LMFDB - Embedded newform 16.7.f.a.3.9

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			3.9
Character	$\chi$	$=$	16.3
Dual form			16.7.f.a.11.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.94882 - 5.34898i) q^{2} +(25.6946 - 25.6946i) q^{3} +(6.77693 - 63.6402i) q^{4} +(-141.826 + 141.826i) q^{5} +(15.4128 - 290.292i) q^{6} +411.977 q^{7} +(-300.095 - 414.834i) q^{8} -591.425i q^{9} +O(q^{10})$	\(q+(5.94882 - 5.34898i) q^{2} +(25.6946 - 25.6946i) q^{3} +(6.77693 - 63.6402i) q^{4} +(-141.826 + 141.826i) q^{5} +(15.4128 - 290.292i) q^{6} +411.977 q^{7} +(-300.095 - 414.834i) q^{8} -591.425i q^{9} +(-85.0738 + 1602.32i) q^{10} +(-44.9619 - 44.9619i) q^{11} +(-1461.08 - 1809.34i) q^{12} +(2355.48 + 2355.48i) q^{13} +(2450.78 - 2203.65i) q^{14} +7288.34i q^{15} +(-4004.15 - 862.570i) q^{16} -3212.26 q^{17} +(-3163.52 - 3518.28i) q^{18} +(-1628.35 + 1628.35i) q^{19} +(8064.70 + 9986.99i) q^{20} +(10585.6 - 10585.6i) q^{21} +(-507.970 - 26.9702i) q^{22} -8469.99 q^{23} +(-18369.8 - 2948.16i) q^{24} -24604.3i q^{25} +(26611.7 + 1412.92i) q^{26} +(3534.93 + 3534.93i) q^{27} +(2791.94 - 26218.3i) q^{28} +(-8578.85 - 8578.85i) q^{29} +(38985.1 + 43357.0i) q^{30} -17162.0i q^{31} +(-28433.8 + 16286.8i) q^{32} -2310.56 q^{33} +(-19109.2 + 17182.3i) q^{34} +(-58429.1 + 58429.1i) q^{35} +(-37638.4 - 4008.05i) q^{36} +(-39117.2 + 39117.2i) q^{37} +(-976.759 + 18396.8i) q^{38} +121046. q^{39} +(101396. + 16272.9i) q^{40} -68881.9i q^{41} +(6349.71 - 119594. i) q^{42} +(-36872.5 - 36872.5i) q^{43} +(-3166.09 + 2556.68i) q^{44} +(83879.6 + 83879.6i) q^{45} +(-50386.4 + 45305.8i) q^{46} -62591.7i q^{47} +(-125048. + 80721.6i) q^{48} +52075.9 q^{49} +(-131608. - 146367. i) q^{50} +(-82537.8 + 82537.8i) q^{51} +(165866. - 133940. i) q^{52} +(-16287.1 + 16287.1i) q^{53} +(39936.9 + 2120.41i) q^{54} +12753.5 q^{55} +(-123632. - 170902. i) q^{56} +83679.7i q^{57} +(-96922.0 - 5145.98i) q^{58} +(56470.6 + 56470.6i) q^{59} +(463831. + 49392.5i) q^{60} +(242781. + 242781. i) q^{61} +(-91799.4 - 102094. i) q^{62} -243653. i q^{63} +(-82029.9 + 248979. i) q^{64} -668136. q^{65} +(-13745.1 + 12359.1i) q^{66} +(337557. - 337557. i) q^{67} +(-21769.3 + 204429. i) q^{68} +(-217633. + 217633. i) q^{69} +(-35048.4 + 660120. i) q^{70} +355567. q^{71} +(-245343. + 177484. i) q^{72} -341935. i q^{73} +(-23464.3 + 441939. i) q^{74} +(-632199. - 632199. i) q^{75} +(92593.4 + 114664. i) q^{76} +(-18523.3 - 18523.3i) q^{77} +(720081. - 647472. i) q^{78} +439742. i q^{79} +(690228. - 445558. i) q^{80} +612806. q^{81} +(-368448. - 409766. i) q^{82} +(-686399. + 686399. i) q^{83} +(-601931. - 745406. i) q^{84} +(455583. - 455583. i) q^{85} +(-416578. - 22117.8i) q^{86} -440860. q^{87} +(-5158.86 + 32144.5i) q^{88} -599060. i q^{89} +(947654. + 50314.8i) q^{90} +(970401. + 970401. i) q^{91} +(-57400.5 + 539032. i) q^{92} +(-440972. - 440972. i) q^{93} +(-334801. - 372347. i) q^{94} -461886. i q^{95} +(-312112. + 1.14908e6i) q^{96} +997682. q^{97} +(309790. - 278553. i) q^{98} +(-26591.6 + 26591.6i) 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 $

$2$	5.94882	−	5.34898i	0.743603	−	0.668622i
$2$	5.94882	−	5.34898i	0.743603	−	0.668622i
$3$	25.6946	−	25.6946i	0.951652	−	0.951652i	−0.0472320	−	0.998884i	$-0.515040\pi$
$3$	25.6946	−	25.6946i	0.951652	−	0.951652i	0.998884	+	0.0472320i	$0.0150400\pi$
$4$	6.77693	−	63.6402i	0.105889	−	0.994378i
$5$	−141.826	+	141.826i	−1.13461	+	1.13461i	−0.145209	+	0.989401i	$0.546385\pi$
$5$	−141.826	+	141.826i	−1.13461	+	1.13461i	−0.989401	+	0.145209i	$0.953615\pi$
$6$	15.4128	−	290.292i	0.0713555	−	1.34395i
$7$	411.977			1.20110			0.600549	−	0.799588i	$-0.294949\pi$
$7$	411.977			1.20110			0.600549	+	0.799588i	$0.294949\pi$
$8$	−300.095	−	414.834i	−0.586123	−	0.810222i
$9$		−	591.425i		−	0.811283i
$10$	−85.0738	+	1602.32i	−0.0850738	+	1.60232i
$11$	−44.9619	−	44.9619i	−0.0337805	−	0.0337805i	0.690015	−	0.723795i	$-0.257604\pi$
$11$	−44.9619	−	44.9619i	−0.0337805	−	0.0337805i	−0.723795	+	0.690015i	$0.757604\pi$
$12$	−1461.08	−	1809.34i	−0.845532	−	1.04707i
$13$	2355.48	+	2355.48i	1.07213	+	1.07213i	0.997188	+	0.0749450i	$0.0238781\pi$
$13$	2355.48	+	2355.48i	1.07213	+	1.07213i	0.0749450	+	0.997188i	$0.476122\pi$
$14$	2450.78	−	2203.65i	0.893140	−	0.803081i
$15$			7288.34i			2.15951i
$16$	−4004.15	−	862.570i	−0.977575	−	0.210588i
$17$	−3212.26			−0.653829			−0.326915	−	0.945054i	$-0.606009\pi$
$17$	−3212.26			−0.653829			−0.326915	+	0.945054i	$0.606009\pi$
$18$	−3163.52	−	3518.28i	−0.542441	−	0.603272i
$19$	−1628.35	+	1628.35i	−0.237404	+	0.237404i	−0.815774	−	0.578370i	$-0.803689\pi$
$19$	−1628.35	+	1628.35i	−0.237404	+	0.237404i	0.578370	+	0.815774i	$0.303689\pi$
$20$	8064.70	+	9986.99i	1.00809	+	1.24837i
$21$	10585.6	−	10585.6i	1.14303	−	1.14303i
$22$	−507.970	−	26.9702i	−0.0477057	−	0.00253289i
$23$	−8469.99			−0.696144			−0.348072	−	0.937468i	$-0.613164\pi$
$23$	−8469.99			−0.696144			−0.348072	+	0.937468i	$0.613164\pi$
$24$	−18369.8	−	2948.16i	−1.32883	−	0.213264i
$25$		−	24604.3i		−	1.57468i
$26$	26611.7	+	1412.92i	1.51409	+	0.0803892i
$27$	3534.93	+	3534.93i	0.179593	+	0.179593i
$28$	2791.94	−	26218.3i	0.127184	−	1.19435i
$29$	−8578.85	−	8578.85i	−0.351751	−	0.351751i	0.509010	−	0.860761i	$-0.330012\pi$
$29$	−8578.85	−	8578.85i	−0.351751	−	0.351751i	−0.860761	+	0.509010i	$0.830012\pi$
$30$	38985.1	+	43357.0i	1.44389	+	1.60581i
$31$		−	17162.0i		−	0.576082i	−0.957618	−	0.288041i	$-0.906996\pi$
$31$		−	17162.0i		−	0.576082i	0.957618	−	0.288041i	$-0.0930039\pi$
$32$	−28433.8	+	16286.8i	−0.867731	+	0.497034i
$33$	−2310.56			−0.0642946
$34$	−19109.2	+	17182.3i	−0.486189	+	0.437164i
$35$	−58429.1	+	58429.1i	−1.36278	+	1.36278i
$36$	−37638.4	−	4008.05i	−0.806722	−	0.0859063i
$37$	−39117.2	+	39117.2i	−0.772259	+	0.772259i	−0.978501	−	0.206242i	$-0.933877\pi$
$37$	−39117.2	+	39117.2i	−0.772259	+	0.772259i	0.206242	+	0.978501i	$0.433877\pi$
$38$	−976.759	+	18396.8i	−0.0178007	+	0.335267i
$39$	121046.			2.04059
$40$	101396.	+	16272.9i	1.58431	+	0.254265i
$41$		−	68881.9i		−	0.999433i	−0.866189	−	0.499716i	$-0.833438\pi$
$41$		−	68881.9i		−	0.999433i	0.866189	−	0.499716i	$-0.166562\pi$
$42$	6349.71	−	119594.i	0.0857050	−	1.61421i
$43$	−36872.5	−	36872.5i	−0.463764	−	0.463764i	0.436123	−	0.899887i	$-0.356351\pi$
$43$	−36872.5	−	36872.5i	−0.463764	−	0.463764i	−0.899887	+	0.436123i	$0.856351\pi$
$44$	−3166.09	+	2556.68i	−0.0371676	+	0.0300136i
$45$	83879.6	+	83879.6i	0.920489	+	0.920489i
$46$	−50386.4	+	45305.8i	−0.517655	+	0.465457i
$47$		−	62591.7i		−	0.602869i	−0.953487	−	0.301435i	$-0.902534\pi$
$47$		−	62591.7i		−	0.602869i	0.953487	−	0.301435i	$-0.0974655\pi$
$48$	−125048.	+	80721.6i	−1.13072	+	0.729904i
$49$	52075.9			0.442638
$50$	−131608.	−	146367.i	−1.05286	−	1.17093i
$51$	−82537.8	+	82537.8i	−0.622218	+	0.622218i
$52$	165866.	−	133940.i	1.17963	−	0.952577i
$53$	−16287.1	+	16287.1i	−0.109400	+	0.109400i	−0.759688	−	0.650288i	$-0.774648\pi$
$53$	−16287.1	+	16287.1i	−0.109400	+	0.109400i	0.650288	+	0.759688i	$0.274648\pi$
$54$	39936.9	+	2120.41i	0.253626	+	0.0134660i
$55$	12753.5			0.0766554
$56$	−123632.	−	170902.i	−0.703992	−	0.973156i
$57$			83679.7i			0.451851i
$58$	−96922.0	−	5145.98i	−0.496751	−	0.0263745i
$59$	56470.6	+	56470.6i	0.274958	+	0.274958i	0.831092	−	0.556134i	$-0.187716\pi$
$59$	56470.6	+	56470.6i	0.274958	+	0.274958i	−0.556134	+	0.831092i	$0.687716\pi$
$60$	463831.	+	49392.5i	2.14737	+	0.228669i
$61$	242781.	+	242781.i	1.06961	+	1.06961i	0.997389	+	0.0722192i	$0.0230081\pi$
$61$	242781.	+	242781.i	1.06961	+	1.06961i	0.0722192	+	0.997389i	$0.476992\pi$
$62$	−91799.4	−	102094.i	−0.385181	−	0.428376i
$63$		−	243653.i		−	0.974431i
$64$	−82029.9	+	248979.i	−0.312919	+	0.949780i
$65$	−668136.			−2.43290
$66$	−13745.1	+	12359.1i	−0.0478096	+	0.0429888i
$67$	337557.	−	337557.i	1.12234	−	1.12234i	0.130946	−	0.991389i	$-0.458198\pi$
$67$	337557.	−	337557.i	1.12234	−	1.12234i	0.991389	−	0.130946i	$-0.0418015\pi$
$68$	−21769.3	+	204429.i	−0.0692336	+	0.650153i
$69$	−217633.	+	217633.i	−0.662487	+	0.662487i
$70$	−35048.4	+	660120.i	−0.102182	+	1.92455i
$71$	355567.			0.993452			0.496726	−	0.867907i	$-0.334535\pi$
$71$	355567.			0.993452			0.496726	+	0.867907i	$0.334535\pi$
$72$	−245343.	+	177484.i	−0.657319	+	0.475512i
$73$		−	341935.i		−	0.878971i	−0.898250	−	0.439486i	$-0.855161\pi$
$73$		−	341935.i		−	0.878971i	0.898250	−	0.439486i	$-0.144839\pi$
$74$	−23464.3	+	441939.i	−0.0579045	+	1.09060i
$75$	−632199.	−	632199.i	−1.49855	−	1.49855i
$76$	92593.4	+	114664.i	0.210930	+	0.261208i
$77$	−18523.3	−	18523.3i	−0.0405737	−	0.0405737i
$78$	720081.	−	647472.i	1.51739	−	1.36439i
$79$			439742.i			0.891901i	0.895058	+	0.445950i	$0.147134\pi$
$79$			439742.i			0.891901i	−0.895058	+	0.445950i	$0.852866\pi$
$80$	690228.	−	445558.i	1.34810	−	0.870230i
$81$	612806.			1.15310
$82$	−368448.	−	409766.i	−0.668243	−	0.743181i
$83$	−686399.	+	686399.i	−1.20045	+	1.20045i	−0.226415	+	0.974031i	$0.572701\pi$
$83$	−686399.	+	686399.i	−1.20045	+	1.20045i	−0.974031	+	0.226415i	$0.927299\pi$
$84$	−601931.	−	745406.i	−1.01557	−	1.25764i
$85$	455583.	−	455583.i	0.741841	−	0.741841i
$86$	−416578.	−	22117.8i	−0.654939	−	0.0347733i
$87$	−440860.			−0.669488
$88$	−5158.86	+	32144.5i	−0.00757018	+	0.0471693i
$89$		−	599060.i		−	0.849768i	−0.905248	−	0.424884i	$-0.860315\pi$
$89$		−	599060.i		−	0.849768i	0.905248	−	0.424884i	$-0.139685\pi$
$90$	947654.	+	50314.8i	1.29994	+	0.0690189i
$91$	970401.	+	970401.i	1.28774	+	1.28774i
$92$	−57400.5	+	539032.i	−0.0737144	+	0.692231i
$93$	−440972.	−	440972.i	−0.548229	−	0.548229i
$94$	−334801.	−	372347.i	−0.403092	−	0.448295i
$95$		−	461886.i		−	0.538721i
$96$	−312112.	+	1.14908e6i	−0.352775	+	1.29878i
$97$	997682.			1.09314			0.546572	−	0.837412i	$-0.315933\pi$
$97$	997682.			1.09314			0.546572	+	0.837412i	$0.315933\pi$
$98$	309790.	−	278553.i	0.329147	−	0.295957i
$99$	−26591.6	+	26591.6i	−0.0274056	+	0.0274056i
$100$	−1.56583e6	−	166742.i	−1.56583	−	0.166742i
$101$	−238723.	+	238723.i	−0.231702	+	0.231702i	−0.813403	−	0.581701i	$-0.802387\pi$
$101$	−238723.	+	238723.i	−0.231702	+	0.231702i	0.581701	+	0.813403i	$0.302387\pi$
$102$	−49509.9	+	932495.i	−0.0466543	+	0.878711i
$103$	−526787.			−0.482085			−0.241042	−	0.970515i	$-0.577489\pi$
$103$	−526787.			−0.482085			−0.241042	+	0.970515i	$0.577489\pi$
$104$	270264.	−	1.68400e6i	0.240264	−	1.49707i
$105$			3.00263e6i			2.59378i
$106$	−9769.76	+	184009.i	−0.00820288	+	0.154497i
$107$	1.20835e6	+	1.20835e6i	0.986375	+	0.986375i	0.999908	−	0.0135332i	$-0.00430787\pi$
$107$	1.20835e6	+	1.20835e6i	0.986375	+	0.986375i	−0.0135332	+	0.999908i	$0.504308\pi$
$108$	248920.	−	201008.i	0.197600	−	0.159566i
$109$	−1.65809e6	−	1.65809e6i	−1.28035	−	1.28035i	−0.940469	−	0.339879i	$-0.889614\pi$
$109$	−1.65809e6	−	1.65809e6i	−1.28035	−	1.28035i	−0.339879	−	0.940469i	$-0.610386\pi$
$110$	75868.6	−	68218.4i	0.0570012	−	0.0512535i
$111$			2.01020e6i			1.46984i
$112$	−1.64962e6	−	355359.i	−1.17416	−	0.252937i
$113$	57104.5			0.0395763			0.0197881	−	0.999804i	$-0.493701\pi$
$113$	57104.5			0.0395763			0.0197881	+	0.999804i	$0.493701\pi$
$114$	447601.	+	497796.i	0.302118	+	0.335998i
$115$	1.20127e6	−	1.20127e6i	0.789852	−	0.789852i
$116$	−604098.	+	487821.i	−0.387020	+	0.312526i
$117$	1.39309e6	−	1.39309e6i	0.869803	−	0.869803i
$118$	637993.	+	33873.6i	0.388303	+	0.0206165i
$119$	−1.32338e6			−0.785313
$120$	3.02345e6	−	2.18719e6i	1.74968	−	1.26574i
$121$		−	1.76752e6i		−	0.997718i
$122$	2.74289e6	+	145631.i	1.51053	+	0.0801999i
$123$	−1.76989e6	−	1.76989e6i	−0.951112	−	0.951112i
$124$	−1.09220e6	−	116306.i	−0.572843	−	0.0610010i
$125$	1.27351e6	+	1.27351e6i	0.652035	+	0.652035i
$126$	−1.30330e6	−	1.44945e6i	−0.651526	−	0.724589i
$127$		−	699514.i		−	0.341496i	−0.985315	−	0.170748i	$-0.945382\pi$
$127$		−	699514.i		−	0.341496i	0.985315	−	0.170748i	$-0.0546183\pi$
$128$	843802.	+	1.91991e6i	0.402356	+	0.915483i
$129$	−1.89485e6			−0.882684
$130$	−3.97462e6	+	3.57384e6i	−1.80911	+	1.62669i
$131$	1.85396e6	−	1.85396e6i	0.824684	−	0.824684i	−0.162092	−	0.986776i	$-0.551824\pi$
$131$	1.85396e6	−	1.85396e6i	0.824684	−	0.824684i	0.986776	+	0.162092i	$0.0518242\pi$
$132$	−15658.5	+	147044.i	−0.00680812	+	0.0639331i
$133$	−670843.	+	670843.i	−0.285145	+	0.285145i
$134$	202482.	−	3.81365e6i	0.0841534	−	1.58499i
$135$	−1.00269e6			−0.407536
$136$	963984.	+	1.33255e6i	0.383224	+	0.529747i
$137$			1.00819e6i			0.392086i	0.980595	+	0.196043i	$0.0628092\pi$
$137$			1.00819e6i			0.392086i	−0.980595	+	0.196043i	$0.937191\pi$
$138$	−130546.	+	2.45877e6i	−0.0496737	+	0.935581i
$139$	−1.56333e6	−	1.56333e6i	−0.582112	−	0.582112i	0.353371	−	0.935483i	$-0.385035\pi$
$139$	−1.56333e6	−	1.56333e6i	−0.582112	−	0.582112i	−0.935483	+	0.353371i	$0.885035\pi$
$140$	3.32247e6	+	4.11441e6i	1.21081	+	1.49942i
$141$	−1.60827e6	−	1.60827e6i	−0.573722	−	0.573722i
$142$	2.11521e6	−	1.90192e6i	0.738733	−	0.664244i
$143$		−	211813.i		−	0.0724344i
$144$	−510145.	+	2.36815e6i	−0.170847	+	0.793090i
$145$	2.43341e6			0.798199
$146$	−1.82900e6	−	2.03411e6i	−0.587699	−	0.653605i
$147$	1.33807e6	−	1.33807e6i	0.421237	−	0.421237i
$148$	2.22433e6	+	2.75452e6i	0.686143	+	0.849691i
$149$	−1.96711e6	+	1.96711e6i	−0.594661	+	0.594661i	−0.938887	−	0.344226i	$-0.888141\pi$
$149$	−1.96711e6	+	1.96711e6i	−0.594661	+	0.594661i	0.344226	+	0.938887i	$0.388141\pi$
$150$	−7.14245e6	−	379221.i	−2.11628	−	0.112362i
$151$	431913.			0.125449			0.0627243	−	0.998031i	$-0.480021\pi$
$151$	431913.			0.125449			0.0627243	+	0.998031i	$0.480021\pi$
$152$	1.16416e6	+	186835.i	0.331498	+	0.0532019i
$153$			1.89981e6i			0.530440i
$154$	−209272.	−	11111.1i	−0.0572992	−	0.00304225i
$155$	2.43403e6	+	2.43403e6i	0.653628	+	0.653628i
$156$	820320.	−	7.70339e6i	0.216078	−	2.02912i
$157$	4.24849e6	+	4.24849e6i	1.09783	+	1.09783i	0.994664	+	0.103166i	$0.0328974\pi$
$157$	4.24849e6	+	4.24849e6i	1.09783	+	1.09783i	0.103166	+	0.994664i	$0.467103\pi$
$158$	2.35217e6	+	2.61595e6i	0.596344	+	0.663220i
$159$			836983.i			0.208221i
$160$	1.72276e6	−	6.34256e6i	0.420597	−	1.54848i
$161$	−3.48944e6			−0.836138
$162$	3.64547e6	−	3.27789e6i	0.857450	−	0.770990i
$163$	−2.55603e6	+	2.55603e6i	−0.590206	+	0.590206i	−0.937687	−	0.347481i	$-0.887037\pi$
$163$	−2.55603e6	+	2.55603e6i	−0.590206	+	0.590206i	0.347481	+	0.937687i	$0.387037\pi$
$164$	−4.38366e6	−	466808.i	−0.993814	−	0.105829i
$165$	327697.	−	327697.i	0.0729493	−	0.0729493i
$166$	−411733.	+	7.75480e6i	−0.0900102	+	1.69530i
$167$	646882.			0.138891			0.0694457	−	0.997586i	$-0.477877\pi$
$167$	646882.			0.138891			0.0694457	+	0.997586i	$0.477877\pi$
$168$	−7.56794e6	−	1.21457e6i	−1.59606	−	0.256151i
$169$			6.26972e6i			1.29894i
$170$	273279.	−	5.14708e6i	0.0556237	−	1.04765i
$171$	963048.	+	963048.i	0.192602	+	0.192602i
$172$	−2.59646e6	+	2.09669e6i	−0.510265	+	0.412049i
$173$	−4.10734e6	−	4.10734e6i	−0.793273	−	0.793273i	0.188752	−	0.982025i	$-0.439556\pi$
$173$	−4.10734e6	−	4.10734e6i	−0.793273	−	0.793273i	−0.982025	+	0.188752i	$0.939556\pi$
$174$	−2.62260e6	+	2.35815e6i	−0.497833	+	0.447635i
$175$		−	1.01364e7i		−	1.89134i
$176$	141251.	+	218817.i	0.0259092	+	0.0401368i
$177$	2.90198e6			0.523329
$178$	−3.20436e6	−	3.56370e6i	−0.568174	−	0.631890i
$179$	1.11716e6	−	1.11716e6i	0.194786	−	0.194786i	−0.602975	−	0.797760i	$-0.706018\pi$
$179$	1.11716e6	−	1.11716e6i	0.194786	−	0.194786i	0.797760	+	0.602975i	$0.206018\pi$
$180$	5.90656e6	−	4.76967e6i	1.01278	−	0.817844i
$181$	2.49437e6	−	2.49437e6i	0.420654	−	0.420654i	−0.464775	−	0.885429i	$-0.653865\pi$
$181$	2.49437e6	−	2.49437e6i	0.420654	−	0.420654i	0.885429	+	0.464775i	$0.153865\pi$
$182$	1.09634e7	+	582091.i	1.81857	+	0.0965554i
$183$	1.24763e7			2.03579
$184$	2.54180e6	+	3.51364e6i	0.408026	+	0.564032i
$185$		−	1.10957e7i		−	1.75243i
$186$	−4.98201e6	−	264515.i	−0.774223	−	0.0411066i
$187$	144429.	+	144429.i	0.0220867	+	0.0220867i
$188$	−3.98335e6	−	424179.i	−0.599480	−	0.0638375i
$189$	1.45631e6	+	1.45631e6i	0.215709	+	0.215709i
$190$	−2.47062e6	−	2.74768e6i	−0.360201	−	0.400594i
$191$			7.12374e6i			1.02237i	0.859471	+	0.511185i	$0.170793\pi$
$191$			7.12374e6i			1.02237i	−0.859471	+	0.511185i	$0.829207\pi$
$192$	4.28969e6	+	8.50514e6i	0.606069	+	1.20165i
$193$	1.63763e6			0.227795			0.113898	−	0.993492i	$-0.463666\pi$
$193$	1.63763e6			0.227795			0.113898	+	0.993492i	$0.463666\pi$
$194$	5.93503e6	−	5.33658e6i	0.812864	−	0.730899i
$195$	−1.71675e7	+	1.71675e7i	−2.31528	+	2.31528i
$196$	352915.	−	3.31412e6i	0.0468707	−	0.440149i
$197$	−8.02811e6	+	8.02811e6i	−1.05006	+	1.05006i	−0.0513818	+	0.998679i	$0.516363\pi$
$197$	−8.02811e6	+	8.02811e6i	−1.05006	+	1.05006i	−0.998679	+	0.0513818i	$0.983637\pi$
$198$	−15950.8	+	300426.i	−0.00205489	+	0.0387028i
$199$	−1.07094e7			−1.35896			−0.679481	−	0.733693i	$-0.737795\pi$
$199$	−1.07094e7			−1.35896			−0.679481	+	0.733693i	$0.737795\pi$
$200$	−1.02067e7	+	7.38364e6i	−1.27584	+	0.922955i
$201$		−	1.73468e7i		−	2.13615i
$202$	−143197.	+	2.69704e6i	−0.0173732	+	0.327215i
$203$	−3.53429e6	−	3.53429e6i	−0.422487	−	0.422487i
$204$	4.69337e6	+	5.81207e6i	0.552833	+	0.684606i
$205$	9.76926e6	+	9.76926e6i	1.13397	+	1.13397i
$206$	−3.13376e6	+	2.81777e6i	−0.358480	+	0.322332i
$207$			5.00936e6i			0.564770i
$208$	−7.39991e6	−	1.14634e7i	−0.822311	−	1.27387i
$209$	146428.			0.0160392
$210$	1.60610e7	+	1.78621e7i	1.73426	+	1.92874i
$211$	−599213.	+	599213.i	−0.0637872	+	0.0637872i	−0.738281	−	0.674494i	$-0.764362\pi$
$211$	−599213.	+	599213.i	−0.0637872	+	0.0637872i	0.674494	+	0.738281i	$0.264362\pi$
$212$	926140.	+	1.14689e6i	0.0972006	+	0.120369i
$213$	9.13616e6	−	9.13616e6i	0.945420	−	0.945420i
$214$	1.36517e7	+	724824.i	1.39298	+	0.0739591i
$215$	1.04590e7			1.05238
$216$	405593.	−	2.52722e6i	0.0402466	−	0.250774i
$217$		−	7.07037e6i		−	0.691931i
$218$	−1.87327e7	−	994596.i	−1.80814	−	0.0960013i
$219$	−8.78588e6	−	8.78588e6i	−0.836475	−	0.836475i
$220$	86429.9	−	811638.i	0.00811700	−	0.0762245i
$221$	−7.56641e6	−	7.56641e6i	−0.700992	−	0.700992i
$222$	1.07525e7	+	1.19583e7i	0.982770	+	1.09298i
$223$		−	4.79044e6i		−	0.431977i	−0.976396	−	0.215989i	$-0.930703\pi$
$223$		−	4.79044e6i		−	0.431977i	0.976396	−	0.215989i	$-0.0692975\pi$
$224$	−1.17141e7	+	6.70979e6i	−1.04223	+	0.596987i
$225$	−1.45516e7			−1.27751
$226$	339704.	−	305451.i	0.0294290	−	0.0264616i
$227$	1.24849e7	−	1.24849e7i	1.06735	−	1.06735i	0.0697866	−	0.997562i	$-0.477768\pi$
$227$	1.24849e7	−	1.24849e7i	1.06735	−	1.06735i	0.997562	−	0.0697866i	$-0.0222318\pi$
$228$	5.32539e6	+	567091.i	0.449311	+	0.0478463i
$229$	4.70901e6	−	4.70901e6i	0.392123	−	0.392123i	−0.483320	−	0.875444i	$-0.660569\pi$
$229$	4.70901e6	−	4.70901e6i	0.392123	−	0.392123i	0.875444	+	0.483320i	$0.160569\pi$
$230$	720574.	−	1.35717e7i	0.0592236	−	1.11545i
$231$	−951895.			−0.0772242
$232$	−984325.	+	6.13326e6i	−0.0788269	+	0.491165i
$233$			7.62544e6i			0.602833i	0.953493	+	0.301417i	$0.0974595\pi$
$233$			7.62544e6i			0.602833i	−0.953493	+	0.301417i	$0.902540\pi$
$234$	835637.	−	1.57388e7i	0.0652184	−	1.22836i
$235$	8.87714e6	+	8.87714e6i	0.684021	+	0.684021i
$236$	3.97650e6	−	3.21110e6i	0.302527	−	0.244297i
$237$	1.12990e7	+	1.12990e7i	0.848779	+	0.848779i
$238$	−7.87254e6	+	7.07871e6i	−0.583961	+	0.525078i
$239$			1.14653e7i			0.839830i	0.907563	+	0.419915i	$0.137940\pi$
$239$			1.14653e7i			0.839830i	−0.907563	+	0.419915i	$0.862060\pi$
$240$	6.28670e6	−	2.91836e7i	0.454767	−	2.11108i
$241$	−1.91183e7			−1.36583			−0.682916	−	0.730497i	$-0.739289\pi$
$241$	−1.91183e7			−1.36583			−0.682916	+	0.730497i	$0.739289\pi$
$242$	−9.45441e6	−	1.05146e7i	−0.667096	−	0.741905i
$243$	1.31688e7	−	1.31688e7i	0.917760	−	0.917760i
$244$	1.70959e7	−	1.38053e7i	1.17685	−	0.950334i
$245$	−7.38573e6	+	7.38573e6i	−0.502221	+	0.502221i
$246$	−1.99959e7	−	1.06166e6i	−1.34318	−	0.0713150i
$247$	−7.67109e6			−0.509057
$248$	−7.11939e6	+	5.15025e6i	−0.466754	+	0.337655i
$249$			3.52735e7i			2.28481i
$250$	1.43878e7	+	763907.i	0.920820	+	0.0488900i
$251$	1.23788e7	+	1.23788e7i	0.782810	+	0.782810i	0.980304	−	0.197494i	$-0.0632804\pi$
$251$	1.23788e7	+	1.23788e7i	0.782810	+	0.782810i	−0.197494	+	0.980304i	$0.563280\pi$
$252$	−1.55061e7	−	1.65122e6i	−0.968952	−	0.103182i
$253$	380827.	+	380827.i	0.0235161	+	0.0235161i
$254$	−3.74168e6	−	4.16128e6i	−0.228331	−	0.253937i
$255$		−	2.34120e7i		−	1.41195i
$256$	1.52892e7	+	6.90771e6i	0.911305	+	0.411732i
$257$	2.58515e7			1.52295			0.761475	−	0.648194i	$-0.224475\pi$
$257$	2.58515e7			1.52295			0.761475	+	0.648194i	$0.224475\pi$
$258$	−1.12721e7	+	1.01355e7i	−0.656366	+	0.590182i
$259$	−1.61154e7	+	1.61154e7i	−0.927559	+	0.927559i
$260$	−4.52791e6	+	4.25203e7i	−0.257619	+	2.41923i
$261$	−5.07374e6	+	5.07374e6i	−0.285369	+	0.285369i
$262$	1.11209e6	−	2.09457e7i	0.0618353	−	1.16464i
$263$	4.58883e6			0.252252			0.126126	−	0.992014i	$-0.459746\pi$
$263$	4.58883e6			0.252252			0.126126	+	0.992014i	$0.459746\pi$
$264$	693386.	+	958496.i	0.0376846	+	0.0520929i
$265$		−	4.61989e6i		−	0.248252i
$266$	−402402.	+	7.57905e6i	−0.0213804	+	0.402689i
$267$	−1.53926e7	−	1.53926e7i	−0.808684	−	0.808684i
$268$	−1.91946e7	−	2.37698e7i	−0.997182	−	1.23487i
$269$	−1.43832e7	−	1.43832e7i	−0.738921	−	0.738921i	0.233448	−	0.972369i	$-0.424999\pi$
$269$	−1.43832e7	−	1.43832e7i	−0.738921	−	0.738921i	−0.972369	+	0.233448i	$0.924999\pi$
$270$	−5.96483e6	+	5.36337e6i	−0.303045	+	0.272488i
$271$			1.56022e7i			0.783932i	0.919980	+	0.391966i	$0.128205\pi$
$271$			1.56022e7i			0.783932i	−0.919980	+	0.391966i	$0.871795\pi$
$272$	1.28624e7	+	2.77080e6i	0.639167	+	0.137689i
$273$	4.98682e7			2.45095
$274$	5.39279e6	+	5.99755e6i	0.262157	+	0.291556i
$275$	−1.10626e6	+	1.10626e6i	−0.0531935	+	0.0531935i
$276$	1.23753e7	+	1.53251e7i	0.588612	+	0.728913i
$277$	−1.49968e7	+	1.49968e7i	−0.705600	+	0.705600i	−0.965607	−	0.260007i	$-0.916275\pi$
$277$	−1.49968e7	+	1.49968e7i	−0.705600	+	0.705600i	0.260007	+	0.965607i	$0.416275\pi$
$278$	−1.76622e7	−	937756.i	−0.822072	−	0.0436471i
$279$	−1.01501e7			−0.467365
$280$	4.17726e7	+	6.70407e6i	1.90291	+	0.305397i
$281$			5.16260e6i			0.232675i	0.993210	+	0.116338i	$0.0371154\pi$
$281$			5.16260e6i			0.232675i	−0.993210	+	0.116338i	$0.962885\pi$
$282$	−1.81699e7	−	964712.i	−0.810224	−	0.0430180i
$283$	7.74606e6	+	7.74606e6i	0.341760	+	0.341760i	0.857029	−	0.515269i	$-0.172308\pi$
$283$	7.74606e6	+	7.74606e6i	0.341760	+	0.341760i	−0.515269	+	0.857029i	$0.672308\pi$
$284$	2.40965e6	−	2.26284e7i	0.105196	−	0.987867i
$285$	−1.18680e7	−	1.18680e7i	−0.512675	−	0.512675i
$286$	−1.13298e6	−	1.26004e6i	−0.0484312	−	0.0538624i
$287$		−	2.83777e7i		−	1.20042i
$288$	9.63243e6	+	1.68165e7i	0.403235	+	0.703975i
$289$	−1.38189e7			−0.572508
$290$	1.44759e7	−	1.30163e7i	0.593543	−	0.533694i
$291$	2.56350e7	−	2.56350e7i	1.04029	−	1.04029i
$292$	−2.17608e7	−	2.31727e6i	−0.874030	−	0.0930738i
$293$	1.94355e7	−	1.94355e7i	0.772668	−	0.772668i	−0.205904	−	0.978572i	$-0.566014\pi$
$293$	1.94355e7	−	1.94355e7i	0.772668	−	0.772668i	0.978572	+	0.205904i	$0.0660136\pi$
$294$	802635.	−	1.51172e7i	0.0315846	−	0.594881i
$295$	−1.60180e7			−0.623940
$296$	2.79660e7	+	4.48826e6i	1.07834	+	0.173062i
$297$		−	317874.i		−	0.0121335i
$298$	−1.17996e6	+	2.22240e7i	−0.0445880	+	0.839794i
$299$	−1.99509e7	−	1.99509e7i	−0.746359	−	0.746359i
$300$	−4.45176e7	+	3.59489e7i	−1.64880	+	1.33144i
$301$	−1.51906e7	−	1.51906e7i	−0.557027	−	0.557027i
$302$	2.56937e6	−	2.31029e6i	0.0932839	−	0.0838777i
$303$			1.22678e7i			0.441000i
$304$	7.92473e6	−	5.11559e6i	0.282074	−	0.182085i
$305$	−6.88653e7			−2.42718
$306$	1.01621e7	+	1.13016e7i	0.354664	+	0.394437i
$307$	1.20617e7	−	1.20617e7i	0.416861	−	0.416861i	−0.467259	−	0.884120i	$-0.654758\pi$
$307$	1.20617e7	−	1.20617e7i	0.416861	−	0.416861i	0.884120	+	0.467259i	$0.154758\pi$
$308$	−1.30435e6	+	1.05329e6i	−0.0446420	+	0.0360493i
$309$	−1.35356e7	+	1.35356e7i	−0.458777	+	0.458777i
$310$	2.74992e7	+	1.46004e6i	0.923069	+	0.0490094i
$311$	2.86256e7			0.951642			0.475821	−	0.879542i	$-0.342151\pi$
$311$	2.86256e7			0.951642			0.475821	+	0.879542i	$0.342151\pi$
$312$	−3.63253e7	−	5.02140e7i	−1.19604	−	1.65333i
$313$			4.36158e7i			1.42236i	0.703009	+	0.711181i	$0.251840\pi$
$313$			4.36158e7i			1.42236i	−0.703009	+	0.711181i	$0.748160\pi$
$314$	4.79985e7	+	2.54843e6i	1.55038	+	0.0823160i
$315$	3.45564e7	+	3.45564e7i	1.10560	+	1.10560i
$316$	2.79853e7	+	2.98010e6i	0.886886	+	0.0944429i
$317$	−1.79251e7	−	1.79251e7i	−0.562708	−	0.562708i	0.367368	−	0.930076i	$-0.380259\pi$
$317$	−1.79251e7	−	1.79251e7i	−0.562708	−	0.562708i	−0.930076	+	0.367368i	$0.880259\pi$
$318$	4.47700e6	+	4.97906e6i	0.139221	+	0.154834i
$319$			771442.i			0.0237646i
$320$	−2.36778e7	−	4.69457e7i	−0.722588	−	1.43267i
$321$	6.20963e7			1.87737
$322$	−2.07580e7	+	1.86649e7i	−0.621754	+	0.559060i
$323$	5.23069e6	−	5.23069e6i	0.155221	−	0.155221i
$324$	4.15294e6	−	3.89991e7i	0.122102	−	1.14662i
$325$	5.79549e7	−	5.79549e7i	1.68826	−	1.68826i
$326$	−1.53322e6	+	2.88776e7i	−0.0442540	+	0.833504i
$327$	−8.52078e7			−2.43689
$328$	−2.85745e7	+	2.06711e7i	−0.809762	+	0.585791i
$329$		−	2.57863e7i		−	0.724106i
$330$	196568.	−	3.70226e6i	0.00546978	−	0.103021i
$331$	−1.49668e7	−	1.49668e7i	−0.412709	−	0.412709i	0.469972	−	0.882681i	$-0.344264\pi$
$331$	−1.49668e7	−	1.49668e7i	−0.412709	−	0.412709i	−0.882681	+	0.469972i	$0.844264\pi$
$332$	3.90309e7	+	4.83343e7i	1.06658	+	1.32081i
$333$	2.31349e7	+	2.31349e7i	0.626520	+	0.626520i
$334$	3.84818e6	−	3.46016e6i	0.103280	−	0.0928659i
$335$			9.57489e7i			2.54683i
$336$	−5.15170e7	+	3.32554e7i	−1.35810	+	0.876687i
$337$	−1.92483e7			−0.502924			−0.251462	−	0.967867i	$-0.580911\pi$
$337$	−1.92483e7			−0.502924			−0.251462	+	0.967867i	$0.580911\pi$
$338$	3.35366e7	+	3.72974e7i	0.868498	+	0.965893i
$339$	1.46728e6	−	1.46728e6i	0.0376629	−	0.0376629i
$340$	−2.59059e7	−	3.20808e7i	−0.659117	−	0.816223i
$341$	−771638.	+	771638.i	−0.0194603	+	0.0194603i
$342$	1.08803e7	+	577680.i	0.271997	+	0.0144414i
$343$	−2.70146e7			−0.669447
$344$	−4.23070e6	+	2.63612e7i	−0.103929	+	0.647575i
$345$		−	6.17321e7i		−	1.50333i
$346$	−4.64039e7	−	2.46377e6i	−1.12028	−	0.0594801i
$347$	5.04931e7	+	5.04931e7i	1.20849	+	1.20849i	0.971516	+	0.236975i	$0.0761560\pi$
$347$	5.04931e7	+	5.04931e7i	1.20849	+	1.20849i	0.236975	+	0.971516i	$0.423844\pi$
$348$	−2.98768e6	+	2.80564e7i	−0.0708918	+	0.665724i
$349$	8.31696e6	+	8.31696e6i	0.195654	+	0.195654i	0.798134	−	0.602480i	$-0.205821\pi$
$349$	8.31696e6	+	8.31696e6i	0.195654	+	0.195654i	−0.602480	+	0.798134i	$0.705821\pi$
$350$	−5.42195e7	−	6.02997e7i	−1.26459	−	1.40641i
$351$			1.66529e7i			0.385095i
$352$	2.01072e6	+	546152.i	0.0461025	+	0.0125223i
$353$	2.48212e7			0.564284			0.282142	−	0.959373i	$-0.408955\pi$
$353$	2.48212e7			0.564284			0.282142	+	0.959373i	$0.408955\pi$
$354$	1.72634e7	−	1.55226e7i	0.389149	−	0.349909i
$355$	−5.04288e7	+	5.04288e7i	−1.12718	+	1.12718i
$356$	−3.81243e7	−	4.05979e6i	−0.844991	−	0.0899815i
$357$	−3.40037e7	+	3.40037e7i	−0.747345	+	0.747345i
$358$	670124.	−	1.26215e7i	0.0146051	−	0.275081i
$359$	8.53598e7			1.84489			0.922444	−	0.386130i	$-0.126188\pi$
$359$	8.53598e7			1.84489			0.922444	+	0.386130i	$0.126188\pi$
$360$	9.62423e6	−	5.99679e7i	0.206281	−	1.28532i
$361$			4.17428e7i			0.887279i
$362$	1.49624e6	−	2.81809e7i	0.0315409	−	0.594059i
$363$	−4.54157e7	−	4.54157e7i	−0.949480	−	0.949480i
$364$	6.83329e7	−	5.51802e7i	1.41686	−	1.14414i
$365$	4.84953e7	+	4.84953e7i	0.997289	+	0.997289i
$366$	7.42193e7	−	6.67355e7i	1.51382	−	1.36117i
$367$		−	5.07928e7i		−	1.02755i	−0.857924	−	0.513777i	$-0.828246\pi$
$367$		−	5.07928e7i		−	1.02755i	0.857924	−	0.513777i	$-0.171754\pi$
$368$	3.39151e7	+	7.30596e6i	0.680533	+	0.146600i
$369$	−4.07385e7			−0.810823
$370$	−5.93506e7	−	6.60063e7i	−1.17171	−	1.30311i
$371$	−6.70992e6	+	6.70992e6i	−0.131400	+	0.131400i
$372$	−3.10520e7	+	2.50751e7i	−0.603199	+	0.487095i
$373$	2.15606e7	−	2.15606e7i	0.415466	−	0.415466i	−0.468172	−	0.883638i	$-0.655087\pi$
$373$	2.15606e7	−	2.15606e7i	0.415466	−	0.415466i	0.883638	+	0.468172i	$0.155087\pi$
$374$	1.63173e6	+	86635.3i	0.0311914	+	0.00165607i
$375$	6.54445e7			1.24102
$376$	−2.59651e7	+	1.87835e7i	−0.488458	+	0.353356i
$377$		−	4.04145e7i		−	0.754247i
$378$	1.64531e7	+	873561.i	0.304630	+	0.0161740i
$379$	−9.50195e6	−	9.50195e6i	−0.174540	−	0.174540i	0.614431	−	0.788971i	$-0.289386\pi$
$379$	−9.50195e6	−	9.50195e6i	−0.174540	−	0.174540i	−0.788971	+	0.614431i	$0.789386\pi$
$380$	−2.93945e7	−	3.13017e6i	−0.535692	−	0.0570449i
$381$	−1.79737e7	−	1.79737e7i	−0.324985	−	0.324985i
$382$	3.81047e7	+	4.23778e7i	0.683578	+	0.760236i
$383$		−	7.09053e7i		−	1.26207i	−0.775755	−	0.631034i	$-0.782631\pi$
$383$		−	7.09053e7i		−	1.26207i	0.775755	−	0.631034i	$-0.217369\pi$
$384$	7.10124e7	+	2.76501e7i	1.25412	+	0.488319i
$385$	5.25417e6			0.0920707
$386$	9.74199e6	−	8.75966e6i	0.169389	−	0.152309i
$387$	−2.18073e7	+	2.18073e7i	−0.376244	+	0.376244i
$388$	6.76122e6	−	6.34927e7i	0.115752	−	1.08700i
$389$	−2.91857e7	+	2.91857e7i	−0.495816	+	0.495816i	−0.910133	−	0.414316i	$-0.864021\pi$
$389$	−2.91857e7	+	2.91857e7i	−0.495816	+	0.495816i	0.414316	+	0.910133i	$0.364021\pi$
$390$	−1.02978e7	+	1.93955e8i	−0.173601	+	3.26969i
$391$	2.72078e7			0.455159
$392$	−1.56277e7	−	2.16028e7i	−0.259440	−	0.358635i
$393$		−	9.52737e7i		−	1.56962i
$394$	−4.81562e6	+	9.06999e7i	−0.0787342	+	1.48292i
$395$	−6.23669e7	−	6.23669e7i	−1.01196	−	1.01196i
$396$	1.51208e6	+	1.87250e6i	0.0243495	+	0.0301534i
$397$	−1.98612e7	−	1.98612e7i	−0.317420	−	0.317420i	0.530356	−	0.847775i	$-0.322058\pi$
$397$	−1.98612e7	−	1.98612e7i	−0.317420	−	0.317420i	−0.847775	+	0.530356i	$0.822058\pi$
$398$	−6.37085e7	+	5.72845e7i	−1.01053	+	0.908631i
$399$			3.44741e7i			0.542718i
$400$	−2.12230e7	+	9.85194e7i	−0.331609	+	1.53937i
$401$	3.50138e7			0.543007			0.271504	−	0.962437i	$-0.412479\pi$
$401$	3.50138e7			0.543007			0.271504	+	0.962437i	$0.412479\pi$
$402$	−9.27875e7	−	1.03193e8i	−1.42827	−	1.58844i
$403$	4.04248e7	−	4.04248e7i	0.617636	−	0.617636i
$404$	1.35746e7	+	1.68102e7i	0.205865	+	0.254934i
$405$	−8.69120e7	+	8.69120e7i	−1.30832	+	1.30832i
$406$	−3.99296e7	−	2.12002e6i	−0.596647	−	0.0316784i
$407$	3.51757e6			0.0521746
$408$	5.90086e7	+	9.47027e6i	0.868831	+	0.139438i
$409$			9.66336e7i			1.41240i	0.708011	+	0.706201i	$0.249592\pi$
$409$			9.66336e7i			1.41240i	−0.708011	+	0.706201i	$0.750408\pi$
$410$	1.10371e8	+	5.86004e6i	1.60141	+	0.0850255i
$411$	2.59051e7	+	2.59051e7i	0.373130	+	0.373130i
$412$	−3.57000e6	+	3.35248e7i	−0.0510477	+	0.479375i
$413$	2.32646e7	+	2.32646e7i	0.330252	+	0.330252i
$414$	2.67950e7	+	2.97998e7i	0.377618	+	0.419964i
$415$		−	1.94699e8i		−	2.72407i
$416$	−1.05338e8	−	2.86120e7i	−1.46321	−	0.397437i
$417$	−8.03383e7			−1.10794
$418$	871071.	−	783237.i	0.0119268	−	0.0107242i
$419$	−9.91922e7	+	9.91922e7i	−1.34845	+	1.34845i	−0.461109	+	0.887344i	$0.652548\pi$
$419$	−9.91922e7	+	9.91922e7i	−1.34845	+	1.34845i	−0.887344	+	0.461109i	$0.847452\pi$
$420$	1.91088e8	+	2.03486e7i	2.57920	+	0.274654i
$421$	1.70314e7	−	1.70314e7i	0.228246	−	0.228246i	−0.583714	−	0.811960i	$-0.698401\pi$
$421$	1.70314e7	−	1.70314e7i	0.228246	−	0.228246i	0.811960	+	0.583714i	$0.198401\pi$
$422$	−359435.	+	6.76978e6i	−0.00478281	+	0.0900819i
$423$	−3.70183e7			−0.489097
$424$	1.16441e7	+	1.86876e6i	0.152760	+	0.0245164i
$425$			7.90356e7i			1.02957i
$426$	5.48028e6	−	1.03218e8i	0.0708882	−	1.33515i
$427$	1.00020e8	+	1.00020e8i	1.28470	+	1.28470i
$428$	8.50887e7	−	6.87108e7i	1.08528	−	0.876383i
$429$	−5.44246e6	−	5.44246e6i	−0.0689324	−	0.0689324i
$430$	6.22186e7	−	5.59448e7i	0.782555	−	0.703646i
$431$		−	6.19323e7i		−	0.773545i	−0.922175	−	0.386772i	$-0.873590\pi$
$431$		−	6.19323e7i		−	0.773545i	0.922175	−	0.386772i	$-0.126410\pi$
$432$	−1.11053e7	−	1.72035e7i	−0.137746	−	0.213386i
$433$	−6.84514e6			−0.0843177			−0.0421588	−	0.999111i	$-0.513424\pi$
$433$	−6.84514e6			−0.0843177			−0.0421588	+	0.999111i	$0.513424\pi$
$434$	−3.78192e7	−	4.20603e7i	−0.462640	−	0.514522i
$435$	6.25255e7	−	6.25255e7i	0.759608	−	0.759608i
$436$	−1.16758e8	+	9.42843e7i	−1.40873	+	1.13757i
$437$	1.37921e7	−	1.37921e7i	0.165267	−	0.165267i
$438$	−9.92611e7	−	5.27017e6i	−1.18129	−	0.0627194i
$439$	1.48097e8			1.75046			0.875232	−	0.483703i	$-0.160708\pi$
$439$	1.48097e8			1.75046			0.875232	+	0.483703i	$0.160708\pi$
$440$	−3.82728e6	−	5.29060e6i	−0.0449295	−	0.0621079i
$441$		−	3.07990e7i		−	0.359104i
$442$	−8.54837e7	−	4.53867e6i	−0.989957	−	0.0525608i
$443$	−1.10015e8	−	1.10015e8i	−1.26543	−	1.26543i	−0.948421	−	0.317013i	$-0.897320\pi$
$443$	−1.10015e8	−	1.10015e8i	−1.26543	−	1.26543i	−0.317013	−	0.948421i	$-0.602680\pi$
$444$	1.27930e8	+	1.36230e7i	1.46158	+	0.155641i
$445$	8.49625e7	+	8.49625e7i	0.964155	+	0.964155i
$446$	−2.56240e7	−	2.84975e7i	−0.288830	−	0.321220i
$447$			1.01088e8i			1.13182i
$448$	−3.37944e7	+	1.02574e8i	−0.375847	+	1.14078i
$449$	−3.03044e7			−0.334785			−0.167393	−	0.985890i	$-0.553535\pi$
$449$	−3.03044e7			−0.334785			−0.167393	+	0.985890i	$0.553535\pi$
$450$	−8.65650e7	+	7.78363e7i	−0.949959	+	0.854171i
$451$	−3.09706e6	+	3.09706e6i	−0.0337614	+	0.0337614i
$452$	386993.	−	3.63414e6i	0.00419071	−	0.0393538i
$453$	1.10978e7	−	1.10978e7i	0.119383	−	0.119383i
$454$	7.48899e6	−	1.41051e8i	0.0800305	−	1.50734i
$455$	−2.75257e8			−2.92216
$456$	3.47132e7	−	2.51119e7i	0.366100	−	0.264841i
$457$		−	1.61100e8i		−	1.68790i	−0.536424	−	0.843949i	$-0.680225\pi$
$457$		−	1.61100e8i		−	1.68790i	0.536424	−	0.843949i	$-0.319775\pi$
$458$	2.82467e6	−	5.32014e7i	0.0294017	−	0.553766i
$459$	−1.13551e7	−	1.13551e7i	−0.117423	−	0.117423i
$460$	−6.83079e7	−	8.45897e7i	−0.701775	−	0.869049i
$461$	1.62650e7	+	1.62650e7i	0.166016	+	0.166016i	0.785226	−	0.619210i	$-0.212547\pi$
$461$	1.62650e7	+	1.62650e7i	0.166016	+	0.166016i	−0.619210	+	0.785226i	$0.712547\pi$
$462$	−5.66265e6	+	5.09166e6i	−0.0574241	+	0.0516338i
$463$			1.68452e8i			1.69720i	0.529038	+	0.848598i	$0.322553\pi$
$463$			1.68452e8i			1.69720i	−0.529038	+	0.848598i	$0.677447\pi$
$464$	2.69511e7	+	4.17508e7i	0.269788	+	0.417937i
$465$	1.25083e8			1.24405
$466$	4.07883e7	+	4.53624e7i	0.403068	+	0.448268i
$467$	7.69239e7	−	7.69239e7i	0.755284	−	0.755284i	−0.220176	−	0.975460i	$-0.570663\pi$
$467$	7.69239e7	−	7.69239e7i	0.755284	−	0.755284i	0.975460	+	0.220176i	$0.0706631\pi$
$468$	−7.92155e7	−	9.80972e7i	−0.772810	−	0.957016i
$469$	1.39066e8	−	1.39066e8i	1.34804	−	1.34804i
$470$	1.00292e8	+	5.32491e6i	0.965992	+	0.0512884i
$471$	2.18326e8			2.08950
$472$	6.47936e6	−	4.03725e7i	0.0616178	−	0.383936i
$473$			3.31571e6i			0.0313324i
$474$	1.27654e8	+	6.77765e6i	1.19867	+	0.0636420i
$475$	4.00645e7	+	4.00645e7i	0.373834	+	0.373834i
$476$	−8.96843e6	+	8.42200e7i	−0.0831564	+	0.780898i
$477$	9.63262e6	+	9.63262e6i	0.0887543	+	0.0887543i
$478$	6.13276e7	+	6.82050e7i	0.561529	+	0.624500i
$479$			1.80538e8i			1.64271i	0.570416	+	0.821356i	$0.306782\pi$
$479$			1.80538e8i			1.64271i	−0.570416	+	0.821356i	$0.693218\pi$
$480$	−1.18704e8	−	2.07235e8i	−1.07335	−	1.87387i
$481$	−1.84279e8			−1.65593
$482$	−1.13731e8	+	1.02263e8i	−1.01564	+	0.913225i
$483$	−8.96598e7	+	8.96598e7i	−0.795712	+	0.795712i
$484$	−1.12485e8	−	1.19783e7i	−0.992108	−	0.105648i
$485$	−1.41497e8	+	1.41497e8i	−1.24029	+	1.24029i
$486$	7.89927e6	−	1.48779e8i	0.0688142	−	1.29608i
$487$	−2.76822e7			−0.239670			−0.119835	−	0.992794i	$-0.538237\pi$
$487$	−2.76822e7			−0.239670			−0.119835	+	0.992794i	$0.538237\pi$
$488$	2.78563e7	−	1.73571e8i	0.239698	−	1.49354i
$489$			1.31353e8i			1.12334i
$490$	−4.43029e6	+	8.34424e7i	−0.0376569	+	0.709249i
$491$	−1.13442e8	−	1.13442e8i	−0.958361	−	0.958361i	0.0408060	−	0.999167i	$-0.487007\pi$
$491$	−1.13442e8	−	1.13442e8i	−0.958361	−	0.958361i	−0.999167	+	0.0408060i	$0.987007\pi$
$492$	−1.24631e8	+	1.00642e8i	−1.04648	+	0.845052i
$493$	2.75575e7	+	2.75575e7i	0.229985	+	0.229985i
$494$	−4.56339e7	+	4.10325e7i	−0.378536	+	0.340366i
$495$		−	7.54277e6i		−	0.0621892i
$496$	−1.48035e7	+	6.87193e7i	−0.121316	+	0.563163i
$497$	1.46486e8			1.19323
$498$	1.88677e8	+	2.09836e8i	1.52768	+	1.69899i
$499$	2.96941e7	−	2.96941e7i	0.238984	−	0.238984i	−0.577445	−	0.816429i	$-0.695950\pi$
$499$	2.96941e7	−	2.96941e7i	0.238984	−	0.238984i	0.816429	+	0.577445i	$0.195950\pi$
$500$	8.96766e7	−	7.24157e7i	0.717413	−	0.579326i
$501$	1.66214e7	−	1.66214e7i	0.132176	−	0.132176i
$502$	1.39853e8	+	7.42534e6i	1.10550	+	0.0586956i
$503$	1.52573e7			0.119888			0.0599438	−	0.998202i	$-0.480908\pi$
$503$	1.52573e7			0.119888			0.0599438	+	0.998202i	$0.480908\pi$
$504$	−1.01076e8	+	7.31192e7i	−0.789505	+	0.571136i
$505$		−	6.77143e7i		−	0.525783i
$506$	4.30250e6	+	228437.i	0.0332101	+	0.00176325i
$507$	1.61098e8	+	1.61098e8i	1.23614	+	1.23614i
$508$	−4.45172e7	−	4.74055e6i	−0.339576	−	0.0361608i
$509$	−1.49274e8	−	1.49274e8i	−1.13196	−	1.13196i	−0.989852	−	0.142104i	$-0.954613\pi$
$509$	−1.49274e8	−	1.49274e8i	−1.13196	−	1.13196i	−0.142104	−	0.989852i	$-0.545387\pi$
$510$	−1.25230e8	−	1.39274e8i	−0.944060	−	1.04993i
$511$		−	1.40869e8i		−	1.05573i
$512$	1.27902e8	−	4.06886e7i	0.952942	−	0.303154i
$513$	−1.15122e7			−0.0852722
$514$	1.53786e8	−	1.38279e8i	1.13247	−	1.01828i
$515$	7.47122e7	−	7.47122e7i	0.546978	−	0.546978i
$516$	−1.28413e7	+	1.20589e8i	−0.0934670	+	0.877722i
$517$	−2.81424e6	+	2.81424e6i	−0.0203652	+	0.0203652i
$518$	−9.66674e6	+	1.82068e8i	−0.0695490	+	1.30992i
$519$	−2.11073e8			−1.50984
$520$	2.00504e8	+	2.77165e8i	1.42598	+	1.97119i
$521$			1.15110e8i			0.813955i	0.913438	+	0.406977i	$0.133417\pi$
$521$			1.15110e8i			0.813955i	−0.913438	+	0.406977i	$0.866583\pi$
$522$	−3.04346e6	+	5.73221e7i	−0.0213972	+	0.403005i
$523$	1.70829e8	+	1.70829e8i	1.19414	+	1.19414i	0.975893	+	0.218250i	$0.0700348\pi$
$523$	1.70829e8	+	1.70829e8i	1.19414	+	1.19414i	0.218250	+	0.975893i	$0.429965\pi$
$524$	−1.05422e8	−	1.30551e8i	−0.732722	−	0.907372i
$525$	−2.60451e8	−	2.60451e8i	−1.79990	−	1.79990i
$526$	2.72981e7	−	2.45455e7i	0.187575	−	0.168661i
$527$			5.51290e7i			0.376659i
$528$	9.25180e6	+	1.99302e6i	0.0628528	+	0.0135397i
$529$	−7.62952e7			−0.515383
$530$	−2.47117e7	−	2.74829e7i	−0.165987	−	0.184601i
$531$	3.33981e7	−	3.33981e7i	0.223069	−	0.223069i
$532$	3.81463e7	+	4.72389e7i	0.253348	+	0.313736i
$533$	1.62250e8	−	1.62250e8i	1.07152	−	1.07152i
$534$	−1.73903e8	−	9.23319e6i	−1.14204	−	0.0606356i
$535$	−3.42752e8			−2.23830
$536$	−2.41329e8	−	3.87308e7i	−1.56717	−	0.251514i
$537$		−	5.74100e7i		−	0.370736i
$538$	−1.62498e8	−	8.62768e6i	−1.04352	−	0.0554048i
$539$	−2.34143e6	−	2.34143e6i	−0.0149525	−	0.0149525i
$540$	−6.79517e6	+	6.38115e7i	−0.0431538	+	0.405245i
$541$	−6.73179e7	−	6.73179e7i	−0.425147	−	0.425147i	0.461825	−	0.886971i	$-0.347195\pi$
$541$	−6.73179e7	−	6.73179e7i	−0.425147	−	0.425147i	−0.886971	+	0.461825i	$0.847195\pi$
$542$	8.34558e7	+	9.28147e7i	0.524154	+	0.582934i
$543$		−	1.28184e8i		−	0.800633i
$544$	9.13369e7	−	5.23175e7i	0.567348	−	0.324975i
$545$	4.70321e8			2.90539
$546$	2.96657e8	−	2.66744e8i	1.82254	−	1.63876i
$547$	−6.44257e7	+	6.44257e7i	−0.393638	+	0.393638i	−0.875982	−	0.482344i	$-0.839786\pi$
$547$	−6.44257e7	+	6.44257e7i	−0.393638	+	0.393638i	0.482344	+	0.875982i	$0.339786\pi$
$548$	6.41615e7	+	6.83244e6i	0.389882	+	0.0415178i
$549$	1.43587e8	−	1.43587e8i	0.867754	−	0.867754i
$550$	−663583.	+	1.24983e7i	−0.00398848	+	0.0751211i
$551$	2.79388e7			0.167014
$552$	1.55592e8	+	2.49709e7i	0.925061	+	0.148463i
$553$			1.81163e8i			1.07126i
$554$	−8.99574e6	+	1.69430e8i	−0.0529063	+	0.996465i
$555$	−2.85100e8	−	2.85100e8i	−1.66770	−	1.66770i
$556$	−1.10085e8	+	8.88960e7i	−0.640479	+	0.517199i
$557$	−2.81484e7	−	2.81484e7i	−0.162888	−	0.162888i	0.620957	−	0.783845i	$-0.286744\pi$
$557$	−2.81484e7	−	2.81484e7i	−0.162888	−	0.162888i	−0.783845	+	0.620957i	$0.786744\pi$
$558$	−6.03809e7	+	5.42924e7i	−0.347534	+	0.312491i
$559$		−	1.73705e8i		−	0.994434i
$560$	2.84358e8	−	1.83560e8i	1.61920	−	1.04523i
$561$	7.42211e6			0.0420377
$562$	2.76146e7	+	3.07114e7i	0.155572	+	0.173018i
$563$	−3.25814e7	+	3.25814e7i	−0.182576	+	0.182576i	−0.792477	−	0.609901i	$-0.791209\pi$
$563$	−3.25814e7	+	3.25814e7i	−0.182576	+	0.182576i	0.609901	+	0.792477i	$0.291209\pi$
$564$	−1.13250e8	+	9.14514e7i	−0.631247	+	0.509745i
$565$	−8.09892e6	+	8.09892e6i	−0.0449036	+	0.0449036i
$566$	8.75134e7	+	4.64644e6i	0.482642	+	0.0256254i
$567$	2.52462e8			1.38499
$568$	−1.06704e8	−	1.47501e8i	−0.582285	−	0.804917i
$569$		−	6.00764e7i		−	0.326112i	−0.986617	−	0.163056i	$-0.947865\pi$
$569$		−	6.00764e7i		−	0.326112i	0.986617	−	0.163056i	$-0.0521351\pi$
$570$	−1.34082e8	−	7.11895e6i	−0.724012	−	0.0384407i
$571$	1.53517e8	+	1.53517e8i	0.824610	+	0.824610i	0.986765	−	0.162155i	$-0.0518446\pi$
$571$	1.53517e8	+	1.53517e8i	0.824610	+	0.824610i	−0.162155	+	0.986765i	$0.551845\pi$
$572$	−1.34798e7	−	1.43544e6i	−0.0720272	−	0.00767004i
$573$	1.83042e8	+	1.83042e8i	0.972939	+	0.972939i
$574$	−1.51792e8	−	1.68814e8i	−0.802625	−	0.892633i
$575$			2.08399e8i			1.09620i
$576$	1.47252e8	+	4.85146e7i	0.770540	+	0.253866i
$577$	−3.34357e8			−1.74054			−0.870269	−	0.492577i	$-0.836055\pi$
$577$	−3.34357e8			−1.74054			−0.870269	+	0.492577i	$0.836055\pi$
$578$	−8.22064e7	+	7.39172e7i	−0.425718	+	0.382791i
$579$	4.20783e7	−	4.20783e7i	0.216782	−	0.216782i
$580$	1.64910e7	−	1.54863e8i	0.0845209	−	0.793712i
$581$	−2.82781e8	+	2.82781e8i	−1.44185	+	1.44185i
$582$	1.53771e7	−	2.89620e8i	0.0780017	−	1.46913i
$583$	1.46460e6			0.00739118
$584$	−1.41846e8	+	1.02613e8i	−0.712162	+	0.515185i
$585$			3.95153e8i			1.97377i
$586$	1.16583e7	−	2.19578e8i	0.0579351	−	1.09118i
$587$	8.00181e7	+	8.00181e7i	0.395616	+	0.395616i	0.876684	−	0.481068i	$-0.159751\pi$
$587$	8.00181e7	+	8.00181e7i	0.395616	+	0.395616i	−0.481068	+	0.876684i	$0.659751\pi$
$588$	−7.60870e7	−	9.42230e7i	−0.374264	−	0.463474i
$589$	2.79459e7	+	2.79459e7i	0.136764	+	0.136764i
$590$	−9.52884e7	+	8.56800e7i	−0.463964	+	0.417180i
$591$			4.12558e8i			1.99858i
$592$	1.90373e8	−	1.22890e8i	0.917570	−	0.592312i
$593$	5.20669e7			0.249688			0.124844	−	0.992176i	$-0.460157\pi$
$593$	5.20669e7			0.249688			0.124844	+	0.992176i	$0.460157\pi$
$594$	−1.70030e6	−	1.89098e6i	−0.00811273	−	0.00902250i
$595$	1.87690e8	−	1.87690e8i	0.891024	−	0.891024i
$596$	1.11856e8	+	1.38518e8i	0.528349	+	0.654286i
$597$	−2.75175e8	+	2.75175e8i	−1.29326	+	1.29326i
$598$	−2.25401e8	−	1.19674e7i	−1.05403	−	0.0559625i
$599$	4.82128e6			0.0224327			0.0112164	−	0.999937i	$-0.496430\pi$
$599$	4.82128e6			0.0224327			0.0112164	+	0.999937i	$0.496430\pi$
$600$	−7.25376e7	+	4.51977e8i	−0.335822	+	2.09249i
$601$		−	4.87391e7i		−	0.224519i	−0.993679	−	0.112260i	$-0.964191\pi$
$601$		−	4.87391e7i		−	0.224519i	0.993679	−	0.112260i	$-0.0358088\pi$
$602$	−1.71621e8	−	9.11202e6i	−0.786647	−	0.0417662i
$603$	−1.99640e8	−	1.99640e8i	−0.910532	−	0.910532i
$604$	2.92705e6	−	2.74870e7i	0.0132837	−	0.124743i
$605$	2.50680e8	+	2.50680e8i	1.13202	+	1.13202i
$606$	6.56201e7	+	7.29788e7i	0.294862	+	0.327928i
$607$		−	3.50813e8i		−	1.56859i	−0.620387	−	0.784296i	$-0.713024\pi$
$607$		−	3.50813e8i		−	1.56859i	0.620387	−	0.784296i	$-0.286976\pi$
$608$	1.97796e7	−	7.28209e7i	0.0880049	−	0.324000i
$609$	−1.81624e8			−0.804121
$610$	−4.09667e8	+	3.68359e8i	−1.80485	+	1.62286i
$611$	1.47433e8	−	1.47433e8i	0.646356	−	0.646356i
$612$	1.20904e8	+	1.28749e7i	0.527458	+	0.0561681i
$613$	1.59265e7	−	1.59265e7i	0.0691413	−	0.0691413i	−0.671691	−	0.740832i	$-0.734432\pi$
$613$	1.59265e7	−	1.59265e7i	0.0691413	−	0.0691413i	0.740832	+	0.671691i	$0.234432\pi$
$614$	7.23512e6	−	1.36270e8i	0.0312565	−	0.588702i
$615$	5.02034e8			2.15828
$616$	−2.12533e6	+	1.32428e7i	−0.00909253	+	0.0566550i
$617$		−	3.70913e8i		−	1.57912i	−0.613671	−	0.789562i	$-0.710308\pi$
$617$		−	3.70913e8i		−	1.57912i	0.613671	−	0.789562i	$-0.289692\pi$
$618$	−8.11926e6	+	1.52922e8i	−0.0343994	+	0.647896i
$619$	−1.41681e7	−	1.41681e7i	−0.0597363	−	0.0597363i	0.676608	−	0.736344i	$-0.263449\pi$
$619$	−1.41681e7	−	1.41681e7i	−0.0597363	−	0.0597363i	−0.736344	+	0.676608i	$0.763449\pi$
$620$	1.71397e8	−	1.38407e8i	0.719165	−	0.580741i
$621$	−2.99408e7	−	2.99408e7i	−0.125023	−	0.125023i
$622$	1.70289e8	−	1.53118e8i	0.707643	−	0.636289i
$623$		−	2.46799e8i		−	1.02066i
$624$	−4.84686e8	−	1.04411e8i	−1.99483	−	0.429725i
$625$	2.32097e7			0.0950670
$626$	2.33300e8	+	2.59462e8i	0.951023	+	1.05767i
$627$	3.76240e6	−	3.76240e6i	0.0152638	−	0.0152638i
$628$	2.99166e8	−	2.41583e8i	1.20791	−	0.975410i
$629$	1.25655e8	−	1.25655e8i	0.504925	−	0.504925i
$630$	3.90412e8	+	2.07285e7i	1.56135	+	0.0828985i
$631$	−1.53432e8			−0.610699			−0.305350	−	0.952240i	$-0.598773\pi$
$631$	−1.53432e8			−0.610699			−0.305350	+	0.952240i	$0.598773\pi$
$632$	1.82420e8	−	1.31964e8i	0.722638	−	0.522764i
$633$			3.07931e7i			0.121406i
$634$	−2.02514e8	−	1.07523e7i	−0.794669	−	0.0421922i
$635$	9.92094e7	+	9.92094e7i	0.387464	+	0.387464i
$636$	5.32658e7	+	5.67217e6i	0.207051	+	0.0220485i
$637$	1.22664e8	+	1.22664e8i	0.474567	+	0.474567i
$638$	4.12643e6	+	4.58917e6i	0.0158896	+	0.0176715i
$639$		−	2.10291e8i		−	0.805970i
$640$	−3.91966e8	−	1.52620e8i	−1.49523	−	0.582199i
$641$	−9.63888e7			−0.365976			−0.182988	−	0.983115i	$-0.558577\pi$
$641$	−9.63888e7			−0.365976			−0.182988	+	0.983115i	$0.558577\pi$
$642$	3.69399e8	−	3.32151e8i	1.39602	−	1.25525i
$643$	−2.96341e8	+	2.96341e8i	−1.11470	+	1.11470i	−0.122198	+	0.992506i	$0.538994\pi$
$643$	−2.96341e8	+	2.96341e8i	−1.11470	+	1.11470i	−0.992506	+	0.122198i	$0.961006\pi$
$644$	−2.36477e7	+	2.22069e8i	−0.0885382	+	0.831437i
$645$	2.68739e8	−	2.68739e8i	1.00150	−	1.00150i
$646$	3.13761e6	−	5.90953e7i	0.0116386	−	0.219208i
$647$	−2.51144e8			−0.927279			−0.463640	−	0.886024i	$-0.653457\pi$
$647$	−2.51144e8			−0.927279			−0.463640	+	0.886024i	$0.653457\pi$
$648$	−1.83900e8	−	2.54213e8i	−0.675860	−	0.934269i
$649$		−	5.07805e6i		−	0.0185765i
$650$	3.47640e7	−	6.54763e8i	0.126587	−	2.38421i
$651$	−1.81670e8	−	1.81670e8i	−0.658477	−	0.658477i
$652$	1.45344e8	+	1.79989e8i	0.524391	+	0.649385i
$653$	1.19499e8	+	1.19499e8i	0.429165	+	0.429165i	0.888344	−	0.459179i	$-0.151856\pi$
$653$	1.19499e8	+	1.19499e8i	0.429165	+	0.429165i	−0.459179	+	0.888344i	$0.651856\pi$
$654$	−5.06886e8	+	4.55775e8i	−1.81208	+	1.62936i
$655$			5.25881e8i			1.87139i
$656$	−5.94155e7	+	2.75813e8i	−0.210469	+	0.977020i
$657$	−2.02229e8			−0.713094
$658$	−1.37930e8	−	1.53398e8i	−0.484153	−	0.538447i
$659$	−1.46053e8	+	1.46053e8i	−0.510333	+	0.510333i	−0.914629	−	0.404295i	$-0.867517\pi$
$659$	−1.46053e8	+	1.46053e8i	−0.510333	+	0.510333i	0.404295	+	0.914629i	$0.367517\pi$
$660$	−1.86339e7	−	2.30755e7i	−0.0648146	−	0.0802637i
$661$	−1.39338e8	+	1.39338e8i	−0.482464	+	0.482464i	−0.905918	−	0.423454i	$-0.860818\pi$
$661$	−1.39338e8	+	1.39338e8i	−0.482464	+	0.482464i	0.423454	+	0.905918i	$0.360818\pi$
$662$	−1.69091e8	−	8.97774e6i	−0.582838	−	0.0309452i
$663$	−3.88832e8			−1.33420
$664$	4.90727e8	+	7.87565e7i	1.67624	+	0.269019i
$665$		−	1.90286e8i		−	0.647057i
$666$	2.61374e8	+	1.38774e7i	0.884787	+	0.0469769i
$667$	7.26627e7	+	7.26627e7i	0.244869	+	0.244869i
$668$	4.38387e6	−	4.11677e7i	0.0147071	−	0.138111i
$669$	−1.23089e8	−	1.23089e8i	−0.411092	−	0.411092i
$670$	5.12158e8	+	5.69593e8i	1.70286	+	1.89383i
$671$		−	2.18318e7i		−	0.0722638i
$672$	−1.28583e8	+	4.73394e8i	−0.423717	+	1.55996i
$673$	1.12659e8			0.369590			0.184795	−	0.982777i	$-0.440838\pi$
$673$	1.12659e8			0.369590			0.184795	+	0.982777i	$0.440838\pi$
$674$	−1.14505e8	+	1.02959e8i	−0.373976	+	0.336266i
$675$	8.69747e7	−	8.69747e7i	0.282801	−	0.282801i
$676$	3.99006e8	+	4.24894e7i	1.29163	+	0.137544i
$677$	2.59382e8	−	2.59382e8i	0.835938	−	0.835938i	−0.152384	−	0.988321i	$-0.548695\pi$
$677$	2.59382e8	−	2.59382e8i	0.835938	−	0.835938i	0.988321	+	0.152384i	$0.0486949\pi$
$678$	880139.	−	1.65770e7i	0.00282398	−	0.0531884i
$679$	4.11022e8			1.31297
$680$	−3.25709e8	−	5.22730e7i	−1.03587	−	0.166246i
$681$		−	6.41587e8i		−	2.03149i
$682$	−462863.	+	8.71781e6i	−0.00145915	+	0.0274824i
$683$	−1.80845e8	−	1.80845e8i	−0.567604	−	0.567604i	0.363853	−	0.931456i	$-0.381461\pi$
$683$	−1.80845e8	−	1.80845e8i	−0.567604	−	0.567604i	−0.931456	+	0.363853i	$0.881461\pi$
$684$	6.78151e7	−	5.47621e7i	0.211913	−	0.171124i
$685$	−1.42988e8	−	1.42988e8i	−0.444865	−	0.444865i
$686$	−1.60705e8	+	1.44500e8i	−0.497802	+	0.447607i
$687$		−	2.41992e8i		−	0.746330i
$688$	1.15838e8	+	1.79448e8i	0.355701	+	0.551028i
$689$	−7.67279e7			−0.234583
$690$	−3.30204e8	−	3.67233e8i	−1.00516	−	1.11788i
$691$	−3.89481e8	+	3.89481e8i	−1.18046	+	1.18046i	−0.200838	+	0.979625i	$0.564366\pi$
$691$	−3.89481e8	+	3.89481e8i	−1.18046	+	1.18046i	−0.979625	+	0.200838i	$0.935634\pi$
$692$	−2.89227e8	+	2.33557e8i	−0.872812	+	0.704814i
$693$	−1.09551e7	+	1.09551e7i	−0.0329168	+	0.0329168i
$694$	5.70460e8	+	3.02880e7i	1.70666	+	0.0906134i
$695$	4.43442e8			1.32094
$696$	1.32300e8	+	1.82884e8i	0.392403	+	0.542434i
$697$			2.21267e8i			0.653458i
$698$	9.39633e7	+	4.98889e6i	0.276307	+	0.0146703i
$699$	1.95933e8	+	1.95933e8i	0.573687	+	0.573687i
$700$	−6.45084e8	−	6.86938e7i	−1.88071	−	0.200273i
$701$	−1.36109e8	−	1.36109e8i	−0.395122	−	0.395122i	0.481386	−	0.876509i	$-0.340133\pi$
$701$	−1.36109e8	−	1.36109e8i	−0.395122	−	0.395122i	−0.876509	+	0.481386i	$0.840133\pi$
$702$	8.90759e7	+	9.90651e7i	0.257483	+	0.286358i
$703$		−	1.27393e8i		−	0.366674i
$704$	1.48828e7	−	7.50635e6i	0.0426546	−	0.0215135i
$705$	4.56189e8			1.30190
$706$	1.47657e8	−	1.32768e8i	0.419603	−	0.377293i
$707$	−9.83483e7	+	9.83483e7i	−0.278297	+	0.278297i
$708$	1.96665e7	−	1.84683e8i	0.0554150	−	0.520387i
$709$	−3.01255e8	+	3.01255e8i	−0.845270	+	0.845270i	−0.989539	−	0.144268i	$-0.953917\pi$
$709$	−3.01255e8	+	3.01255e8i	−0.845270	+	0.845270i	0.144268	+	0.989539i	$0.453917\pi$
$710$	−3.02495e7	+	5.69734e8i	−0.0845167	+	1.59183i
$711$	2.60074e8			0.723584
$712$	−2.48510e8	+	1.79775e8i	−0.688501	+	0.498069i
$713$			1.45362e8i			0.401036i
$714$	−2.03969e7	+	3.84166e8i	−0.0560364	+	1.05542i
$715$	3.00407e7	+	3.00407e7i	0.0821848	+	0.0821848i
$716$	−6.35254e7	−	7.86672e7i	−0.173065	−	0.214316i
$717$	2.94596e8	+	2.94596e8i	0.799226	+	0.799226i
$718$	5.07790e8	−	4.56588e8i	1.37186	−	1.23353i
$719$		−	3.57293e8i		−	0.961253i	−0.876925	−	0.480626i	$-0.840409\pi$
$719$		−	3.57293e8i		−	0.961253i	0.876925	−	0.480626i	$-0.159591\pi$
$720$	−2.63514e8	−	4.08218e8i	−0.706003	−	1.09369i
$721$	−2.17024e8			−0.579031
$722$	2.23281e8	+	2.48321e8i	0.593254	+	0.659783i
$723$	−4.91236e8	+	4.91236e8i	−1.29980	+	1.29980i
$724$	−1.41838e8	−	1.75646e8i	−0.373747	−	0.462832i
$725$	−2.11077e8	+	2.11077e8i	−0.553894	+	0.553894i
$726$	−5.13097e8	−	2.72424e7i	−1.34088	−	0.0711926i
$727$	7.94049e7			0.206654			0.103327	−	0.994647i	$-0.467051\pi$
$727$	7.94049e7			0.206654			0.103327	+	0.994647i	$0.467051\pi$
$728$	1.11342e8	−	6.93768e8i	0.288580	−	1.79813i
$729$		−	2.30001e8i		−	0.593672i
$730$	5.47890e8	+	2.90897e7i	1.40840	+	0.0747774i
$731$	1.18444e8	+	1.18444e8i	0.303223	+	0.303223i
$732$	8.45510e7	−	7.93994e8i	0.215569	−	2.02434i
$733$	−2.46020e8	−	2.46020e8i	−0.624680	−	0.624680i	0.322044	−	0.946725i	$-0.395630\pi$
$733$	−2.46020e8	−	2.46020e8i	−0.624680	−	0.624680i	−0.946725	+	0.322044i	$0.895630\pi$
$734$	−2.71690e8	−	3.02157e8i	−0.687045	−	0.764091i
$735$			3.79547e8i			0.955879i
$736$	2.40834e8	−	1.37949e8i	0.604066	−	0.346007i
$737$	−3.03544e7			−0.0758262
$738$	−2.42346e8	+	2.17909e8i	−0.602930	+	0.542134i
$739$	2.05535e8	−	2.05535e8i	0.509276	−	0.509276i	−0.405028	−	0.914304i	$-0.632738\pi$
$739$	2.05535e8	−	2.05535e8i	0.509276	−	0.509276i	0.914304	+	0.405028i	$0.132738\pi$
$740$	−7.06132e8	−	7.51948e7i	−1.74257	−	0.185563i
$741$	−1.97106e8	+	1.97106e8i	−0.484445	+	0.484445i
$742$	−4.02491e6	+	7.58073e7i	−0.00985247	+	0.185566i
$743$	−1.49313e8			−0.364024			−0.182012	−	0.983296i	$-0.558261\pi$
$743$	−1.49313e8			−0.364024			−0.182012	+	0.983296i	$0.558261\pi$
$744$	−5.05965e7	+	3.15264e8i	−0.122858	+	0.765517i
$745$		−	5.57975e8i		−	1.34942i
$746$	1.29330e7	−	2.43588e8i	0.0311519	−	0.586731i
$747$	4.05954e8	+	4.05954e8i	0.973901	+	0.973901i
$748$	1.01703e7	−	8.21272e6i	0.0243013	−	0.0196238i
$749$	4.97813e8	+	4.97813e8i	1.18473	+	1.18473i
$750$	3.89317e8	−	3.50061e8i	0.922827	−	0.829774i
$751$			2.61119e8i			0.616478i	0.951309	+	0.308239i	$0.0997397\pi$
$751$			2.61119e8i			0.616478i	−0.951309	+	0.308239i	$0.900260\pi$
$752$	−5.39897e7	+	2.50626e8i	−0.126957	+	0.589350i
$753$	6.36135e8			1.48992
$754$	−2.16176e8	−	2.40419e8i	−0.504306	−	0.560860i
$755$	−6.12566e7	+	6.12566e7i	−0.142335	+	0.142335i
$756$	1.02549e8	−	8.28105e7i	0.237338	−	0.191655i
$757$	4.05024e8	−	4.05024e8i	0.933670	−	0.933670i	−0.0642632	−	0.997933i	$-0.520470\pi$
$757$	4.05024e8	−	4.05024e8i	0.933670	−	0.933670i	0.997933	+	0.0642632i	$0.0204697\pi$
$758$	−1.07351e8	−	5.69970e6i	−0.246490	−	0.0130871i
$759$	1.95704e7			0.0447583
$760$	−1.91606e8	+	1.38610e8i	−0.436484	+	0.315757i
$761$			1.35070e8i			0.306481i	0.988189	+	0.153240i	$0.0489709\pi$
$761$			1.35070e8i			0.306481i	−0.988189	+	0.153240i	$0.951029\pi$
$762$	−2.03063e8	−	1.07815e7i	−0.458952	−	0.0243676i
$763$	−6.83094e8	−	6.83094e8i	−1.53782	−	1.53782i
$764$	4.53356e8	+	4.82770e7i	1.01662	+	0.108258i
$765$	−2.69443e8	−	2.69443e8i	−0.601843	−	0.601843i
$766$	−3.79271e8	−	4.21803e8i	−0.843846	−	0.938477i
$767$			2.66030e8i			0.589583i
$768$	5.70340e8	−	2.15358e8i	1.25907	−	0.475420i
$769$	3.00152e8			0.660028			0.330014	−	0.943976i	$-0.392946\pi$
$769$	3.00152e8			0.660028			0.330014	+	0.943976i	$0.392946\pi$
$770$	3.12561e7	−	2.81044e7i	0.0684640	−	0.0615605i
$771$	6.64243e8	−	6.64243e8i	1.44932	−	1.44932i
$772$	1.10981e7	−	1.04219e8i	0.0241211	−	0.226515i
$773$	3.89585e7	−	3.89585e7i	0.0843458	−	0.0843458i	−0.663675	−	0.748021i	$-0.731004\pi$
$773$	3.89585e7	−	3.89585e7i	0.0843458	−	0.0843458i	0.748021	+	0.663675i	$0.231004\pi$
$774$	−1.30810e7	+	2.46375e8i	−0.0282110	+	0.531341i
$775$	−4.22261e8			−0.907143
$776$	−2.99399e8	−	4.13872e8i	−0.640716	−	0.885689i
$777$			8.28157e8i			1.76543i
$778$	−1.75069e7	+	3.29734e8i	−0.0371766	+	0.700204i
$779$	1.12164e8	+	1.12164e8i	0.237269	+	0.237269i
$780$	9.76200e8	+	1.20889e9i	2.05710	+	2.54742i
$781$	−1.59870e7	−	1.59870e7i	−0.0335593	−	0.0335593i
$782$	1.61854e8	−	1.45534e8i	0.338458	−	0.304330i
$783$		−	6.06513e7i		−	0.126344i
$784$	−2.08520e8	−	4.49191e7i	−0.432712	−	0.0932144i
$785$	−1.20509e9			−2.49122
$786$	−5.09617e8	−	5.66766e8i	−1.04948	−	1.16718i
$787$	4.96033e8	−	4.96033e8i	1.01762	−	1.01762i	0.0177796	−	0.999842i	$-0.494340\pi$
$787$	4.96033e8	−	4.96033e8i	1.01762	−	1.01762i	0.999842	−	0.0177796i	$-0.00565973\pi$
$788$	4.56504e8	+	5.65316e8i	0.932967	+	1.15535i
$789$	1.17908e8	−	1.17908e8i	0.240056	−	0.240056i
$790$	−7.04609e8	−	3.74105e7i	−1.42911	−	0.0758774i
$791$	2.35257e7			0.0475350
$792$	1.90111e7	+	3.05108e6i	0.0382676	+	0.00614155i
$793$			1.14373e9i			2.29352i
$794$	−2.24388e8	−	1.19136e7i	−0.448268	−	0.0238003i
$795$	−1.18706e8	−	1.18706e8i	−0.236250	−	0.236250i
$796$	−7.25770e7	+	6.81550e8i	−0.143900	+	1.35132i
$797$	−3.36288e8	−	3.36288e8i	−0.664257	−	0.664257i	0.292123	−	0.956381i	$-0.405638\pi$
$797$	−3.36288e8	−	3.36288e8i	−0.664257	−	0.664257i	−0.956381	+	0.292123i	$0.905638\pi$
$798$	1.84401e8	+	2.05080e8i	0.362873	+	0.403567i
$799$			2.01061e8i			0.394174i
$800$	4.00726e8	+	6.99595e8i	0.782668	+	1.36640i
$801$	−3.54299e8			−0.689402
$802$	2.08291e8	−	1.87288e8i	0.403782	−	0.363067i
$803$	−1.53740e7	+	1.53740e7i	−0.0296921	+	0.0296921i
$804$	−1.10395e9	−	1.17558e8i	−2.12414	−	0.226195i
$805$	4.94894e8	−	4.94894e8i	0.948690	−	0.948690i
$806$	2.42486e7	−	4.56711e8i	0.0463107	−	0.872241i
$807$	−7.39140e8			−1.40639
$808$	1.70670e8	+	2.73907e7i	0.323536	+	0.0519242i
$809$		−	2.41708e8i		−	0.456506i	−0.973602	−	0.228253i	$-0.926699\pi$
$809$		−	2.41708e8i		−	0.456506i	0.973602	−	0.228253i	$-0.0733013\pi$
$810$	−5.21337e7	+	9.81914e8i	−0.0980988	+	1.84764i
$811$	4.40043e8	+	4.40043e8i	0.824959	+	0.824959i	0.986814	−	0.161855i	$-0.0517478\pi$
$811$	4.40043e8	+	4.40043e8i	0.824959	+	0.824959i	−0.161855	+	0.986814i	$0.551748\pi$
$812$	−2.48874e8	+	2.00971e8i	−0.464849	+	0.375375i
$813$	4.00893e8	+	4.00893e8i	0.746030	+	0.746030i
$814$	2.09254e7	−	1.88154e7i	0.0387972	−	0.0348851i
$815$		−	7.25025e8i		−	1.33931i
$816$	4.01688e8	−	2.59299e8i	0.739296	−	0.477233i
$817$	1.20083e8			0.220199
$818$	5.16891e8	+	5.74856e8i	0.944363	+	1.05027i
$819$	5.73920e8	−	5.73920e8i	1.04472	−	1.04472i
$820$	6.87923e8	−	5.55512e8i	1.24767	−	1.00752i
$821$	−2.57117e8	+	2.57117e8i	−0.464624	+	0.464624i	−0.900168	−	0.435544i	$-0.856556\pi$
$821$	−2.57117e8	+	2.57117e8i	−0.464624	+	0.464624i	0.435544	+	0.900168i	$0.356556\pi$
$822$	2.92670e8	+	1.55390e7i	0.526943	+	0.0279775i
$823$	−9.19926e8			−1.65026			−0.825132	−	0.564940i	$-0.808899\pi$
$823$	−9.19926e8			−1.65026			−0.825132	+	0.564940i	$0.808899\pi$
$824$	1.58086e8	+	2.18529e8i	0.282561	+	0.390596i
$825$			5.68497e7i			0.101243i
$826$	2.62839e8	+	1.39551e7i	0.466390	+	0.0247625i
$827$	−4.44970e8	−	4.44970e8i	−0.786709	−	0.786709i	0.194245	−	0.980953i	$-0.437774\pi$
$827$	−4.44970e8	−	4.44970e8i	−0.786709	−	0.786709i	−0.980953	+	0.194245i	$0.937774\pi$
$828$	3.18797e8	+	3.39481e7i	0.561595	+	0.0598032i
$829$	3.19132e8	+	3.19132e8i	0.560153	+	0.560153i	0.929351	−	0.369198i	$-0.120368\pi$
$829$	3.19132e8	+	3.19132e8i	0.560153	+	0.560153i	−0.369198	+	0.929351i	$0.620368\pi$
$830$	−1.04144e9	−	1.15823e9i	−1.82138	−	2.02563i
$831$			7.70672e8i			1.34297i
$832$	−7.79684e8	+	3.93245e8i	−1.35378	+	0.682799i
$833$	−1.67281e8			−0.289410
$834$	−4.77918e8	+	4.29728e8i	−0.823864	+	0.740790i
$835$	−9.17448e7	+	9.17448e7i	−0.157588	+	0.157588i
$836$	992329.	−	9.31868e6i	0.00169839	−	0.0159491i
$837$	6.06667e7	−	6.06667e7i	0.103460	−	0.103460i
$838$	−5.95000e7	+	1.12065e9i	−0.101108	+	1.90432i
$839$	3.41595e8			0.578397			0.289198	−	0.957269i	$-0.406611\pi$
$839$	3.41595e8			0.578397			0.289198	+	0.957269i	$0.406611\pi$
$840$	1.24559e9	−	9.01073e8i	2.10154	−	1.52027i
$841$		−	4.47630e8i		−	0.752543i
$842$	1.02162e7	−	1.92417e8i	0.0171140	−	0.322335i
$843$	1.32651e8	+	1.32651e8i	0.221426	+	0.221426i
$844$	3.40732e7	+	4.21948e7i	0.0566742	+	0.0701830i
$845$	−8.89211e8	−	8.89211e8i	−1.47379	−	1.47379i
$846$	−2.20215e8	+	1.98010e8i	−0.363694	+	0.327021i
$847$		−	7.28176e8i		−	1.19836i
$848$	7.92649e7	−	5.11673e7i	0.129985	−	0.0839083i
$849$	3.98064e8			0.650473
$850$	4.22760e8	+	4.70169e8i	0.688393	+	0.765591i
$851$	3.31323e8	−	3.31323e8i	0.537604	−	0.537604i
$852$	−5.19512e8	−	6.43342e8i	−0.839995	−	1.04022i
$853$	−7.26055e8	+	7.26055e8i	−1.16983	+	1.16983i	−0.187580	+	0.982249i	$0.560064\pi$
$853$	−7.26055e8	+	7.26055e8i	−1.16983	+	1.16983i	−0.982249	+	0.187580i	$0.939936\pi$
$854$	1.13001e9	+	5.99965e7i	1.81429	+	0.0963280i
$855$	−2.73171e8			−0.437055
$856$	1.38645e8	−	8.63886e8i	0.221046	−	1.37732i
$857$			1.03657e9i			1.64686i	0.567414	+	0.823432i	$0.307944\pi$
$857$			1.03657e9i			1.64686i	−0.567414	+	0.823432i	$0.692056\pi$
$858$	−6.14878e7	−	3.26463e6i	−0.0973480	−	0.00516859i
$859$	−3.46895e8	−	3.46895e8i	−0.547291	−	0.547291i	0.378366	−	0.925656i	$-0.376486\pi$
$859$	−3.46895e8	−	3.46895e8i	−0.547291	−	0.547291i	−0.925656	+	0.378366i	$0.876486\pi$
$860$	7.08797e7	−	6.65611e8i	0.111436	−	1.04647i
$861$	−7.29155e8	−	7.29155e8i	−1.14238	−	1.14238i
$862$	−3.31274e8	−	3.68424e8i	−0.517209	−	0.575210i
$863$			2.30709e8i			0.358948i	0.983763	+	0.179474i	$0.0574396\pi$
$863$			2.30709e8i			0.358948i	−0.983763	+	0.179474i	$0.942560\pi$
$864$	−1.58084e8	−	4.29388e7i	−0.245102	−	0.0665747i
$865$	1.16506e9			1.80011
$866$	−4.07205e7	+	3.66145e7i	−0.0626989	+	0.0563767i
$867$	−3.55072e8	+	3.55072e8i	−0.544828	+	0.544828i
$868$	−4.49959e8	−	4.79154e7i	−0.688041	−	0.0732682i
$869$	1.97716e7	−	1.97716e7i	0.0301289	−	0.0301289i
$870$	3.75056e7	−	7.06400e8i	0.0569559	−	1.07274i
$871$	1.59021e9			2.40659
$872$	−1.90247e8	+	1.18541e9i	−0.286925	+	1.78781i
$873$		−	5.90054e8i		−	0.886848i
$874$	8.27314e6	−	1.55821e8i	0.0123918	−	0.233395i
$875$	5.24655e8	+	5.24655e8i	0.783159	+	0.783159i
$876$	−6.18676e8	+	4.99594e8i	−0.920346	+	0.743198i
$877$	1.79911e7	+	1.79911e7i	0.0266722	+	0.0266722i	0.720317	−	0.693645i	$-0.243996\pi$
$877$	1.79911e7	+	1.79911e7i	0.0266722	+	0.0266722i	−0.693645	+	0.720317i	$0.743996\pi$
$878$	8.81004e8	−	7.92168e8i	1.30165	−	1.17040i
$879$		−	9.98775e8i		−	1.47062i
$880$	−5.10671e7	−	1.10008e7i	−0.0749364	−	0.0161427i
$881$	6.42117e8			0.939045			0.469523	−	0.882920i	$-0.344426\pi$
$881$	6.42117e8			0.939045			0.469523	+	0.882920i	$0.344426\pi$
$882$	−1.64743e8	−	1.83218e8i	−0.240105	−	0.267031i
$883$	4.47721e8	−	4.47721e8i	0.650317	−	0.650317i	−0.302752	−	0.953069i	$-0.597905\pi$
$883$	4.47721e8	−	4.47721e8i	0.650317	−	0.650317i	0.953069	+	0.302752i	$0.0979054\pi$
$884$	−5.32804e8	+	4.30250e8i	−0.771278	+	0.622823i
$885$	−4.11577e8	+	4.11577e8i	−0.593774	+	0.593774i
$886$	−1.24292e9	−	6.59918e7i	−1.78708	−	0.0948831i
$887$	5.17347e8			0.741329			0.370664	−	0.928767i	$-0.379130\pi$
$887$	5.17347e8			0.741329			0.370664	+	0.928767i	$0.379130\pi$
$888$	8.33900e8	−	6.03252e8i	1.19090	−	0.861509i
$889$		−	2.88183e8i		−	0.410170i
$890$	9.59888e8	+	5.09643e7i	1.36160	+	0.0722930i
$891$	−2.75529e7	−	2.75529e7i	−0.0389524	−	0.0389524i
$892$	−3.04865e8	−	3.24645e7i	−0.429549	−	0.0457419i
$893$	1.01921e8	+	1.01921e8i	0.143123	+	0.143123i
$894$	5.40718e8	+	6.01355e8i	0.756760	+	0.841624i
$895$			3.16885e8i			0.442011i
$896$	3.47627e8	+	7.90957e8i	0.483269	+	1.09959i
$897$	−1.02526e9			−1.42055
$898$	−1.80275e8	+	1.62097e8i	−0.248947	+	0.223845i
$899$	−1.47231e8	+	1.47231e8i	−0.202637	+	0.202637i
$900$	−9.86153e7	+	9.26068e8i	−0.135275	+	1.27033i
$901$	5.23186e7	−	5.23186e7i	0.0715289	−	0.0715289i
$902$	−1.85776e6	+	3.49900e7i	−0.00253145	+	0.0476786i
$903$	−7.80634e8			−1.06019
$904$	−1.71368e7	−	2.36889e7i	−0.0231966	−	0.0320656i
$905$			7.07535e8i			0.954557i
$906$	6.65699e6	−	1.25381e8i	0.00895144	−	0.168596i
$907$	−2.47278e8	−	2.47278e8i	−0.331409	−	0.331409i	0.521713	−	0.853121i	$-0.325293\pi$
$907$	−2.47278e8	−	2.47278e8i	−0.331409	−	0.331409i	−0.853121	+	0.521713i	$0.825293\pi$
$908$	−7.09930e8	−	8.79148e8i	−0.948327	−	1.17437i
$909$	1.41187e8	+	1.41187e8i	0.187976	+	0.187976i
$910$	−1.63745e9	+	1.47234e9i	−2.17292	+	1.95382i
$911$			1.40425e9i			1.85733i	0.370919	+	0.928665i	$0.379043\pi$
$911$			1.40425e9i			1.85733i	−0.370919	+	0.928665i	$0.620957\pi$
$912$	7.21796e7	−	3.35066e8i	0.0951547	−	0.441719i
$913$	6.17236e7			0.0811034
$914$	−8.61718e8	−	9.58353e8i	−1.12857	−	1.25512i
$915$	−1.76947e9	+	1.76947e9i	−2.30983	+	2.30983i
$916$	−2.67769e8	−	3.31595e8i	−0.348397	−	0.431441i
$917$	7.63790e8	−	7.63790e8i	0.990526	−	0.990526i
$918$	−1.28288e8	−	6.81132e6i	−0.165828	−	0.00880447i
$919$	−8.17828e8			−1.05370			−0.526848	−	0.849959i	$-0.676626\pi$
$919$	−8.17828e8			−1.05370			−0.526848	+	0.849959i	$0.676626\pi$
$920$	−8.58820e8	−	1.37832e8i	−1.10291	−	0.177005i
$921$		−	6.19839e8i		−	0.793414i
$922$	1.83758e8	+	9.75645e6i	0.234452	+	0.0124480i
$923$	8.37530e8	+	8.37530e8i	1.06511	+	1.06511i
$924$	−6.45093e6	+	6.05788e7i	−0.00817723	+	0.0767900i
$925$	9.62454e8	+	9.62454e8i	1.21606	+	1.21606i
$926$	9.01043e8	+	1.00209e9i	1.13478	+	1.26204i
$927$			3.11555e8i			0.391107i
$928$	3.83651e8	+	1.04207e8i	0.480057	+	0.130393i
$929$	9.02460e8			1.12559			0.562796	−	0.826596i	$-0.309726\pi$
$929$	9.02460e8			1.12559			0.562796	+	0.826596i	$0.309726\pi$
$930$	7.44095e8	−	6.69065e8i	0.925080	−	0.831801i
$931$	−8.47979e7	+	8.47979e7i	−0.105084	+	0.105084i
$932$	4.85285e8	+	5.16771e7i	0.599444	+	0.0638337i
$933$	7.35524e8	−	7.35524e8i	0.905632	−	0.905632i
$934$	4.61424e7	−	8.69070e8i	0.0566317	−	1.06663i
$935$	−4.09677e7			−0.0501195
$936$	−9.95958e8	−	1.59841e8i	−1.21454	−	0.194922i
$937$			8.55187e8i			1.03954i	0.854305	+	0.519771i	$0.173983\pi$
$937$			8.55187e8i			1.03954i	−0.854305	+	0.519771i	$0.826017\pi$
$938$	8.34179e7	−	1.57114e9i	0.101077	−	1.90373i
$939$	1.12069e9	+	1.12069e9i	1.35359	+	1.35359i
$940$	6.25103e8	−	5.04783e8i	0.752606	−	0.607745i
$941$	−6.02375e8	−	6.02375e8i	−0.722933	−	0.722933i	0.246269	−	0.969202i	$-0.420795\pi$
$941$	−6.02375e8	−	6.02375e8i	−0.722933	−	0.722933i	−0.969202	+	0.246269i	$0.920795\pi$
$942$	1.29878e9	−	1.16782e9i	1.55376	−	1.39709i
$943$			5.83429e8i			0.695750i
$944$	−1.77407e8	−	2.74826e8i	−0.210889	−	0.326695i
$945$	−4.13086e8			−0.489491
$946$	1.77357e7	+	1.97246e7i	0.0209495	+	0.0232989i
$947$	−4.57925e8	+	4.57925e8i	−0.539193	+	0.539193i	−0.923292	−	0.384099i	$-0.874512\pi$
$947$	−4.57925e8	+	4.57925e8i	−0.539193	+	0.539193i	0.384099	+	0.923292i	$0.374512\pi$
$948$	7.95642e8	−	6.42498e8i	0.933884	−	0.754130i
$949$	8.05419e8	−	8.05419e8i	0.942374	−	0.942374i
$950$	4.52641e8	+	2.40325e7i	0.527938	+	0.0280303i
$951$	−9.21155e8			−1.07100
$952$	3.97139e8	+	5.48982e8i	0.460290	+	0.636278i
$953$		−	1.03047e9i		−	1.19057i	−0.803513	−	0.595287i	$-0.797038\pi$
$953$		−	1.03047e9i		−	1.19057i	0.803513	−	0.595287i	$-0.202962\pi$
$954$	1.08827e8	+	5.77808e6i	0.125341	+	0.00665485i
$955$	−1.01033e9	−	1.01033e9i	−1.15999	−	1.15999i
$956$	7.29654e8	+	7.76995e7i	0.835109	+	0.0889292i
$957$	1.98219e7	+	1.98219e7i	0.0226157	+	0.0226157i
$958$	9.65692e8	+	1.07399e9i	1.09835	+	1.22152i
$959$			4.15352e8i			0.470934i
$960$	−1.81464e9	−	5.97862e8i	−2.05106	−	0.675751i
$961$	5.92968e8			0.668130
$962$	−1.09625e9	+	9.85706e8i	−1.23135	+	1.10719i
$963$	7.14650e8	−	7.14650e8i	0.800229	−	0.800229i
$964$	−1.29563e8	+	1.21669e9i	−0.144627	+	1.35815i
$965$	−2.32259e8	+	2.32259e8i	−0.258459	+	0.258459i
$966$	−5.37820e7	+	1.01296e9i	−0.0596630	+	1.12372i
$967$	1.42057e9			1.57103			0.785513	−	0.618845i	$-0.212399\pi$
$967$	1.42057e9			1.57103			0.785513	+	0.618845i	$0.212399\pi$
$968$	−7.33226e8	+	5.30423e8i	−0.808373	+	0.584785i
$969$		−	2.68801e8i		−	0.295434i
$970$	−8.48766e7	+	1.59861e9i	−0.0929978	+	1.75157i
$971$	−5.17352e8	−	5.17352e8i	−0.565104	−	0.565104i	0.365649	−	0.930753i	$-0.380847\pi$
$971$	−5.17352e8	−	5.17352e8i	−0.565104	−	0.565104i	−0.930753	+	0.365649i	$0.880847\pi$
$972$	−7.48824e8	−	9.27312e8i	−0.815419	−	1.00978i
$973$	−6.44056e8	−	6.44056e8i	−0.699174	−	0.699174i
$974$	−1.64677e8	+	1.48071e8i	−0.178219	+	0.160249i
$975$		−	2.97826e9i		−	3.21328i
$976$	−7.62714e8	−	1.18154e9i	−0.820375	−	1.27087i
$977$	−1.73570e9			−1.86119			−0.930594	−	0.366054i	$-0.880709\pi$
$977$	−1.73570e9			−1.86119			−0.930594	+	0.366054i	$0.880709\pi$
$978$	7.02602e8	+	7.81393e8i	0.751091	+	0.835320i
$979$	−2.69349e7	+	2.69349e7i	−0.0287056	+	0.0287056i
$980$	4.19977e8	+	5.20082e8i	0.446218	+	0.552578i
$981$	−9.80635e8	+	9.80635e8i	−1.03872	+	1.03872i
$982$	−1.28164e9	−	6.80476e7i	−1.35342	−	0.0718585i
$983$	5.18747e8			0.546129			0.273064	−	0.961996i	$-0.411963\pi$
$983$	5.18747e8			0.546129			0.273064	+	0.961996i	$0.411963\pi$
$984$	−2.03075e8	+	1.26535e9i	−0.213143	+	1.32808i
$985$		−	2.27719e9i		−	2.38282i
$986$	3.11339e8	+	1.65302e7i	0.324790	+	0.0172444i
$987$	−6.62569e8	−	6.62569e8i	−0.689096	−	0.689096i
$988$	−5.19864e7	+	4.88189e8i	−0.0539038	+	0.506195i
$989$	3.12310e8	+	3.12310e8i	0.322847	+	0.322847i
$990$	−4.03461e7	−	4.48706e7i	−0.0415811	−	0.0462441i
$991$			6.01846e8i			0.618392i	0.950998	+	0.309196i	$0.100060\pi$
$991$			6.01846e8i			0.618392i	−0.950998	+	0.309196i	$0.899940\pi$
$992$	2.79515e8	+	4.87982e8i	0.286332	+	0.499884i
$993$	−7.69130e8			−0.785510
$994$	8.71416e8	−	7.83547e8i	0.887292	−	0.797822i
$995$	1.51888e9	−	1.51888e9i	1.54189	−	1.54189i
$996$	2.24481e9	+	2.39046e8i	2.27197	+	0.241938i
$997$	−7.87235e8	+	7.87235e8i	−0.794363	+	0.794363i	−0.982200	−	0.187837i	$-0.939852\pi$
$997$	−7.87235e8	+	7.87235e8i	−0.794363	+	0.794363i	0.187837	+	0.982200i	$0.439852\pi$
$998$	1.78119e7	−	3.35478e8i	0.0179192	−	0.337499i
$999$	−2.76554e8			−0.277385

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.7.f.a.3.9	✓	22
4.3	odd	2		64.7.f.a.47.2		22
8.3	odd	2		128.7.f.a.95.10		22
8.5	even	2		128.7.f.b.95.2		22
16.3	odd	4		128.7.f.b.31.2		22
16.5	even	4		64.7.f.a.15.2		22
16.11	odd	4	inner	16.7.f.a.11.9	yes	22
16.13	even	4		128.7.f.a.31.10		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.7.f.a.3.9	✓	22	1.1	even	1	trivial
16.7.f.a.11.9	yes	22	16.11	odd	4	inner
64.7.f.a.15.2		22	16.5	even	4
64.7.f.a.47.2		22	4.3	odd	2
128.7.f.a.31.10		22	16.13	even	4
128.7.f.a.95.10		22	8.3	odd	2
128.7.f.b.31.2		22	16.3	odd	4
128.7.f.b.95.2		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)

\(f(q)\)	\(=\)	\(q+(5.94882 - 5.34898i) q^{2} +(25.6946 - 25.6946i) q^{3} +(6.77693 - 63.6402i) q^{4} +(-141.826 + 141.826i) q^{5} +(15.4128 - 290.292i) q^{6} +411.977 q^{7} +(-300.095 - 414.834i) q^{8} -591.425i q^{9} +O(q^{10})\)	\(q+(5.94882 - 5.34898i) q^{2} +(25.6946 - 25.6946i) q^{3} +(6.77693 - 63.6402i) q^{4} +(-141.826 + 141.826i) q^{5} +(15.4128 - 290.292i) q^{6} +411.977 q^{7} +(-300.095 - 414.834i) q^{8} -591.425i q^{9} +(-85.0738 + 1602.32i) q^{10} +(-44.9619 - 44.9619i) q^{11} +(-1461.08 - 1809.34i) q^{12} +(2355.48 + 2355.48i) q^{13} +(2450.78 - 2203.65i) q^{14} +7288.34i q^{15} +(-4004.15 - 862.570i) q^{16} -3212.26 q^{17} +(-3163.52 - 3518.28i) q^{18} +(-1628.35 + 1628.35i) q^{19} +(8064.70 + 9986.99i) q^{20} +(10585.6 - 10585.6i) q^{21} +(-507.970 - 26.9702i) q^{22} -8469.99 q^{23} +(-18369.8 - 2948.16i) q^{24} -24604.3i q^{25} +(26611.7 + 1412.92i) q^{26} +(3534.93 + 3534.93i) q^{27} +(2791.94 - 26218.3i) q^{28} +(-8578.85 - 8578.85i) q^{29} +(38985.1 + 43357.0i) q^{30} -17162.0i q^{31} +(-28433.8 + 16286.8i) q^{32} -2310.56 q^{33} +(-19109.2 + 17182.3i) q^{34} +(-58429.1 + 58429.1i) q^{35} +(-37638.4 - 4008.05i) q^{36} +(-39117.2 + 39117.2i) q^{37} +(-976.759 + 18396.8i) q^{38} +121046. q^{39} +(101396. + 16272.9i) q^{40} -68881.9i q^{41} +(6349.71 - 119594. i) q^{42} +(-36872.5 - 36872.5i) q^{43} +(-3166.09 + 2556.68i) q^{44} +(83879.6 + 83879.6i) q^{45} +(-50386.4 + 45305.8i) q^{46} -62591.7i q^{47} +(-125048. + 80721.6i) q^{48} +52075.9 q^{49} +(-131608. - 146367. i) q^{50} +(-82537.8 + 82537.8i) q^{51} +(165866. - 133940. i) q^{52} +(-16287.1 + 16287.1i) q^{53} +(39936.9 + 2120.41i) q^{54} +12753.5 q^{55} +(-123632. - 170902. i) q^{56} +83679.7i q^{57} +(-96922.0 - 5145.98i) q^{58} +(56470.6 + 56470.6i) q^{59} +(463831. + 49392.5i) q^{60} +(242781. + 242781. i) q^{61} +(-91799.4 - 102094. i) q^{62} -243653. i q^{63} +(-82029.9 + 248979. i) q^{64} -668136. q^{65} +(-13745.1 + 12359.1i) q^{66} +(337557. - 337557. i) q^{67} +(-21769.3 + 204429. i) q^{68} +(-217633. + 217633. i) q^{69} +(-35048.4 + 660120. i) q^{70} +355567. q^{71} +(-245343. + 177484. i) q^{72} -341935. i q^{73} +(-23464.3 + 441939. i) q^{74} +(-632199. - 632199. i) q^{75} +(92593.4 + 114664. i) q^{76} +(-18523.3 - 18523.3i) q^{77} +(720081. - 647472. i) q^{78} +439742. i q^{79} +(690228. - 445558. i) q^{80} +612806. q^{81} +(-368448. - 409766. i) q^{82} +(-686399. + 686399. i) q^{83} +(-601931. - 745406. i) q^{84} +(455583. - 455583. i) q^{85} +(-416578. - 22117.8i) q^{86} -440860. q^{87} +(-5158.86 + 32144.5i) q^{88} -599060. i q^{89} +(947654. + 50314.8i) q^{90} +(970401. + 970401. i) q^{91} +(-57400.5 + 539032. i) q^{92} +(-440972. - 440972. i) q^{93} +(-334801. - 372347. i) q^{94} -461886. i q^{95} +(-312112. + 1.14908e6i) q^{96} +997682. q^{97} +(309790. - 278553. i) q^{98} +(-26591.6 + 26591.6i) 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

Groups

Database

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