111. + 235111. i) q^{75} +(431568. + 487609. i) q^{76} +(-279568. - 279568. i) q^{77} +(-921.911 + 867.415i) q^{78} -637548. i q^{79} +(-722990. + 565312. i) q^{80} -337787. q^{81} +(-110742. - 117699. i) q^{82} +(467104. - 467104. i) q^{83} +(-87080.5 - 98388.3i) q^{84} +(449026. - 449026. i) q^{85} +(335100. + 10205.8i) q^{86} +1524.10 q^{87} +(86480.1 - 944160. i) q^{88} +240298. i q^{89} +(1.14048e6 + 34734.6i) q^{90} +(-2484.37 - 2484.37i) q^{91} +(30532.2 - 500785. i) q^{92} +(-53560.2 - 53560.2i) q^{93} +(-436593. - 464022. i) q^{94} +2.27972e6i q^{95} +(47780.3 - 311434. i) q^{96} +869115. q^{97} +(-419874. + 395054. i) q^{98} +(-833495. + 833495. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 2 q^{2} - 2 q^{3} + 88 q^{4} - 2 q^{5} - 512 q^{6} - 4 q^{7} + 964 q^{8}+O(q^{10}) $ 22 * q - 2 * q^2 - 2 * q^3 + 88 * q^4 - 2 * q^5 - 512 * q^6 - 4 * q^7 + 964 * q^8	\( 22 q - 2 q^{2} - 2 q^{3} + 88 q^{4} - 2 q^{5} - 512 q^{6} - 4 q^{7} + 964 q^{8} - 1124 q^{10} + 1358 q^{11} - 2348 q^{12} - 2 q^{13} + 7564 q^{14} - 7976 q^{16} - 4 q^{17} - 1874 q^{18} + 3934 q^{19} - 16564 q^{20} - 1460 q^{21} + 25252 q^{22} - 13124 q^{23} - 32592 q^{24} + 58952 q^{26} + 35776 q^{27} + 45176 q^{28} - 33202 q^{29} + 8452 q^{30} - 39672 q^{32} - 4 q^{33} - 52588 q^{34} - 112420 q^{35} - 138484 q^{36} + 3598 q^{37} - 187280 q^{38} + 254396 q^{39} + 165160 q^{40} + 353496 q^{42} - 267986 q^{43} + 380724 q^{44} + 32706 q^{45} + 248156 q^{46} - 460824 q^{48} + 168066 q^{49} - 719674 q^{50} + 301788 q^{51} - 784892 q^{52} - 221842 q^{53} - 547552 q^{54} - 232708 q^{55} + 366424 q^{56} + 1441912 q^{58} + 39150 q^{59} + 2405600 q^{60} + 326494 q^{61} + 182832 q^{62} - 318656 q^{64} + 186412 q^{65} - 3392732 q^{66} - 122786 q^{67} - 2504400 q^{68} - 543188 q^{69} - 1186816 q^{70} - 267012 q^{71} + 1748596 q^{72} + 3610396 q^{74} - 275278 q^{75} + 4245988 q^{76} + 231180 q^{77} + 3179052 q^{78} - 2898968 q^{80} - 354298 q^{81} - 5004624 q^{82} - 288322 q^{83} - 7602776 q^{84} + 340748 q^{85} - 3240476 q^{86} + 2029884 q^{87} + 3308152 q^{88} + 10273400 q^{90} + 302396 q^{91} + 7253656 q^{92} - 1173344 q^{93} + 3859056 q^{94} - 5689424 q^{96} - 4 q^{97} - 9176950 q^{98} - 271522 q^{99}+O(q^{100}) \) 22 * q - 2 * q^2 - 2 * q^3 + 88 * q^4 - 2 * q^5 - 512 * q^6 - 4 * q^7 + 964 * q^8 - 1124 * q^10 + 1358 * q^11 - 2348 * q^12 - 2 * q^13 + 7564 * q^14 - 7976 * q^16 - 4 * q^17 - 1874 * q^18 + 3934 * q^19 - 16564 * q^20 - 1460 * q^21 + 25252 * q^22 - 13124 * q^23 - 32592 * q^24 + 58952 * q^26 + 35776 * q^27 + 45176 * q^28 - 33202 * q^29 + 8452 * q^30 - 39672 * q^32 - 4 * q^33 - 52588 * q^34 - 112420 * q^35 - 138484 * q^36 + 3598 * q^37 - 187280 * q^38 + 254396 * q^39 + 165160 * q^40 + 353496 * q^42 - 267986 * q^43 + 380724 * q^44 + 32706 * q^45 + 248156 * q^46 - 460824 * q^48 + 168066 * q^49 - 719674 * q^50 + 301788 * q^51 - 784892 * q^52 - 221842 * q^53 - 547552 * q^54 - 232708 * q^55 + 366424 * q^56 + 1441912 * q^58 + 39150 * q^59 + 2405600 * q^60 + 326494 * q^61 + 182832 * q^62 - 318656 * q^64 + 186412 * q^65 - 3392732 * q^66 - 122786 * q^67 - 2504400 * q^68 - 543188 * q^69 - 1186816 * q^70 - 267012 * q^71 + 1748596 * q^72 + 3610396 * q^74 - 275278 * q^75 + 4245988 * q^76 + 231180 * q^77 + 3179052 * q^78 - 2898968 * q^80 - 354298 * q^81 - 5004624 * q^82 - 288322 * q^83 - 7602776 * q^84 + 340748 * q^85 - 3240476 * q^86 + 2029884 * q^87 + 3308152 * q^88 + 10273400 * q^90 + 302396 * q^91 + 7253656 * q^92 - 1173344 * q^93 + 3859056 * q^94 - 5689424 * q^96 - 4 * q^97 - 9176950 * q^98 - 271522 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	5.82644	−	5.48203i	0.728305	−	0.685253i
$2$	5.82644	−	5.48203i	0.728305	−	0.685253i
$3$	−6.79913	+	6.79913i	−0.251820	+	0.251820i	−0.821716	−	0.569897i	$-0.806983\pi$
$3$	−6.79913	+	6.79913i	−0.251820	+	0.251820i	0.569897	+	0.821716i	$0.306983\pi$
$4$	3.89476	−	63.8814i	0.0608556	−	0.998147i
$5$	158.437	−	158.437i	1.26750	−	1.26750i	0.320119	−	0.947377i	$-0.396277\pi$
$5$	158.437	−	158.437i	1.26750	−	1.26750i	0.947377	−	0.320119i	$-0.103723\pi$
$6$	−2.34170	+	76.8878i	−0.0108412	+	0.355962i
$7$	−213.507			−0.622471			−0.311235	−	0.950333i	$-0.600743\pi$
$7$	−213.507			−0.622471			−0.311235	+	0.950333i	$0.600743\pi$
$8$	−327.507	−	393.552i	−0.639662	−	0.768656i
$9$			636.544i			0.873174i
$10$	54.5675	−	1791.68i	0.0545675	−	1.79168i
$11$	1309.41	+	1309.41i	0.983777	+	0.983777i	0.999870	−	0.0160934i	$-0.00512291\pi$
$11$	1309.41	+	1309.41i	0.983777	+	0.983777i	−0.0160934	+	0.999870i	$0.505123\pi$
$12$	407.857	+	460.819i	0.236028	+	0.266678i
$13$	11.6360	+	11.6360i	0.00529630	+	0.00529630i	0.709750	−	0.704454i	$-0.248808\pi$
$13$	11.6360	+	11.6360i	0.00529630	+	0.00529630i	−0.704454	+	0.709750i	$0.748808\pi$
$14$	−1243.99	+	1170.45i	−0.453348	+	0.426550i
$15$			2154.47i			0.638361i
$16$	−4065.66	−	497.605i	−0.992593	−	0.121486i
$17$	2834.10			0.576857			0.288429	−	0.957501i	$-0.406867\pi$
$17$	2834.10			0.576857			0.288429	+	0.957501i	$0.406867\pi$
$18$	3489.55	+	3708.78i	0.598345	+	0.635937i
$19$	−7194.40	+	7194.40i	−1.04890	+	1.04890i	−0.0501577	+	0.998741i	$0.515972\pi$
$19$	−7194.40	+	7194.40i	−1.04890	+	1.04890i	−0.998741	+	0.0501577i	$0.984028\pi$
$20$	−9504.10	−	10738.3i	−1.18801	−	1.34228i
$21$	1451.67	−	1451.67i	0.156750	−	0.156750i
$22$	14807.4	+	450.974i	1.39063	+	0.0423530i
$23$	7839.29			0.644308			0.322154	−	0.946687i	$-0.395593\pi$
$23$	7839.29			0.644308			0.322154	+	0.946687i	$0.395593\pi$
$24$	4902.58	+	449.050i	0.354642	+	0.0324834i
$25$		−	34579.6i		−	2.21309i
$26$	131.585	+	4.00756i	0.00748662	+	0.000228013i
$27$	−9284.51	−	9284.51i	−0.471702	−	0.471702i
$28$	−831.561	+	13639.2i	−0.0378809	+	0.621317i
$29$	−112.081	−	112.081i	−0.00459554	−	0.00459554i	0.704805	−	0.709401i	$-0.251034\pi$
$29$	−112.081	−	112.081i	−0.00459554	−	0.00459554i	−0.709401	+	0.704805i	$0.751034\pi$
$30$	11810.9	+	12552.9i	0.437439	+	0.464921i
$31$			7877.51i			0.264426i	0.991221	+	0.132213i	$0.0422083\pi$
$31$			7877.51i			0.264426i	−0.991221	+	0.132213i	$0.957792\pi$
$32$	−26416.2	+	19388.8i	−0.806159	+	0.591699i
$33$	−17805.7			−0.495469
$34$	16512.7	−	15536.6i	0.420128	−	0.395293i
$35$	−33827.5	+	33827.5i	−0.788979	+	0.788979i
$36$	40663.3	+	2479.19i	0.871555	+	0.0531375i
$37$	22766.4	−	22766.4i	0.449457	−	0.449457i	−0.445717	−	0.895174i	$-0.647051\pi$
$37$	22766.4	−	22766.4i	0.449457	−	0.449457i	0.895174	+	0.445717i	$0.147051\pi$
$38$	−2477.83	+	81357.6i	−0.0451566	+	1.48268i
$39$	−158.229			−0.00266742
$40$	−114242.	−	10464.0i	−1.78504	−	0.163500i
$41$		−	20200.8i		−	0.293101i	−0.989203	−	0.146551i	$-0.953183\pi$
$41$		−	20200.8i		−	0.293101i	0.989203	−	0.146551i	$-0.0468172\pi$
$42$	499.970	−	16416.1i	0.00674833	−	0.221576i
$43$	29632.7	+	29632.7i	0.372705	+	0.372705i	0.868462	−	0.495756i	$-0.165109\pi$
$43$	29632.7	+	29632.7i	0.372705	+	0.372705i	−0.495756	+	0.868462i	$0.665109\pi$
$44$	88746.6	−	78546.9i	1.04182	−	0.922085i
$45$	100852.	+	100852.i	1.10674	+	1.10674i
$46$	45675.2	−	42975.2i	0.469252	−	0.441514i
$47$		−	79640.8i		−	0.767083i	−0.923524	−	0.383541i	$-0.874704\pi$
$47$		−	79640.8i		−	0.767083i	0.923524	−	0.383541i	$-0.125296\pi$
$48$	31026.3	−	24259.7i	0.280547	−	0.219362i
$49$	−72063.5			−0.612530
$50$	−189566.	−	201476.i	−1.51653	−	1.61181i
$51$	−19269.4	+	19269.4i	−0.145264	+	0.145264i
$52$	788.641	−	698.002i	0.00560879	−	0.00496417i
$53$	−189013.	+	189013.i	−1.26959	+	1.26959i	−0.323292	+	0.946299i	$0.604790\pi$
$53$	−189013.	+	189013.i	−1.26959	+	1.26959i	−0.946299	+	0.323292i	$0.895210\pi$
$54$	−104994.	−	3197.69i	−0.666778	−	0.0203074i
$55$	414917.			2.49387
$56$	69925.2	+	84026.3i	0.398171	+	0.478466i
$57$		−	97831.3i		−	0.528267i
$58$	−1267.46	−	38.6018i	−0.00649606	−	0.000197844i
$59$	−251413.	−	251413.i	−1.22414	−	1.22414i	−0.966145	−	0.257998i	$-0.916937\pi$
$59$	−251413.	−	251413.i	−1.22414	−	1.22414i	−0.257998	−	0.966145i	$-0.583063\pi$
$60$	137630.	+	8391.14i	0.637178	+	0.0388479i
$61$	197272.	+	197272.i	0.869113	+	0.869113i	0.992374	−	0.123261i	$-0.0393353\pi$
$61$	197272.	+	197272.i	0.869113	+	0.869113i	−0.123261	+	0.992374i	$0.539335\pi$
$62$	43184.7	+	45897.8i	0.181199	+	0.192583i
$63$		−	135907.i		−	0.543525i
$64$	−47622.5	+	257782.i	−0.181665	+	0.983360i
$65$	3687.14			0.0134261
$66$	−103744.	+	97611.1i	−0.360852	+	0.339522i
$67$	−214576.	+	214576.i	−0.713439	+	0.713439i	−0.967253	−	0.253814i	$-0.918315\pi$
$67$	−214576.	+	214576.i	−0.713439	+	0.713439i	0.253814	+	0.967253i	$0.418315\pi$
$68$	11038.1	−	181046.i	0.0351050	−	0.575788i
$69$	−53300.4	+	53300.4i	−0.162249	+	0.162249i
$70$	−11650.6	+	382537.i	−0.0339667	+	1.11527i
$71$	−275257.			−0.769066			−0.384533	−	0.923111i	$-0.625638\pi$
$71$	−275257.			−0.769066			−0.384533	+	0.923111i	$0.625638\pi$
$72$	250513.	−	208472.i	0.671171	−	0.558536i
$73$		−	106038.i		−	0.272580i	−0.990669	−	0.136290i	$-0.956482\pi$
$73$		−	106038.i		−	0.272580i	0.990669	−	0.136290i	$-0.0435179\pi$
$74$	7840.99	−	257453.i	0.0193498	−	0.635334i
$75$	235111.	+	235111.i	0.557301	+	0.557301i
$76$	431568.	+	487609.i	0.983124	+	1.11079i
$77$	−279568.	−	279568.i	−0.612373	−	0.612373i
$78$	−921.911	+	867.415i	−0.00194270	+	0.00182786i
$79$		−	637548.i		−	1.29310i	−0.762873	−	0.646549i	$-0.776212\pi$
$79$		−	637548.i		−	1.29310i	0.762873	−	0.646549i	$-0.223788\pi$
$80$	−722990.	+	565312.i	−1.41209	+	1.10413i
$81$	−337787.			−0.635606
$82$	−110742.	−	117699.i	−0.200849	−	0.213467i
$83$	467104.	−	467104.i	0.816919	−	0.816919i	−0.168741	−	0.985660i	$-0.553970\pi$
$83$	467104.	−	467104.i	0.816919	−	0.816919i	0.985660	+	0.168741i	$0.0539702\pi$
$84$	−87080.5	−	98388.3i	−0.146921	−	0.165999i
$85$	449026.	−	449026.i	0.731164	−	0.731164i
$86$	335100.	+	10205.8i	0.526841	+	0.0160455i
$87$	1524.10			0.00231449
$88$	86480.1	−	944160.i	0.126902	−	1.38547i
$89$			240298.i			0.340863i	0.985370	+	0.170432i	$0.0545162\pi$
$89$			240298.i			0.340863i	−0.985370	+	0.170432i	$0.945484\pi$
$90$	1.14048e6	+	34734.6i	1.56445	+	0.0476469i
$91$	−2484.37	−	2484.37i	−0.00329679	−	0.00329679i
$92$	30532.2	−	500785.i	0.0392098	−	0.643114i
$93$	−53560.2	−	53560.2i	−0.0665876	−	0.0665876i
$94$	−436593.	−	464022.i	−0.525646	−	0.558670i
$95$			2.27972e6i			2.65895i
$96$	47780.3	−	311434.i	0.0540052	−	0.352008i
$97$	869115.			0.952274			0.476137	−	0.879371i	$-0.342037\pi$
$97$	869115.			0.952274			0.476137	+	0.879371i	$0.342037\pi$
$98$	−419874.	+	395054.i	−0.446109	+	0.419738i
$99$	−833495.	+	833495.i	−0.859008	+	0.859008i
$100$	−2.20899e6	−	134679.i	−2.20899	−	0.134679i
$101$	81235.1	−	81235.1i	0.0788459	−	0.0788459i	−0.666584	−	0.745430i	$-0.732244\pi$
$101$	81235.1	−	81235.1i	0.0788459	−	0.0788459i	0.745430	+	0.666584i	$0.232244\pi$
$102$	−6636.60	+	217908.i	−0.00625382	+	0.205339i
$103$	−738426.			−0.675764			−0.337882	−	0.941188i	$-0.609711\pi$
$103$	−738426.			−0.675764			−0.337882	+	0.941188i	$0.609711\pi$
$104$	768.500	−	8390.22i	0.000683194	−	0.00745887i
$105$		−	459995.i		−	0.397361i
$106$	−65098.2	+	2.13745e6i	−0.0546577	+	1.79464i
$107$	498199.	+	498199.i	0.406679	+	0.406679i	0.880579	−	0.473900i	$-0.157154\pi$
$107$	498199.	+	498199.i	0.406679	+	0.406679i	−0.473900	+	0.880579i	$0.657154\pi$
$108$	−629268.	+	556946.i	−0.499534	+	0.442122i
$109$	113037.	+	113037.i	0.0872849	+	0.0872849i	0.749401	−	0.662116i	$-0.230341\pi$
$109$	113037.	+	113037.i	0.0872849	+	0.0872849i	−0.662116	+	0.749401i	$0.730341\pi$
$110$	2.41749e6	−	2.27459e6i	1.81630	−	1.70893i
$111$			309583.i			0.226364i
$112$	868049.	+	106243.i	0.617860	+	0.0756213i
$113$	623127.			0.431858			0.215929	−	0.976409i	$-0.430722\pi$
$113$	623127.			0.431858			0.215929	+	0.976409i	$0.430722\pi$
$114$	−536314.	−	570008.i	−0.361997	−	0.384739i
$115$	1.24203e6	−	1.24203e6i	0.816658	−	0.816658i
$116$	−7596.39	+	6723.33i	−0.00486668	+	0.00430735i
$117$	−7406.80	+	7406.80i	−0.00462459	+	0.00462459i
$118$	−2.84310e6	−	86589.6i	−1.73040	−	0.0527011i
$119$	−605101.			−0.359077
$120$	847896.	−	705603.i	0.490680	−	0.408335i
$121$			1.65753e6i			0.935635i
$122$	2.23085e6	+	67942.7i	1.22854	+	0.0374165i
$123$	137348.	+	137348.i	0.0738087	+	0.0738087i
$124$	503226.	+	30681.0i	0.263936	+	0.0160918i
$125$	−3.00311e6	−	3.00311e6i	−1.53759	−	1.53759i
$126$	−745045.	−	791853.i	−0.372452	−	0.395852i
$127$		−	2.20299e6i		−	1.07548i	−0.843111	−	0.537740i	$-0.819278\pi$
$127$		−	2.20299e6i		−	1.07548i	0.843111	−	0.537740i	$-0.180722\pi$
$128$	1.13570e6	+	1.76302e6i	0.541543	+	0.840673i
$129$	−402953.			−0.187709
$130$	21482.9	−	20213.0i	0.00977827	−	0.00920026i
$131$	1.79275e6	−	1.79275e6i	0.797455	−	0.797455i	−0.185238	−	0.982694i	$-0.559306\pi$
$131$	1.79275e6	−	1.79275e6i	0.797455	−	0.797455i	0.982694	+	0.185238i	$0.0593057\pi$
$132$	−69348.8	+	1.13745e6i	−0.0301521	+	0.494551i
$133$	1.53606e6	−	1.53606e6i	0.652909	−	0.652909i
$134$	−73902.4	+	2.42652e6i	−0.0307145	+	1.00849i
$135$	−2.94202e6			−1.19576
$136$	−928187.	−	1.11537e6i	−0.368993	−	0.443405i
$137$			2.77226e6i			1.07813i	0.842263	+	0.539066i	$0.181223\pi$
$137$			2.77226e6i			1.07813i	−0.842263	+	0.539066i	$0.818777\pi$
$138$	−18357.3	+	602746.i	−0.00698506	+	0.229349i
$139$	−550090.	−	550090.i	−0.204828	−	0.204828i	0.597237	−	0.802065i	$-0.296265\pi$
$139$	−550090.	−	550090.i	−0.204828	−	0.204828i	−0.802065	+	0.597237i	$0.796265\pi$
$140$	2.02920e6	+	2.29270e6i	0.739503	+	0.835531i
$141$	541489.	+	541489.i	0.193167	+	0.193167i
$142$	−1.60377e6	+	1.50897e6i	−0.560115	+	0.527005i
$143$			30472.4i			0.0104208i
$144$	316748.	−	2.58797e6i	0.106078	−	0.866706i
$145$	−35515.4			−0.0116497
$146$	−581305.	−	617825.i	−0.186786	−	0.198521i
$147$	489970.	−	489970.i	0.154247	−	0.154247i
$148$	−1.36568e6	−	1.54302e6i	−0.421272	−	0.475976i
$149$	−2.51113e6	+	2.51113e6i	−0.759121	+	0.759121i	−0.976162	−	0.217041i	$-0.930359\pi$
$149$	−2.51113e6	+	2.51113e6i	−0.759121	+	0.759121i	0.217041	+	0.976162i	$0.430359\pi$
$150$	2.65875e6	+	80974.9i	0.787777	+	0.0239926i
$151$	1.07459e6			0.312112			0.156056	−	0.987748i	$-0.450122\pi$
$151$	1.07459e6			0.312112			0.156056	+	0.987748i	$0.450122\pi$
$152$	5.18759e6	+	475156.i	1.47718	+	0.135302i
$153$			1.80403e6i			0.503696i
$154$	−3.16149e6	−	96286.4i	−0.865624	−	0.0263635i
$155$	1.24809e6	+	1.24809e6i	0.335159	+	0.335159i
$156$	−616.264	+	10107.9i	−0.000162328	+	0.00266248i
$157$	2.31833e6	+	2.31833e6i	0.599069	+	0.599069i	0.940065	−	0.340996i	$-0.110764\pi$
$157$	2.31833e6	+	2.31833e6i	0.599069	+	0.599069i	−0.340996	+	0.940065i	$0.610764\pi$
$158$	−3.49505e6	−	3.71463e6i	−0.886099	−	0.941769i
$159$		−	2.57025e6i		−	0.639416i
$160$	−1.11340e6	+	7.25721e6i	−0.271827	+	1.77178i
$161$	−1.67375e6			−0.401063
$162$	−1.96810e6	+	1.85176e6i	−0.462915	+	0.435551i
$163$	−60152.4	+	60152.4i	−0.0138896	+	0.0138896i	−0.714017	−	0.700128i	$-0.753126\pi$
$163$	−60152.4	+	60152.4i	−0.0138896	+	0.0138896i	0.700128	+	0.714017i	$0.253126\pi$
$164$	−1.29046e6	−	78677.5i	−0.292558	−	0.0178369i
$165$	−2.82108e6	+	2.82108e6i	−0.628005	+	0.628005i
$166$	160876.	−	5.28223e6i	0.0351695	−	1.15476i
$167$	8.63569e6			1.85416			0.927081	−	0.374861i	$-0.122309\pi$
$167$	8.63569e6			1.85416			0.927081	+	0.374861i	$0.122309\pi$
$168$	−1.04674e6	−	95875.6i	−0.220755	−	0.0202200i
$169$		−	4.82654e6i		−	0.999944i
$170$	154650.	−	5.07780e6i	0.0314776	−	1.03354i
$171$	−4.57955e6	−	4.57955e6i	−0.915871	−	0.915871i
$172$	2.00839e6	−	1.77756e6i	0.394696	−	0.349333i
$173$	2.87166e6	+	2.87166e6i	0.554618	+	0.554618i	0.927770	−	0.373152i	$-0.121723\pi$
$173$	2.87166e6	+	2.87166e6i	0.554618	+	0.554618i	−0.373152	+	0.927770i	$0.621723\pi$
$174$	8880.08	−	8355.16i	0.00168566	−	0.00158601i
$175$			7.38300e6i			1.37759i
$176$	−4.67204e6	−	5.97518e6i	−0.856976	−	1.09601i
$177$	3.41879e6			0.616527
$178$	1.31732e6	+	1.40008e6i	0.233578	+	0.248252i
$179$	−6.03905e6	+	6.03905e6i	−1.05296	+	1.05296i	−0.0544379	+	0.998517i	$0.517337\pi$
$179$	−6.03905e6	+	6.03905e6i	−1.05296	+	1.05296i	−0.998517	+	0.0544379i	$0.982663\pi$
$180$	6.83536e6	−	6.04978e6i	1.17204	−	1.03734i
$181$	2.29298e6	−	2.29298e6i	0.386691	−	0.386691i	−0.486814	−	0.873505i	$-0.661841\pi$
$181$	2.29298e6	−	2.29298e6i	0.386691	−	0.386691i	0.873505	+	0.486814i	$0.161841\pi$
$182$	−28094.4	−	855.643i	−0.00466021	−	0.000141931i
$183$	−2.68256e6			−0.437720
$184$	−2.56742e6	−	3.08517e6i	−0.412139	−	0.495251i
$185$		−	7.21407e6i		−	1.13937i
$186$	−605684.	−	18446.7i	−0.0941255	−	0.00286669i
$187$	3.71099e6	+	3.71099e6i	0.567499	+	0.567499i
$188$	−5.08757e6	−	310182.i	−0.765661	−	0.0466813i
$189$	1.98231e6	+	1.98231e6i	0.293621	+	0.293621i
$190$	1.24975e7	+	1.32826e7i	1.82206	+	1.93653i
$191$		−	7.15510e6i		−	1.02687i	−0.858128	−	0.513435i	$-0.828373\pi$
$191$		−	7.15510e6i		−	1.02687i	0.858128	−	0.513435i	$-0.171627\pi$
$192$	−1.42890e6	−	2.07649e6i	−0.201883	−	0.293376i
$193$	−1.93248e6			−0.268809			−0.134404	−	0.990927i	$-0.542912\pi$
$193$	−1.93248e6			−0.268809			−0.134404	+	0.990927i	$0.542912\pi$
$194$	5.06385e6	−	4.76451e6i	0.693546	−	0.652549i
$195$	−25069.3	+	25069.3i	−0.00338095	+	0.00338095i
$196$	−280670.	+	4.60352e6i	−0.0372759	+	0.611395i
$197$	3.89019e6	−	3.89019e6i	0.508830	−	0.508830i	−0.405338	−	0.914167i	$-0.632846\pi$
$197$	3.89019e6	−	3.89019e6i	0.508830	−	0.508830i	0.914167	+	0.405338i	$0.132846\pi$
$198$	−287065.	+	9.42555e6i	−0.0369815	+	1.21426i
$199$	−3.70221e6			−0.469788			−0.234894	−	0.972021i	$-0.575474\pi$
$199$	−3.70221e6			−0.469788			−0.234894	+	0.972021i	$0.575474\pi$
$200$	−1.36089e7	+	1.13251e7i	−1.70111	+	1.41563i
$201$		−	2.91786e6i		−	0.359316i
$202$	27978.3	−	918644.i	0.00339443	−	0.111453i
$203$	23930.0	+	23930.0i	0.00286059	+	0.00286059i
$204$	1.15591e6	+	1.30601e6i	0.136155	+	0.153835i
$205$	−3.20056e6	−	3.20056e6i	−0.371505	−	0.371505i
$206$	−4.30239e6	+	4.04807e6i	−0.492162	+	0.463070i
$207$			4.99005e6i			0.562593i
$208$	−41517.8	−	53098.0i	−0.00461364	−	0.00590049i
$209$	−1.88408e7			−2.06377
$210$	−2.52171e6	−	2.68013e6i	−0.272293	−	0.289400i
$211$	−6.80392e6	+	6.80392e6i	−0.724289	+	0.724289i	−0.969476	−	0.245187i	$-0.921151\pi$
$211$	−6.80392e6	+	6.80392e6i	−0.724289	+	0.724289i	0.245187	+	0.969476i	$0.421151\pi$
$212$	1.13382e7	+	1.28106e7i	1.18998	+	1.34450i
$213$	1.87151e6	−	1.87151e6i	0.193666	−	0.193666i
$214$	5.63387e6	+	171585.i	0.574865	+	0.0175081i
$215$	9.38983e6			0.944805
$216$	−613198.	+	6.69468e6i	−0.0608470	+	0.664307i
$217$		−	1.68191e6i		−	0.164597i
$218$	1.27827e6	+	38931.0i	0.123382	+	0.00375774i
$219$	720968.	+	720968.i	0.0686410	+	0.0686410i
$220$	1.61600e6	−	2.65055e7i	0.151766	−	2.48925i
$221$	32977.5	+	32977.5i	0.00305521	+	0.00305521i
$222$	1.69714e6	+	1.80377e6i	0.155117	+	0.164862i
$223$		−	1.17213e7i		−	1.05696i	−0.848944	−	0.528482i	$-0.822761\pi$
$223$		−	1.17213e7i		−	1.05696i	0.848944	−	0.528482i	$-0.177239\pi$
$224$	5.64006e6	−	4.13965e6i	0.501810	−	0.368315i
$225$	2.20114e7			1.93241
$226$	3.63061e6	−	3.41600e6i	0.314524	−	0.295932i
$227$	−5.78763e6	+	5.78763e6i	−0.494792	+	0.494792i	−0.909812	−	0.415020i	$-0.863775\pi$
$227$	−5.78763e6	+	5.78763e6i	−0.494792	+	0.494792i	0.415020	+	0.909812i	$0.363775\pi$
$228$	−6.24960e6	−	381030.i	−0.527288	−	0.0321480i
$229$	−4.21573e6	+	4.21573e6i	−0.351048	+	0.351048i	−0.860499	−	0.509451i	$-0.829848\pi$
$229$	−4.21573e6	+	4.21573e6i	−0.351048	+	0.351048i	0.509451	+	0.860499i	$0.329848\pi$
$230$	427771.	−	1.40455e7i	0.0351583	−	1.15439i
$231$	3.80164e6			0.308415
$232$	−7402.39	+	80816.7i	−0.000592799	+	0.00647198i
$233$		−	1.68651e7i		−	1.33328i	−0.745380	−	0.666640i	$-0.767732\pi$
$233$		−	1.68651e7i		−	1.33328i	0.745380	−	0.666640i	$-0.232268\pi$
$234$	−2550.98	+	83759.5i	−0.000199095	+	0.00653712i
$235$	−1.26181e7	−	1.26181e7i	−0.972275	−	0.972275i
$236$	−1.70398e7	+	1.50814e7i	−1.29637	+	1.14738i
$237$	4.33477e6	+	4.33477e6i	0.325627	+	0.325627i
$238$	−3.52559e6	+	3.31718e6i	−0.261517	+	0.246059i
$239$			8.76368e6i			0.641938i	0.947090	+	0.320969i	$0.104008\pi$
$239$			8.76368e6i			0.641938i	−0.947090	+	0.320969i	$0.895992\pi$
$240$	1.07208e6	−	8.75934e6i	0.0775518	−	0.633633i
$241$	9.78461e6			0.699025			0.349512	−	0.936932i	$-0.386347\pi$
$241$	9.78461e6			0.699025			0.349512	+	0.936932i	$0.386347\pi$
$242$	9.08665e6	+	9.65752e6i	0.641147	+	0.681427i
$243$	9.06507e6	−	9.06507e6i	0.631760	−	0.631760i
$244$	1.33703e7	−	1.18337e7i	0.920393	−	0.814612i
$245$	−1.14175e7	+	1.14175e7i	−0.776380	+	0.776380i
$246$	1.55320e6	+	47304.3i	0.104333	+	0.00317757i
$247$	−167428.			−0.0111106
$248$	3.10021e6	−	2.57994e6i	0.203253	−	0.169143i
$249$			6.35180e6i			0.411433i
$250$	−3.39605e7	−	1.03430e6i	−2.17347	−	0.0661955i
$251$	1.28892e7	+	1.28892e7i	0.815089	+	0.815089i	0.985392	−	0.170303i	$-0.0544745\pi$
$251$	1.28892e7	+	1.28892e7i	0.815089	+	0.815089i	−0.170303	+	0.985392i	$0.554475\pi$
$252$	−8.68192e6	−	529325.i	−0.542518	−	0.0330766i
$253$	1.02648e7	+	1.02648e7i	0.633855	+	0.633855i
$254$	−1.20769e7	−	1.28356e7i	−0.736976	−	0.783277i
$255$			6.10598e6i			0.368243i
$256$	1.62820e7	+	4.04619e6i	0.970482	+	0.241172i
$257$	−2.14023e7			−1.26084			−0.630422	−	0.776252i	$-0.717118\pi$
$257$	−2.14023e7			−1.26084			−0.630422	+	0.776252i	$0.717118\pi$
$258$	−2.34778e6	+	2.20900e6i	−0.136709	+	0.128628i
$259$	−4.86079e6	+	4.86079e6i	−0.279774	+	0.279774i
$260$	14360.5	−	235539.i	0.000817053	−	0.0134012i
$261$	71344.1	−	71344.1i	0.00401270	−	0.00401270i
$262$	617444.	−	2.02733e7i	0.0343316	−	1.12725i
$263$	−785705.			−0.0431909			−0.0215955	−	0.999767i	$-0.506875\pi$
$263$	−785705.			−0.0431909			−0.0215955	+	0.999767i	$0.506875\pi$
$264$	5.83148e6	+	7.00746e6i	0.316933	+	0.380845i
$265$			5.98933e7i			3.21840i
$266$	529036.	−	1.73705e7i	0.0281086	−	0.922925i
$267$	−1.63382e6	−	1.63382e6i	−0.0858360	−	0.0858360i
$268$	1.28717e7	+	1.45431e7i	0.668700	+	0.755533i
$269$	−1.24683e7	−	1.24683e7i	−0.640546	−	0.640546i	0.310143	−	0.950690i	$-0.399623\pi$
$269$	−1.24683e7	−	1.24683e7i	−0.640546	−	0.640546i	−0.950690	+	0.310143i	$0.899623\pi$
$270$	−1.71415e7	+	1.61282e7i	−0.870879	+	0.819399i
$271$		−	1.55043e7i		−	0.779012i	−0.921024	−	0.389506i	$-0.872646\pi$
$271$		−	1.55043e7i		−	0.779012i	0.921024	−	0.389506i	$-0.127354\pi$
$272$	−1.15225e7	−	1.41026e6i	−0.572584	−	0.0700799i
$273$	33783.1			0.00166039
$274$	1.51976e7	+	1.61524e7i	0.738794	+	0.785209i
$275$	4.52788e7	−	4.52788e7i	2.17719	−	2.17719i
$276$	3.19731e6	+	3.61250e6i	0.152075	+	0.171823i
$277$	1.24335e7	−	1.24335e7i	0.584998	−	0.584998i	−0.351275	−	0.936272i	$-0.614252\pi$
$277$	1.24335e7	−	1.24335e7i	0.584998	−	0.584998i	0.936272	+	0.351275i	$0.114252\pi$
$278$	−6.22068e6	−	189457.i	−0.289537	−	0.00881814i
$279$	−5.01438e6			−0.230890
$280$	2.43916e7	+	2.23414e6i	1.11113	+	0.101774i
$281$			8.37508e6i			0.377459i	0.982029	+	0.188729i	$0.0604369\pi$
$281$			8.37508e6i			0.377459i	−0.982029	+	0.188729i	$0.939563\pi$
$282$	6.12341e6	+	186495.i	0.273052	+	0.00831609i
$283$	6.71417e6	+	6.71417e6i	0.296233	+	0.296233i	0.839536	−	0.543304i	$-0.182827\pi$
$283$	6.71417e6	+	6.71417e6i	0.296233	+	0.296233i	−0.543304	+	0.839536i	$0.682827\pi$
$284$	−1.07206e6	+	1.75838e7i	−0.0468020	+	0.767641i
$285$	−1.55001e7	−	1.55001e7i	−0.669576	−	0.669576i
$286$	167051.	+	177546.i	0.00714086	+	0.00758948i
$287$			4.31303e6i			0.182447i
$288$	−1.23418e7	−	1.68151e7i	−0.516656	−	0.703917i
$289$	−1.61055e7			−0.667236
$290$	−206928.	+	194696.i	−0.00848450	+	0.00798296i
$291$	−5.90923e6	+	5.90923e6i	−0.239801	+	0.239801i
$292$	−6.77387e6	−	412994.i	−0.272075	−	0.0165880i
$293$	5.01259e6	−	5.01259e6i	0.199278	−	0.199278i	−0.600412	−	0.799691i	$-0.704997\pi$
$293$	5.01259e6	−	5.01259e6i	0.199278	−	0.199278i	0.799691	+	0.600412i	$0.204997\pi$
$294$	168751.	−	5.54080e6i	0.00664056	−	0.218037i
$295$	−7.96664e7			−3.10320
$296$	−1.64159e7	−	1.50361e6i	−0.632979	−	0.0579776i
$297$		−	2.43144e7i		−	0.928099i
$298$	−864863.	+	2.83971e7i	−0.0326812	+	1.07306i
$299$	91217.8	+	91217.8i	0.00341245	+	0.00341245i
$300$	1.59349e7	−	1.41035e7i	0.590183	−	0.522353i
$301$	−6.32680e6	−	6.32680e6i	−0.231998	−	0.231998i
$302$	6.26101e6	−	5.89091e6i	0.227313	−	0.213876i
$303$			1.10466e6i			0.0397099i
$304$	3.28300e7	−	2.56700e7i	1.16856	−	0.913704i
$305$	6.25104e7			2.20320
$306$	9.88973e6	+	1.05111e7i	0.345160	+	0.366845i
$307$	5.38397e6	−	5.38397e6i	0.186075	−	0.186075i	−0.607922	−	0.793997i	$-0.707997\pi$
$307$	5.38397e6	−	5.38397e6i	0.186075	−	0.186075i	0.793997	+	0.607922i	$0.207997\pi$
$308$	−1.89481e7	+	1.67704e7i	−0.648504	+	0.573971i
$309$	5.02066e6	−	5.02066e6i	0.170171	−	0.170171i
$310$	1.41140e7	+	429856.i	0.473766	+	0.0144290i
$311$	4.70346e7			1.56364			0.781819	−	0.623506i	$-0.214292\pi$
$311$	4.70346e7			1.56364			0.781819	+	0.623506i	$0.214292\pi$
$312$	51821.1	+	62271.3i	0.00170625	+	0.00205033i
$313$		−	1.98492e7i		−	0.647306i	−0.946176	−	0.323653i	$-0.895089\pi$
$313$		−	1.98492e7i		−	0.647306i	0.946176	−	0.323653i	$-0.104911\pi$
$314$	2.62168e7	+	798460.i	0.846819	+	0.0257908i
$315$	−2.15327e7	−	2.15327e7i	−0.688916	−	0.688916i
$316$	−4.07274e7	−	2.48310e6i	−1.29070	−	0.0786923i
$317$	−2.53957e7	−	2.53957e7i	−0.797229	−	0.797229i	0.185429	−	0.982658i	$-0.440633\pi$
$317$	−2.53957e7	−	2.53957e7i	−0.797229	−	0.797229i	−0.982658	+	0.185429i	$0.940633\pi$
$318$	−1.40902e7	−	1.49754e7i	−0.438162	−	0.465690i
$319$		−	293518.i		−	0.00904197i
$320$	3.32970e7	+	4.83874e7i	1.01615	+	1.47667i
$321$	−6.77465e6			−0.204820
$322$	−9.75199e6	+	9.17553e6i	−0.292096	+	0.274830i
$323$	−2.03896e7	+	2.03896e7i	−0.605065	+	0.605065i
$324$	−1.31560e6	+	2.15783e7i	−0.0386802	+	0.634428i
$325$	402367.	−	402367.i	0.0117212	−	0.0117212i
$326$	−20717.2	+	680232.i	−0.000597968	+	0.0196338i
$327$	−1.53710e6			−0.0439601
$328$	−7.95009e6	+	6.61592e6i	−0.225294	+	0.187486i
$329$			1.70039e7i			0.477487i
$330$	−971610.	+	3.19021e7i	−0.0270365	+	0.887722i
$331$	2.88736e7	+	2.88736e7i	0.796189	+	0.796189i	0.982492	−	0.186303i	$-0.0596506\pi$
$331$	2.88736e7	+	2.88736e7i	0.796189	+	0.796189i	−0.186303	+	0.982492i	$0.559651\pi$
$332$	−2.80200e7	−	3.16585e7i	−0.765691	−	0.865119i
$333$	1.44918e7	+	1.44918e7i	0.392454	+	0.392454i
$334$	5.03153e7	−	4.73411e7i	1.35040	−	1.27057i
$335$			6.79936e7i			1.80856i
$336$	−6.62434e6	+	5.17963e6i	−0.174632	+	0.136546i
$337$	−5.14079e7			−1.34320			−0.671599	−	0.740915i	$-0.734392\pi$
$337$	−5.14079e7			−1.34320			−0.671599	+	0.740915i	$0.734392\pi$
$338$	−2.64592e7	−	2.81215e7i	−0.685215	−	0.728264i
$339$	−4.23672e6	+	4.23672e6i	−0.108750	+	0.108750i
$340$	−2.69356e7	−	3.04333e7i	−0.685314	−	0.774305i
$341$	−1.03149e7	+	1.03149e7i	−0.260136	+	0.260136i
$342$	−5.17877e7	−	1.57725e6i	−1.29464	−	0.0394295i
$343$	4.05051e7			1.00375
$344$	1.95710e6	−	2.13669e7i	0.0480770	−	0.524888i
$345$			1.68895e7i			0.411301i
$346$	3.24740e7	+	989030.i	0.783985	+	0.0238771i
$347$	8.11640e6	+	8.11640e6i	0.194256	+	0.194256i	0.797532	−	0.603276i	$-0.206138\pi$
$347$	8.11640e6	+	8.11640e6i	0.194256	+	0.194256i	−0.603276	+	0.797532i	$0.706138\pi$
$348$	5936.01	−	97361.7i	0.000140850	−	0.00231020i
$349$	2.31407e7	+	2.31407e7i	0.544378	+	0.544378i	0.924809	−	0.380431i	$-0.124224\pi$
$349$	2.31407e7	+	2.31407e7i	0.544378	+	0.544378i	−0.380431	+	0.924809i	$0.624224\pi$
$350$	4.04738e7	+	4.30166e7i	0.943996	+	1.00330i
$351$		−	216069.i		−	0.00499655i
$352$	−5.99774e7	−	9.20175e6i	−1.37518	−	0.210980i
$353$	7.13339e7			1.62171			0.810853	−	0.585250i	$-0.199004\pi$
$353$	7.13339e7			1.62171			0.810853	+	0.585250i	$0.199004\pi$
$354$	1.99193e7	−	1.87419e7i	0.449020	−	0.422477i
$355$	−4.36110e7	+	4.36110e7i	−0.974789	+	0.974789i
$356$	1.53506e7	+	935903.i	0.340231	+	0.0207434i
$357$	4.11416e6	−	4.11416e6i	0.0904226	−	0.0904226i
$358$	−2.07992e6	+	6.82924e7i	−0.0453312	+	1.48841i
$359$	−7.03447e7			−1.52037			−0.760183	−	0.649709i	$-0.774891\pi$
$359$	−7.03447e7			−1.52037			−0.760183	+	0.649709i	$0.774891\pi$
$360$	6.66080e6	−	7.27203e7i	0.142764	−	1.55865i
$361$		−	5.64729e7i		−	1.20038i
$362$	789727.	−	2.59301e7i	0.0166476	−	0.546610i
$363$	−1.12698e7	−	1.12698e7i	−0.235611	−	0.235611i
$364$	−168381.	+	149029.i	−0.00349131	+	0.00309005i
$365$	−1.68004e7	−	1.68004e7i	−0.345494	−	0.345494i
$366$	−1.56298e7	+	1.47059e7i	−0.318793	+	0.299949i
$367$		−	3.10050e7i		−	0.627239i	−0.949549	−	0.313620i	$-0.898458\pi$
$367$		−	3.10050e7i		−	0.627239i	0.949549	−	0.313620i	$-0.101542\pi$
$368$	−3.18719e7	−	3.90088e6i	−0.639536	−	0.0782742i
$369$	1.28587e7			0.255928
$370$	−3.95477e7	−	4.20323e7i	−0.780758	−	0.829809i
$371$	4.03557e7	−	4.03557e7i	0.790284	−	0.790284i
$372$	−3.63011e6	+	3.21290e6i	−0.0705164	+	0.0624120i
$373$	6.29288e7	−	6.29288e7i	1.21262	−	1.21262i	0.242452	−	0.970163i	$-0.422048\pi$
$373$	6.29288e7	−	6.29288e7i	1.21262	−	1.21262i	0.970163	−	0.242452i	$-0.0779517\pi$
$374$	4.19656e7	+	1.27811e6i	0.802193	+	0.0244316i
$375$	4.08371e7			0.774392
$376$	−3.13428e7	+	2.60829e7i	−0.589623	+	0.490674i
$377$		−	2608.33i		−	4.86787e-5i
$378$	2.24169e7	+	682731.i	0.415050	+	0.0126408i
$379$	5.96910e7	+	5.96910e7i	1.09646	+	1.09646i	0.994822	+	0.101634i	$0.0324072\pi$
$379$	5.96910e7	+	5.96910e7i	1.09646	+	1.09646i	0.101634	+	0.994822i	$0.467593\pi$
$380$	1.45632e8	+	8.87896e6i	2.65402	+	0.161812i
$381$	1.49784e7	+	1.49784e7i	0.270827	+	0.270827i
$382$	−3.92245e7	−	4.16888e7i	−0.703667	−	0.747875i
$383$		−	5.76504e7i		−	1.02614i	−0.858347	−	0.513069i	$-0.828508\pi$
$383$		−	5.76504e7i		−	1.02614i	0.858347	−	0.513069i	$-0.171492\pi$
$384$	−1.97088e7	−	4.26524e6i	−0.348069	−	0.0753268i
$385$	−8.85879e7			−1.55236
$386$	−1.12595e7	+	1.05939e7i	−0.195775	+	0.184202i
$387$	−1.88625e7	+	1.88625e7i	−0.325436	+	0.325436i
$388$	3.38500e6	−	5.55203e7i	0.0579513	−	0.950509i
$389$	−6.44525e7	+	6.44525e7i	−1.09494	+	1.09494i	−0.0999496	+	0.994992i	$0.531868\pi$
$389$	−6.44525e7	+	6.44525e7i	−1.09494	+	1.09494i	−0.994992	+	0.0999496i	$0.968132\pi$
$390$	−8634.16	+	283496.i	−0.000145555	+	0.00477917i
$391$	2.22173e7			0.371674
$392$	2.36013e7	+	2.83608e7i	0.391812	+	0.470825i
$393$			2.43783e7i			0.401630i
$394$	1.33983e6	−	4.39921e7i	0.0219058	−	0.719260i
$395$	−1.01011e8	−	1.01011e8i	−1.63900	−	1.63900i
$396$	4.99985e7	+	5.64911e7i	0.805141	+	0.909692i
$397$	3.32033e7	+	3.32033e7i	0.530652	+	0.530652i	0.920766	−	0.390114i	$-0.127565\pi$
$397$	3.32033e7	+	3.32033e7i	0.530652	+	0.530652i	−0.390114	+	0.920766i	$0.627565\pi$
$398$	−2.15707e7	+	2.02956e7i	−0.342149	+	0.321924i
$399$			2.08877e7i			0.328831i
$400$	−1.72070e7	+	1.40589e8i	−0.268859	+	2.19670i
$401$	−6.57507e7			−1.01969			−0.509844	−	0.860267i	$-0.670297\pi$
$401$	−6.57507e7			−1.01969			−0.509844	+	0.860267i	$0.670297\pi$
$402$	−1.59958e7	−	1.70007e7i	−0.246222	−	0.261691i
$403$	−91662.4	+	91662.4i	−0.00140048	+	0.00140048i
$404$	−4.87302e6	−	5.50580e6i	−0.0739016	−	0.0834980i
$405$	−5.35180e7	+	5.35180e7i	−0.805628	+	0.805628i
$406$	270612.	+	8241.77i	0.00404361	+	0.000123152i
$407$	5.96209e7			0.884332
$408$	1.38944e7	+	1.27265e6i	0.204578	+	0.0187383i
$409$		−	3.16009e7i		−	0.461881i	−0.972968	−	0.230940i	$-0.925820\pi$
$409$		−	3.16009e7i		−	0.461881i	0.972968	−	0.230940i	$-0.0741802\pi$
$410$	−3.61934e7	−	1.10231e6i	−0.525144	−	0.0159938i
$411$	−1.88490e7	−	1.88490e7i	−0.271495	−	0.271495i
$412$	−2.87599e6	+	4.71717e7i	−0.0411241	+	0.674512i
$413$	5.36787e7	+	5.36787e7i	0.761994	+	0.761994i
$414$	2.73556e7	+	2.90742e7i	0.385518	+	0.409739i
$415$		−	1.48013e8i		−	2.07088i
$416$	−532986.	−	81770.7i	−0.00740347	−	0.00113584i
$417$	7.48028e6			0.103160
$418$	−1.09775e8	+	1.03286e8i	−1.50305	+	1.41420i
$419$	−3.02706e7	+	3.02706e7i	−0.411509	+	0.411509i	−0.882264	−	0.470755i	$-0.843982\pi$
$419$	−3.02706e7	+	3.02706e7i	−0.411509	+	0.411509i	0.470755	+	0.882264i	$0.343982\pi$
$420$	−2.93851e7	−	1.79157e6i	−0.396625	−	0.0241817i
$421$	1.29835e7	−	1.29835e7i	0.173999	−	0.173999i	−0.614735	−	0.788734i	$-0.710737\pi$
$421$	1.29835e7	−	1.29835e7i	0.173999	−	0.173999i	0.788734	+	0.614735i	$0.210737\pi$
$422$	−2.34335e6	+	7.69419e7i	−0.0311816	+	1.02382i
$423$	5.06949e7			0.669797
$424$	1.36289e8	+	1.24834e7i	1.78799	+	0.163770i
$425$		−	9.80020e7i		−	1.27664i
$426$	644569.	−	2.11639e7i	0.00833760	−	0.273758i
$427$	−4.21191e7	−	4.21191e7i	−0.540998	−	0.540998i
$428$	3.37660e7	−	2.98853e7i	0.430674	−	0.381177i
$429$	−207186.	−	207186.i	−0.00262415	−	0.00262415i
$430$	5.47093e7	−	5.14753e7i	0.688106	−	0.647431i
$431$			1.28691e8i			1.60737i	0.595054	+	0.803686i	$0.297131\pi$
$431$			1.28691e8i			1.60737i	−0.595054	+	0.803686i	$0.702869\pi$
$432$	3.31277e7	+	4.23677e7i	0.410903	+	0.525513i
$433$	4.42637e7			0.545236			0.272618	−	0.962122i	$-0.412110\pi$
$433$	4.42637e7			0.545236			0.272618	+	0.962122i	$0.412110\pi$
$434$	−9.22026e6	−	9.79953e6i	−0.112791	−	0.119877i
$435$	241474.	−	241474.i	0.00293361	−	0.00293361i
$436$	7.66118e6	−	6.78068e6i	0.0924349	−	0.0818114i
$437$	−5.63990e7	+	5.63990e7i	−0.675814	+	0.675814i
$438$	8.15304e6	+	248309.i	0.0970281	+	0.00295509i
$439$	2.93985e7			0.347481			0.173741	−	0.984791i	$-0.444415\pi$
$439$	2.93985e7			0.347481			0.173741	+	0.984791i	$0.444415\pi$
$440$	−1.35888e8	−	1.63292e8i	−1.59523	−	1.91693i
$441$		−	4.58716e7i		−	0.534845i
$442$	372925.	+	11357.8i	0.00431871	+	0.000131531i
$443$	7.00084e6	+	7.00084e6i	0.0805265	+	0.0805265i	0.746223	−	0.665696i	$-0.231865\pi$
$443$	7.00084e6	+	7.00084e6i	0.0805265	+	0.0805265i	−0.665696	+	0.746223i	$0.731865\pi$
$444$	1.97766e7	+	1.20575e6i	0.225945	+	0.0137756i
$445$	3.80721e7	+	3.80721e7i	0.432043	+	0.432043i
$446$	−6.42563e7	−	6.82933e7i	−0.724288	−	0.769792i
$447$		−	3.41471e7i		−	0.382323i
$448$	1.01678e7	−	5.50384e7i	0.113081	−	0.612113i
$449$	1.34157e7			0.148209			0.0741043	−	0.997250i	$-0.476390\pi$
$449$	1.34157e7			0.148209			0.0741043	+	0.997250i	$0.476390\pi$
$450$	1.28248e8	−	1.20667e8i	1.40739	−	1.32419i
$451$	2.64511e7	−	2.64511e7i	0.288347	−	0.288347i
$452$	2.42693e6	−	3.98062e7i	0.0262810	−	0.431058i
$453$	−7.30626e6	+	7.30626e6i	−0.0785960	+	0.0785960i
$454$	−1.99332e6	+	6.54492e7i	−0.0213015	+	0.699418i
$455$	−787231.			−0.00835734
$456$	−3.85017e7	+	3.20404e7i	−0.406056	+	0.337912i
$457$			1.61973e8i			1.69705i	0.529156	+	0.848524i	$0.322509\pi$
$457$			1.61973e8i			1.69705i	−0.529156	+	0.848524i	$0.677491\pi$
$458$	−1.45194e6	+	4.76734e7i	−0.0151131	+	0.496227i
$459$	−2.63132e7	−	2.63132e7i	−0.272105	−	0.272105i
$460$	−7.45054e7	−	8.41803e7i	−0.765446	−	0.864842i
$461$	−1.16319e7	−	1.16319e7i	−0.118727	−	0.118727i	0.645247	−	0.763974i	$-0.276754\pi$
$461$	−1.16319e7	−	1.16319e7i	−0.118727	−	0.118727i	−0.763974	+	0.645247i	$0.776754\pi$
$462$	2.21500e7	−	2.08407e7i	0.224620	−	0.211342i
$463$		−	4.02011e7i		−	0.405037i	−0.979278	−	0.202519i	$-0.935087\pi$
$463$		−	4.02011e7i		−	0.405037i	0.979278	−	0.202519i	$-0.0649127\pi$
$464$	399910.	+	511453.i	0.00400321	+	0.00511979i
$465$	−1.69718e7			−0.168799
$466$	−9.24550e7	−	9.82635e7i	−0.913634	−	0.971034i
$467$	−3.28960e7	+	3.28960e7i	−0.322992	+	0.322992i	−0.849914	−	0.526922i	$-0.823346\pi$
$467$	−3.28960e7	+	3.28960e7i	−0.322992	+	0.322992i	0.526922	+	0.849914i	$0.323346\pi$
$468$	444309.	+	502004.i	0.00433458	+	0.00489745i
$469$	4.58136e7	−	4.58136e7i	0.444095	−	0.444095i
$470$	−1.42691e8	−	4.34580e6i	−1.37437	−	0.0418578i
$471$	−3.15253e7			−0.301715
$472$	−1.66047e7	+	1.81284e8i	−0.157908	+	1.72398i
$473$			7.76025e7i			0.733318i
$474$	4.90196e7	+	1.49294e6i	0.460293	+	0.0140187i
$475$	2.48779e8	+	2.48779e8i	2.32131	+	2.32131i
$476$	−2.35673e6	+	3.86547e7i	−0.0218518	+	0.358411i
$477$	−1.20315e8	−	1.20315e8i	−1.10857	−	1.10857i
$478$	4.80427e7	+	5.10610e7i	0.439890	+	0.467526i
$479$		−	4.78638e7i		−	0.435512i	−0.976003	−	0.217756i	$-0.930126\pi$
$479$		−	4.78638e7i		−	0.435512i	0.976003	−	0.217756i	$-0.0698738\pi$
$480$	−4.17726e7	−	5.69129e7i	−0.377718	−	0.514620i
$481$	529817.			0.00476092
$482$	5.70094e7	−	5.36395e7i	0.509103	−	0.479009i
$483$	1.13800e7	−	1.13800e7i	0.100996	−	0.100996i
$484$	1.05886e8	+	6.45570e6i	0.933901	+	0.0569387i
$485$	1.37700e8	−	1.37700e8i	1.20700	−	1.20700i
$486$	3.12211e6	−	1.02512e8i	0.0271982	−	0.893030i
$487$	−6.83549e7			−0.591810			−0.295905	−	0.955217i	$-0.595621\pi$
$487$	−6.83549e7			−0.591810			−0.295905	+	0.955217i	$0.595621\pi$
$488$	1.30289e7	−	1.42245e8i	0.112111	−	1.22399i
$489$		−	817969.i		−	0.00699536i
$490$	−3.93233e6	+	1.29115e8i	−0.0334242	+	1.09746i
$491$	−4.09317e7	−	4.09317e7i	−0.345793	−	0.345793i	0.512747	−	0.858540i	$-0.328628\pi$
$491$	−4.09317e7	−	4.09317e7i	−0.345793	−	0.345793i	−0.858540	+	0.512747i	$0.828628\pi$
$492$	9.30893e6	−	8.23906e6i	0.0781636	−	0.0691803i
$493$	−317647.	−	317647.i	−0.00265097	−	0.00265097i
$494$	−975506.	+	917842.i	−0.00809188	+	0.00761355i
$495$			2.64113e8i			2.17758i
$496$	3.91989e6	−	3.20273e7i	0.0321240	−	0.262467i
$497$	5.87695e7			0.478721
$498$	3.48208e7	+	3.70084e7i	0.281936	+	0.299648i
$499$	3.26564e7	−	3.26564e7i	0.262825	−	0.262825i	−0.563376	−	0.826201i	$-0.690498\pi$
$499$	3.26564e7	−	3.26564e7i	0.262825	−	0.262825i	0.826201	+	0.563376i	$0.190498\pi$
$500$	−2.03539e8	+	1.80146e8i	−1.62831	+	1.44117i
$501$	−5.87152e7	+	5.87152e7i	−0.466915	+	0.466915i
$502$	1.45757e8	+	4.43919e6i	1.15218	+	0.0350907i
$503$	−2.43128e8			−1.91043			−0.955216	−	0.295908i	$-0.904378\pi$
$503$	−2.43128e8			−1.91043			−0.955216	+	0.295908i	$0.904378\pi$
$504$	−5.34864e7	+	4.45104e7i	−0.417784	+	0.347672i
$505$		−	2.57413e7i		−	0.199874i
$506$	1.16079e8	+	3.53532e6i	0.895991	+	0.0272884i
$507$	3.28163e7	+	3.28163e7i	0.251806	+	0.251806i
$508$	−1.40730e8	−	8.58013e6i	−1.07349	−	0.0654490i
$509$	−9.12226e6	−	9.12226e6i	−0.0691750	−	0.0691750i	0.671673	−	0.740848i	$-0.265576\pi$
$509$	−9.12226e6	−	9.12226e6i	−0.0691750	−	0.0691750i	−0.740848	+	0.671673i	$0.765576\pi$
$510$	3.34731e7	+	3.55761e7i	0.252340	+	0.268193i
$511$			2.26400e7i			0.169673i
$512$	1.17047e8	−	6.56834e7i	0.872071	−	0.489380i
$513$	1.33593e8			0.989536
$514$	−1.24699e8	+	1.17328e8i	−0.918279	+	0.863998i
$515$	−1.16994e8	+	1.16994e8i	−0.856529	+	0.856529i
$516$	−1.56941e6	+	2.57412e7i	−0.0114232	+	0.187361i
$517$	1.04282e8	−	1.04282e8i	0.754639	−	0.754639i
$518$	−1.67411e6	+	5.49681e7i	−0.0120447	+	0.395477i
$519$	−3.90495e7			−0.279328
$520$	−1.20756e6	−	1.45108e6i	−0.00858815	−	0.0103200i
$521$		−	1.20851e8i		−	0.854548i	−0.904122	−	0.427274i	$-0.859474\pi$
$521$		−	1.20851e8i		−	0.854548i	0.904122	−	0.427274i	$-0.140526\pi$
$522$	24571.7	−	806793.i	0.000172752	−	0.00567219i
$523$	−1.56314e8	−	1.56314e8i	−1.09268	−	1.09268i	−0.995242	−	0.0974367i	$-0.968936\pi$
$523$	−1.56314e8	−	1.56314e8i	−1.09268	−	1.09268i	−0.0974367	−	0.995242i	$-0.531064\pi$
$524$	−1.07541e8	−	1.21506e8i	−0.747448	−	0.844507i
$525$	−5.01980e7	−	5.01980e7i	−0.346903	−	0.346903i
$526$	−4.57786e6	+	4.30726e6i	−0.0314562	+	0.0295967i
$527$			2.23256e7i			0.152536i
$528$	7.23918e7	+	8.86020e6i	0.491799	+	0.0601924i
$529$	−8.65814e7			−0.584867
$530$	3.28337e8	+	3.48965e8i	2.20542	+	2.34398i
$531$	1.60036e8	−	1.60036e8i	1.06889	−	1.06889i
$532$	−9.21429e7	−	1.04108e8i	−0.611966	−	0.691432i
$533$	235056.	−	235056.i	0.00155235	−	0.00155235i
$534$	−1.84760e7	−	562705.i	−0.121334	−	0.00369536i
$535$	1.57866e8			1.03093
$536$	1.54722e8	+	1.41717e7i	1.00475	+	0.0920297i
$537$		−	8.21207e7i		−	0.530310i
$538$	−1.40997e8	−	4.29422e6i	−0.905450	−	0.0275764i
$539$	−9.43605e7	−	9.43605e7i	−0.602593	−	0.602593i
$540$	−1.14585e7	+	1.87940e8i	−0.0727688	+	1.19354i
$541$	−1.95480e8	−	1.95480e8i	−1.23455	−	1.23455i	−0.962196	−	0.272359i	$-0.912196\pi$
$541$	−1.95480e8	−	1.95480e8i	−1.23455	−	1.23455i	−0.272359	−	0.962196i	$-0.587804\pi$
$542$	−8.49950e7	−	9.03348e7i	−0.533821	−	0.567358i
$543$			3.11805e7i			0.194753i
$544$	−7.48662e7	+	5.49498e7i	−0.465038	+	0.341326i
$545$	3.58183e7			0.221267
$546$	196835.	−	185200.i	0.00120927	−	0.00113779i
$547$	1.05737e8	−	1.05737e8i	0.646050	−	0.646050i	−0.305986	−	0.952036i	$-0.598986\pi$
$547$	1.05737e8	−	1.05737e8i	0.646050	−	0.646050i	0.952036	+	0.305986i	$0.0989862\pi$
$548$	1.77096e8	+	1.07973e7i	1.07613	+	0.0656104i
$549$	−1.25572e8	+	1.25572e8i	−0.758887	+	0.758887i
$550$	1.55945e7	−	5.12033e8i	0.0937311	−	3.07759i
$551$	1.61270e6			0.00964051
$552$	3.84327e7	+	3.52024e6i	0.228499	+	0.0209293i
$553$			1.36121e8i			0.804916i
$554$	4.28224e6	−	1.40604e8i	0.0251850	−	0.826929i
$555$	4.90494e7	+	4.90494e7i	0.286916	+	0.286916i
$556$	−3.72830e7	+	3.29981e7i	−0.216913	+	0.191984i
$557$	9.55244e7	+	9.55244e7i	0.552776	+	0.552776i	0.927241	−	0.374465i	$-0.122174\pi$
$557$	9.55244e7	+	9.55244e7i	0.552776	+	0.552776i	−0.374465	+	0.927241i	$0.622174\pi$
$558$	−2.92160e7	+	2.74890e7i	−0.168158	+	0.158218i
$559$			689610.i			0.00394792i
$560$	1.54364e8	−	1.20698e8i	0.878985	−	0.687286i
$561$	−5.04630e7			−0.285815
$562$	4.59124e7	+	4.87969e7i	0.258655	+	0.274905i
$563$	7.31393e7	−	7.31393e7i	0.409851	−	0.409851i	−0.471836	−	0.881686i	$-0.656408\pi$
$563$	7.31393e7	−	7.31393e7i	0.409851	−	0.409851i	0.881686	+	0.471836i	$0.156408\pi$
$564$	3.67000e7	−	3.24821e7i	0.204564	−	0.181053i
$565$	9.87264e7	−	9.87264e7i	0.547379	−	0.547379i
$566$	7.59270e7	+	2.31244e6i	0.418742	+	0.0127532i
$567$	7.21201e7			0.395646
$568$	9.01487e7	+	1.08328e8i	0.491942	+	0.591148i
$569$			2.55687e8i			1.38794i	0.720002	+	0.693972i	$0.244141\pi$
$569$			2.55687e8i			1.38794i	−0.720002	+	0.693972i	$0.755859\pi$
$570$	−1.75282e8	−	5.33841e6i	−0.946485	−	0.0288262i
$571$	1.59086e8	+	1.59086e8i	0.854524	+	0.854524i	0.990686	−	0.136163i	$-0.0434770\pi$
$571$	1.59086e8	+	1.59086e8i	0.854524	+	0.854524i	−0.136163	+	0.990686i	$0.543477\pi$
$572$	1.94662e6	+	118683.i	0.0104014	+	0.000634162i
$573$	4.86485e7	+	4.86485e7i	0.258586	+	0.258586i
$574$	2.36442e7	+	2.51296e7i	0.125022	+	0.132877i
$575$		−	2.71080e8i		−	1.42591i
$576$	−1.64089e8	−	3.03138e7i	−0.858644	−	0.158625i
$577$	−1.52809e8			−0.795464			−0.397732	−	0.917502i	$-0.630203\pi$
$577$	−1.52809e8			−0.795464			−0.397732	+	0.917502i	$0.630203\pi$
$578$	−9.38374e7	+	8.82905e7i	−0.485951	+	0.457226i
$579$	1.31392e7	−	1.31392e7i	0.0676913	−	0.0676913i
$580$	−138324.	+	2.26877e6i	−0.000708947	+	0.0116281i
$581$	−9.97302e7	+	9.97302e7i	−0.508508	+	0.508508i
$582$	−2.03520e6	+	6.68243e7i	−0.0103238	+	0.338973i
$583$	−4.94990e8			−2.49799
$584$	−4.17316e7	+	3.47283e7i	−0.209520	+	0.174359i
$585$			2.34702e6i			0.0117233i
$586$	1.72639e6	−	5.66847e7i	0.00857920	−	0.281691i
$587$	1.42595e8	+	1.42595e8i	0.705002	+	0.705002i	0.965480	−	0.260478i	$-0.0838802\pi$
$587$	1.42595e8	+	1.42595e8i	0.705002	+	0.705002i	−0.260478	+	0.965480i	$0.583880\pi$
$588$	−2.93916e7	−	3.32083e7i	−0.144574	−	0.163348i
$589$	−5.66739e7	−	5.66739e7i	−0.277356	−	0.277356i
$590$	−4.64171e8	+	4.36733e8i	−2.26007	+	2.12648i
$591$			5.28999e7i			0.256267i
$592$	−1.03889e8	+	8.12317e7i	−0.500731	+	0.391526i
$593$	3.24485e8			1.55607			0.778037	−	0.628219i	$-0.216216\pi$
$593$	3.24485e8			1.55607			0.778037	+	0.628219i	$0.216216\pi$
$594$	−1.33292e8	−	1.41666e8i	−0.635983	−	0.675939i
$595$	−9.58705e7	+	9.58705e7i	−0.455128	+	0.455128i
$596$	1.50634e8	+	1.70195e8i	0.711517	+	0.803911i
$597$	2.51718e7	−	2.51718e7i	0.118302	−	0.118302i
$598$	1.03153e6	+	31416.4i	0.00482369	+	0.000146911i
$599$	1.79608e8			0.835689			0.417844	−	0.908519i	$-0.362786\pi$
$599$	1.79608e8			0.835689			0.417844	+	0.908519i	$0.362786\pi$
$600$	1.55280e7	−	1.69529e8i	0.0718888	−	0.784857i
$601$			2.78315e8i			1.28207i	0.767510	+	0.641037i	$0.221495\pi$
$601$			2.78315e8i			1.28207i	−0.767510	+	0.641037i	$0.778505\pi$
$602$	−7.15464e7	−	2.17902e6i	−0.327943	−	0.00998785i
$603$	−1.36587e8	−	1.36587e8i	−0.622956	−	0.622956i
$604$	4.18526e6	−	6.86461e7i	0.0189938	−	0.311534i
$605$	2.62615e8	+	2.62615e8i	1.18591	+	1.18591i
$606$	6.05575e6	+	6.43621e6i	0.0272114	+	0.0289209i
$607$			1.38550e8i			0.619499i	0.950818	+	0.309750i	$0.100245\pi$
$607$			1.38550e8i			0.619499i	−0.950818	+	0.309750i	$0.899755\pi$
$608$	5.05580e7	−	3.29540e8i	0.224947	−	1.46621i
$609$	−325407.			−0.00144070
$610$	3.64213e8	−	3.42684e8i	1.60460	−	1.50975i
$611$	926698.	−	926698.i	0.00406270	−	0.00406270i
$612$	1.15244e8	+	7.02626e6i	0.502763	+	0.0306528i
$613$	−6.90262e7	+	6.90262e7i	−0.299663	+	0.299663i	−0.840882	−	0.541219i	$-0.817963\pi$
$613$	−6.90262e7	+	6.90262e7i	−0.299663	+	0.299663i	0.541219	+	0.840882i	$0.317963\pi$
$614$	1.85430e6	−	6.08845e7i	0.00801078	−	0.263028i
$615$	4.35221e7			0.187105
$616$	−1.84642e7	+	2.01585e8i	−0.0789928	+	0.862415i
$617$			1.22553e8i			0.521758i	0.965372	+	0.260879i	$0.0840124\pi$
$617$			1.22553e8i			0.521758i	−0.965372	+	0.260879i	$0.915988\pi$
$618$	1.72917e6	−	5.67759e7i	0.00732609	−	0.240546i
$619$	9.63080e7	+	9.63080e7i	0.406060	+	0.406060i	0.880362	−	0.474302i	$-0.157300\pi$
$619$	9.63080e7	+	9.63080e7i	0.406060	+	0.406060i	−0.474302	+	0.880362i	$0.657300\pi$
$620$	8.45907e7	−	7.48686e7i	0.354934	−	0.314141i
$621$	−7.27840e7	−	7.27840e7i	−0.303921	−	0.303921i
$622$	2.74044e8	−	2.57845e8i	1.13880	−	1.07149i
$623$		−	5.13054e7i		−	0.212177i
$624$	643305.	+	78735.6i	0.00264767	+	0.000324054i
$625$	−4.11301e8			−1.68469
$626$	−1.08814e8	−	1.15650e8i	−0.443568	−	0.471436i
$627$	1.28101e8	−	1.28101e8i	0.519697	−	0.519697i
$628$	1.57128e8	−	1.39069e8i	0.634415	−	0.561502i
$629$	6.45221e7	−	6.45221e7i	0.259273	−	0.259273i
$630$	−2.43501e8	−	7.41609e6i	−0.973823	−	0.0296588i
$631$	4.49697e8			1.78991			0.894957	−	0.446153i	$-0.147206\pi$
$631$	4.49697e8			1.78991			0.894957	+	0.446153i	$0.147206\pi$
$632$	−2.50908e8	+	2.08801e8i	−0.993948	+	0.827145i
$633$		−	9.25215e7i		−	0.364780i
$634$	−2.87187e8	−	8.74658e6i	−1.12693	−	0.0343218i
$635$	−3.49036e8	−	3.49036e8i	−1.36317	−	1.36317i
$636$	−1.64191e8	−	1.00105e7i	−0.638231	−	0.0389121i
$637$	−838529.	−	838529.i	−0.00324414	−	0.00324414i
$638$	−1.60907e6	−	1.71017e6i	−0.00619604	−	0.00658531i
$639$		−	1.75213e8i		−	0.671528i
$640$	4.59264e8	+	9.93908e7i	1.75195	+	0.379146i
$641$	1.60286e8			0.608586			0.304293	−	0.952579i	$-0.401580\pi$
$641$	1.60286e8			0.608586			0.304293	+	0.952579i	$0.401580\pi$
$642$	−3.94721e7	+	3.71388e7i	−0.149171	+	0.140353i
$643$	−2.80798e8	+	2.80798e8i	−1.05624	+	1.05624i	−0.0579139	+	0.998322i	$0.518445\pi$
$643$	−2.80798e8	+	2.80798e8i	−1.05624	+	1.05624i	−0.998322	+	0.0579139i	$0.981555\pi$
$644$	−6.51885e6	+	1.06921e8i	−0.0244069	+	0.400320i
$645$	−6.38427e7	+	6.38427e7i	−0.237921	+	0.237921i
$646$	−7.02242e6	+	2.30575e8i	−0.0260489	+	0.855294i
$647$	2.66079e8			0.982422			0.491211	−	0.871041i	$-0.336554\pi$
$647$	2.66079e8			0.982422			0.491211	+	0.871041i	$0.336554\pi$
$648$	1.10628e8	+	1.32937e8i	0.406573	+	0.488563i
$649$		−	6.58405e8i		−	2.40857i
$650$	138580.	−	4.55015e6i	0.000504614	−	0.0165686i
$651$	1.14355e7	+	1.14355e7i	0.0414489	+	0.0414489i
$652$	3.60834e6	+	4.07690e6i	0.0130186	+	0.0147091i
$653$	−4.39341e6	−	4.39341e6i	−0.0157784	−	0.0157784i	0.699174	−	0.714952i	$-0.253551\pi$
$653$	−4.39341e6	−	4.39341e6i	−0.0157784	−	0.0157784i	−0.714952	+	0.699174i	$0.753551\pi$
$654$	−8.95582e6	+	8.42643e6i	−0.0320164	+	0.0301238i
$655$		−	5.68077e8i		−	2.02154i
$656$	−1.00521e7	+	8.21298e7i	−0.0356076	+	0.290931i
$657$	6.74980e7			0.238010
$658$	9.32159e7	+	9.90723e7i	0.327199	+	0.347756i
$659$	9.60616e7	−	9.60616e7i	0.335655	−	0.335655i	−0.519074	−	0.854729i	$-0.673723\pi$
$659$	9.60616e7	−	9.60616e7i	0.335655	−	0.335655i	0.854729	+	0.519074i	$0.173723\pi$
$660$	1.69227e8	+	1.91202e8i	0.588623	+	0.665059i
$661$	−3.32344e8	+	3.32344e8i	−1.15076	+	1.15076i	−0.164354	+	0.986401i	$0.552554\pi$
$661$	−3.32344e8	+	3.32344e8i	−1.15076	+	1.15076i	−0.986401	+	0.164354i	$0.947446\pi$
$662$	3.26516e8	+	9.94437e6i	1.12546	+	0.0342771i
$663$	−448437.			−0.00153872
$664$	−3.36809e8	−	3.08500e7i	−1.15048	−	0.105378i
$665$		−	4.86737e8i		−	1.65512i
$666$	1.63880e8	+	4.99113e6i	0.554757	+	0.0168957i
$667$	−878632.	−	878632.i	−0.00296094	−	0.00296094i
$668$	3.36340e7	−	5.51660e8i	0.112836	−	1.85073i
$669$	7.96945e7	+	7.96945e7i	0.266164	+	0.266164i
$670$	3.72742e8	+	3.96160e8i	1.23932	+	1.31718i
$671$			5.16619e8i			1.71003i
$672$	−1.02015e7	+	6.64936e7i	−0.0336166	+	0.219115i
$673$	−2.59342e8			−0.850801			−0.425400	−	0.905005i	$-0.639867\pi$
$673$	−2.59342e8			−0.850801			−0.425400	+	0.905005i	$0.639867\pi$
$674$	−2.99525e8	+	2.81819e8i	−0.978257	+	0.920430i
$675$	−3.21055e8	+	3.21055e8i	−1.04392	+	1.04392i
$676$	−3.08326e8	−	1.87982e7i	−0.998091	−	0.0608522i
$677$	7.93397e7	−	7.93397e7i	0.255697	−	0.255697i	−0.567605	−	0.823301i	$-0.692130\pi$
$677$	7.93397e7	−	7.93397e7i	0.255697	−	0.255697i	0.823301	+	0.567605i	$0.192130\pi$
$678$	−1.45917e6	+	4.79108e7i	−0.00468186	+	0.153725i
$679$	−1.85563e8			−0.592763
$680$	−3.23774e8	−	2.96560e7i	−1.02971	−	0.0943162i
$681$		−	7.87017e7i		−	0.249197i
$682$	−3.55256e6	+	1.16645e8i	−0.0111992	+	0.367717i
$683$	−9.83571e7	−	9.83571e7i	−0.308705	−	0.308705i	0.535702	−	0.844407i	$-0.320047\pi$
$683$	−9.83571e7	−	9.83571e7i	−0.308705	−	0.308705i	−0.844407	+	0.535702i	$0.820047\pi$
$684$	−3.10384e8	+	2.74712e8i	−0.969909	+	0.858438i
$685$	4.39228e8	+	4.39228e8i	1.36653	+	1.36653i
$686$	2.36000e8	−	2.22050e8i	0.731038	−	0.687825i
$687$		−	5.73266e7i		−	0.176802i
$688$	−1.05731e8	−	1.35222e8i	−0.324666	−	0.415223i
$689$	−4.39870e6			−0.0134483
$690$	9.25888e7	+	9.84057e7i	0.281845	+	0.299553i
$691$	−2.67048e8	+	2.67048e8i	−0.809386	+	0.809386i	−0.984541	−	0.175155i	$-0.943957\pi$
$691$	−2.67048e8	+	2.67048e8i	−0.809386	+	0.809386i	0.175155	+	0.984541i	$0.443957\pi$
$692$	1.94630e8	−	1.72261e8i	0.587342	−	0.519839i
$693$	1.77957e8	−	1.77957e8i	0.534708	−	0.534708i
$694$	9.17840e7	+	2.79538e6i	0.274592	+	0.00836300i
$695$	−1.74309e8			−0.519238
$696$	−499154.	−	599813.i	−0.00148049	−	0.00177905i
$697$		−	5.72512e7i		−	0.169078i
$698$	2.61686e8	+	7.96992e6i	0.769510	+	0.0234362i
$699$	1.14668e8	+	1.14668e8i	0.335746	+	0.335746i
$700$	4.71636e8	+	2.87550e7i	1.37503	+	0.0838339i
$701$	−3.87585e8	−	3.87585e8i	−1.12516	−	1.12516i	−0.990954	−	0.134202i	$-0.957153\pi$
$701$	−3.87585e8	−	3.87585e8i	−1.12516	−	1.12516i	−0.134202	−	0.990954i	$-0.542847\pi$
$702$	−1.18449e6	−	1.25891e6i	−0.00342390	−	0.00363901i
$703$			3.27581e8i			0.942871i
$704$	−3.99899e8	+	2.75184e8i	−1.14613	+	0.788689i
$705$	1.71584e8			0.489676
$706$	4.15623e8	−	3.91054e8i	1.18110	−	1.11128i
$707$	−1.73443e7	+	1.73443e7i	−0.0490793	+	0.0490793i
$708$	1.33154e7	−	2.18397e8i	0.0375192	−	0.615384i
$709$	3.44165e8	−	3.44165e8i	0.965667	−	0.965667i	−0.0337624	−	0.999430i	$-0.510749\pi$
$709$	3.44165e8	−	3.44165e8i	0.965667	−	0.965667i	0.999430	+	0.0337624i	$0.0107490\pi$
$710$	−1.50201e7	+	4.93173e8i	−0.0419660	+	1.37792i
$711$	4.05827e8			1.12910
$712$	9.45697e7	−	7.86992e7i	0.262007	−	0.218037i
$713$			6.17541e7i			0.170372i
$714$	1.41696e6	−	4.65249e7i	0.00389282	−	0.127818i
$715$	4.82796e6	+	4.82796e6i	0.0132083	+	0.0132083i
$716$	3.62262e8	+	4.09304e8i	0.986925	+	1.11508i
$717$	−5.95854e7	−	5.95854e7i	−0.161653	−	0.161653i
$718$	−4.09859e8	+	3.85632e8i	−1.10729	+	1.04184i
$719$			2.26972e8i			0.610641i	0.952250	+	0.305321i	$0.0987637\pi$
$719$			2.26972e8i			0.610641i	−0.952250	+	0.305321i	$0.901236\pi$
$720$	−3.59846e8	−	4.60215e8i	−0.964093	−	1.23300i
$721$	1.57659e8			0.420644
$722$	−3.09586e8	−	3.29036e8i	−0.822563	−	0.874241i
$723$	−6.65269e7	+	6.65269e7i	−0.176028	+	0.176028i
$724$	−1.37548e8	−	1.55409e8i	−0.362442	−	0.409507i
$725$	−3.87570e6	+	3.87570e6i	−0.0101704	+	0.0101704i
$726$	−1.27444e8	−	3.88144e6i	−0.333050	−	0.0101434i
$727$	−1.42830e8			−0.371719			−0.185860	−	0.982576i	$-0.559507\pi$
$727$	−1.42830e8			−0.371719			−0.185860	+	0.982576i	$0.559507\pi$
$728$	−164081.	+	1.79137e6i	−0.000425268	+	0.00464293i
$729$		−	1.22978e8i		−	0.317427i
$730$	−1.89987e8	−	5.78624e6i	−0.488376	−	0.0148740i
$731$	8.39820e7	+	8.39820e7i	0.214998	+	0.214998i
$732$	−1.04479e7	+	1.71366e8i	−0.0266377	+	0.436908i
$733$	2.54471e8	+	2.54471e8i	0.646139	+	0.646139i	0.952058	−	0.305919i	$-0.0989636\pi$
$733$	2.54471e8	+	2.54471e8i	0.646139	+	0.646139i	−0.305919	+	0.952058i	$0.598964\pi$
$734$	−1.69970e8	−	1.80649e8i	−0.429818	−	0.456821i
$735$		−	1.55259e8i		−	0.391015i
$736$	−2.07084e8	+	1.51994e8i	−0.519414	+	0.381236i
$737$	−5.61935e8			−1.40373
$738$	7.49205e7	−	7.04918e7i	0.186394	−	0.175376i
$739$	2.61656e8	−	2.61656e8i	0.648333	−	0.648333i	−0.304257	−	0.952590i	$-0.598408\pi$
$739$	2.61656e8	−	2.61656e8i	0.648333	−	0.648333i	0.952590	+	0.304257i	$0.0984081\pi$
$740$	−4.60845e8	−	2.80971e7i	−1.13726	−	0.0693372i
$741$	1.13836e6	−	1.13836e6i	0.00279786	−	0.00279786i
$742$	1.38989e7	−	4.56361e8i	0.0340228	−	1.11711i
$743$	−1.90483e8			−0.464397			−0.232198	−	0.972668i	$-0.574592\pi$
$743$	−1.90483e8			−0.464397			−0.232198	+	0.972668i	$0.574592\pi$
$744$	−3.53740e6	+	3.86201e7i	−0.00858944	+	0.0937766i
$745$			7.95713e8i			1.92437i
$746$	2.16734e7	−	7.11628e8i	0.0522048	−	1.71410i
$747$	2.97332e8	+	2.97332e8i	0.713312	+	0.713312i
$748$	2.51517e8	−	2.22610e8i	0.600982	−	0.531911i
$749$	−1.06369e8	−	1.06369e8i	−0.253146	−	0.253146i
$750$	2.37935e8	−	2.23870e8i	0.563993	−	0.530654i
$751$		−	1.15685e8i		−	0.273122i	−0.990632	−	0.136561i	$-0.956395\pi$
$751$		−	1.15685e8i		−	0.273122i	0.990632	−	0.136561i	$-0.0436050\pi$
$752$	−3.96297e7	+	3.23793e8i	−0.0931896	+	0.761401i
$753$	−1.75271e8			−0.410511
$754$	−14298.9	−	15197.3i	−3.33572e−5	−	3.54529e-5i
$755$	1.70254e8	−	1.70254e8i	0.395601	−	0.395601i
$756$	1.34354e8	−	1.18912e8i	0.310945	−	0.275208i
$757$	7.45004e7	−	7.45004e7i	0.171740	−	0.171740i	−0.616004	−	0.787743i	$-0.711249\pi$
$757$	7.45004e7	−	7.45004e7i	0.171740	−	0.171740i	0.787743	+	0.616004i	$0.211249\pi$
$758$	6.75014e8	+	2.05583e7i	1.54990	+	0.0472040i
$759$	−1.39584e8			−0.319235
$760$	8.97188e8	−	7.46623e8i	2.04382	−	1.70083i
$761$		−	2.60939e8i		−	0.592086i	−0.955175	−	0.296043i	$-0.904333\pi$
$761$		−	2.60939e8i		−	0.592086i	0.955175	−	0.296043i	$-0.0956672\pi$
$762$	1.69383e8	+	5.15874e6i	0.382829	+	0.0116595i
$763$	−2.41341e7	−	2.41341e7i	−0.0543323	−	0.0543323i
$764$	−4.57078e8	−	2.78674e7i	−1.02497	−	0.0624909i
$765$	2.85825e8	+	2.85825e8i	0.638433	+	0.638433i
$766$	−3.16041e8	−	3.35897e8i	−0.703165	−	0.747342i
$767$		−	5.85088e6i		−	0.0129669i
$768$	−1.38214e8	+	8.31928e7i	−0.305118	+	0.183655i
$769$	5.34401e8			1.17514			0.587568	−	0.809175i	$-0.300085\pi$
$769$	5.34401e8			1.17514			0.587568	+	0.809175i	$0.300085\pi$
$770$	−5.16152e8	+	4.85641e8i	−1.13059	+	1.06376i
$771$	1.45517e8	−	1.45517e8i	0.317506	−	0.317506i
$772$	−7.52655e6	+	1.23449e8i	−0.0163585	+	0.268310i
$773$	−3.55344e8	+	3.55344e8i	−0.769325	+	0.769325i	−0.977988	−	0.208662i	$-0.933089\pi$
$773$	−3.55344e8	+	3.55344e8i	−0.769325	+	0.769325i	0.208662	+	0.977988i	$0.433089\pi$
$774$	−6.49645e6	+	2.13306e8i	−0.0140105	+	0.460023i
$775$	2.72401e8			0.585199
$776$	−2.84641e8	−	3.42042e8i	−0.609134	−	0.731972i
$777$		−	6.60983e7i		−	0.140905i
$778$	−2.21982e7	+	7.28859e8i	−0.0471388	+	1.54776i
$779$	1.45333e8	+	1.45333e8i	0.307434	+	0.307434i
$780$	1.50382e6	+	1.69910e6i	0.00316893	+	0.00358043i
$781$	−3.60424e8	−	3.60424e8i	−0.756590	−	0.756590i
$782$	1.29448e8	−	1.21796e8i	0.270692	−	0.254691i
$783$			2.08123e6i			0.00433545i
$784$	2.92986e8	+	3.58592e7i	0.607993	+	0.0744137i
$785$	7.34619e8			1.51864
$786$	1.33643e8	+	1.42039e8i	0.275218	+	0.292509i
$787$	−3.27339e8	+	3.27339e8i	−0.671542	+	0.671542i	−0.958071	−	0.286529i	$-0.907498\pi$
$787$	−3.27339e8	+	3.27339e8i	−0.671542	+	0.671542i	0.286529	+	0.958071i	$0.407498\pi$
$788$	−2.33359e8	−	2.63662e8i	−0.476921	−	0.538852i
$789$	5.34212e6	−	5.34212e6i	0.0108763	−	0.0108763i
$790$	−1.14228e9	−	3.47894e7i	−2.31682	−	0.0705611i
$791$	−1.33042e8			−0.268819
$792$	6.00999e8	+	5.50484e7i	1.20976	+	0.110807i
$793$			4.59090e6i			0.00920616i
$794$	3.75478e8	+	1.14356e7i	0.750108	+	0.0228453i
$795$	−4.07223e8	−	4.07223e8i	−0.810458	−	0.810458i
$796$	−1.44192e7	+	2.36502e8i	−0.0285893	+	0.468917i
$797$	−2.74877e8	−	2.74877e8i	−0.542955	−	0.542955i	0.381439	−	0.924394i	$-0.375429\pi$
$797$	−2.74877e8	−	2.74877e8i	−0.542955	−	0.542955i	−0.924394	+	0.381439i	$0.875429\pi$
$798$	1.14507e8	+	1.21701e8i	0.225332	+	0.239489i
$799$		−	2.25710e8i		−	0.442497i
$800$	6.70457e8	+	9.13462e8i	1.30949	+	1.78410i
$801$	−1.52960e8			−0.297633
$802$	−3.83093e8	+	3.60447e8i	−0.742644	+	0.698745i
$803$	1.38847e8	−	1.38847e8i	0.268158	−	0.268158i
$804$	−1.86397e8	−	1.13644e7i	−0.358650	−	0.0218664i
$805$	−2.65184e8	+	2.65184e8i	−0.508346	+	0.508346i
$806$	−31569.6	+	1.03656e6i	−6.02925e−5	+	0.00197966i
$807$	1.69547e8			0.322604
$808$	−5.85753e7	−	5.36519e6i	−0.111040	−	0.0101707i
$809$			7.49473e8i			1.41550i	0.706462	+	0.707751i	$0.250290\pi$
$809$			7.49473e8i			1.41550i	−0.706462	+	0.707751i	$0.749710\pi$
$810$	−1.84322e7	+	6.05206e8i	−0.0346834	+	1.13880i
$811$	−5.97328e8	−	5.97328e8i	−1.11983	−	1.11983i	−0.991767	−	0.128058i	$-0.959125\pi$
$811$	−5.97328e8	−	5.97328e8i	−1.11983	−	1.11983i	−0.128058	−	0.991767i	$-0.540875\pi$
$812$	1.62189e6	−	1.43548e6i	0.00302937	−	0.00268120i
$813$	1.05416e8	+	1.05416e8i	0.196171	+	0.196171i
$814$	3.47377e8	−	3.26843e8i	0.644063	−	0.605991i
$815$			1.90607e7i			0.0352101i
$816$	8.79315e7	−	6.87544e7i	0.161836	−	0.126541i
$817$	−4.26379e8			−0.781861
$818$	−1.73237e8	−	1.84121e8i	−0.316505	−	0.336390i
$819$	1.58141e6	−	1.58141e6i	0.00287867	−	0.00287867i
$820$	−2.16922e8	+	1.91991e8i	−0.393425	+	0.348208i
$821$	−3.66612e8	+	3.66612e8i	−0.662488	+	0.662488i	−0.955966	−	0.293478i	$-0.905187\pi$
$821$	−3.66612e8	+	3.66612e8i	−0.662488	+	0.662488i	0.293478	+	0.955966i	$0.405187\pi$
$822$	−2.13153e8	−	6.49179e6i	−0.383774	−	0.0116882i
$823$	−5.77764e8			−1.03646			−0.518228	−	0.855243i	$-0.673408\pi$
$823$	−5.77764e8			−1.03646			−0.518228	+	0.855243i	$0.673408\pi$
$824$	2.41840e8	+	2.90609e8i	0.432261	+	0.519431i
$825$			6.15713e8i			1.09652i
$826$	6.07023e8	+	1.84875e7i	1.07712	+	0.0328049i
$827$	3.54236e8	+	3.54236e8i	0.626290	+	0.626290i	0.947133	−	0.320842i	$-0.103966\pi$
$827$	3.54236e8	+	3.54236e8i	0.626290	+	0.626290i	−0.320842	+	0.947133i	$0.603966\pi$
$828$	3.18771e8	+	1.94351e7i	0.561550	+	0.0342369i
$829$	−8.00560e7	−	8.00560e7i	−0.140517	−	0.140517i	0.633349	−	0.773866i	$-0.281680\pi$
$829$	−8.00560e7	−	8.00560e7i	−0.140517	−	0.140517i	−0.773866	+	0.633349i	$0.781680\pi$
$830$	−8.11412e8	−	8.62389e8i	−1.41908	−	1.50824i
$831$			1.69074e8i			0.294628i
$832$	−3.55368e6	+	2.44541e6i	−0.00617032	+	0.00424602i
$833$	−2.04235e8			−0.353342
$834$	4.35834e7	−	4.10071e7i	0.0751316	−	0.0706904i
$835$	1.36821e9	−	1.36821e9i	2.35014	−	2.35014i
$836$	−7.33804e7	+	1.20358e9i	−0.125592	+	2.05994i
$837$	7.31388e7	−	7.31388e7i	0.124730	−	0.124730i
$838$	−1.04255e7	+	3.42314e8i	−0.0177160	+	0.581691i
$839$	6.76738e8			1.14587			0.572934	−	0.819602i	$-0.305805\pi$
$839$	6.76738e8			1.14587			0.572934	+	0.819602i	$0.305805\pi$
$840$	−1.81032e8	+	1.50652e8i	−0.305434	+	0.254177i
$841$		−	5.94798e8i		−	0.999958i
$842$	4.47167e6	−	1.46824e8i	0.00749089	−	0.245957i
$843$	−5.69433e7	−	5.69433e7i	−0.0950516	−	0.0950516i
$844$	4.08144e8	+	4.61143e8i	0.678869	+	0.767023i
$845$	−7.64702e8	−	7.64702e8i	−1.26743	−	1.26743i
$846$	2.95371e8	−	2.77911e8i	0.487816	−	0.458980i
$847$		−	3.53896e8i		−	0.582405i
$848$	8.62517e8	−	6.74409e8i	1.41442	−	1.10595i
$849$	−9.13011e7			−0.149195
$850$	−5.37249e8	−	5.71002e8i	−0.874821	−	0.929782i
$851$	1.78472e8	−	1.78472e8i	0.289589	−	0.289589i
$852$	−1.12266e8	−	1.26844e8i	−0.181521	−	0.205093i
$853$	3.99632e8	−	3.99632e8i	0.643892	−	0.643892i	−0.307618	−	0.951510i	$-0.599532\pi$
$853$	3.99632e8	−	3.99632e8i	0.643892	−	0.643892i	0.951510	+	0.307618i	$0.0995317\pi$
$854$	−4.76302e8	−	1.45063e7i	−0.764731	−	0.0232907i
$855$	−1.45114e9			−2.32173
$856$	3.29037e7	−	3.59231e8i	0.0524594	−	0.572734i
$857$			4.22100e8i			0.670615i	0.942109	+	0.335307i	$0.108840\pi$
$857$			4.22100e8i			0.670615i	−0.942109	+	0.335307i	$0.891160\pi$
$858$	−2.34296e6	−	71357.2i	−0.00370939	−	0.000112973i
$859$	3.35359e8	+	3.35359e8i	0.529090	+	0.529090i	0.920301	−	0.391211i	$-0.127944\pi$
$859$	3.35359e8	+	3.35359e8i	0.529090	+	0.529090i	−0.391211	+	0.920301i	$0.627944\pi$
$860$	3.65711e7	−	5.99835e8i	0.0574967	−	0.943054i
$861$	−2.93249e7	−	2.93249e7i	−0.0459438	−	0.0459438i
$862$	7.05487e8	+	7.49810e8i	1.10146	+	1.17066i
$863$		−	7.06487e8i		−	1.09919i	−0.835432	−	0.549593i	$-0.814783\pi$
$863$		−	7.06487e8i		−	1.09919i	0.835432	−	0.549593i	$-0.185217\pi$
$864$	4.25277e8	+	6.52461e7i	0.659373	+	0.101161i
$865$	9.09953e8			1.40595
$866$	2.57900e8	−	2.42655e8i	0.397098	−	0.373625i
$867$	1.09503e8	−	1.09503e8i	0.168023	−	0.168023i
$868$	−1.07443e8	−	6.55063e6i	−0.164292	−	0.0100167i
$869$	8.34809e8	−	8.34809e8i	1.27212	−	1.27212i
$870$	83166.3	−	2.73070e6i	0.000126296	−	0.00414683i
$871$	−4.99360e6			−0.00755717
$872$	7.46552e6	−	8.15060e7i	0.0112593	−	0.122925i
$873$			5.53230e8i			0.831501i
$874$	−1.94244e7	+	6.37786e8i	−0.0290947	+	0.955302i
$875$	6.41186e8	+	6.41186e8i	0.957106	+	0.957106i
$876$	4.88644e7	−	4.32484e7i	0.0726910	−	0.0643366i
$877$	1.18842e8	+	1.18842e8i	0.176185	+	0.176185i	0.789691	−	0.613505i	$-0.210241\pi$
$877$	1.18842e8	+	1.18842e8i	0.176185	+	0.176185i	−0.613505	+	0.789691i	$0.710241\pi$
$878$	1.71288e8	−	1.61163e8i	0.253072	−	0.238113i
$879$			6.81626e7i			0.100364i
$880$	−1.68691e9	−	2.06465e8i	−2.47540	−	0.302969i
$881$	−8.18267e8			−1.19665			−0.598326	−	0.801253i	$-0.704167\pi$
$881$	−8.18267e8			−1.19665			−0.598326	+	0.801253i	$0.704167\pi$
$882$	−2.51469e8	−	2.67268e8i	−0.366504	−	0.389530i
$883$	−8.74250e8	+	8.74250e8i	−1.26985	+	1.26985i	−0.323690	+	0.946163i	$0.604924\pi$
$883$	−8.74250e8	+	8.74250e8i	−1.26985	+	1.26985i	−0.946163	+	0.323690i	$0.895076\pi$
$884$	2.23509e6	−	1.97821e6i	0.00323547	−	0.00286362i
$885$	5.41662e8	−	5.41662e8i	0.781446	−	0.781446i
$886$	7.91687e7	+	2.41117e6i	0.113829	+	0.00346678i
$887$	−9.08568e8			−1.30193			−0.650963	−	0.759109i	$-0.725635\pi$
$887$	−9.08568e8			−1.30193			−0.650963	+	0.759109i	$0.725635\pi$
$888$	1.21837e8	−	1.01391e8i	0.173997	−	0.144797i
$889$			4.70356e8i			0.669454i
$890$	4.30537e8	+	1.31124e7i	0.610717	+	0.0186000i
$891$	−4.42301e8	−	4.42301e8i	−0.625294	−	0.625294i
$892$	−7.48771e8	−	4.56516e7i	−1.05501	−	0.0643222i
$893$	5.72968e8	+	5.72968e8i	0.804593	+	0.804593i
$894$	−1.87195e8	−	1.98956e8i	−0.261988	−	0.278448i
$895$			1.91362e9i			2.66923i
$896$	−2.42480e8	−	3.76418e8i	−0.337095	−	0.523294i
$897$	−1.24040e6			−0.00171864
$898$	7.81656e7	−	7.35451e7i	0.107941	−	0.101560i
$899$	882915.	−	882915.i	0.00121518	−	0.00121518i
$900$	8.57292e7	−	1.40612e9i	0.117598	−	1.92883i
$901$	−5.35681e8	+	5.35681e8i	−0.732373	+	0.732373i
$902$	9.11007e6	−	2.99122e8i	0.0124137	−	0.407595i
$903$	8.60335e7			0.116843
$904$	−2.04078e8	−	2.45233e8i	−0.276243	−	0.331951i
$905$		−	7.26585e8i		−	0.980259i
$906$	−2.51636e6	+	8.26226e7i	−0.00338367	+	0.111100i
$907$	4.33430e8	+	4.33430e8i	0.580895	+	0.580895i	0.935149	−	0.354254i	$-0.115265\pi$
$907$	4.33430e8	+	4.33430e8i	0.580895	+	0.580895i	−0.354254	+	0.935149i	$0.615265\pi$
$908$	3.47180e8	+	3.92263e8i	0.463764	+	0.523986i
$909$	5.17097e7	+	5.17097e7i	0.0688462	+	0.0688462i
$910$	−4.58675e6	+	4.31562e6i	−0.00608669	+	0.00572690i
$911$			8.08779e8i			1.06973i	0.844937	+	0.534865i	$0.179638\pi$
$911$			8.08779e8i			1.06973i	−0.844937	+	0.534865i	$0.820362\pi$
$912$	−4.86814e7	+	3.97749e8i	−0.0641769	+	0.524354i
$913$	1.22326e9			1.60733
$914$	8.87941e8	+	9.43726e8i	1.16291	+	1.23597i
$915$	−4.25017e8	+	4.25017e8i	−0.554808	+	0.554808i
$916$	2.52887e8	+	2.85726e8i	0.329034	+	0.371760i
$917$	−3.82766e8	+	3.82766e8i	−0.496393	+	0.496393i
$918$	−2.97562e8	−	9.06257e6i	−0.384636	−	0.0117145i
$919$	9.98417e8			1.28637			0.643184	−	0.765711i	$-0.277613\pi$
$919$	9.98417e8			1.28637			0.643184	+	0.765711i	$0.277613\pi$
$920$	−8.95580e8	−	8.20305e7i	−1.15011	−	0.105344i
$921$			7.32127e7i			0.0937146i
$922$	−1.31539e8	−	4.00617e6i	−0.167827	−	0.00511136i
$923$	−3.20288e6	−	3.20288e6i	−0.00407320	−	0.00407320i
$924$	1.48065e7	−	2.42854e8i	0.0187688	−	0.307843i
$925$	−7.87251e8	−	7.87251e8i	−0.994691	−	0.994691i
$926$	−2.20384e8	−	2.34229e8i	−0.277553	−	0.294991i
$927$		−	4.70040e8i		−	0.590060i
$928$	5.13385e6	+	787636.i	0.00642391	+	0.000985557i
$929$	−1.15058e9			−1.43506			−0.717531	−	0.696527i	$-0.754728\pi$
$929$	−1.15058e9			−1.43506			−0.717531	+	0.696527i	$0.754728\pi$
$930$	−9.88854e7	+	9.30401e7i	−0.122937	+	0.115670i
$931$	5.18454e8	−	5.18454e8i	0.642482	−	0.642482i
$932$	−1.07737e9	−	6.56856e7i	−1.33081	−	0.0811376i
$933$	−3.19794e8	+	3.19794e8i	−0.393755	+	0.393755i
$934$	−1.13297e7	+	3.72003e8i	−0.0139053	+	0.456568i
$935$	1.17592e9			1.43861
$936$	5.34074e6	+	489184.i	0.00651289	+	0.000596547i
$937$		−	1.04563e9i		−	1.27104i	−0.772086	−	0.635518i	$-0.780787\pi$
$937$		−	1.04563e9i		−	1.27104i	0.772086	−	0.635518i	$-0.219213\pi$
$938$	1.57787e7	−	5.18081e8i	0.0191189	−	0.627754i
$939$	1.34957e8	+	1.34957e8i	0.163004	+	0.163004i
$940$	−8.55203e8	+	7.56915e8i	−1.02964	+	0.911304i
$941$	9.38599e8	+	9.38599e8i	1.12645	+	1.12645i	0.990750	+	0.135698i	$0.0433278\pi$
$941$	9.38599e8	+	9.38599e8i	1.12645	+	1.12645i	0.135698	+	0.990750i	$0.456672\pi$
$942$	−1.83680e8	+	1.72823e8i	−0.219740	+	0.206751i
$943$		−	1.58360e8i		−	0.188848i
$944$	8.97057e8	+	1.14727e9i	1.06636	+	1.36379i
$945$	6.28144e8			0.744326
$946$	4.25419e8	+	4.52146e8i	0.502509	+	0.534079i
$947$	−8.73243e8	+	8.73243e8i	−1.02822	+	1.02822i	−0.0286279	+	0.999590i	$0.509114\pi$
$947$	−8.73243e8	+	8.73243e8i	−1.02822	+	1.02822i	−0.999590	+	0.0286279i	$0.990886\pi$
$948$	2.93794e8	−	2.60028e8i	0.344840	−	0.305208i
$949$	1.23386e6	−	1.23386e6i	0.00144366	−	0.00144366i
$950$	2.81331e9	+	8.56824e7i	3.28131	+	0.0999357i
$951$	3.45338e8			0.401516
$952$	1.98175e8	+	2.38139e8i	0.229688	+	0.276007i
$953$		−	1.04703e9i		−	1.20970i	−0.796338	−	0.604852i	$-0.793232\pi$
$953$		−	1.04703e9i		−	1.20970i	0.796338	−	0.604852i	$-0.206768\pi$
$954$	−1.36058e9	−	4.14378e7i	−1.56703	−	0.0477256i
$955$	−1.13363e9	−	1.13363e9i	−1.30156	−	1.30156i
$956$	5.59836e8	+	3.41325e7i	0.640748	+	0.0390655i
$957$	1.99567e6	+	1.99567e6i	0.00227695	+	0.00227695i
$958$	−2.62391e8	−	2.78875e8i	−0.298436	−	0.317186i
$959$		−	5.91898e8i		−	0.671106i
$960$	−5.55383e8	−	1.02601e8i	−0.627739	−	0.115968i
$961$	8.25449e8			0.930079
$962$	3.08695e6	−	2.90447e6i	0.00346740	−	0.00326244i
$963$	−3.17126e8	+	3.17126e8i	−0.355102	+	0.355102i
$964$	3.81087e7	−	6.25055e8i	0.0425396	−	0.697729i
$965$	−3.06176e8	+	3.06176e8i	−0.340714	+	0.340714i
$966$	3.91941e6	−	1.28691e8i	0.00434800	−	0.142763i
$967$	−2.11963e8			−0.234412			−0.117206	−	0.993108i	$-0.537394\pi$
$967$	−2.11963e8			−0.234412			−0.117206	+	0.993108i	$0.537394\pi$
$968$	6.52326e8	−	5.42854e8i	0.719182	−	0.598490i
$969$		−	2.77264e8i		−	0.304735i
$970$	4.74254e7	−	1.55718e9i	0.0519632	−	1.70617i
$971$	4.03408e8	+	4.03408e8i	0.440643	+	0.440643i	0.892228	−	0.451585i	$-0.149141\pi$
$971$	4.03408e8	+	4.03408e8i	0.440643	+	0.440643i	−0.451585	+	0.892228i	$0.649141\pi$
$972$	−5.43783e8	−	6.14395e8i	−0.592143	−	0.669035i
$973$	1.17448e8	+	1.17448e8i	0.127500	+	0.127500i
$974$	−3.98265e8	+	3.74723e8i	−0.431018	+	0.405540i
$975$			5.47149e6i			0.00590326i
$976$	−7.03878e8	−	9.00206e8i	−0.757091	−	0.968261i
$977$	−1.56036e9			−1.67317			−0.836586	−	0.547836i	$-0.815452\pi$
$977$	−1.56036e9			−1.67317			−0.836586	+	0.547836i	$0.815452\pi$
$978$	−4.48413e6	−	4.76584e6i	−0.00479359	−	0.00509475i
$979$	−3.14648e8	+	3.14648e8i	−0.335333	+	0.335333i
$980$	6.84899e8	+	7.73836e8i	0.727693	+	0.822188i
$981$	−7.19527e7	+	7.19527e7i	−0.0762149	+	0.0762149i
$982$	−4.62875e8	−	1.40973e7i	−0.488798	−	0.0148869i
$983$	3.49167e7			0.0367598			0.0183799	−	0.999831i	$-0.494149\pi$
$983$	3.49167e7			0.0367598			0.0183799	+	0.999831i	$0.494149\pi$
$984$	9.07120e6	−	9.90362e7i	0.00952093	−	0.103946i
$985$		−	1.23270e9i		−	1.28988i
$986$	−3.59210e6	−	109401.i	−0.00374730	−	0.000114128i
$987$	−1.15612e8	−	1.15612e8i	−0.120241	−	0.120241i
$988$	−652090.	+	1.06955e7i	−0.000676141	+	0.0110900i
$989$	2.32299e8	+	2.32299e8i	0.240137	+	0.240137i
$990$	1.44787e9	+	1.53884e9i	1.49219	+	1.58594i
$991$			1.02328e9i			1.05142i	0.850664	+	0.525709i	$0.176200\pi$
$991$			1.02328e9i			1.05142i	−0.850664	+	0.525709i	$0.823800\pi$
$992$	−1.52735e8	−	2.08094e8i	−0.156461	−	0.213169i
$993$	−3.92630e8			−0.400992
$994$	3.42417e8	−	3.22176e8i	0.348655	−	0.328045i
$995$	−5.86568e8	+	5.86568e8i	−0.595455	+	0.595455i
$996$	4.05762e8	+	2.47388e7i	0.410670	+	0.0250380i
$997$	9.21368e8	−	9.21368e8i	0.929711	−	0.929711i	−0.0679761	−	0.997687i	$-0.521654\pi$
$997$	9.21368e8	−	9.21368e8i	0.929711	−	0.929711i	0.997687	+	0.0679761i	$0.0216542\pi$
$998$	1.12472e7	−	3.69294e8i	0.0113150	−	0.371519i
$999$	−4.22749e8			−0.424020

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.7.f.a.3.8	✓	22
4.3	odd	2		64.7.f.a.47.6		22
8.3	odd	2		128.7.f.a.95.6		22
8.5	even	2		128.7.f.b.95.6		22
16.3	odd	4		128.7.f.b.31.6		22
16.5	even	4		64.7.f.a.15.6		22
16.11	odd	4	inner	16.7.f.a.11.8	yes	22
16.13	even	4		128.7.f.a.31.6		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.7.f.a.3.8	✓	22	1.1	even	1	trivial
16.7.f.a.11.8	yes	22	16.11	odd	4	inner
64.7.f.a.15.6		22	16.5	even	4
64.7.f.a.47.6		22	4.3	odd	2
128.7.f.a.31.6		22	16.13	even	4
128.7.f.a.95.6		22	8.3	odd	2
128.7.f.b.31.6		22	16.3	odd	4
128.7.f.b.95.6		22	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:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	16.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(5.82644 - 5.48203i) q^{2} +(-6.79913 + 6.79913i) q^{3} +(3.89476 - 63.8814i) q^{4} +(158.437 - 158.437i) q^{5} +(-2.34170 + 76.8878i) q^{6} -213.507 q^{7} +(-327.507 - 393.552i) q^{8} +636.544i q^{9} +O(q^{10})\)	\(q+(5.82644 - 5.48203i) q^{2} +(-6.79913 + 6.79913i) q^{3} +(3.89476 - 63.8814i) q^{4} +(158.437 - 158.437i) q^{5} +(-2.34170 + 76.8878i) q^{6} -213.507 q^{7} +(-327.507 - 393.552i) q^{8} +636.544i q^{9} +(54.5675 - 1791.68i) q^{10} +(1309.41 + 1309.41i) q^{11} +(407.857 + 460.819i) q^{12} +(11.6360 + 11.6360i) q^{13} +(-1243.99 + 1170.45i) q^{14} +2154.47i q^{15} +(-4065.66 - 497.605i) q^{16} +2834.10 q^{17} +(3489.55 + 3708.78i) q^{18} +(-7194.40 + 7194.40i) q^{19} +(-9504.10 - 10738.3i) q^{20} +(1451.67 - 1451.67i) q^{21} +(14807.4 + 450.974i) q^{22} +7839.29 q^{23} +(4902.58 + 449.050i) q^{24} -34579.6i q^{25} +(131.585 + 4.00756i) q^{26} +(-9284.51 - 9284.51i) q^{27} +(-831.561 + 13639.2i) q^{28} +(-112.081 - 112.081i) q^{29} +(11810.9 + 12552.9i) q^{30} +7877.51i q^{31} +(-26416.2 + 19388.8i) q^{32} -17805.7 q^{33} +(16512.7 - 15536.6i) q^{34} +(-33827.5 + 33827.5i) q^{35} +(40663.3 + 2479.19i) q^{36} +(22766.4 - 22766.4i) q^{37} +(-2477.83 + 81357.6i) q^{38} -158.229 q^{39} +(-114242. - 10464.0i) q^{40} -20200.8i q^{41} +(499.970 - 16416.1i) q^{42} +(29632.7 + 29632.7i) q^{43} +(88746.6 - 78546.9i) q^{44} +(100852. + 100852. i) q^{45} +(45675.2 - 42975.2i) q^{46} -79640.8i q^{47} +(31026.3 - 24259.7i) q^{48} -72063.5 q^{49} +(-189566. - 201476. i) q^{50} +(-19269.4 + 19269.4i) q^{51} +(788.641 - 698.002i) q^{52} +(-189013. + 189013. i) q^{53} +(-104994. - 3197.69i) q^{54} +414917. q^{55} +(69925.2 + 84026.3i) q^{56} -97831.3i q^{57} +(-1267.46 - 38.6018i) q^{58} +(-251413. - 251413. i) q^{59} +(137630. + 8391.14i) q^{60} +(197272. + 197272. i) q^{61} +(43184.7 + 45897.8i) q^{62} -135907. i q^{63} +(-47622.5 + 257782. i) q^{64} +3687.14 q^{65} +(-103744. + 97611.1i) q^{66} +(-214576. + 214576. i) q^{67} +(11038.1 - 181046. i) q^{68} +(-53300.4 + 53300.4i) q^{69} +(-11650.6 + 382537. i) q^{70} -275257. q^{71} +(250513. - 208472. i) q^{72} -106038. i q^{73} +(7840.99 - 257453. i) q^{74} +(235111. + 235111. i) q^{75} +(431568. + 487609. i) q^{76} +(-279568. - 279568. i) q^{77} +(-921.911 + 867.415i) q^{78} -637548. i q^{79} +(-722990. + 565312. i) q^{80} -337787. q^{81} +(-110742. - 117699. i) q^{82} +(467104. - 467104. i) q^{83} +(-87080.5 - 98388.3i) q^{84} +(449026. - 449026. i) q^{85} +(335100. + 10205.8i) q^{86} +1524.10 q^{87} +(86480.1 - 944160. i) q^{88} +240298. i q^{89} +(1.14048e6 + 34734.6i) q^{90} +(-2484.37 - 2484.37i) q^{91} +(30532.2 - 500785. i) q^{92} +(-53560.2 - 53560.2i) q^{93} +(-436593. - 464022. i) q^{94} +2.27972e6i q^{95} +(47780.3 - 311434. i) q^{96} +869115. q^{97} +(-419874. + 395054. i) q^{98} +(-833495. + 833495. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 2 q^{2} - 2 q^{3} + 88 q^{4} - 2 q^{5} - 512 q^{6} - 4 q^{7} + 964 q^{8}+O(q^{10}) \) 22 * q - 2 * q^2 - 2 * q^3 + 88 * q^4 - 2 * q^5 - 512 * q^6 - 4 * q^7 + 964 * q^8	\( 22 q - 2 q^{2} - 2 q^{3} + 88 q^{4} - 2 q^{5} - 512 q^{6} - 4 q^{7} + 964 q^{8} - 1124 q^{10} + 1358 q^{11} - 2348 q^{12} - 2 q^{13} + 7564 q^{14} - 7976 q^{16} - 4 q^{17} - 1874 q^{18} + 3934 q^{19} - 16564 q^{20} - 1460 q^{21} + 25252 q^{22} - 13124 q^{23} - 32592 q^{24} + 58952 q^{26} + 35776 q^{27} + 45176 q^{28} - 33202 q^{29} + 8452 q^{30} - 39672 q^{32} - 4 q^{33} - 52588 q^{34} - 112420 q^{35} - 138484 q^{36} + 3598 q^{37} - 187280 q^{38} + 254396 q^{39} + 165160 q^{40} + 353496 q^{42} - 267986 q^{43} + 380724 q^{44} + 32706 q^{45} + 248156 q^{46} - 460824 q^{48} + 168066 q^{49} - 719674 q^{50} + 301788 q^{51} - 784892 q^{52} - 221842 q^{53} - 547552 q^{54} - 232708 q^{55} + 366424 q^{56} + 1441912 q^{58} + 39150 q^{59} + 2405600 q^{60} + 326494 q^{61} + 182832 q^{62} - 318656 q^{64} + 186412 q^{65} - 3392732 q^{66} - 122786 q^{67} - 2504400 q^{68} - 543188 q^{69} - 1186816 q^{70} - 267012 q^{71} + 1748596 q^{72} + 3610396 q^{74} - 275278 q^{75} + 4245988 q^{76} + 231180 q^{77} + 3179052 q^{78} - 2898968 q^{80} - 354298 q^{81} - 5004624 q^{82} - 288322 q^{83} - 7602776 q^{84} + 340748 q^{85} - 3240476 q^{86} + 2029884 q^{87} + 3308152 q^{88} + 10273400 q^{90} + 302396 q^{91} + 7253656 q^{92} - 1173344 q^{93} + 3859056 q^{94} - 5689424 q^{96} - 4 q^{97} - 9176950 q^{98} - 271522 q^{99}+O(q^{100}) \) 22 * q - 2 * q^2 - 2 * q^3 + 88 * q^4 - 2 * q^5 - 512 * q^6 - 4 * q^7 + 964 * q^8 - 1124 * q^10 + 1358 * q^11 - 2348 * q^12 - 2 * q^13 + 7564 * q^14 - 7976 * q^16 - 4 * q^17 - 1874 * q^18 + 3934 * q^19 - 16564 * q^20 - 1460 * q^21 + 25252 * q^22 - 13124 * q^23 - 32592 * q^24 + 58952 * q^26 + 35776 * q^27 + 45176 * q^28 - 33202 * q^29 + 8452 * q^30 - 39672 * q^32 - 4 * q^33 - 52588 * q^34 - 112420 * q^35 - 138484 * q^36 + 3598 * q^37 - 187280 * q^38 + 254396 * q^39 + 165160 * q^40 + 353496 * q^42 - 267986 * q^43 + 380724 * q^44 + 32706 * q^45 + 248156 * q^46 - 460824 * q^48 + 168066 * q^49 - 719674 * q^50 + 301788 * q^51 - 784892 * q^52 - 221842 * q^53 - 547552 * q^54 - 232708 * q^55 + 366424 * q^56 + 1441912 * q^58 + 39150 * q^59 + 2405600 * q^60 + 326494 * q^61 + 182832 * q^62 - 318656 * q^64 + 186412 * q^65 - 3392732 * q^66 - 122786 * q^67 - 2504400 * q^68 - 543188 * q^69 - 1186816 * q^70 - 267012 * q^71 + 1748596 * q^72 + 3610396 * q^74 - 275278 * q^75 + 4245988 * q^76 + 231180 * q^77 + 3179052 * q^78 - 2898968 * q^80 - 354298 * q^81 - 5004624 * q^82 - 288322 * q^83 - 7602776 * q^84 + 340748 * q^85 - 3240476 * q^86 + 2029884 * q^87 + 3308152 * q^88 + 10273400 * q^90 + 302396 * q^91 + 7253656 * q^92 - 1173344 * q^93 + 3859056 * q^94 - 5689424 * q^96 - 4 * q^97 - 9176950 * q^98 - 271522 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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