LMFDB - Embedded newform 16.7.f.a.11.6

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			11.6
Character	$\chi$	$=$	16.11
Dual form			16.7.f.a.3.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.392939 + 7.99034i) q^{2} +(-15.4507 - 15.4507i) q^{3} +(-63.6912 - 6.27943i) q^{4} +(-66.8872 - 66.8872i) q^{5} +(129.527 - 117.385i) q^{6} -121.702 q^{7} +(75.2016 - 506.447i) q^{8} -251.553i q^{9} +O(q^{10})$	\(q+(-0.392939 + 7.99034i) q^{2} +(-15.4507 - 15.4507i) q^{3} +(-63.6912 - 6.27943i) q^{4} +(-66.8872 - 66.8872i) q^{5} +(129.527 - 117.385i) q^{6} -121.702 q^{7} +(75.2016 - 506.447i) q^{8} -251.553i q^{9} +(560.735 - 508.169i) q^{10} +(-1652.52 + 1652.52i) q^{11} +(887.051 + 1081.09i) q^{12} +(-836.906 + 836.906i) q^{13} +(47.8216 - 972.444i) q^{14} +2066.91i q^{15} +(4017.14 + 799.889i) q^{16} +3619.86 q^{17} +(2009.99 + 98.8449i) q^{18} +(-5241.94 - 5241.94i) q^{19} +(3840.11 + 4680.14i) q^{20} +(1880.38 + 1880.38i) q^{21} +(-12554.9 - 13853.6i) q^{22} -77.1116 q^{23} +(-8986.87 + 6663.04i) q^{24} -6677.19i q^{25} +(-6358.32 - 7016.02i) q^{26} +(-15150.2 + 15150.2i) q^{27} +(7751.37 + 764.222i) q^{28} +(31731.0 - 31731.0i) q^{29} +(-16515.3 - 812.168i) q^{30} -3585.24i q^{31} +(-7969.88 + 31784.0i) q^{32} +51065.3 q^{33} +(-1422.38 + 28923.9i) q^{34} +(8140.34 + 8140.34i) q^{35} +(-1579.61 + 16021.7i) q^{36} +(-44437.9 - 44437.9i) q^{37} +(43944.6 - 39825.1i) q^{38} +25861.6 q^{39} +(-38904.9 + 28844.8i) q^{40} +121940. i q^{41} +(-15763.8 + 14286.0i) q^{42} +(-62148.8 + 62148.8i) q^{43} +(115628. - 94874.3i) q^{44} +(-16825.7 + 16825.7i) q^{45} +(30.3001 - 616.148i) q^{46} -99656.9i q^{47} +(-49708.7 - 74426.4i) q^{48} -102838. q^{49} +(53353.1 + 2623.73i) q^{50} +(-55929.3 - 55929.3i) q^{51} +(58558.9 - 48048.3i) q^{52} +(-123740. - 123740. i) q^{53} +(-115102. - 127009. i) q^{54} +221066. q^{55} +(-9152.21 + 61635.8i) q^{56} +161983. i q^{57} +(241073. + 266010. i) q^{58} +(-1066.08 + 1066.08i) q^{59} +(12979.0 - 131644. i) q^{60} +(-103557. + 103557. i) q^{61} +(28647.3 + 1408.78i) q^{62} +30614.6i q^{63} +(-250833. - 76171.3i) q^{64} +111957. q^{65} +(-20065.5 + 408029. i) q^{66} +(-11914.8 - 11914.8i) q^{67} +(-230553. - 22730.7i) q^{68} +(1191.43 + 1191.43i) q^{69} +(-68242.7 + 61845.4i) q^{70} +603474. q^{71} +(-127398. - 18917.2i) q^{72} -102254. i q^{73} +(372536. - 337613. i) q^{74} +(-103167. + 103167. i) q^{75} +(300949. + 366782. i) q^{76} +(201116. - 201116. i) q^{77} +(-10162.0 + 206643. i) q^{78} -387379. i q^{79} +(-215193. - 322198. i) q^{80} +284780. q^{81} +(-974342. - 47915.0i) q^{82} +(-84597.7 - 84597.7i) q^{83} +(-107956. - 131572. i) q^{84} +(-242122. - 242122. i) q^{85} +(-472169. - 521011. i) q^{86} -980532. q^{87} +(712644. + 961189. i) q^{88} +34522.8i q^{89} +(-127831. - 141054. i) q^{90} +(101853. - 101853. i) q^{91} +(4911.33 + 484.217i) q^{92} +(-55394.5 + 55394.5i) q^{93} +(796293. + 39159.1i) q^{94} +701237. i q^{95} +(614225. - 367944. i) q^{96} -331728. q^{97} +(40408.9 - 821707. i) q^{98} +(415697. + 415697. 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 $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.392939	+	7.99034i	−0.0491174	+	0.998793i
$2$	−0.392939	+	7.99034i	−0.0491174	+	0.998793i
$3$	−15.4507	−	15.4507i	−0.572248	−	0.572248i	0.360508	−	0.932756i	$-0.382603\pi$
$3$	−15.4507	−	15.4507i	−0.572248	−	0.572248i	−0.932756	+	0.360508i	$0.882603\pi$
$4$	−63.6912	−	6.27943i	−0.995175	−	0.0981162i
$5$	−66.8872	−	66.8872i	−0.535098	−	0.535098i	0.386987	−	0.922085i	$-0.373516\pi$
$5$	−66.8872	−	66.8872i	−0.535098	−	0.535098i	−0.922085	+	0.386987i	$0.873516\pi$
$6$	129.527	−	117.385i	0.599664	−	0.543450i
$7$	−121.702			−0.354817			−0.177409	−	0.984137i	$-0.556771\pi$
$7$	−121.702			−0.354817			−0.177409	+	0.984137i	$0.556771\pi$
$8$	75.2016	−	506.447i	0.146878	−	0.989155i
$9$		−	251.553i		−	0.345065i
$10$	560.735	−	508.169i	0.560735	−	0.508169i
$11$	−1652.52	+	1652.52i	−1.24157	+	1.24157i	−0.282215	+	0.959351i	$0.591069\pi$
$11$	−1652.52	+	1652.52i	−1.24157	+	1.24157i	−0.959351	+	0.282215i	$0.908931\pi$
$12$	887.051	+	1081.09i	0.513340	+	0.625633i
$13$	−836.906	+	836.906i	−0.380931	+	0.380931i	−0.871438	−	0.490506i	$-0.836812\pi$
$13$	−836.906	+	836.906i	−0.380931	+	0.380931i	0.490506	+	0.871438i	$0.336812\pi$
$14$	47.8216	−	972.444i	0.0174277	−	0.354389i
$15$			2066.91i			0.612417i
$16$	4017.14	+	799.889i	0.980746	+	0.195286i
$17$	3619.86			0.736792			0.368396	−	0.929669i	$-0.379907\pi$
$17$	3619.86			0.736792			0.368396	+	0.929669i	$0.379907\pi$
$18$	2009.99	+	98.8449i	0.344649	+	0.0169487i
$19$	−5241.94	−	5241.94i	−0.764242	−	0.764242i	0.212844	−	0.977086i	$-0.431727\pi$
$19$	−5241.94	−	5241.94i	−0.764242	−	0.764242i	−0.977086	+	0.212844i	$0.931727\pi$
$20$	3840.11	+	4680.14i	0.480014	+	0.585018i
$21$	1880.38	+	1880.38i	0.203043	+	0.203043i
$22$	−12554.9	−	13853.6i	−1.17909	−	1.30105i
$23$	−77.1116			−0.00633776			−0.00316888	−	0.999995i	$-0.501009\pi$
$23$	−77.1116			−0.00633776			−0.00316888	+	0.999995i	$0.501009\pi$
$24$	−8986.87	+	6663.04i	−0.650092	+	0.481991i
$25$		−	6677.19i		−	0.427340i
$26$	−6358.32	−	7016.02i	−0.361761	−	0.399182i
$27$	−15150.2	+	15150.2i	−0.769710	+	0.769710i
$28$	7751.37	+	764.222i	0.353105	+	0.0348133i
$29$	31731.0	−	31731.0i	1.30104	−	1.30104i	0.373346	−	0.927692i	$-0.378211\pi$
$29$	31731.0	−	31731.0i	1.30104	−	1.30104i	0.927692	−	0.373346i	$-0.121789\pi$
$30$	−16515.3	−	812.168i	−0.611678	−	0.0300803i
$31$		−	3585.24i		−	0.120347i	−0.998188	−	0.0601733i	$-0.980835\pi$
$31$		−	3585.24i		−	0.120347i	0.998188	−	0.0601733i	$-0.0191653\pi$
$32$	−7969.88	+	31784.0i	−0.243221	+	0.969971i
$33$	51065.3			1.42097
$34$	−1422.38	+	28923.9i	−0.0361893	+	0.735903i
$35$	8140.34	+	8140.34i	0.189862	+	0.189862i
$36$	−1579.61	+	16021.7i	−0.0338565	+	0.343401i
$37$	−44437.9	−	44437.9i	−0.877301	−	0.877301i	0.115954	−	0.993255i	$-0.463008\pi$
$37$	−44437.9	−	44437.9i	−0.877301	−	0.877301i	−0.993255	+	0.115954i	$0.963008\pi$
$38$	43944.6	−	39825.1i	0.800857	−	0.725782i
$39$	25861.6			0.435974
$40$	−38904.9	+	28844.8i	−0.607889	+	0.450700i
$41$			121940.i			1.76927i	0.466283	+	0.884636i	$0.345593\pi$
$41$			121940.i			1.76927i	−0.466283	+	0.884636i	$0.654407\pi$
$42$	−15763.8	+	14286.0i	−0.212771	+	0.192825i
$43$	−62148.8	+	62148.8i	−0.781677	+	0.781677i	−0.980114	−	0.198437i	$-0.936414\pi$
$43$	−62148.8	+	62148.8i	−0.781677	+	0.781677i	0.198437	+	0.980114i	$0.436414\pi$
$44$	115628.	−	94874.3i	1.35739	−	1.11376i
$45$	−16825.7	+	16825.7i	−0.184644	+	0.184644i
$46$	30.3001	−	616.148i	0.000311294	−	0.00633011i
$47$		−	99656.9i		−	0.959873i	−0.877303	−	0.479937i	$-0.840660\pi$
$47$		−	99656.9i		−	0.959873i	0.877303	−	0.479937i	$-0.159340\pi$
$48$	−49708.7	−	74426.4i	−0.449478	−	0.672981i
$49$	−102838.			−0.874105
$50$	53353.1	+	2623.73i	0.426825	+	0.0209898i
$51$	−55929.3	−	55929.3i	−0.421627	−	0.421627i
$52$	58558.9	−	48048.3i	0.416469	−	0.341718i
$53$	−123740.	−	123740.i	−0.831158	−	0.831158i	0.156517	−	0.987675i	$-0.449973\pi$
$53$	−123740.	−	123740.i	−0.831158	−	0.831158i	−0.987675	+	0.156517i	$0.949973\pi$
$54$	−115102.	−	127009.i	−0.730975	−	0.806588i
$55$	221066.			1.32872
$56$	−9152.21	+	61635.8i	−0.0521149	+	0.350969i
$57$			161983.i			0.874671i
$58$	241073.	+	266010.i	1.23556	+	1.36337i
$59$	−1066.08	+	1066.08i	−0.00519078	+	0.00519078i	−0.709697	−	0.704507i	$-0.751168\pi$
$59$	−1066.08	+	1066.08i	−0.00519078	+	0.00519078i	0.704507	+	0.709697i	$0.251168\pi$
$60$	12979.0	−	131644.i	0.0600880	−	0.609462i
$61$	−103557.	+	103557.i	−0.456238	+	0.456238i	−0.897418	−	0.441181i	$-0.854560\pi$
$61$	−103557.	+	103557.i	−0.456238	+	0.456238i	0.441181	+	0.897418i	$0.354560\pi$
$62$	28647.3	+	1408.78i	0.120201	+	0.00591110i
$63$			30614.6i			0.122435i
$64$	−250833.	−	76171.3i	−0.956854	−	0.290570i
$65$	111957.			0.407671
$66$	−20065.5	+	408029.i	−0.0697941	+	1.41925i
$67$	−11914.8	−	11914.8i	−0.0396154	−	0.0396154i	0.687022	−	0.726637i	$-0.258918\pi$
$67$	−11914.8	−	11914.8i	−0.0396154	−	0.0396154i	−0.726637	+	0.687022i	$0.758918\pi$
$68$	−230553.	−	22730.7i	−0.733237	−	0.0722912i
$69$	1191.43	+	1191.43i	0.00362677	+	0.00362677i
$70$	−68242.7	+	61845.4i	−0.198958	+	0.180307i
$71$	603474.			1.68610			0.843051	−	0.537834i	$-0.180757\pi$
$71$	603474.			1.68610			0.843051	+	0.537834i	$0.180757\pi$
$72$	−127398.	−	18917.2i	−0.341323	−	0.0506826i
$73$		−	102254.i		−	0.262851i	−0.991326	−	0.131426i	$-0.958045\pi$
$73$		−	102254.i		−	0.262851i	0.991326	−	0.131426i	$-0.0419555\pi$
$74$	372536.	−	337613.i	0.919333	−	0.833151i
$75$	−103167.	+	103167.i	−0.244544	+	0.244544i
$76$	300949.	+	366782.i	0.685570	+	0.835539i
$77$	201116.	−	201116.i	0.440529	−	0.440529i
$78$	−10162.0	+	206643.i	−0.0214139	+	0.435448i
$79$		−	387379.i		−	0.785696i	−0.919603	−	0.392848i	$-0.871490\pi$
$79$		−	387379.i		−	0.785696i	0.919603	−	0.392848i	$-0.128510\pi$
$80$	−215193.	−	322198.i	−0.420299	−	0.629292i
$81$	284780.			0.535864
$82$	−974342.	−	47915.0i	−1.76714	−	0.0869019i
$83$	−84597.7	−	84597.7i	−0.147953	−	0.147953i	0.629250	−	0.777203i	$-0.283362\pi$
$83$	−84597.7	−	84597.7i	−0.147953	−	0.147953i	−0.777203	+	0.629250i	$0.783362\pi$
$84$	−107956.	−	131572.i	−0.182142	−	0.221986i
$85$	−242122.	−	242122.i	−0.394256	−	0.394256i
$86$	−472169.	−	521011.i	−0.742339	−	0.819127i
$87$	−980532.			−1.48903
$88$	712644.	+	961189.i	1.04574	+	1.41046i
$89$			34522.8i			0.0489707i	0.999700	+	0.0244853i	$0.00779470\pi$
$89$			34522.8i			0.0489707i	−0.999700	+	0.0244853i	$0.992205\pi$
$90$	−127831.	−	141054.i	−0.175352	−	0.193490i
$91$	101853.	−	101853.i	0.135161	−	0.135161i
$92$	4911.33	+	484.217i	0.00630718	+	0.000621837i
$93$	−55394.5	+	55394.5i	−0.0688680	+	0.0688680i
$94$	796293.	+	39159.1i	0.958715	+	0.0471465i
$95$			701237.i			0.817889i
$96$	614225.	−	367944.i	0.694246	−	0.415881i
$97$	−331728.			−0.363469			−0.181734	−	0.983348i	$-0.558171\pi$
$97$	−331728.			−0.363469			−0.181734	+	0.983348i	$0.558171\pi$
$98$	40408.9	−	821707.i	0.0429337	−	0.873050i
$99$	415697.	+	415697.i	0.428422	+	0.428422i
$100$	−41929.0	+	425278.i	−0.0419290	+	0.425278i
$101$	1.15559e6	+	1.15559e6i	1.12161	+	1.12161i	0.991500	+	0.130106i	$0.0415318\pi$
$101$	1.15559e6	+	1.15559e6i	1.12161	+	1.12161i	0.130106	+	0.991500i	$0.458468\pi$
$102$	468871.	−	424917.i	0.441828	−	0.400409i
$103$	−1.83079e6			−1.67543			−0.837717	−	0.546105i	$-0.816110\pi$
$103$	−1.83079e6			−1.67543			−0.837717	+	0.546105i	$0.816110\pi$
$104$	360912.	+	486786.i	0.320850	+	0.432751i
$105$		−	251548.i		−	0.217296i
$106$	1.03735e6	−	940105.i	0.870979	−	0.789331i
$107$	−283121.	+	283121.i	−0.231111	+	0.231111i	−0.813156	−	0.582046i	$-0.802253\pi$
$107$	−283121.	+	283121.i	−0.231111	+	0.231111i	0.582046	+	0.813156i	$0.302253\pi$
$108$	1.06007e6	−	869800.i	0.841518	−	0.690476i
$109$	790298.	−	790298.i	0.610255	−	0.610255i	−0.332758	−	0.943012i	$-0.607979\pi$
$109$	790298.	−	790298.i	0.610255	−	0.610255i	0.943012	+	0.332758i	$0.107979\pi$
$110$	−86865.3	+	1.76639e6i	−0.0652632	+	1.32712i
$111$			1.37319e6i			1.00407i
$112$	−488895.	−	97348.4i	−0.347986	−	0.0692907i
$113$	−860645.			−0.596470			−0.298235	−	0.954492i	$-0.596398\pi$
$113$	−860645.			−0.596470			−0.298235	+	0.954492i	$0.596398\pi$
$114$	−1.29430e6	−	63649.4i	−0.873615	−	0.0429615i
$115$	5157.78	+	5157.78i	0.00339132	+	0.00339132i
$116$	−2.22024e6	+	1.82173e6i	−1.42241	+	1.16711i
$117$	210526.	+	210526.i	0.131446	+	0.131446i
$118$	−8099.42	−	8937.23i	−0.00492956	−	0.00543947i
$119$	−440545.			−0.261427
$120$	1.04678e6	+	155435.i	0.605775	+	0.0899507i
$121$		−	3.69011e6i		−	2.08297i
$122$	−786766.	−	868150.i	−0.433278	−	0.478096i
$123$	1.88406e6	−	1.88406e6i	1.01246	−	1.01246i
$124$	−22513.3	+	228348.i	−0.0118079	+	0.119766i
$125$	−1.49173e6	+	1.49173e6i	−0.763767	+	0.763767i
$126$	−244621.	−	12029.7i	−0.122287	−	0.00601370i
$127$		−	679010.i		−	0.331486i	−0.986169	−	0.165743i	$-0.946998\pi$
$127$		−	679010.i		−	0.331486i	0.986169	−	0.165743i	$-0.0530022\pi$
$128$	707197.	−	1.97431e6i	0.337218	−	0.941427i
$129$	1.92048e6			0.894625
$130$	−43992.2	+	894573.i	−0.0200237	+	0.407179i
$131$	−311623.	−	311623.i	−0.138617	−	0.138617i	0.634394	−	0.773010i	$-0.281250\pi$
$131$	−311623.	−	311623.i	−0.138617	−	0.138617i	−0.773010	+	0.634394i	$0.781250\pi$
$132$	−3.25241e6	−	320661.i	−1.41411	−	0.139420i
$133$	637956.	+	637956.i	0.271166	+	0.271166i
$134$	99885.5	−	90521.9i	0.0415134	−	0.0376218i
$135$	2.02671e6			0.823741
$136$	272219.	−	1.83327e6i	0.108219	−	0.728801i
$137$			2.15854e6i			0.839459i	0.907649	+	0.419729i	$0.137875\pi$
$137$			2.15854e6i			0.839459i	−0.907649	+	0.419729i	$0.862125\pi$
$138$	−9988.07	+	9051.75i	−0.00380053	+	0.00344425i
$139$	1.48545e6	−	1.48545e6i	0.553114	−	0.553114i	−0.374224	−	0.927338i	$-0.622091\pi$
$139$	1.48545e6	−	1.48545e6i	0.553114	−	0.553114i	0.927338	+	0.374224i	$0.122091\pi$
$140$	−467351.	−	569584.i	−0.170317	−	0.207575i
$141$	−1.53977e6	+	1.53977e6i	−0.549285	+	0.549285i
$142$	−237129.	+	4.82197e6i	−0.0828169	+	1.68407i
$143$		−	2.76602e6i		−	0.945903i
$144$	201214.	−	1.01052e6i	0.0673863	−	0.338422i
$145$	−4.24480e6			−1.39237
$146$	817042.	+	40179.5i	0.262534	+	0.0129106i
$147$	1.58891e6	+	1.58891e6i	0.500204	+	0.500204i
$148$	2.55126e6	+	3.10935e6i	0.786990	+	0.959145i
$149$	1.39411e6	+	1.39411e6i	0.421442	+	0.421442i	0.885700	−	0.464258i	$-0.153679\pi$
$149$	1.39411e6	+	1.39411e6i	0.421442	+	0.421442i	−0.464258	+	0.885700i	$0.653679\pi$
$150$	−783803.	−	864880.i	−0.232238	−	0.256261i
$151$	2.86091e6			0.830946			0.415473	−	0.909605i	$-0.363616\pi$
$151$	2.86091e6			0.830946			0.415473	+	0.909605i	$0.363616\pi$
$152$	−3.04897e6	+	2.26056e6i	−0.868204	+	0.643703i
$153$		−	910585.i		−	0.254241i
$154$	1.52796e6	+	1.68601e6i	0.418360	+	0.461635i
$155$	−239807.	+	239807.i	−0.0643972	+	0.0643972i
$156$	−1.64715e6	−	162396.i	−0.433871	−	0.0427761i
$157$	−305105.	+	305105.i	−0.0788407	+	0.0788407i	−0.745427	−	0.666587i	$-0.767755\pi$
$157$	−305105.	+	305105.i	−0.0788407	+	0.0788407i	0.666587	+	0.745427i	$0.267755\pi$
$158$	3.09529e6	+	152216.i	0.784748	+	0.0385913i
$159$			3.82375e6i			0.951256i
$160$	2.65903e6	−	1.59286e6i	0.649177	−	0.388882i
$161$	9384.66			0.00224875
$162$	−111901.	+	2.27549e6i	−0.0263202	+	0.535218i
$163$	−1.46892e6	−	1.46892e6i	−0.339184	−	0.339184i	0.516876	−	0.856060i	$-0.327095\pi$
$163$	−1.46892e6	−	1.46892e6i	−0.339184	−	0.339184i	−0.856060	+	0.516876i	$0.827095\pi$
$164$	765714.	−	7.76650e6i	0.173594	−	1.76073i
$165$	−3.41561e6	−	3.41561e6i	−0.760356	−	0.760356i
$166$	709206.	−	642723.i	0.155042	−	0.140507i
$167$	−6.13253e6			−1.31671			−0.658356	−	0.752707i	$-0.728748\pi$
$167$	−6.13253e6			−1.31671			−0.658356	+	0.752707i	$0.728748\pi$
$168$	1.09372e6	−	810908.i	0.230664	−	0.171019i
$169$			3.42598e6i			0.709782i
$170$	2.02978e6	−	1.83950e6i	0.413145	−	0.374415i
$171$	−1.31862e6	+	1.31862e6i	−0.263714	+	0.263714i
$172$	4.34859e6	−	3.56807e6i	0.854600	−	0.701210i
$173$	2.23000e6	−	2.23000e6i	0.430693	−	0.430693i	−0.458171	−	0.888864i	$-0.651495\pi$
$173$	2.23000e6	−	2.23000e6i	0.430693	−	0.430693i	0.888864	+	0.458171i	$0.151495\pi$
$174$	385289.	−	7.83479e6i	0.0731373	−	1.48723i
$175$			812630.i			0.151628i
$176$	−7.96025e6	+	5.31658e6i	−1.46012	+	0.975202i
$177$	32943.2			0.00594082
$178$	−275849.	−	13565.4i	−0.0489116	−	0.00240531i
$179$	366903.	+	366903.i	0.0639723	+	0.0639723i	0.738369	−	0.674397i	$-0.235596\pi$
$179$	366903.	+	366903.i	0.0639723	+	0.0639723i	−0.674397	+	0.738369i	$0.735596\pi$
$180$	1.17730e6	−	965991.i	0.201869	−	0.165636i
$181$	−4.61849e6	−	4.61849e6i	−0.778869	−	0.778869i	0.200769	−	0.979639i	$-0.435656\pi$
$181$	−4.61849e6	−	4.61849e6i	−0.778869	−	0.778869i	−0.979639	+	0.200769i	$0.935656\pi$
$182$	773822.	+	853867.i	0.128359	+	0.141637i
$183$	3.20006e6			0.522162
$184$	−5798.91	+	39052.9i	−0.000930879	+	0.00626903i
$185$			5.94466e6i			0.938884i
$186$	−420854.	−	464387.i	−0.0654023	−	0.0721675i
$187$	−5.98190e6	+	5.98190e6i	−0.914776	+	0.914776i
$188$	−625789.	+	6.34727e6i	−0.0941791	+	0.955242i
$189$	1.84382e6	−	1.84382e6i	0.273107	−	0.273107i
$190$	−5.60313e6	−	275543.i	−0.816901	−	0.0401725i
$191$		−	9.81862e6i		−	1.40913i	−0.709640	−	0.704564i	$-0.751143\pi$
$191$		−	9.81862e6i		−	1.40913i	0.709640	−	0.704564i	$-0.248857\pi$
$192$	2.69865e6	+	5.05245e6i	0.381279	+	0.713835i
$193$	4.76197e6			0.662391			0.331196	−	0.943562i	$-0.392548\pi$
$193$	4.76197e6			0.662391			0.331196	+	0.943562i	$0.392548\pi$
$194$	130349.	−	2.65062e6i	0.0178526	−	0.363030i
$195$	−1.72981e6	−	1.72981e6i	−0.233289	−	0.233289i
$196$	6.54985e6	+	645762.i	0.869887	+	0.0857638i
$197$	4.92013e6	+	4.92013e6i	0.643543	+	0.643543i	0.951425	−	0.307882i	$-0.0996201\pi$
$197$	4.92013e6	+	4.92013e6i	0.643543	+	0.643543i	−0.307882	+	0.951425i	$0.599620\pi$
$198$	−3.48491e6	+	3.15822e6i	−0.448947	+	0.406862i
$199$	4.98525e6			0.632598			0.316299	−	0.948659i	$-0.397560\pi$
$199$	4.98525e6			0.632598			0.316299	+	0.948659i	$0.397560\pi$
$200$	−3.38165e6	−	502136.i	−0.422706	−	0.0627670i
$201$			368185.i			0.0453396i
$202$	−9.68765e6	+	8.77950e6i	−1.17534	+	1.06516i
$203$	−3.86174e6	+	3.86174e6i	−0.461631	+	0.461631i
$204$	3.21100e6	+	3.91341e6i	0.378224	+	0.460961i
$205$	8.15623e6	−	8.15623e6i	0.946733	−	0.946733i
$206$	719389.	−	1.46287e7i	0.0822929	−	1.67341i
$207$			19397.6i			0.00218694i
$208$	−4.03140e6	+	2.69254e6i	−0.447988	+	0.299207i
$209$	1.73249e7			1.89771
$210$	2.00995e6	+	98842.8i	0.217034	+	0.0106730i
$211$	1.36570e6	+	1.36570e6i	0.145381	+	0.145381i	0.776051	−	0.630670i	$-0.217220\pi$
$211$	1.36570e6	+	1.36570e6i	0.145381	+	0.145381i	−0.630670	+	0.776051i	$0.717220\pi$
$212$	7.10415e6	+	8.65819e6i	0.745598	+	0.908698i
$213$	−9.32409e6	−	9.32409e6i	−0.964868	−	0.964868i
$214$	−2.15098e6	−	2.37348e6i	−0.219480	−	0.242183i
$215$	8.31392e6			0.836547
$216$	6.53346e6	+	8.81210e6i	0.648309	+	0.874416i
$217$			436333.i			0.0427010i
$218$	6.00421e6	+	6.62529e6i	0.579544	+	0.639492i
$219$	−1.57989e6	+	1.57989e6i	−0.150416	+	0.150416i
$220$	−1.40799e7	−	1.38817e6i	−1.32231	−	0.130369i
$221$	−3.02948e6	+	3.02948e6i	−0.280667	+	0.280667i
$222$	−1.09723e7	−	539581.i	−1.00285	−	0.0493171i
$223$			1.32424e7i			1.19413i	0.802192	+	0.597066i	$0.203667\pi$
$223$			1.32424e7i			1.19413i	−0.802192	+	0.597066i	$0.796333\pi$
$224$	969953.	−	3.86819e6i	0.0862992	−	0.344163i
$225$	−1.67967e6			−0.147460
$226$	338181.	−	6.87685e6i	0.0292970	−	0.595750i
$227$	−1.21388e7	−	1.21388e7i	−1.03776	−	1.03776i	−0.999258	−	0.0385062i	$-0.987740\pi$
$227$	−1.21388e7	−	1.21388e7i	−1.03776	−	1.03776i	−0.0385062	−	0.999258i	$-0.512260\pi$
$228$	1.01716e6	−	1.03169e7i	0.0858194	−	0.870451i
$229$	2.33223e6	+	2.33223e6i	0.194207	+	0.194207i	0.797511	−	0.603304i	$-0.206149\pi$
$229$	2.33223e6	+	2.33223e6i	0.194207	+	0.194207i	−0.603304	+	0.797511i	$0.706149\pi$
$230$	−43239.1	+	39185.7i	−0.00355380	+	0.00322066i
$231$	−6.21476e6			−0.504184
$232$	−1.36839e7	−	1.84563e7i	−1.09583	−	1.47802i
$233$		−	9.93521e6i		−	0.785433i	−0.919660	−	0.392717i	$-0.871535\pi$
$233$		−	9.93521e6i		−	0.785433i	0.919660	−	0.392717i	$-0.128465\pi$
$234$	−1.76490e6	+	1.59945e6i	−0.137744	+	0.124831i
$235$	−6.66578e6	+	6.66578e6i	−0.513626	+	0.513626i
$236$	74594.1	−	61205.4i	0.00567503	−	0.00465644i
$237$	−5.98527e6	+	5.98527e6i	−0.449613	+	0.449613i
$238$	173107.	−	3.52011e6i	0.0128406	−	0.261111i
$239$		−	1.31680e7i		−	0.964556i	−0.876018	−	0.482278i	$-0.839810\pi$
$239$		−	1.31680e7i		−	0.964556i	0.876018	−	0.482278i	$-0.160190\pi$
$240$	−1.65330e6	+	8.30305e6i	−0.119596	+	0.600626i
$241$	−1.93349e7			−1.38131			−0.690654	−	0.723185i	$-0.742677\pi$
$241$	−1.93349e7			−1.38131			−0.690654	+	0.723185i	$0.742677\pi$
$242$	2.94853e7	+	1.44999e6i	2.08046	+	0.102310i
$243$	6.64445e6	+	6.64445e6i	0.463063	+	0.463063i
$244$	7.24597e6	−	5.94540e6i	0.498800	−	0.409272i
$245$	6.87852e6	+	6.87852e6i	0.467732	+	0.467732i
$246$	1.43139e7	+	1.57946e7i	0.961510	+	1.06097i
$247$	8.77402e6			0.582248
$248$	−1.81574e6	−	269616.i	−0.119041	−	0.0176763i
$249$			2.61418e6i			0.169332i
$250$	−1.13333e7	−	1.25056e7i	−0.725331	−	0.800359i
$251$	1.63941e7	−	1.63941e7i	1.03673	−	1.03673i	0.0374309	−	0.999299i	$-0.488083\pi$
$251$	1.63941e7	−	1.63941e7i	1.03673	−	1.03673i	0.999299	−	0.0374309i	$-0.0119174\pi$
$252$	192242.	−	1.94988e6i	0.0120129	−	0.121844i
$253$	127429.	−	127429.i	0.00786875	−	0.00786875i
$254$	5.42553e6	+	266810.i	0.331086	+	0.0162817i
$255$			7.48191e6i			0.451224i
$256$	1.54976e7	+	6.42653e6i	0.923727	+	0.383051i
$257$	−9.18776e6			−0.541265			−0.270633	−	0.962683i	$-0.587233\pi$
$257$	−9.18776e6			−0.541265			−0.270633	+	0.962683i	$0.587233\pi$
$258$	−754632.	+	1.53453e7i	−0.0439416	+	0.893545i
$259$	5.40820e6	+	5.40820e6i	0.311282	+	0.311282i
$260$	−7.13066e6	−	703025.i	−0.405704	−	0.0399991i
$261$	−7.98202e6	−	7.98202e6i	−0.448943	−	0.448943i
$262$	2.61242e6	−	2.36752e6i	0.145258	−	0.131641i
$263$	−1.95854e7			−1.07662			−0.538312	−	0.842745i	$-0.680938\pi$
$263$	−1.95854e7			−1.07662			−0.538312	+	0.842745i	$0.680938\pi$
$264$	3.84019e6	−	2.58619e7i	0.208709	−	1.40556i
$265$			1.65533e7i			0.889502i
$266$	−5.34817e6	+	4.84681e6i	−0.284158	+	0.257520i
$267$	533401.	−	533401.i	0.0280233	−	0.0280233i
$268$	684052.	+	833689.i	0.0355373	+	0.0433111i
$269$	−2.11137e7	+	2.11137e7i	−1.08469	+	1.08469i	−0.0886277	+	0.996065i	$0.528248\pi$
$269$	−2.11137e7	+	2.11137e7i	−1.08469	+	1.08469i	−0.996065	+	0.0886277i	$0.971752\pi$
$270$	−796374.	+	1.61941e7i	−0.0404600	+	0.822747i
$271$			5.87787e6i			0.295333i	0.989037	+	0.147667i	$0.0471763\pi$
$271$			5.87787e6i			0.295333i	−0.989037	+	0.147667i	$0.952824\pi$
$272$	1.45415e7	+	2.89549e6i	0.722606	+	0.143885i
$273$	−3.14741e6			−0.154691
$274$	−1.72475e7	−	848176.i	−0.838445	−	0.0412320i
$275$	1.10342e7	+	1.10342e7i	0.530571	+	0.530571i
$276$	−68401.9	−	83364.9i	−0.00325343	−	0.00396511i
$277$	1.63950e7	+	1.63950e7i	0.771385	+	0.771385i	0.978349	−	0.206963i	$-0.0663581\pi$
$277$	1.63950e7	+	1.63950e7i	0.771385	+	0.771385i	−0.206963	+	0.978349i	$0.566358\pi$
$278$	1.12856e7	+	1.24530e7i	0.525279	+	0.579614i
$279$	−901878.			−0.0415274
$280$	4.73482e6	−	3.51048e6i	0.215690	−	0.159916i
$281$			5.78838e6i			0.260878i	0.991456	+	0.130439i	$0.0416387\pi$
$281$			5.78838e6i			0.260878i	−0.991456	+	0.130439i	$0.958361\pi$
$282$	−1.16982e7	−	1.29083e7i	−0.521643	−	0.575602i
$283$	3.06081e7	−	3.06081e7i	1.35045	−	1.35045i	0.465288	−	0.885159i	$-0.345951\pi$
$283$	3.06081e7	−	3.06081e7i	1.35045	−	1.35045i	0.885159	−	0.465288i	$-0.154049\pi$
$284$	−3.84360e7	−	3.78948e6i	−1.67797	−	0.165434i
$285$	1.08346e7	−	1.08346e7i	0.468035	−	0.468035i
$286$	2.21014e7	+	1.08688e6i	0.944761	+	0.0464603i
$287$		−	1.48404e7i		−	0.627768i
$288$	7.99535e6	+	2.00485e6i	0.334703	+	0.0839273i
$289$	−1.10342e7			−0.457138
$290$	1.66795e6	−	3.39174e7i	0.0683893	−	1.39068i
$291$	5.12543e6	+	5.12543e6i	0.207994	+	0.207994i
$292$	−642095.	+	6.51266e6i	−0.0257900	+	0.261583i
$293$	−9.11890e6	−	9.11890e6i	−0.362527	−	0.362527i	0.502216	−	0.864742i	$-0.332518\pi$
$293$	−9.11890e6	−	9.11890e6i	−0.362527	−	0.362527i	−0.864742	+	0.502216i	$0.832518\pi$
$294$	−1.33203e7	+	1.20716e7i	−0.524169	+	0.475032i
$295$	142614.			0.00555515
$296$	−2.58473e7	+	1.91637e7i	−0.996642	+	0.738930i
$297$		−	5.00722e7i		−	1.91129i
$298$	−1.16872e7	+	1.05916e7i	−0.441634	+	0.400234i
$299$	64535.2	−	64535.2i	0.00241425	−	0.00241425i
$300$	7.21867e6	−	5.92301e6i	0.267358	−	0.219371i
$301$	7.56365e6	−	7.56365e6i	0.277353	−	0.277353i
$302$	−1.12416e6	+	2.28596e7i	−0.0408139	+	0.829943i
$303$		−	3.57094e7i		−	1.28367i
$304$	−1.68646e7	−	2.52505e7i	−0.600282	−	0.898773i
$305$	1.38533e7			0.488264
$306$	7.27589e6	+	357804.i	0.253935	+	0.0124877i
$307$	169532.	+	169532.i	0.00585918	+	0.00585918i	0.710030	−	0.704171i	$-0.248681\pi$
$307$	169532.	+	169532.i	0.00585918	+	0.00585918i	−0.704171	+	0.710030i	$0.748681\pi$
$308$	−1.40722e7	+	1.15464e7i	−0.481627	+	0.395181i
$309$	2.82870e7	+	2.82870e7i	0.958763	+	0.958763i
$310$	−1.82191e6	−	2.01037e6i	−0.0611564	−	0.0674825i
$311$	−2.53265e7			−0.841964			−0.420982	−	0.907069i	$-0.638314\pi$
$311$	−2.53265e7			−0.841964			−0.420982	+	0.907069i	$0.638314\pi$
$312$	1.94483e6	−	1.30975e7i	0.0640351	−	0.431246i
$313$		−	3.13305e7i		−	1.02172i	−0.859662	−	0.510862i	$-0.829326\pi$
$313$		−	3.13305e7i		−	1.02172i	0.859662	−	0.510862i	$-0.170674\pi$
$314$	−2.31801e6	−	2.55778e6i	−0.0748731	−	0.0826180i
$315$	2.04772e6	−	2.04772e6i	0.0655148	−	0.0655148i
$316$	−2.43252e6	+	2.46726e7i	−0.0770895	+	0.781905i
$317$	8.59619e6	−	8.59619e6i	0.269854	−	0.269854i	−0.559188	−	0.829041i	$-0.688887\pi$
$317$	8.59619e6	−	8.59619e6i	0.269854	−	0.269854i	0.829041	+	0.559188i	$0.188887\pi$
$318$	−3.05530e7	−	1.50250e6i	−0.950108	−	0.0467232i
$319$			1.04873e8i			3.23065i
$320$	1.16827e7	+	2.18724e7i	0.356527	+	0.667494i
$321$	8.74881e6			0.264505
$322$	−3687.60	+	74986.7i	−0.000110453	+	0.00224603i
$323$	−1.89751e7	−	1.89751e7i	−0.563087	−	0.563087i
$324$	−1.81380e7	−	1.78826e6i	−0.533279	−	0.0525770i
$325$	5.58819e6	+	5.58819e6i	0.162787	+	0.162787i
$326$	1.23144e7	−	1.11600e7i	0.355435	−	0.322115i
$327$	−2.44213e7			−0.698434
$328$	6.17561e7	+	9.17008e6i	1.75008	+	0.259867i
$329$			1.21285e7i			0.340580i
$330$	2.86341e7	−	2.59498e7i	0.796785	−	0.722092i
$331$	−1.68223e7	+	1.68223e7i	−0.463875	+	0.463875i	−0.899923	−	0.436048i	$-0.856378\pi$
$331$	−1.68223e7	+	1.68223e7i	−0.463875	+	0.463875i	0.436048	+	0.899923i	$0.356378\pi$
$332$	4.85690e6	+	5.91935e6i	0.132723	+	0.161756i
$333$	−1.11785e7	+	1.11785e7i	−0.302726	+	0.302726i
$334$	2.40971e6	−	4.90011e7i	0.0646734	−	1.31512i
$335$			1.59390e6i			0.0423962i
$336$	6.04966e6	+	9.05786e6i	0.159483	+	0.238786i
$337$	7.98258e6			0.208571			0.104285	−	0.994547i	$-0.466744\pi$
$337$	7.98258e6			0.208571			0.104285	+	0.994547i	$0.466744\pi$
$338$	−2.73748e7	−	1.34620e6i	−0.708926	−	0.0348626i
$339$	1.32976e7	+	1.32976e7i	0.341329	+	0.341329i
$340$	1.39007e7	+	1.69415e7i	0.353671	+	0.431036i
$341$	5.92470e6	+	5.92470e6i	0.149418	+	0.149418i
$342$	−1.00181e7	−	1.10544e7i	−0.250442	−	0.276348i
$343$	2.68337e7			0.664965
$344$	2.68014e7	+	3.61488e7i	0.658388	+	0.888010i
$345$		−	159382.i		−	0.00388135i
$346$	1.69422e7	+	1.86948e7i	0.409018	+	0.451327i
$347$	−1.15339e7	+	1.15339e7i	−0.276049	+	0.276049i	−0.831530	−	0.555480i	$-0.812534\pi$
$347$	−1.15339e7	+	1.15339e7i	−0.276049	+	0.276049i	0.555480	+	0.831530i	$0.312534\pi$
$348$	6.24512e7	+	6.15719e6i	1.48185	+	0.146098i
$349$	1.93783e6	−	1.93783e6i	0.0455868	−	0.0455868i	−0.683946	−	0.729533i	$-0.739738\pi$
$349$	1.93783e6	−	1.93783e6i	0.0455868	−	0.0455868i	0.729533	+	0.683946i	$0.239738\pi$
$350$	−6.49320e6	−	319314.i	−0.151445	−	0.00744756i
$351$		−	2.53586e7i		−	0.586414i
$352$	−3.93534e7	−	6.56943e7i	−0.902307	−	1.50626i
$353$	−1.27870e7			−0.290700			−0.145350	−	0.989380i	$-0.546431\pi$
$353$	−1.27870e7			−0.290700			−0.145350	+	0.989380i	$0.546431\pi$
$354$	−12944.7	+	263228.i	−0.000291798	+	0.00593365i
$355$	−4.03647e7	−	4.03647e7i	−0.902230	−	0.902230i
$356$	216784.	−	2.19880e6i	0.00480481	−	0.0487344i
$357$	6.80673e6	+	6.80673e6i	0.149601	+	0.149601i
$358$	−3.07585e6	+	2.78751e6i	−0.0670372	+	0.0607529i
$359$	−3.11361e7			−0.672947			−0.336473	−	0.941693i	$-0.609234\pi$
$359$	−3.11361e7			−0.672947			−0.336473	+	0.941693i	$0.609234\pi$
$360$	7.25599e6	+	9.78663e6i	0.155521	+	0.209761i
$361$			7.90990e6i			0.168132i
$362$	3.87181e7	−	3.50886e7i	0.816185	−	0.739673i
$363$	−5.70148e7	+	5.70148e7i	−1.19198	+	1.19198i
$364$	−7.12675e6	+	5.84759e6i	−0.147770	+	0.121247i
$365$	−6.83947e6	+	6.83947e6i	−0.140651	+	0.140651i
$366$	−1.25743e6	+	2.55696e7i	−0.0256472	+	0.521531i
$367$		−	7.10844e7i		−	1.43806i	−0.694981	−	0.719028i	$-0.744587\pi$
$367$		−	7.10844e7i		−	1.43806i	0.694981	−	0.719028i	$-0.255413\pi$
$368$	−309768.	−	61680.7i	−0.00621574	−	0.00123767i
$369$	3.06743e7			0.610514
$370$	−4.74999e7	−	2.33589e6i	−0.937750	−	0.0461155i
$371$	1.50595e7	+	1.50595e7i	0.294909	+	0.294909i
$372$	3.87599e6	−	3.18029e6i	0.0752928	−	0.0617786i
$373$	−5.52051e7	−	5.52051e7i	−1.06378	−	1.06378i	−0.997822	−	0.0659603i	$-0.978989\pi$
$373$	−5.52051e7	−	5.52051e7i	−1.06378	−	1.06378i	−0.0659603	−	0.997822i	$-0.521011\pi$
$374$	−4.54469e7	−	5.01480e7i	−0.868740	−	0.958603i
$375$	4.60966e7			0.874127
$376$	−5.04710e7	−	7.49436e6i	−0.949463	−	0.140984i
$377$			5.31118e7i			0.991213i
$378$	1.40082e7	+	1.54572e7i	0.259363	+	0.286191i
$379$	3.89682e7	−	3.89682e7i	0.715801	−	0.715801i	−0.251941	−	0.967743i	$-0.581069\pi$
$379$	3.89682e7	−	3.89682e7i	0.715801	−	0.715801i	0.967743	+	0.251941i	$0.0810690\pi$
$380$	4.40337e6	−	4.46626e7i	0.0802481	−	0.813942i
$381$	−1.04912e7	+	1.04912e7i	−0.189692	+	0.189692i
$382$	7.84542e7	+	3.85812e6i	1.40743	+	0.0692127i
$383$			3.33754e7i			0.594060i	0.954868	+	0.297030i	$0.0959962\pi$
$383$			3.33754e7i			0.594060i	−0.954868	+	0.297030i	$0.904004\pi$
$384$	−4.14312e7	+	1.95778e7i	−0.731701	+	0.345757i
$385$	−2.69042e7			−0.471453
$386$	−1.87116e6	+	3.80498e7i	−0.0325349	+	0.661592i
$387$	1.56337e7	+	1.56337e7i	0.269730	+	0.269730i
$388$	2.11282e7	+	2.08307e6i	0.361715	+	0.0356622i
$389$	−4.29114e7	−	4.29114e7i	−0.728994	−	0.728994i	0.241426	−	0.970419i	$-0.422385\pi$
$389$	−4.29114e7	−	4.29114e7i	−0.728994	−	0.728994i	−0.970419	+	0.241426i	$0.922385\pi$
$390$	1.45015e7	−	1.31421e7i	0.244466	−	0.221549i
$391$	−279133.			−0.00466961
$392$	−7.73355e6	+	5.20818e7i	−0.128387	+	0.864625i
$393$			9.62957e6i			0.158646i
$394$	−4.12468e7	+	3.73802e7i	−0.674375	+	0.611157i
$395$	−2.59107e7	+	2.59107e7i	−0.420424	+	0.420424i
$396$	−2.38659e7	−	2.90866e7i	−0.384319	−	0.468390i
$397$	7.31474e7	−	7.31474e7i	1.16904	−	1.16904i	0.186599	−	0.982436i	$-0.440253\pi$
$397$	7.31474e7	−	7.31474e7i	1.16904	−	1.16904i	0.982436	−	0.186599i	$-0.0597466\pi$
$398$	−1.95890e6	+	3.98339e7i	−0.0310716	+	0.631835i
$399$		−	1.97137e7i		−	0.310349i
$400$	5.34102e6	−	2.68232e7i	0.0834534	−	0.419113i
$401$	8.45758e7			1.31164			0.655818	−	0.754919i	$-0.272324\pi$
$401$	8.45758e7			1.31164			0.655818	+	0.754919i	$0.272324\pi$
$402$	−2.94192e6	−	144674.i	−0.0452849	−	0.00222696i
$403$	3.00051e6	+	3.00051e6i	0.0458438	+	0.0458438i
$404$	−6.63446e7	−	8.08575e7i	−1.00615	−	1.22624i
$405$	−1.90482e7	−	1.90482e7i	−0.286740	−	0.286740i
$406$	−2.93392e7	−	3.23741e7i	−0.438400	−	0.483748i
$407$	1.46869e8			2.17845
$408$	−3.25312e7	+	2.41193e7i	−0.478982	+	0.355127i
$409$			9.99205e7i			1.46044i	0.683210	+	0.730222i	$0.260583\pi$
$409$			9.99205e7i			1.46044i	−0.683210	+	0.730222i	$0.739417\pi$
$410$	6.19662e7	+	6.83760e7i	0.899090	+	0.992092i
$411$	3.33510e7	−	3.33510e7i	0.480378	−	0.480378i
$412$	1.16605e8	+	1.14963e7i	1.66735	+	0.164387i
$413$	129744.	−	129744.i	0.00184178	−	0.00184178i
$414$	−154994.	−	7622.08i	−0.00218430	−	0.000107417i
$415$			1.13170e7i			0.158339i
$416$	−1.99302e7	−	3.32703e7i	−0.276842	−	0.462143i
$417$	−4.59025e7			−0.633036
$418$	−6.80761e6	+	1.38432e8i	−0.0932107	+	1.89542i
$419$	8.00776e6	+	8.00776e6i	0.108860	+	0.108860i	0.759439	−	0.650579i	$-0.225474\pi$
$419$	8.00776e6	+	8.00776e6i	0.108860	+	0.108860i	−0.650579	+	0.759439i	$0.725474\pi$
$420$	−1.57958e6	+	1.60214e7i	−0.0213203	+	0.216248i
$421$	2.60923e7	+	2.60923e7i	0.349676	+	0.349676i	0.859989	−	0.510313i	$-0.170470\pi$
$421$	2.60923e7	+	2.60923e7i	0.349676	+	0.349676i	−0.510313	+	0.859989i	$0.670470\pi$
$422$	−1.14491e7	+	1.03758e7i	−0.152347	+	0.138065i
$423$	−2.50690e7			−0.331219
$424$	−7.19734e7	+	5.33625e7i	−0.944223	+	0.700065i
$425$		−	2.41705e7i		−	0.314861i
$426$	7.81665e7	−	7.08389e7i	1.01109	−	0.916311i
$427$	1.26032e7	−	1.26032e7i	0.161881	−	0.161881i
$428$	1.98101e7	−	1.62545e7i	0.252671	−	0.207320i
$429$	−4.27368e7	+	4.27368e7i	−0.541291	+	0.541291i
$430$	−3.26686e6	+	6.64311e7i	−0.0410890	+	0.835538i
$431$		−	1.08961e8i		−	1.36094i	−0.732777	−	0.680468i	$-0.761776\pi$
$431$		−	1.08961e8i		−	1.36094i	0.732777	−	0.680468i	$-0.238224\pi$
$432$	−7.29790e7	+	4.87420e7i	−0.905204	+	0.604577i
$433$	−1.43136e8			−1.76313			−0.881567	−	0.472058i	$-0.843511\pi$
$433$	−1.43136e8			−1.76313			−0.881567	+	0.472058i	$0.843511\pi$
$434$	−3.48645e6	−	171452.i	−0.0426495	−	0.00209736i
$435$	6.55851e7	+	6.55851e7i	0.796778	+	0.796778i
$436$	−5.52976e7	+	4.53724e7i	−0.667186	+	0.547435i
$437$	404214.	+	404214.i	0.00484358	+	0.00484358i
$438$	−1.20031e7	−	1.32447e7i	−0.142846	−	0.157623i
$439$	3.90563e7			0.461634			0.230817	−	0.972997i	$-0.425860\pi$
$439$	3.90563e7			0.461634			0.230817	+	0.972997i	$0.425860\pi$
$440$	1.66245e7	−	1.11958e8i	0.195160	−	1.31431i
$441$			2.58691e7i			0.301623i
$442$	−2.30162e7	−	2.53970e7i	−0.266543	−	0.294114i
$443$	1.85718e6	−	1.85718e6i	0.0213620	−	0.0213620i	−0.696345	−	0.717707i	$-0.745192\pi$
$443$	1.85718e6	−	1.85718e6i	0.0213620	−	0.0213620i	0.717707	+	0.696345i	$0.245192\pi$
$444$	8.62287e6	−	8.74603e7i	0.0985152	−	0.999222i
$445$	2.30913e6	−	2.30913e6i	0.0262041	−	0.0262041i
$446$	−1.05811e8	−	5.20346e6i	−1.19269	−	0.0586527i
$447$		−	4.30799e7i		−	0.482339i
$448$	3.05270e7	+	9.27022e6i	0.339508	+	0.103099i
$449$	1.03229e8			1.14042			0.570209	−	0.821500i	$-0.306862\pi$
$449$	1.03229e8			1.14042			0.570209	+	0.821500i	$0.306862\pi$
$450$	660006.	−	1.34211e7i	0.00724287	−	0.147282i
$451$	−2.01509e8	−	2.01509e8i	−2.19667	−	2.19667i
$452$	5.48155e7	+	5.40436e6i	0.593592	+	0.0585234i
$453$	−4.42030e7	−	4.42030e7i	−0.475507	−	0.475507i
$454$	1.01763e8	−	9.22235e7i	1.08748	−	0.985540i
$455$	−1.36254e7			−0.144649
$456$	8.20358e7	+	1.21814e7i	0.865185	+	0.128470i
$457$			6.37499e7i			0.667930i	0.942585	+	0.333965i	$0.108387\pi$
$457$			6.37499e7i			0.667930i	−0.942585	+	0.333965i	$0.891613\pi$
$458$	−1.95517e7	+	1.77189e7i	−0.203512	+	0.184434i
$459$	−5.48416e7	+	5.48416e7i	−0.567116	+	0.567116i
$460$	−296117.	−	360893.i	−0.00304222	−	0.00370770i
$461$	−8.61182e7	+	8.61182e7i	−0.879007	+	0.879007i	−0.993432	−	0.114425i	$-0.963497\pi$
$461$	−8.61182e7	+	8.61182e7i	−0.879007	+	0.879007i	0.114425	+	0.993432i	$0.463497\pi$
$462$	2.44202e6	−	4.96581e7i	0.0247642	−	0.503575i
$463$			1.27955e8i			1.28918i	0.764528	+	0.644591i	$0.222972\pi$
$463$			1.27955e8i			1.28918i	−0.764528	+	0.644591i	$0.777028\pi$
$464$	1.52849e8	−	1.02087e8i	1.53006	−	1.02191i
$465$	7.41037e6			0.0737023
$466$	7.93857e7	+	3.90393e6i	0.784485	+	0.0385784i
$467$	8.68130e7	+	8.68130e7i	0.852382	+	0.852382i	0.990426	−	0.138044i	$-0.0440815\pi$
$467$	8.68130e7	+	8.68130e7i	0.852382	+	0.852382i	−0.138044	+	0.990426i	$0.544082\pi$
$468$	−1.20867e7	−	1.47306e7i	−0.117915	−	0.143709i
$469$	1.45006e6	+	1.45006e6i	0.0140562	+	0.0140562i
$470$	−5.06426e7	−	5.58811e7i	−0.487778	−	0.538234i
$471$	9.42817e6			0.0902328
$472$	459741.	+	620083.i	0.00437207	+	0.00589690i
$473$		−	2.05405e8i		−	1.94101i
$474$	−4.54725e7	−	5.01762e7i	−0.426986	−	0.471154i
$475$	−3.50014e7	+	3.50014e7i	−0.326591	+	0.326591i
$476$	2.80589e7	+	2.76638e6i	0.260165	+	0.0256502i
$477$	−3.11272e7	+	3.11272e7i	−0.286804	+	0.286804i
$478$	1.05217e8	+	5.17424e6i	0.963392	+	0.0473765i
$479$			1.27810e8i			1.16295i	0.813565	+	0.581474i	$0.197524\pi$
$479$			1.27810e8i			1.16295i	−0.813565	+	0.581474i	$0.802476\pi$
$480$	−6.56946e7	−	1.64730e7i	−0.594027	−	0.148953i
$481$	7.43808e7			0.668383
$482$	7.59744e6	−	1.54493e8i	0.0678463	−	1.37964i
$483$	−144999.	−	144999.i	−0.00128684	−	0.00128684i
$484$	−2.31718e7	+	2.35028e8i	−0.204373	+	2.07292i
$485$	2.21884e7	+	2.21884e7i	0.194491	+	0.194491i
$486$	−5.57023e7	+	5.04806e7i	−0.485249	+	0.439760i
$487$	−1.62214e8			−1.40443			−0.702217	−	0.711963i	$-0.747806\pi$
$487$	−1.62214e8			−1.40443			−0.702217	+	0.711963i	$0.747806\pi$
$488$	4.46586e7	+	6.02340e7i	0.384278	+	0.518301i
$489$			4.53917e7i			0.388195i
$490$	−5.76646e7	+	5.22589e7i	−0.490141	+	0.444193i
$491$	−5.29699e7	+	5.29699e7i	−0.447491	+	0.447491i	−0.894520	−	0.447028i	$-0.852482\pi$
$491$	−5.29699e7	+	5.29699e7i	−0.447491	+	0.447491i	0.447028	+	0.894520i	$0.352482\pi$
$492$	−1.31829e8	+	1.08167e8i	−1.10691	+	0.908237i
$493$	1.14862e8	−	1.14862e8i	0.958594	−	0.958594i
$494$	−3.44765e6	+	7.01074e7i	−0.0285985	+	0.581545i
$495$		−	5.56097e7i		−	0.458495i
$496$	2.86780e6	−	1.44024e7i	0.0235019	−	0.118029i
$497$	−7.34443e7			−0.598258
$498$	−2.08882e7	−	1.02721e6i	−0.169127	−	0.00831712i
$499$	−1.61475e7	−	1.61475e7i	−0.129958	−	0.129958i	0.639136	−	0.769094i	$-0.279292\pi$
$499$	−1.61475e7	−	1.61475e7i	−0.129958	−	0.129958i	−0.769094	+	0.639136i	$0.779292\pi$
$500$	1.04377e8	−	8.56430e7i	0.835020	−	0.685144i
$501$	9.47518e7	+	9.47518e7i	0.753485	+	0.753485i
$502$	1.24552e8	+	1.37436e8i	0.984557	+	1.08640i
$503$	−6.19657e7			−0.486908			−0.243454	−	0.969912i	$-0.578281\pi$
$503$	−6.19657e7			−0.486908			−0.243454	+	0.969912i	$0.578281\pi$
$504$	1.55047e7	+	2.30226e6i	0.121107	+	0.0179831i
$505$		−	1.54589e8i		−	1.20034i
$506$	968128.	+	1.06827e6i	0.00747276	+	0.00824575i
$507$	5.29338e7	−	5.29338e7i	0.406171	−	0.406171i
$508$	−4.26380e6	+	4.32470e7i	−0.0325241	+	0.329887i
$509$	5.79647e7	−	5.79647e7i	0.439552	−	0.439552i	−0.452309	−	0.891861i	$-0.649400\pi$
$509$	5.79647e7	−	5.79647e7i	0.439552	−	0.439552i	0.891861	+	0.452309i	$0.149400\pi$
$510$	−5.97830e7	−	2.93993e6i	−0.450679	−	0.0221629i
$511$			1.24445e7i			0.0932643i
$512$	−5.74398e7	+	1.21306e8i	−0.427960	+	0.903798i
$513$	1.58833e8			1.17649
$514$	3.61023e6	−	7.34134e7i	0.0265855	−	0.540612i
$515$	1.22457e8	+	1.22457e8i	0.896521	+	0.896521i
$516$	−1.22318e8	−	1.20595e7i	−0.890309	−	0.0877772i
$517$	1.64686e8	+	1.64686e8i	1.19175	+	1.19175i
$518$	−4.53385e7	+	4.10883e7i	−0.326195	+	0.295617i
$519$	−6.89102e7			−0.492926
$520$	8.41932e6	−	5.67002e7i	0.0598780	−	0.403250i
$521$		−	6.20493e7i		−	0.438757i	−0.975640	−	0.219378i	$-0.929597\pi$
$521$		−	6.20493e7i		−	0.438757i	0.975640	−	0.219378i	$-0.0704029\pi$
$522$	6.69156e7	−	6.06427e7i	0.470452	−	0.426350i
$523$	7.63295e7	−	7.63295e7i	0.533565	−	0.533565i	−0.388066	−	0.921631i	$-0.626857\pi$
$523$	7.63295e7	−	7.63295e7i	0.533565	−	0.533565i	0.921631	+	0.388066i	$0.126857\pi$
$524$	1.78908e7	+	2.18044e7i	0.124347	+	0.151548i
$525$	1.25557e7	−	1.25557e7i	0.0867686	−	0.0867686i
$526$	7.69585e6	−	1.56494e8i	0.0528810	−	1.07533i
$527$		−	1.29781e7i		−	0.0886703i
$528$	2.05136e8	+	4.08466e7i	1.39361	+	0.277494i
$529$	−1.48030e8			−0.999960
$530$	−1.32267e8	−	6.50444e6i	−0.888428	−	0.0436900i
$531$	268175.	+	268175.i	0.00179116	+	0.00179116i
$532$	−3.66262e7	−	4.46382e7i	−0.243252	−	0.296464i
$533$	−1.02052e8	−	1.02052e8i	−0.673971	−	0.673971i
$534$	4.05246e6	+	4.47165e6i	0.0266131	+	0.0293660i
$535$	3.78743e7			0.247334
$536$	−6.93025e6	+	5.13822e6i	−0.0450044	+	0.0333671i
$537$		−	1.13378e7i		−	0.0732159i
$538$	−1.60409e8	−	1.77002e8i	−1.03011	−	1.13666i
$539$	1.69942e8	−	1.69942e8i	1.08526	−	1.08526i
$540$	−1.29084e8	−	1.27266e7i	−0.819766	−	0.0808223i
$541$	1.29543e7	−	1.29543e7i	0.0818132	−	0.0818132i	−0.665016	−	0.746829i	$-0.731575\pi$
$541$	1.29543e7	−	1.29543e7i	0.0818132	−	0.0818132i	0.746829	+	0.665016i	$0.231575\pi$
$542$	−4.69662e7	−	2.30965e6i	−0.294977	−	0.0145060i
$543$			1.42718e8i			0.891412i
$544$	−2.88498e7	+	1.15054e8i	−0.179204	+	0.714667i
$545$	−1.05722e8			−0.653092
$546$	1.23674e6	−	2.51489e7i	0.00759803	−	0.154505i
$547$	−1.31621e8	−	1.31621e8i	−0.804200	−	0.804200i	0.179549	−	0.983749i	$-0.442536\pi$
$547$	−1.31621e8	−	1.31621e8i	−0.804200	−	0.804200i	−0.983749	+	0.179549i	$0.942536\pi$
$548$	1.35544e7	−	1.37480e8i	0.0823645	−	0.835408i
$549$	2.60501e7	+	2.60501e7i	0.157432	+	0.157432i
$550$	−9.25030e7	+	8.38315e7i	−0.555991	+	0.503871i
$551$	−3.32664e8			−1.98862
$552$	692992.	−	513797.i	0.00412013	−	0.00305474i
$553$			4.71449e7i			0.278779i
$554$	−1.37444e8	+	1.24559e8i	−0.808343	+	0.732566i
$555$	9.18491e7	−	9.18491e7i	0.537274	−	0.537274i
$556$	−1.03938e8	+	8.52825e7i	−0.604715	+	0.496176i
$557$	1.49279e7	−	1.49279e7i	0.0863841	−	0.0863841i	−0.662594	−	0.748978i	$-0.730545\pi$
$557$	1.49279e7	−	1.49279e7i	0.0863841	−	0.0863841i	0.748978	+	0.662594i	$0.230545\pi$
$558$	354383.	−	7.20631e6i	0.00203972	−	0.0414773i
$559$		−	1.04025e8i		−	0.595531i
$560$	2.61895e7	+	3.92122e7i	0.149129	+	0.223284i
$561$	1.84849e8			1.04696
$562$	−4.62511e7	−	2.27448e6i	−0.260563	−	0.0128137i
$563$	2.05259e8	+	2.05259e8i	1.15021	+	1.15021i	0.986511	+	0.163698i	$0.0523423\pi$
$563$	2.05259e8	+	2.05259e8i	1.15021	+	1.15021i	0.163698	+	0.986511i	$0.447658\pi$
$564$	1.07739e8	−	8.84008e7i	0.600529	−	0.492741i
$565$	5.75662e7	+	5.75662e7i	0.319170	+	0.319170i
$566$	2.32542e8	+	2.56597e8i	1.28249	+	1.41515i
$567$	−3.46584e7			−0.190134
$568$	4.53822e7	−	3.05628e8i	0.247651	−	1.66782i
$569$		−	6.06159e7i		−	0.329041i	−0.986374	−	0.164520i	$-0.947392\pi$
$569$		−	6.06159e7i		−	0.329041i	0.986374	−	0.164520i	$-0.0526076\pi$
$570$	8.23148e7	+	9.08295e7i	0.444481	+	0.490458i
$571$	4.61937e7	−	4.61937e7i	0.248127	−	0.248127i	−0.572075	−	0.820202i	$-0.693861\pi$
$571$	4.61937e7	−	4.61937e7i	0.248127	−	0.248127i	0.820202	+	0.572075i	$0.193861\pi$
$572$	−1.73690e7	+	1.76171e8i	−0.0928084	+	0.941339i
$573$	−1.51704e8	+	1.51704e8i	−0.806370	+	0.806370i
$574$	1.18580e8	+	5.83136e6i	0.627011	+	0.0308343i
$575$			514889.i			0.00270838i
$576$	−1.91611e7	+	6.30978e7i	−0.100266	+	0.330177i
$577$	−3.13721e8			−1.63311			−0.816557	−	0.577265i	$-0.804120\pi$
$577$	−3.13721e8			−1.63311			−0.816557	+	0.577265i	$0.804120\pi$
$578$	4.33577e6	−	8.81670e7i	0.0224534	−	0.456586i
$579$	−7.35757e7	−	7.35757e7i	−0.379052	−	0.379052i
$580$	2.70356e8	+	2.66549e7i	1.38565	+	0.136614i
$581$	1.02957e7	+	1.02957e7i	0.0524963	+	0.0524963i
$582$	−4.29679e7	+	3.89400e7i	−0.217959	+	0.197527i
$583$	4.08968e8			2.06388
$584$	−5.17861e7	−	7.68964e6i	−0.260001	−	0.0386071i
$585$		−	2.81630e7i		−	0.140673i
$586$	7.64464e7	−	6.92800e7i	0.379895	−	0.344283i
$587$	−2.13000e8	+	2.13000e8i	−1.05309	+	1.05309i	−0.0545786	+	0.998509i	$0.517382\pi$
$587$	−2.13000e8	+	2.13000e8i	−1.05309	+	1.05309i	−0.998509	+	0.0545786i	$0.982618\pi$
$588$	−9.12221e7	−	1.11177e8i	−0.448713	−	0.546869i
$589$	−1.87936e7	+	1.87936e7i	−0.0919739	+	0.0919739i
$590$	−56038.6	+	1.13953e6i	−0.000272854	+	0.00554845i
$591$		−	1.52039e8i		−	0.736532i
$592$	−1.42968e8	−	2.14059e8i	−0.689085	−	1.03173i
$593$	−9.60508e7			−0.460614			−0.230307	−	0.973118i	$-0.573973\pi$
$593$	−9.60508e7			−0.460614			−0.230307	+	0.973118i	$0.573973\pi$
$594$	4.00094e8	+	1.96753e7i	1.90899	+	0.0938777i
$595$	2.94669e7	+	2.94669e7i	0.139889	+	0.139889i
$596$	−8.00383e7	−	9.75467e7i	−0.378059	−	0.460759i
$597$	−7.70256e7	−	7.70256e7i	−0.362003	−	0.362003i
$598$	490300.	+	541017.i	0.00229276	+	0.00252992i
$599$	1.89080e8			0.879761			0.439880	−	0.898056i	$-0.355021\pi$
$599$	1.89080e8			0.879761			0.439880	+	0.898056i	$0.355021\pi$
$600$	4.44904e7	+	6.00071e7i	0.205974	+	0.277811i
$601$			3.05658e8i			1.40803i	0.710185	+	0.704015i	$0.248611\pi$
$601$			3.05658e8i			1.40803i	−0.710185	+	0.704015i	$0.751389\pi$
$602$	5.74641e7	+	6.34082e7i	0.263395	+	0.290641i
$603$	−2.99721e6	+	2.99721e6i	−0.0136699	+	0.0136699i
$604$	−1.82215e8	−	1.79649e7i	−0.826937	−	0.0815293i
$605$	−2.46821e8	+	2.46821e8i	−1.11459	+	1.11459i
$606$	2.85330e8	+	1.40316e7i	1.28212	+	0.0630506i
$607$			1.84885e8i			0.826676i	0.910578	+	0.413338i	$0.135637\pi$
$607$			1.84885e8i			0.826676i	−0.910578	+	0.413338i	$0.864363\pi$
$608$	2.08387e8	−	1.24832e8i	0.927172	−	0.555412i
$609$	1.19333e8			0.528334
$610$	−5.44351e6	+	1.10693e8i	−0.0239822	+	0.487674i
$611$	8.34035e7	+	8.34035e7i	0.365646	+	0.365646i
$612$	−5.71796e6	+	5.79963e7i	−0.0249452	+	0.253015i
$613$	−2.84487e7	−	2.84487e7i	−0.123504	−	0.123504i	0.642653	−	0.766157i	$-0.277834\pi$
$613$	−2.84487e7	−	2.84487e7i	−0.123504	−	0.123504i	−0.766157	+	0.642653i	$0.777834\pi$
$614$	−1.42123e6	+	1.28800e6i	−0.00613989	+	0.00556432i
$615$	−2.52039e8			−1.08353
$616$	−8.67304e7	−	1.16979e8i	−0.371047	−	0.500456i
$617$		−	5.23788e7i		−	0.222998i	−0.993765	−	0.111499i	$-0.964435\pi$
$617$		−	5.23788e7i		−	0.222998i	0.993765	−	0.111499i	$-0.0355651\pi$
$618$	−2.37138e8	+	2.14908e8i	−1.00470	+	0.910514i
$619$	−1.64781e7	+	1.64781e7i	−0.0694760	+	0.0694760i	−0.740991	−	0.671515i	$-0.765644\pi$
$619$	−1.64781e7	+	1.64781e7i	−0.0694760	+	0.0694760i	0.671515	+	0.740991i	$0.265644\pi$
$620$	1.67794e7	−	1.37677e7i	0.0704049	−	0.0577681i
$621$	1.16826e6	−	1.16826e6i	0.00487824	−	0.00487824i
$622$	9.95176e6	−	2.02367e8i	0.0413551	−	0.840948i
$623$		−	4.20151e6i		−	0.0173756i
$624$	1.03889e8	+	2.06864e7i	0.427580	+	0.0851394i
$625$	9.52246e7			0.390040
$626$	2.50341e8	+	1.23110e7i	1.02049	+	0.0501844i
$627$	−2.67681e8	−	2.67681e8i	−1.08596	−	1.08596i
$628$	2.13484e7	−	1.75166e7i	0.0861959	−	0.0707248i
$629$	−1.60859e8	−	1.60859e8i	−0.646388	−	0.646388i
$630$	1.55574e7	+	1.71666e7i	0.0622178	+	0.0686537i
$631$	6.27154e7			0.249624			0.124812	−	0.992180i	$-0.460167\pi$
$631$	6.27154e7			0.249624			0.124812	+	0.992180i	$0.460167\pi$
$632$	−1.96187e8	−	2.91315e7i	−0.777175	−	0.115402i
$633$		−	4.22021e7i		−	0.166388i
$634$	6.53087e7	+	7.20643e7i	0.256273	+	0.282782i
$635$	−4.54171e7	+	4.54171e7i	−0.177378	+	0.177378i
$636$	2.40110e7	−	2.43539e8i	0.0933336	−	0.946667i
$637$	8.60654e7	−	8.60654e7i	0.332974	−	0.332974i
$638$	−8.37968e8	−	4.12085e7i	−3.22675	−	0.158681i
$639$		−	1.51806e8i		−	0.581815i
$640$	−1.79359e8	+	8.47540e7i	−0.684200	+	0.323311i
$641$	−855209.			−0.00324712			−0.00162356	−	0.999999i	$-0.500517\pi$
$641$	−855209.			−0.00324712			−0.00162356	+	0.999999i	$0.500517\pi$
$642$	−3.43775e6	+	6.99060e7i	−0.0129918	+	0.264186i
$643$	1.12918e8	+	1.12918e8i	0.424747	+	0.424747i	0.886834	−	0.462087i	$-0.152899\pi$
$643$	1.12918e8	+	1.12918e8i	0.424747	+	0.424747i	−0.462087	+	0.886834i	$0.652899\pi$
$644$	−597720.	−	58930.4i	−0.00223790	−	0.000220639i
$645$	−1.28456e8	−	1.28456e8i	−0.478712	−	0.478712i
$646$	1.59073e8	−	1.44161e8i	0.590065	−	0.534750i
$647$	4.66920e8			1.72397			0.861985	−	0.506933i	$-0.169221\pi$
$647$	4.66920e8			1.72397			0.861985	+	0.506933i	$0.169221\pi$
$648$	2.14159e7	−	1.44226e8i	0.0787068	−	0.530053i
$649$		−	3.52344e6i		−	0.0128894i
$650$	−4.68473e7	+	4.24557e7i	−0.170587	+	0.154595i
$651$	6.74164e6	−	6.74164e6i	0.0244356	−	0.0244356i
$652$	8.43333e7	+	1.02781e8i	0.304268	+	0.370827i
$653$	1.27870e8	−	1.27870e8i	0.459227	−	0.459227i	−0.439174	−	0.898402i	$-0.644729\pi$
$653$	1.27870e8	−	1.27870e8i	0.459227	−	0.459227i	0.898402	+	0.439174i	$0.144729\pi$
$654$	9.59607e6	−	1.95134e8i	0.0343052	−	0.697591i
$655$			4.16872e7i			0.148347i
$656$	−9.75385e7	+	4.89850e8i	−0.345513	+	1.73521i
$657$	−2.57222e7			−0.0907009
$658$	−9.69108e7	−	4.76575e6i	−0.340169	−	0.0167284i
$659$	−2.91571e8	−	2.91571e8i	−1.01880	−	1.01880i	−0.999820	−	0.0189772i	$-0.993959\pi$
$659$	−2.91571e8	−	2.91571e8i	−1.01880	−	1.01880i	−0.0189772	−	0.999820i	$-0.506041\pi$
$660$	1.96096e8	+	2.38993e8i	0.682084	+	0.831291i
$661$	1.61409e8	+	1.61409e8i	0.558886	+	0.558886i	0.928990	−	0.370104i	$-0.120678\pi$
$661$	1.61409e8	+	1.61409e8i	0.558886	+	0.558886i	−0.370104	+	0.928990i	$0.620678\pi$
$662$	−1.27806e8	−	1.41026e8i	−0.440531	−	0.486100i
$663$	9.36152e7			0.321222
$664$	−4.92061e7	+	3.64824e7i	−0.168080	+	0.124617i
$665$		−	8.53422e7i		−	0.290201i
$666$	−8.49274e7	−	9.37123e7i	−0.287492	−	0.317230i
$667$	−2.44683e6	+	2.44683e6i	−0.00824567	+	0.00824567i
$668$	3.90588e8	+	3.85088e7i	1.31036	+	0.129191i
$669$	2.04604e8	−	2.04604e8i	0.683340	−	0.683340i
$670$	−1.27358e7	−	626306.i	−0.0423450	−	0.00208239i
$671$		−	3.42262e8i		−	1.13290i
$672$	−7.47526e7	+	4.47797e7i	−0.246331	+	0.147562i
$673$	2.09562e8			0.687490			0.343745	−	0.939063i	$-0.388304\pi$
$673$	2.09562e8			0.687490			0.343745	+	0.939063i	$0.388304\pi$
$674$	−3.13667e6	+	6.37836e7i	−0.0102445	+	0.208319i
$675$	1.01161e8	+	1.01161e8i	0.328928	+	0.328928i
$676$	2.15132e7	−	2.18205e8i	0.0696411	−	0.706358i
$677$	4.71272e7	+	4.71272e7i	0.151882	+	0.151882i	0.778958	−	0.627076i	$-0.215749\pi$
$677$	4.71272e7	+	4.71272e7i	0.151882	+	0.151882i	−0.627076	+	0.778958i	$0.715749\pi$
$678$	−1.11477e8	+	1.01027e8i	−0.357682	+	0.324151i
$679$	4.03721e7			0.128965
$680$	−1.40830e8	+	1.04414e8i	−0.447887	+	0.332072i
$681$			3.75106e8i			1.18772i
$682$	−4.96685e7	+	4.50124e7i	−0.156577	+	0.141899i
$683$	−1.52125e8	+	1.52125e8i	−0.477462	+	0.477462i	−0.904319	−	0.426857i	$-0.859621\pi$
$683$	−1.52125e8	+	1.52125e8i	−0.477462	+	0.477462i	0.426857	+	0.904319i	$0.359621\pi$
$684$	9.22649e7	−	7.57045e7i	0.288316	−	0.236567i
$685$	1.44379e8	−	1.44379e8i	0.449193	−	0.449193i
$686$	−1.05440e7	+	2.14411e8i	−0.0326613	+	0.664162i
$687$		−	7.20691e7i		−	0.222269i
$688$	−2.99372e8	+	1.99948e8i	−0.919277	+	0.613977i
$689$	2.07118e8			0.633229
$690$	1.27352e6	+	62627.6i	0.00387667	+	0.000190642i
$691$	1.50684e8	+	1.50684e8i	0.456703	+	0.456703i	0.897572	−	0.440869i	$-0.145330\pi$
$691$	1.50684e8	+	1.50684e8i	0.456703	+	0.456703i	−0.440869	+	0.897572i	$0.645330\pi$
$692$	−1.56035e8	+	1.28028e8i	−0.470872	+	0.386357i
$693$	−5.05913e7	−	5.05913e7i	−0.152011	−	0.152011i
$694$	−8.76275e7	−	9.66917e7i	−0.262157	−	0.289275i
$695$	−1.98716e8			−0.591940
$696$	−7.37376e7	+	4.96588e8i	−0.218706	+	1.47288i
$697$			4.41405e8i			1.30358i
$698$	1.47225e7	+	1.62454e7i	0.0432927	+	0.0477709i
$699$	−1.53506e8	+	1.53506e8i	−0.449462	+	0.449462i
$700$	5.10286e6	−	5.17574e7i	0.0148771	−	0.150896i
$701$	1.51241e8	−	1.51241e8i	0.439052	−	0.439052i	−0.452641	−	0.891693i	$-0.649518\pi$
$701$	1.51241e8	−	1.51241e8i	0.439052	−	0.439052i	0.891693	+	0.452641i	$0.149518\pi$
$702$	2.02624e8	+	9.96439e6i	0.585706	+	0.0288031i
$703$			4.65881e8i			1.34094i
$704$	5.40383e8	−	2.88634e8i	1.54876	−	0.827235i
$705$	2.05982e8			0.587843
$706$	5.02452e6	−	1.02173e8i	0.0142784	−	0.290349i
$707$	−1.40638e8	−	1.40638e8i	−0.397965	−	0.397965i
$708$	−2.09820e6	−	206865.i	−0.00591216	−	0.000582891i
$709$	−2.71311e8	−	2.71311e8i	−0.761252	−	0.761252i	0.215297	−	0.976549i	$-0.430928\pi$
$709$	−2.71311e8	−	2.71311e8i	−0.761252	−	0.761252i	−0.976549	+	0.215297i	$0.930928\pi$
$710$	3.38389e8	−	3.06667e8i	0.945456	−	0.856825i
$711$	−9.74462e7			−0.271117
$712$	1.74840e7	+	2.59617e6i	0.0484396	+	0.00719272i
$713$			276464.i			0.000762728i
$714$	−5.70627e7	+	5.17135e7i	−0.156768	+	0.142072i
$715$	−1.85011e8	+	1.85011e8i	−0.506151	+	0.506151i
$716$	−2.10645e7	−	2.56724e7i	−0.0573869	−	0.0699403i
$717$	−2.03455e8	+	2.03455e8i	−0.551965	+	0.551965i
$718$	1.22346e7	−	2.48788e8i	0.0330534	−	0.672135i
$719$			1.13751e8i			0.306034i	0.988224	+	0.153017i	$0.0488990\pi$
$719$			1.13751e8i			0.306034i	−0.988224	+	0.153017i	$0.951101\pi$
$720$	−8.10497e7	+	5.41323e7i	−0.217147	+	0.145031i
$721$	2.22812e8			0.594473
$722$	−6.32028e7	−	3.10811e6i	−0.167929	−	0.00825818i
$723$	2.98737e8	+	2.98737e8i	0.790451	+	0.790451i
$724$	2.65156e8	+	3.23159e8i	0.698692	+	0.851531i
$725$	−2.11874e8	−	2.11874e8i	−0.555986	−	0.555986i
$726$	−4.33164e8	−	4.77971e8i	−1.13199	−	1.24908i
$727$	−4.67014e8			−1.21542			−0.607710	−	0.794159i	$-0.707912\pi$
$727$	−4.67014e8			−1.21542			−0.607710	+	0.794159i	$0.707912\pi$
$728$	−4.39239e7	−	5.92430e7i	−0.113843	−	0.153547i
$729$		−	4.12928e8i		−	1.06584i
$730$	−5.19622e7	−	5.73372e7i	−0.133573	−	0.147390i
$731$	−2.24970e8	+	2.24970e8i	−0.575933	+	0.575933i
$732$	−2.03816e8	−	2.00946e7i	−0.519642	−	0.0512325i
$733$	2.99863e8	−	2.99863e8i	0.761396	−	0.761396i	−0.215179	−	0.976575i	$-0.569033\pi$
$733$	2.99863e8	−	2.99863e8i	0.761396	−	0.761396i	0.976575	+	0.215179i	$0.0690334\pi$
$734$	5.67989e8	+	2.79318e7i	1.43632	+	0.0706336i
$735$		−	2.12556e8i		−	0.535317i
$736$	614570.	−	2.45091e6i	0.00154148	−	0.00614745i
$737$	3.93791e7			0.0983702
$738$	−1.20531e7	+	2.45098e8i	−0.0299869	+	0.609778i
$739$	−1.55914e8	−	1.55914e8i	−0.386323	−	0.386323i	0.487051	−	0.873374i	$-0.338073\pi$
$739$	−1.55914e8	−	1.55914e8i	−0.386323	−	0.386323i	−0.873374	+	0.487051i	$0.838073\pi$
$740$	3.73291e7	−	3.78622e8i	0.0921197	−	0.934354i
$741$	−1.35565e8	−	1.35565e8i	−0.333190	−	0.333190i
$742$	−1.26248e8	+	1.14413e8i	−0.309039	+	0.280068i
$743$	1.51890e8			0.370307			0.185153	−	0.982710i	$-0.440722\pi$
$743$	1.51890e8			0.370307			0.185153	+	0.982710i	$0.440722\pi$
$744$	2.38886e7	+	3.22201e7i	0.0580059	+	0.0782363i
$745$		−	1.86496e8i		−	0.451026i
$746$	4.62800e8	−	4.19416e8i	1.11475	−	1.01025i
$747$	−2.12808e7	+	2.12808e7i	−0.0510535	+	0.0510535i
$748$	4.18558e8	−	3.43432e8i	1.00012	−	0.820608i
$749$	3.44564e7	−	3.44564e7i	0.0820021	−	0.0820021i
$750$	−1.81131e7	+	3.68327e8i	−0.0429348	+	0.873072i
$751$		−	4.03068e8i		−	0.951610i	−0.879551	−	0.475805i	$-0.842157\pi$
$751$		−	4.03068e8i		−	0.951610i	0.879551	−	0.475805i	$-0.157843\pi$
$752$	7.97145e7	−	4.00336e8i	0.187449	−	0.941392i
$753$	−5.06599e8			−1.18653
$754$	−4.24381e8	−	2.08697e7i	−0.990016	−	0.0486858i
$755$	−1.91358e8	−	1.91358e8i	−0.444638	−	0.444638i
$756$	−1.29013e8	+	1.05857e8i	−0.298585	+	0.244993i
$757$	3.97871e8	+	3.97871e8i	0.917180	+	0.917180i	0.996823	−	0.0796438i	$-0.0253783\pi$
$757$	3.97871e8	+	3.97871e8i	0.917180	+	0.917180i	−0.0796438	+	0.996823i	$0.525378\pi$
$758$	2.96057e8	+	3.26681e8i	0.679779	+	0.750096i
$759$	−3.93772e6			−0.00900575
$760$	3.55140e8	+	5.27342e7i	0.809018	+	0.120130i
$761$			3.38573e8i			0.768242i	0.923283	+	0.384121i	$0.125495\pi$
$761$			3.38573e8i			0.768242i	−0.923283	+	0.384121i	$0.874505\pi$
$762$	−7.97057e7	−	8.79505e7i	−0.180146	−	0.198780i
$763$	−9.61811e7	+	9.61811e7i	−0.216529	+	0.216529i
$764$	−6.16554e7	+	6.25360e8i	−0.138258	+	1.40233i
$765$	−6.09065e7	+	6.09065e7i	−0.136044	+	0.136044i
$766$	−2.66681e8	−	1.31145e7i	−0.593343	−	0.0291787i
$767$		−	1.78441e6i		−	0.00395466i
$768$	−1.40154e8	−	3.38742e8i	−0.309401	−	0.747801i
$769$	−6.17719e8			−1.35835			−0.679175	−	0.733976i	$-0.737662\pi$
$769$	−6.17719e8			−1.35835			−0.679175	+	0.733976i	$0.737662\pi$
$770$	1.05717e7	−	2.14974e8i	0.0231565	−	0.470884i
$771$	1.41957e8	+	1.41957e8i	0.309738	+	0.309738i
$772$	−3.03295e8	−	2.99025e7i	−0.659195	−	0.0649913i
$773$	1.29098e8	+	1.29098e8i	0.279500	+	0.279500i	0.832910	−	0.553409i	$-0.186673\pi$
$773$	1.29098e8	+	1.29098e8i	0.279500	+	0.279500i	−0.553409	+	0.832910i	$0.686673\pi$
$774$	−1.31062e8	+	1.18776e8i	−0.282653	+	0.256156i
$775$	−2.39394e7			−0.0514289
$776$	−2.49465e7	+	1.68003e8i	−0.0533856	+	0.359527i
$777$		−	1.67121e8i		−	0.356260i
$778$	3.59738e8	−	3.26015e8i	0.763920	−	0.692308i
$779$	6.39201e8	−	6.39201e8i	1.35215	−	1.35215i
$780$	9.93113e7	+	1.21036e8i	0.209274	+	0.255053i
$781$	−9.97256e8	+	9.97256e8i	−2.09341	+	2.09341i
$782$	109682.	−	2.23037e6i	0.000229359	−	0.00466398i
$783$			9.61463e8i			2.00284i
$784$	−4.13113e8	−	8.22587e7i	−0.857275	−	0.170700i
$785$	4.08153e7			0.0843750
$786$	−7.69436e7	−	3.78383e6i	−0.158455	−	0.00779228i
$787$	−2.09507e8	−	2.09507e8i	−0.429808	−	0.429808i	0.458755	−	0.888563i	$-0.348296\pi$
$787$	−2.09507e8	−	2.09507e8i	−0.429808	−	0.429808i	−0.888563	+	0.458755i	$0.848296\pi$
$788$	−2.82473e8	−	3.44264e8i	−0.577296	−	0.703580i
$789$	3.02607e8	+	3.02607e8i	0.616096	+	0.616096i
$790$	−1.96854e8	−	2.17217e8i	−0.399267	−	0.440567i
$791$	1.04743e8			0.211638
$792$	2.41790e8	−	1.79267e8i	0.486701	−	0.360849i
$793$		−	1.73335e8i		−	0.347590i
$794$	5.55731e8	+	6.13216e8i	1.11020	+	1.22504i
$795$	2.55760e8	−	2.55760e8i	0.509015	−	0.509015i
$796$	−3.17517e8	−	3.13046e7i	−0.629546	−	0.0620681i
$797$	2.47632e6	−	2.47632e6i	0.00489138	−	0.00489138i	−0.704657	−	0.709548i	$-0.748899\pi$
$797$	2.47632e6	−	2.47632e6i	0.00489138	−	0.00489138i	0.709548	+	0.704657i	$0.248899\pi$
$798$	1.57519e8	+	7.74629e6i	0.309974	+	0.0152435i
$799$		−	3.60744e8i		−	0.707227i
$800$	2.12228e8	+	5.32164e7i	0.414508	+	0.103938i
$801$	8.68430e6			0.0168981
$802$	−3.32331e7	+	6.75790e8i	−0.0644241	+	1.31005i
$803$	1.68977e8	+	1.68977e8i	0.326347	+	0.326347i
$804$	2.31199e6	−	2.34501e7i	0.00444855	−	0.0451208i
$805$	−627714.	−	627714.i	−0.00120330	−	0.00120330i
$806$	−2.51542e7	+	2.27961e7i	−0.0480402	+	0.0435367i
$807$	6.52441e8			1.24143
$808$	6.72149e8	−	4.98344e8i	1.27418	−	0.944702i
$809$		−	4.11008e7i		−	0.0776255i	−0.999247	−	0.0388128i	$-0.987642\pi$
$809$		−	4.11008e7i		−	0.0776255i	0.999247	−	0.0388128i	$-0.0123576\pi$
$810$	1.59686e8	−	1.44717e8i	0.300478	−	0.272310i
$811$	5.53374e8	−	5.53374e8i	1.03742	−	1.03742i	0.0381526	−	0.999272i	$-0.487853\pi$
$811$	5.53374e8	−	5.53374e8i	1.03742	−	1.03742i	0.999272	−	0.0381526i	$-0.0121473\pi$
$812$	2.70208e8	−	2.21709e8i	0.504697	−	0.414110i
$813$	9.08172e7	−	9.08172e7i	0.169004	−	0.169004i
$814$	−5.77107e7	+	1.17354e9i	−0.107000	+	2.17582i
$815$			1.96504e8i			0.362993i
$816$	−1.79938e8	−	2.69413e8i	−0.331172	−	0.495847i
$817$	6.51560e8			1.19478
$818$	−7.98399e8	−	3.92627e7i	−1.45868	−	0.0717331i
$819$	−2.56215e7	−	2.56215e7i	−0.0466394	−	0.0466394i
$820$	−5.70696e8	+	4.68263e8i	−1.03506	+	0.849276i
$821$	4.55915e8	+	4.55915e8i	0.823862	+	0.823862i	0.986659	−	0.162798i	$-0.0520518\pi$
$821$	4.55915e8	+	4.55915e8i	0.823862	+	0.823862i	−0.162798	+	0.986659i	$0.552052\pi$
$822$	2.53381e8	+	2.79591e8i	0.456203	+	0.503393i
$823$	−4.45550e7			−0.0799276			−0.0399638	−	0.999201i	$-0.512724\pi$
$823$	−4.45550e7			−0.0799276			−0.0399638	+	0.999201i	$0.512724\pi$
$824$	−1.37678e8	+	9.27199e8i	−0.246085	+	1.65726i
$825$		−	3.40973e8i		−	0.607236i
$826$	985719.	+	1.08768e6i	0.00174909	+	0.00193002i
$827$	4.25439e8	−	4.25439e8i	0.752178	−	0.752178i	−0.222708	−	0.974885i	$-0.571490\pi$
$827$	4.25439e8	−	4.25439e8i	0.752178	−	0.752178i	0.974885	+	0.222708i	$0.0714896\pi$
$828$	121806.	−	1.23546e6i	0.000214574	−	0.00217639i
$829$	−4.28560e7	+	4.28560e7i	−0.0752225	+	0.0752225i	−0.743717	−	0.668495i	$-0.766939\pi$
$829$	−4.28560e7	+	4.28560e7i	−0.0752225	+	0.0752225i	0.668495	+	0.743717i	$0.266939\pi$
$830$	−9.04268e7	−	4.44689e6i	−0.158148	−	0.00777719i
$831$		−	5.06627e8i		−	0.882847i
$832$	2.73672e8	−	1.46176e8i	0.475183	−	0.253808i
$833$	−3.72257e8			−0.644033
$834$	1.80369e7	−	3.66777e8i	0.0310931	−	0.632272i
$835$	4.10188e8	+	4.10188e8i	0.704569	+	0.704569i
$836$	−1.10344e9	−	1.08790e8i	−1.88856	−	0.186196i
$837$	5.43172e7	+	5.43172e7i	0.0926320	+	0.0926320i
$838$	−6.71313e7	+	6.08382e7i	−0.114076	+	0.103382i
$839$	−7.90041e8			−1.33772			−0.668858	−	0.743390i	$-0.733216\pi$
$839$	−7.90041e8			−1.33772			−0.668858	+	0.743390i	$0.733216\pi$
$840$	−1.27396e8	−	1.89168e7i	−0.214940	−	0.0319161i
$841$		−	1.41889e9i		−	2.38540i
$842$	−2.18739e8	+	1.98233e8i	−0.366429	+	0.332079i
$843$	8.94344e7	−	8.94344e7i	0.149287	−	0.149287i
$844$	−7.84074e7	−	9.55591e7i	−0.130416	−	0.158944i
$845$	2.29155e8	−	2.29155e8i	0.379803	−	0.379803i
$846$	9.85058e6	−	2.00310e8i	0.0162686	−	0.330819i
$847$			4.49096e8i			0.739075i
$848$	−3.98103e8	−	5.96060e8i	−0.652842	−	0.977468i
$849$	−9.45834e8			−1.54558
$850$	1.93131e8	+	9.49753e6i	0.314481	+	0.0154651i
$851$	3.42668e6	+	3.42668e6i	0.00556012	+	0.00556012i
$852$	5.35313e8	+	6.52413e8i	0.865543	+	1.05488i
$853$	−6.74914e8	−	6.74914e8i	−1.08743	−	1.08743i	−0.995792	−	0.0916372i	$-0.970790\pi$
$853$	−6.74914e8	−	6.74914e8i	−1.08743	−	1.08743i	−0.0916372	−	0.995792i	$-0.529210\pi$
$854$	9.57513e7	+	1.05656e8i	0.153734	+	0.169637i
$855$	1.76398e8			0.282225
$856$	1.22094e8	+	1.64677e8i	0.194659	+	0.262549i
$857$			8.46030e8i			1.34414i	0.740489	+	0.672068i	$0.234594\pi$
$857$			8.46030e8i			1.34414i	−0.740489	+	0.672068i	$0.765406\pi$
$858$	−3.24689e8	−	3.58275e8i	−0.514051	−	0.567224i
$859$	−6.04869e8	+	6.04869e8i	−0.954293	+	0.954293i	−0.999000	−	0.0447076i	$-0.985764\pi$
$859$	−6.04869e8	+	6.04869e8i	−0.954293	+	0.954293i	0.0447076	+	0.999000i	$0.485764\pi$
$860$	−5.29524e8	−	5.22067e7i	−0.832511	−	0.0820788i
$861$	−2.29294e8	+	2.29294e8i	−0.359239	+	0.359239i
$862$	8.70633e8	+	4.28149e7i	1.35929	+	0.0668456i
$863$		−	5.32769e8i		−	0.828908i	−0.910070	−	0.414454i	$-0.863973\pi$
$863$		−	5.32769e8i		−	0.828908i	0.910070	−	0.414454i	$-0.136027\pi$
$864$	−3.60789e8	−	6.02280e8i	−0.559387	−	0.933807i
$865$	−2.98318e8			−0.460926
$866$	5.62438e7	−	1.14371e9i	0.0866005	−	1.76101i
$867$	1.70486e8	+	1.70486e8i	0.261596	+	0.261596i
$868$	2.73992e6	−	2.77905e7i	0.00418966	−	0.0424950i
$869$	6.40153e8	+	6.40153e8i	0.975494	+	0.975494i
$870$	−5.49818e8	+	4.98276e8i	−0.834952	+	0.756680i
$871$	1.99432e7			0.0301815
$872$	−3.40812e8	−	4.59676e8i	−0.514003	−	0.693270i
$873$			8.34471e7i			0.125421i
$874$	−3.38864e6	+	3.07098e6i	−0.00507564	+	0.00459983i
$875$	1.81547e8	−	1.81547e8i	0.270998	−	0.270998i
$876$	1.10546e8	−	9.07042e7i	0.164449	−	0.134932i
$877$	5.99876e8	−	5.99876e8i	0.889329	−	0.889329i	−0.105130	−	0.994459i	$-0.533526\pi$
$877$	5.99876e8	−	5.99876e8i	0.889329	−	0.889329i	0.994459	+	0.105130i	$0.0335258\pi$
$878$	−1.53467e7	+	3.12073e8i	−0.0226742	+	0.461077i
$879$			2.81787e8i			0.414910i
$880$	8.88051e8	+	1.76828e8i	1.30314	+	0.259480i
$881$	8.62180e8			1.26087			0.630435	−	0.776242i	$-0.282877\pi$
$881$	8.62180e8			1.26087			0.630435	+	0.776242i	$0.282877\pi$
$882$	−2.06703e8	−	1.01650e7i	−0.301259	−	0.0148149i
$883$	3.51358e7	+	3.51358e7i	0.0510350	+	0.0510350i	0.732164	−	0.681129i	$-0.238511\pi$
$883$	3.51358e7	+	3.51358e7i	0.0510350	+	0.0510350i	−0.681129	+	0.732164i	$0.738511\pi$
$884$	2.11975e8	−	1.73928e8i	0.306851	−	0.251775i
$885$	−2.20348e6	−	2.20348e6i	−0.00317892	−	0.00317892i
$886$	1.41097e7	+	1.55692e7i	0.0202870	+	0.0223855i
$887$	−1.21889e9			−1.74660			−0.873300	−	0.487182i	$-0.838025\pi$
$887$	−1.21889e9			−1.74660			−0.873300	+	0.487182i	$0.838025\pi$
$888$	6.95449e8	+	1.03266e8i	0.993177	+	0.147475i
$889$			8.26372e7i			0.117617i
$890$	1.75434e7	+	1.93581e7i	0.0248854	+	0.0274596i
$891$	−4.70606e8	+	4.70606e8i	−0.665311	+	0.665311i
$892$	8.31549e7	−	8.43425e8i	0.117164	−	1.18837i
$893$	−5.22395e8	+	5.22395e8i	−0.733576	+	0.733576i
$894$	3.44223e8	+	1.69278e7i	0.481757	+	0.0236912i
$895$		−	4.90822e7i		−	0.0684629i
$896$	−8.60675e7	+	2.40279e8i	−0.119651	+	0.334035i
$897$	−1.99422e6			−0.00276310
$898$	−4.05628e7	+	8.24838e8i	−0.0560143	+	1.13904i
$899$	−1.13763e8	−	1.13763e8i	−0.156575	−	0.156575i
$900$	1.06980e8	+	1.05474e7i	0.146749	+	0.0144682i
$901$	−4.47922e8	−	4.47922e8i	−0.612390	−	0.612390i
$902$	1.68930e9	−	1.53094e9i	2.30191	−	2.08612i
$903$	−2.33727e8			−0.317429
$904$	−6.47219e7	+	4.35871e8i	−0.0876084	+	0.590001i
$905$			6.17837e8i			0.833543i
$906$	3.70566e8	−	3.35828e8i	0.498289	−	0.451577i
$907$	7.76440e8	−	7.76440e8i	1.04061	−	1.04061i	0.0414655	−	0.999140i	$-0.486797\pi$
$907$	7.76440e8	−	7.76440e8i	1.04061	−	1.04061i	0.999140	−	0.0414655i	$-0.0132027\pi$
$908$	6.96911e8	+	8.49361e8i	0.930936	+	1.13458i
$909$	2.90692e8	−	2.90692e8i	0.387028	−	0.387028i
$910$	5.35395e6	−	1.08872e8i	0.00710477	−	0.144474i
$911$			4.63788e8i			0.613429i	0.951802	+	0.306715i	$0.0992297\pi$
$911$			4.63788e8i			0.613429i	−0.951802	+	0.306715i	$0.900770\pi$
$912$	−1.29568e8	+	6.50708e8i	−0.170811	+	0.857831i
$913$	2.79599e8			0.367387
$914$	−5.09384e8	−	2.50498e7i	−0.667124	−	0.0328070i
$915$	−2.14043e8	−	2.14043e8i	−0.279408	−	0.279408i
$916$	−1.33897e8	−	1.63188e8i	−0.174215	−	0.212325i
$917$	3.79252e7	+	3.79252e7i	0.0491836	+	0.0491836i
$918$	−4.16654e8	−	4.59753e8i	−0.538577	−	0.594287i
$919$	−5.25334e8			−0.676844			−0.338422	−	0.940994i	$-0.609893\pi$
$919$	−5.25334e8			−0.676844			−0.338422	+	0.940994i	$0.609893\pi$
$920$	3.00002e6	−	2.22427e6i	0.00385266	−	0.00285643i
$921$		−	5.23877e6i		−	0.00670580i
$922$	−6.54275e8	−	7.21953e8i	−0.834771	−	0.921120i
$923$	−5.05052e8	+	5.05052e8i	−0.642289	+	0.642289i
$924$	3.95826e8	+	3.90252e7i	0.501751	+	0.0494686i
$925$	−2.96721e8	+	2.96721e8i	−0.374906	+	0.374906i
$926$	−1.02240e9	−	5.02785e7i	−1.28763	−	0.0633212i
$927$			4.60541e8i			0.578134i
$928$	7.55646e8	+	1.26143e9i	0.945528	+	1.57841i
$929$	−3.93973e7			−0.0491382			−0.0245691	−	0.999698i	$-0.507821\pi$
$929$	−3.93973e7			−0.0491382			−0.0245691	+	0.999698i	$0.507821\pi$
$930$	−2.91182e6	+	5.92114e7i	−0.00362006	+	0.0736133i
$931$	5.39068e8	+	5.39068e8i	0.668027	+	0.668027i
$932$	−6.23875e7	+	6.32785e8i	−0.0770637	+	0.781643i
$933$	3.91311e8	+	3.91311e8i	0.481812	+	0.481812i
$934$	−7.27778e8	+	6.59554e8i	−0.893220	+	0.809487i
$935$	8.00226e8			0.978989
$936$	1.22452e8	−	9.07884e7i	0.149327	−	0.110714i
$937$			1.63628e8i			0.198902i	0.995042	+	0.0994508i	$0.0317086\pi$
$937$			1.63628e8i			0.198902i	−0.995042	+	0.0994508i	$0.968291\pi$
$938$	−1.21563e7	+	1.10167e7i	−0.0147297	+	0.0133489i
$939$	−4.84077e8	+	4.84077e8i	−0.584680	+	0.584680i
$940$	4.66409e8	−	3.82694e8i	0.561543	−	0.460753i
$941$	−1.49735e8	+	1.49735e8i	−0.179702	+	0.179702i	−0.791226	−	0.611524i	$-0.790557\pi$
$941$	−1.49735e8	+	1.49735e8i	−0.179702	+	0.179702i	0.611524	+	0.791226i	$0.290557\pi$
$942$	−3.70469e6	+	7.53343e7i	−0.00443200	+	0.0901239i
$943$		−	9.40298e6i		−	0.0112132i
$944$	−5.13532e6	+	3.42984e6i	−0.00610452	+	0.00407716i
$945$	−2.46656e8			−0.292278
$946$	1.64125e9	+	8.07115e7i	1.93866	+	0.0953371i
$947$	−1.00429e9	−	1.00429e9i	−1.18252	−	1.18252i	−0.979090	−	0.203428i	$-0.934792\pi$
$947$	−1.00429e9	−	1.00429e9i	−1.18252	−	1.18252i	−0.203428	−	0.979090i	$-0.565208\pi$
$948$	4.18793e8	−	3.43625e8i	0.491558	−	0.403329i
$949$	8.55768e7	+	8.55768e7i	0.100128	+	0.100128i
$950$	−2.65920e8	−	2.93427e8i	−0.310156	−	0.342239i
$951$	−2.65634e8			−0.308846
$952$	−3.31297e7	+	2.23113e8i	−0.0383978	+	0.258591i
$953$		−	7.04794e8i		−	0.814299i	−0.913362	−	0.407149i	$-0.866523\pi$
$953$		−	7.04794e8i		−	0.814299i	0.913362	−	0.407149i	$-0.133477\pi$
$954$	−2.36486e8	−	2.60948e8i	−0.272371	−	0.300545i
$955$	−6.56741e8	+	6.56741e8i	−0.754022	+	0.754022i
$956$	−8.26878e7	+	8.38688e8i	−0.0946385	+	0.959902i
$957$	1.62035e9	−	1.62035e9i	1.84873	−	1.84873i
$958$	−1.02125e9	−	5.02217e7i	−1.16154	−	0.0571209i
$959$		−	2.62700e8i		−	0.297855i
$960$	1.57439e8	−	5.18449e8i	0.177950	−	0.585993i
$961$	8.74650e8			0.985517
$962$	−2.92271e7	+	5.94328e8i	−0.0328292	+	0.667576i
$963$	7.12197e7	+	7.12197e7i	0.0797483	+	0.0797483i
$964$	1.23146e9	+	1.21412e8i	1.37464	+	0.135529i
$965$	−3.18515e8	−	3.18515e8i	−0.354444	−	0.354444i
$966$	1.21557e6	−	1.10162e6i	0.00134849	−	0.00122208i
$967$	6.23901e8			0.689980			0.344990	−	0.938606i	$-0.387882\pi$
$967$	6.23901e8			0.689980			0.344990	+	0.938606i	$0.387882\pi$
$968$	−1.86885e9	−	2.77502e8i	−2.06038	−	0.305943i
$969$			5.86355e8i			0.644451i
$970$	−1.86012e8	+	1.68574e8i	−0.203810	+	0.184704i
$971$	−3.29180e8	+	3.29180e8i	−0.359564	+	0.359564i	−0.863652	−	0.504088i	$-0.831829\pi$
$971$	−3.29180e8	+	3.29180e8i	−0.359564	+	0.359564i	0.504088	+	0.863652i	$0.331829\pi$
$972$	−3.81470e8	−	4.64917e8i	−0.415395	−	0.506263i
$973$	−1.80783e8	+	1.80783e8i	−0.196254	+	0.196254i
$974$	6.37402e7	−	1.29614e9i	0.0689821	−	1.40274i
$975$		−	1.72683e8i		−	0.186309i
$976$	−4.98838e8	+	3.33169e8i	−0.536550	+	0.358357i
$977$	−1.08225e8			−0.116050			−0.0580248	−	0.998315i	$-0.518480\pi$
$977$	−1.08225e8			−0.116050			−0.0580248	+	0.998315i	$0.518480\pi$
$978$	−3.62695e8	−	1.78361e7i	−0.387726	−	0.0190671i
$979$	−5.70498e7	−	5.70498e7i	−0.0608003	−	0.0608003i
$980$	−3.94908e8	−	4.81294e8i	−0.419583	−	0.511367i
$981$	−1.98802e8	−	1.98802e8i	−0.210578	−	0.210578i
$982$	−4.02434e8	−	4.44062e8i	−0.424972	−	0.468931i
$983$	5.07802e8			0.534606			0.267303	−	0.963612i	$-0.413868\pi$
$983$	5.07802e8			0.534606			0.267303	+	0.963612i	$0.413868\pi$
$984$	−8.12491e8	−	1.09586e9i	−0.852772	−	1.15019i
$985$		−	6.58187e8i		−	0.688717i
$986$	8.72651e8	+	9.62919e8i	0.910353	+	1.00452i
$987$	1.87393e8	−	1.87393e8i	0.194896	−	0.194896i
$988$	−5.58828e8	−	5.50959e7i	−0.579438	−	0.0571279i
$989$	4.79239e6	−	4.79239e6i	0.00495408	−	0.00495408i
$990$	4.44340e8	+	2.18512e7i	0.457942	+	0.0225201i
$991$		−	1.50199e9i		−	1.54328i	−0.636057	−	0.771642i	$-0.719436\pi$
$991$		−	1.50199e9i		−	1.54328i	0.636057	−	0.771642i	$-0.280564\pi$
$992$	1.13953e8	+	2.85740e7i	0.116733	+	0.0292709i
$993$	5.19832e8			0.530903
$994$	2.88591e7	−	5.86845e8i	0.0293849	−	0.597536i
$995$	−3.33450e8	−	3.33450e8i	−0.338502	−	0.338502i
$996$	1.64156e7	−	1.66501e8i	0.0166142	−	0.168515i
$997$	−8.34985e8	−	8.34985e8i	−0.842545	−	0.842545i	0.146644	−	0.989189i	$-0.453153\pi$
$997$	−8.34985e8	−	8.34985e8i	−0.842545	−	0.842545i	−0.989189	+	0.146644i	$0.953153\pi$
$998$	1.35369e8	−	1.22679e8i	0.136184	−	0.123418i
$999$	1.34649e9			1.35054

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.7.f.a.11.6	yes	22
4.3	odd	2		64.7.f.a.15.9		22
8.3	odd	2		128.7.f.a.31.3		22
8.5	even	2		128.7.f.b.31.9		22
16.3	odd	4	inner	16.7.f.a.3.6	✓	22
16.5	even	4		128.7.f.a.95.3		22
16.11	odd	4		128.7.f.b.95.9		22
16.13	even	4		64.7.f.a.47.9		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.7.f.a.3.6	✓	22	16.3	odd	4	inner
16.7.f.a.11.6	yes	22	1.1	even	1	trivial
64.7.f.a.15.9		22	4.3	odd	2
64.7.f.a.47.9		22	16.13	even	4
128.7.f.a.31.3		22	8.3	odd	2
128.7.f.a.95.3		22	16.5	even	4
128.7.f.b.31.9		22	8.5	even	2
128.7.f.b.95.9		22	16.11	odd	4

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)

\(f(q)\)	\(=\)	\(q+(-0.392939 + 7.99034i) q^{2} +(-15.4507 - 15.4507i) q^{3} +(-63.6912 - 6.27943i) q^{4} +(-66.8872 - 66.8872i) q^{5} +(129.527 - 117.385i) q^{6} -121.702 q^{7} +(75.2016 - 506.447i) q^{8} -251.553i q^{9} +O(q^{10})\)	\(q+(-0.392939 + 7.99034i) q^{2} +(-15.4507 - 15.4507i) q^{3} +(-63.6912 - 6.27943i) q^{4} +(-66.8872 - 66.8872i) q^{5} +(129.527 - 117.385i) q^{6} -121.702 q^{7} +(75.2016 - 506.447i) q^{8} -251.553i q^{9} +(560.735 - 508.169i) q^{10} +(-1652.52 + 1652.52i) q^{11} +(887.051 + 1081.09i) q^{12} +(-836.906 + 836.906i) q^{13} +(47.8216 - 972.444i) q^{14} +2066.91i q^{15} +(4017.14 + 799.889i) q^{16} +3619.86 q^{17} +(2009.99 + 98.8449i) q^{18} +(-5241.94 - 5241.94i) q^{19} +(3840.11 + 4680.14i) q^{20} +(1880.38 + 1880.38i) q^{21} +(-12554.9 - 13853.6i) q^{22} -77.1116 q^{23} +(-8986.87 + 6663.04i) q^{24} -6677.19i q^{25} +(-6358.32 - 7016.02i) q^{26} +(-15150.2 + 15150.2i) q^{27} +(7751.37 + 764.222i) q^{28} +(31731.0 - 31731.0i) q^{29} +(-16515.3 - 812.168i) q^{30} -3585.24i q^{31} +(-7969.88 + 31784.0i) q^{32} +51065.3 q^{33} +(-1422.38 + 28923.9i) q^{34} +(8140.34 + 8140.34i) q^{35} +(-1579.61 + 16021.7i) q^{36} +(-44437.9 - 44437.9i) q^{37} +(43944.6 - 39825.1i) q^{38} +25861.6 q^{39} +(-38904.9 + 28844.8i) q^{40} +121940. i q^{41} +(-15763.8 + 14286.0i) q^{42} +(-62148.8 + 62148.8i) q^{43} +(115628. - 94874.3i) q^{44} +(-16825.7 + 16825.7i) q^{45} +(30.3001 - 616.148i) q^{46} -99656.9i q^{47} +(-49708.7 - 74426.4i) q^{48} -102838. q^{49} +(53353.1 + 2623.73i) q^{50} +(-55929.3 - 55929.3i) q^{51} +(58558.9 - 48048.3i) q^{52} +(-123740. - 123740. i) q^{53} +(-115102. - 127009. i) q^{54} +221066. q^{55} +(-9152.21 + 61635.8i) q^{56} +161983. i q^{57} +(241073. + 266010. i) q^{58} +(-1066.08 + 1066.08i) q^{59} +(12979.0 - 131644. i) q^{60} +(-103557. + 103557. i) q^{61} +(28647.3 + 1408.78i) q^{62} +30614.6i q^{63} +(-250833. - 76171.3i) q^{64} +111957. q^{65} +(-20065.5 + 408029. i) q^{66} +(-11914.8 - 11914.8i) q^{67} +(-230553. - 22730.7i) q^{68} +(1191.43 + 1191.43i) q^{69} +(-68242.7 + 61845.4i) q^{70} +603474. q^{71} +(-127398. - 18917.2i) q^{72} -102254. i q^{73} +(372536. - 337613. i) q^{74} +(-103167. + 103167. i) q^{75} +(300949. + 366782. i) q^{76} +(201116. - 201116. i) q^{77} +(-10162.0 + 206643. i) q^{78} -387379. i q^{79} +(-215193. - 322198. i) q^{80} +284780. q^{81} +(-974342. - 47915.0i) q^{82} +(-84597.7 - 84597.7i) q^{83} +(-107956. - 131572. i) q^{84} +(-242122. - 242122. i) q^{85} +(-472169. - 521011. i) q^{86} -980532. q^{87} +(712644. + 961189. i) q^{88} +34522.8i q^{89} +(-127831. - 141054. i) q^{90} +(101853. - 101853. i) q^{91} +(4911.33 + 484.217i) q^{92} +(-55394.5 + 55394.5i) q^{93} +(796293. + 39159.1i) q^{94} +701237. i q^{95} +(614225. - 367944. i) q^{96} -331728. q^{97} +(40408.9 - 821707. i) q^{98} +(415697. + 415697. 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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