LMFDB - Embedded newform 21.7.f.a.10.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,7,Mod(10,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("21.10");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	21.f (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.83113575602$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 212x^{6} + 473x^{5} + 39800x^{4} + 36821x^{3} + 985651x^{2} - 601290x + 21068100 $ x^8 - x^7 + 212x^6 + 473x^5 + 39800x^4 + 36821x^3 + 985651x^2 - 601290x + 21068100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.4
Root			$-6.30797 - 10.9257i$ of defining polynomial
Character	$\chi$	$=$	21.10
Dual form			21.7.f.a.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.80797 + 10.0597i) q^{2} +(-13.5000 - 7.79423i) q^{3} +(-35.4650 + 61.4271i) q^{4} +(-165.302 + 95.4373i) q^{5} -181.074i q^{6} +(-103.254 + 327.089i) q^{7} -80.4975 q^{8} +(121.500 + 210.444i) q^{9} +O(q^{10})$	\(q+(5.80797 + 10.0597i) q^{2} +(-13.5000 - 7.79423i) q^{3} +(-35.4650 + 61.4271i) q^{4} +(-165.302 + 95.4373i) q^{5} -181.074i q^{6} +(-103.254 + 327.089i) q^{7} -80.4975 q^{8} +(121.500 + 210.444i) q^{9} +(-1920.14 - 1108.59i) q^{10} +(1027.55 - 1779.77i) q^{11} +(957.554 - 552.844i) q^{12} +3059.97i q^{13} +(-3890.12 + 861.018i) q^{14} +2975.44 q^{15} +(1802.23 + 3121.55i) q^{16} +(2468.38 + 1425.12i) q^{17} +(-1411.34 + 2444.51i) q^{18} +(-3420.04 + 1974.56i) q^{19} -13538.7i q^{20} +(3943.34 - 3610.92i) q^{21} +23872.0 q^{22} +(-330.272 - 572.047i) q^{23} +(1086.72 + 627.416i) q^{24} +(10404.0 - 18020.3i) q^{25} +(-30782.3 + 17772.2i) q^{26} -3788.00i q^{27} +(-16430.3 - 17942.8i) q^{28} -9282.66 q^{29} +(17281.3 + 29932.0i) q^{30} +(2426.36 + 1400.86i) q^{31} +(-23510.5 + 40721.4i) q^{32} +(-27743.9 + 16018.0i) q^{33} +33108.2i q^{34} +(-14148.4 - 63922.9i) q^{35} -17236.0 q^{36} +(18466.2 + 31984.5i) q^{37} +(-39727.0 - 22936.4i) q^{38} +(23850.1 - 41309.5i) q^{39} +(13306.4 - 7682.46i) q^{40} -67941.3i q^{41} +(59227.6 + 18696.7i) q^{42} +12336.3 q^{43} +(72884.2 + 126239. i) q^{44} +(-40168.4 - 23191.3i) q^{45} +(3836.41 - 6644.86i) q^{46} +(127836. - 73806.3i) q^{47} -56188.0i q^{48} +(-96326.1 - 67546.8i) q^{49} +241705. q^{50} +(-22215.4 - 38478.3i) q^{51} +(-187965. - 108522. i) q^{52} +(-109818. + 190210. i) q^{53} +(38106.1 - 22000.6i) q^{54} +392267. i q^{55} +(8311.72 - 26329.9i) q^{56} +61560.8 q^{57} +(-53913.4 - 93380.8i) q^{58} +(166725. + 96258.8i) q^{59} +(-105524. + 182773. i) q^{60} +(288244. - 166418. i) q^{61} +32544.5i q^{62} +(-81379.5 + 18012.1i) q^{63} -315508. q^{64} +(-292035. - 505819. i) q^{65} +(-322271. - 186063. i) q^{66} +(-174592. + 302402. i) q^{67} +(-175082. + 101084. i) q^{68} +10296.9i q^{69} +(560872. - 513590. i) q^{70} +305650. q^{71} +(-9780.45 - 16940.2i) q^{72} +(-204814. - 118249. i) q^{73} +(-214503. + 371529. i) q^{74} +(-280909. + 162183. i) q^{75} -280111. i q^{76} +(476046. + 519871. i) q^{77} +554082. q^{78} +(293218. + 507869. i) q^{79} +(-595825. - 344000. i) q^{80} +(-29524.5 + 51137.9i) q^{81} +(683468. - 394601. i) q^{82} +106377. i q^{83} +(81957.9 + 370289. i) q^{84} -544039. q^{85} +(71648.8 + 124099. i) q^{86} +(125316. + 72351.2i) q^{87} +(-82715.4 + 143267. i) q^{88} +(11308.5 - 6528.95i) q^{89} -538776. i q^{90} +(-1.00088e6 - 315955. i) q^{91} +46852.3 q^{92} +(-21837.2 - 37823.2i) q^{93} +(1.48494e6 + 857329. i) q^{94} +(376894. - 652799. i) q^{95} +(634784. - 366493. i) q^{96} +205209. i q^{97} +(120042. - 1.36132e6i) q^{98} +499390. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 5 q^{2} - 108 q^{3} - 173 q^{4} - 294 q^{5} - 656 q^{7} + 3326 q^{8} + 972 q^{9}+O(q^{10}) $ 8 * q - 5 * q^2 - 108 * q^3 - 173 * q^4 - 294 * q^5 - 656 * q^7 + 3326 * q^8 + 972 * q^9	\( 8 q - 5 q^{2} - 108 q^{3} - 173 q^{4} - 294 q^{5} - 656 q^{7} + 3326 q^{8} + 972 q^{9} - 3411 q^{10} - 314 q^{11} + 4671 q^{12} - 5360 q^{14} + 5292 q^{15} - 12721 q^{16} - 5532 q^{17} + 1215 q^{18} - 18234 q^{19} + 9342 q^{21} + 86106 q^{22} + 3928 q^{23} - 44901 q^{24} - 17038 q^{25} + 12366 q^{26} + 85037 q^{28} - 8300 q^{29} + 30699 q^{30} - 89508 q^{31} - 186207 q^{32} + 8478 q^{33} - 25860 q^{35} - 84078 q^{36} + 64706 q^{37} - 77136 q^{38} + 29106 q^{39} + 221823 q^{40} + 173583 q^{42} + 45740 q^{43} + 92529 q^{44} - 71442 q^{45} - 111504 q^{46} + 483276 q^{47} - 310684 q^{49} + 967216 q^{50} + 49788 q^{51} - 1673988 q^{52} - 540974 q^{53} - 32805 q^{54} - 241885 q^{56} + 328212 q^{57} + 539799 q^{58} - 181770 q^{59} - 146367 q^{60} + 418224 q^{61} - 92826 q^{63} + 2378626 q^{64} - 414204 q^{65} - 1162431 q^{66} - 1158902 q^{67} - 821250 q^{68} + 1087917 q^{70} + 1442344 q^{71} + 404109 q^{72} - 378666 q^{73} - 432940 q^{74} + 460026 q^{75} + 1065994 q^{77} - 222588 q^{78} + 611452 q^{79} - 2094945 q^{80} - 236196 q^{81} - 1561266 q^{82} - 1579716 q^{84} - 275112 q^{85} + 816224 q^{86} + 112050 q^{87} - 366441 q^{88} - 989196 q^{89} + 304446 q^{91} + 678720 q^{92} + 805572 q^{93} - 716148 q^{94} - 591792 q^{95} + 5027589 q^{96} + 3509629 q^{98} - 152604 q^{99}+O(q^{100}) \) 8 * q - 5 * q^2 - 108 * q^3 - 173 * q^4 - 294 * q^5 - 656 * q^7 + 3326 * q^8 + 972 * q^9 - 3411 * q^10 - 314 * q^11 + 4671 * q^12 - 5360 * q^14 + 5292 * q^15 - 12721 * q^16 - 5532 * q^17 + 1215 * q^18 - 18234 * q^19 + 9342 * q^21 + 86106 * q^22 + 3928 * q^23 - 44901 * q^24 - 17038 * q^25 + 12366 * q^26 + 85037 * q^28 - 8300 * q^29 + 30699 * q^30 - 89508 * q^31 - 186207 * q^32 + 8478 * q^33 - 25860 * q^35 - 84078 * q^36 + 64706 * q^37 - 77136 * q^38 + 29106 * q^39 + 221823 * q^40 + 173583 * q^42 + 45740 * q^43 + 92529 * q^44 - 71442 * q^45 - 111504 * q^46 + 483276 * q^47 - 310684 * q^49 + 967216 * q^50 + 49788 * q^51 - 1673988 * q^52 - 540974 * q^53 - 32805 * q^54 - 241885 * q^56 + 328212 * q^57 + 539799 * q^58 - 181770 * q^59 - 146367 * q^60 + 418224 * q^61 - 92826 * q^63 + 2378626 * q^64 - 414204 * q^65 - 1162431 * q^66 - 1158902 * q^67 - 821250 * q^68 + 1087917 * q^70 + 1442344 * q^71 + 404109 * q^72 - 378666 * q^73 - 432940 * q^74 + 460026 * q^75 + 1065994 * q^77 - 222588 * q^78 + 611452 * q^79 - 2094945 * q^80 - 236196 * q^81 - 1561266 * q^82 - 1579716 * q^84 - 275112 * q^85 + 816224 * q^86 + 112050 * q^87 - 366441 * q^88 - 989196 * q^89 + 304446 * q^91 + 678720 * q^92 + 805572 * q^93 - 716148 * q^94 - 591792 * q^95 + 5027589 * q^96 + 3509629 * q^98 - 152604 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	5.80797	+	10.0597i	0.725996	+	1.25746i	0.958563	+	0.284881i	$0.0919542\pi$
$2$	5.80797	+	10.0597i	0.725996	+	1.25746i	−0.232567	+	0.972580i	$0.574712\pi$
$3$	−13.5000	−	7.79423i	−0.500000	−	0.288675i
$3$	−13.5000	−	7.79423i	−0.500000	−	0.288675i
$4$	−35.4650	+	61.4271i	−0.554140	+	0.959799i
$5$	−165.302	+	95.4373i	−1.32242	+	0.763498i	−0.984114	−	0.177539i	$-0.943186\pi$
$5$	−165.302	+	95.4373i	−1.32242	+	0.763498i	−0.338304	+	0.941037i	$0.609853\pi$
$6$		−	181.074i		−	0.838308i
$7$	−103.254	+	327.089i	−0.301033	+	0.953614i
$7$	−103.254	+	327.089i	−0.301033	+	0.953614i
$8$	−80.4975			−0.157222
$9$	121.500	+	210.444i	0.166667	+	0.288675i
$10$	−1920.14	−	1108.59i	−1.92014	−	1.10859i
$11$	1027.55	−	1779.77i	0.772015	−	1.33717i	−0.164442	−	0.986387i	$-0.552582\pi$
$11$	1027.55	−	1779.77i	0.772015	−	1.33717i	0.936457	−	0.350783i	$-0.114084\pi$
$12$	957.554	−	552.844i	0.554140	−	0.319933i
$13$			3059.97i			1.39279i	0.717657	+	0.696396i	$0.245214\pi$
$13$			3059.97i			1.39279i	−0.717657	+	0.696396i	$0.754786\pi$
$14$	−3890.12	+	861.018i	−1.41768	+	0.313782i
$15$	2975.44			0.881612
$16$	1802.23	+	3121.55i	0.439998	+	0.762098i
$17$	2468.38	+	1425.12i	0.502419	+	0.290072i	0.729712	−	0.683755i	$-0.239654\pi$
$17$	2468.38	+	1425.12i	0.502419	+	0.290072i	−0.227293	+	0.973826i	$0.572988\pi$
$18$	−1411.34	+	2444.51i	−0.241999	+	0.419154i
$19$	−3420.04	+	1974.56i	−0.498622	+	0.287879i	−0.728144	−	0.685424i	$-0.759617\pi$
$19$	−3420.04	+	1974.56i	−0.498622	+	0.287879i	0.229523	+	0.973303i	$0.426284\pi$
$20$		−	13538.7i		−	1.69234i
$21$	3943.34	−	3610.92i	0.425801	−	0.389906i
$22$	23872.0			2.24192
$23$	−330.272	−	572.047i	−0.0271449	−	0.0470163i	0.852134	−	0.523324i	$-0.175308\pi$
$23$	−330.272	−	572.047i	−0.0271449	−	0.0470163i	−0.879279	+	0.476308i	$0.841975\pi$
$24$	1086.72	+	627.416i	0.0786109	+	0.0453860i
$25$	10404.0	−	18020.3i	0.665859	−	1.15330i
$26$	−30782.3	+	17772.2i	−1.75138	+	1.01116i
$27$		−	3788.00i		−	0.192450i
$28$	−16430.3	−	17942.8i	−0.748463	−	0.817367i
$29$	−9282.66			−0.380609			−0.190304	−	0.981725i	$-0.560947\pi$
$29$	−9282.66			−0.380609			−0.190304	+	0.981725i	$0.560947\pi$
$30$	17281.3	+	29932.0i	0.640046	+	1.10859i
$31$	2426.36	+	1400.86i	0.0814460	+	0.0470229i	0.540170	−	0.841556i	$-0.318360\pi$
$31$	2426.36	+	1400.86i	0.0814460	+	0.0470229i	−0.458724	+	0.888579i	$0.651693\pi$
$32$	−23510.5	+	40721.4i	−0.717484	+	1.24272i
$33$	−27743.9	+	16018.0i	−0.772015	+	0.445723i
$34$			33108.2i			0.842363i
$35$	−14148.4	−	63922.9i	−0.329991	−	1.49091i
$36$	−17236.0			−0.369427
$37$	18466.2	+	31984.5i	0.364563	+	0.631442i	0.988706	−	0.149868i	$-0.0478849\pi$
$37$	18466.2	+	31984.5i	0.364563	+	0.631442i	−0.624143	+	0.781310i	$0.714552\pi$
$38$	−39727.0	−	22936.4i	−0.723994	−	0.417998i
$39$	23850.1	−	41309.5i	0.402065	−	0.696396i
$40$	13306.4	−	7682.46i	0.207913	−	0.120039i
$41$		−	67941.3i		−	0.985785i	−0.870090	−	0.492892i	$-0.835940\pi$
$41$		−	67941.3i		−	0.985785i	0.870090	−	0.492892i	$-0.164060\pi$
$42$	59227.6	+	18696.7i	0.799422	+	0.252358i
$43$	12336.3			0.155160			0.0775799	−	0.996986i	$-0.475281\pi$
$43$	12336.3			0.155160			0.0775799	+	0.996986i	$0.475281\pi$
$44$	72884.2	+	126239.i	0.855609	+	1.48196i
$45$	−40168.4	−	23191.3i	−0.440806	−	0.254499i
$46$	3836.41	−	6644.86i	0.0394141	−	0.0682673i
$47$	127836.	−	73806.3i	1.23129	−	0.710886i	0.263991	−	0.964525i	$-0.414961\pi$
$47$	127836.	−	73806.3i	1.23129	−	0.710886i	0.967299	+	0.253639i	$0.0816277\pi$
$48$		−	56188.0i		−	0.508066i
$49$	−96326.1	−	67546.8i	−0.818758	−	0.574139i
$50$	241705.			1.93364
$51$	−22215.4	−	38478.3i	−0.167473	−	0.290072i
$52$	−187965.	−	108522.i	−1.33680	−	0.771802i
$53$	−109818.	+	190210.i	−0.737641	+	1.27763i	0.215914	+	0.976412i	$0.430727\pi$
$53$	−109818.	+	190210.i	−0.737641	+	1.27763i	−0.953555	+	0.301219i	$0.902607\pi$
$54$	38106.1	−	22000.6i	0.241999	−	0.139718i
$55$			392267.i			2.35773i
$56$	8311.72	−	26329.9i	0.0473290	−	0.149929i
$57$	61560.8			0.332414
$58$	−53913.4	−	93380.8i	−0.276320	−	0.478601i
$59$	166725.	+	96258.8i	0.811792	+	0.468689i	0.847578	−	0.530671i	$-0.178060\pi$
$59$	166725.	+	96258.8i	0.811792	+	0.468689i	−0.0357855	+	0.999359i	$0.511393\pi$
$60$	−105524.	+	182773.i	−0.488536	+	0.846170i
$61$	288244.	−	166418.i	1.26990	−	0.733180i	0.294935	−	0.955517i	$-0.404702\pi$
$61$	288244.	−	166418.i	1.26990	−	0.733180i	0.974970	+	0.222338i	$0.0713688\pi$
$62$			32544.5i			0.136554i
$63$	−81379.5	+	18012.1i	−0.325457	+	0.0720348i
$64$	−315508.			−1.20357
$65$	−292035.	−	505819.i	−1.06339	−	1.84185i
$66$	−322271.	−	186063.i	−1.12096	−	0.647186i
$67$	−174592.	+	302402.i	−0.580496	+	1.00545i	0.414924	+	0.909856i	$0.363808\pi$
$67$	−174592.	+	302402.i	−0.580496	+	1.00545i	−0.995420	+	0.0955931i	$0.969525\pi$
$68$	−175082.	+	101084.i	−0.556821	+	0.321481i
$69$			10296.9i			0.0313442i
$70$	560872.	−	513590.i	1.63519	−	1.49735i
$71$	305650.			0.853984			0.426992	−	0.904255i	$-0.359573\pi$
$71$	305650.			0.853984			0.426992	+	0.904255i	$0.359573\pi$
$72$	−9780.45	−	16940.2i	−0.0262036	−	0.0453860i
$73$	−204814.	−	118249.i	−0.526490	−	0.303969i	0.213096	−	0.977031i	$-0.431645\pi$
$73$	−204814.	−	118249.i	−0.526490	−	0.303969i	−0.739586	+	0.673062i	$0.764979\pi$
$74$	−214503.	+	371529.i	−0.529343	+	0.916849i
$75$	−280909.	+	162183.i	−0.665859	+	0.384434i
$76$		−	280111.i		−	0.638102i
$77$	476046.	+	519871.i	1.04274	+	1.13874i
$78$	554082.			1.16759
$79$	293218.	+	507869.i	0.594716	+	1.03008i	0.993587	+	0.113072i	$0.0360690\pi$
$79$	293218.	+	507869.i	0.594716	+	1.03008i	−0.398871	+	0.917007i	$0.630598\pi$
$80$	−595825.	−	344000.i	−1.16372	−	0.671875i
$81$	−29524.5	+	51137.9i	−0.0555556	+	0.0962250i
$82$	683468.	−	394601.i	1.23959	−	0.715675i
$83$			106377.i			0.186044i	0.995664	+	0.0930218i	$0.0296526\pi$
$83$			106377.i			0.186044i	−0.995664	+	0.0930218i	$0.970347\pi$
$84$	81957.9	+	370289.i	0.138278	+	0.624746i
$85$	−544039.			−0.885876
$86$	71648.8	+	124099.i	0.112645	+	0.195108i
$87$	125316.	+	72351.2i	0.190304	+	0.109872i
$88$	−82715.4	+	143267.i	−0.121378	+	0.210232i
$89$	11308.5	−	6528.95i	0.0160411	−	0.00926134i	−0.491958	−	0.870619i	$-0.663719\pi$
$89$	11308.5	−	6528.95i	0.0160411	−	0.00926134i	0.507999	+	0.861358i	$0.330385\pi$
$90$		−	538776.i		−	0.739062i
$91$	−1.00088e6	−	315955.i	−1.32819	−	0.419277i
$92$	46852.3			0.0601682
$93$	−21837.2	−	37823.2i	−0.0271487	−	0.0470229i
$94$	1.48494e6	+	857329.i	1.78782	+	1.03220i
$95$	376894.	−	652799.i	0.439591	−	0.761393i
$96$	634784.	−	366493.i	0.717484	−	0.414240i
$97$			205209.i			0.224844i	0.993661	+	0.112422i	$0.0358609\pi$
$97$			205209.i			0.224844i	−0.993661	+	0.112422i	$0.964139\pi$
$98$	120042.	−	1.36132e6i	0.127542	−	1.44638i
$99$	499390.			0.514677
$100$	737958.	+	1.27818e6i	0.737958	+	1.27818i
$101$	−1.21339e6	−	700549.i	−1.17770	−	0.679946i	−0.222220	−	0.974997i	$-0.571330\pi$
$101$	−1.21339e6	−	700549.i	−1.17770	−	0.679946i	−0.955482	+	0.295050i	$0.904664\pi$
$102$	258053.	−	446961.i	0.243169	−	0.421182i
$103$	448291.	−	258821.i	0.410250	−	0.236858i	−0.280647	−	0.959811i	$-0.590549\pi$
$103$	448291.	−	258821.i	0.410250	−	0.236858i	0.690897	+	0.722953i	$0.257216\pi$
$104$		−	246320.i		−	0.218977i
$105$	−307227.	+	973235.i	−0.265394	+	0.840717i
$106$	−2.55127e6			−2.14210
$107$	−323372.	−	560097.i	−0.263968	−	0.457206i	0.703325	−	0.710869i	$-0.251698\pi$
$107$	−323372.	−	560097.i	−0.263968	−	0.457206i	−0.967293	+	0.253663i	$0.918365\pi$
$108$	232686.	+	134341.i	0.184713	+	0.106644i
$109$	343631.	−	595186.i	0.265346	−	0.459593i	−0.702308	−	0.711873i	$-0.747847\pi$
$109$	343631.	−	595186.i	0.265346	−	0.459593i	0.967654	+	0.252280i	$0.0811805\pi$
$110$	−3.94609e6	+	2.27827e6i	−2.96475	+	1.71170i
$111$		−	575720.i		−	0.420962i
$112$	−1.20712e6	+	267177.i	−0.859201	+	0.190171i
$113$	2.11668e6			1.46697			0.733483	−	0.679708i	$-0.237893\pi$
$113$	2.11668e6			1.46697			0.733483	+	0.679708i	$0.237893\pi$
$114$	357543.	+	619283.i	0.241331	+	0.417998i
$115$	109189.	+	63040.4i	0.0717937	+	0.0414501i
$116$	329209.	−	570207.i	0.210910	−	0.365308i
$117$	−643952.	+	371786.i	−0.402065	+	0.232132i
$118$			2.23627e6i			1.36106i
$119$	−721014.	+	660232.i	−0.427861	+	0.391792i
$120$	−239516.			−0.138609
$121$	−1.22595e6	−	2.12340e6i	−0.692015	−	1.19860i
$122$	3.34823e6	+	1.93310e6i	1.84389	+	1.06457i
$123$	−529550.	+	917207.i	−0.284571	+	0.492892i
$124$	−172101.	+	99362.7i	−0.0902649	+	0.0521145i
$125$			989318.i			0.506531i
$126$	−653846.	−	714039.i	−0.326861	−	0.356952i
$127$	3.29012e6			1.60620			0.803102	−	0.595841i	$-0.203181\pi$
$127$	3.29012e6			1.60620			0.803102	+	0.595841i	$0.203181\pi$
$128$	−327785.	−	567740.i	−0.156300	−	0.270720i
$129$	−166540.	−	96151.9i	−0.0775799	−	0.0447908i
$130$	3.39226e6	−	5.87556e6i	1.54404	−	2.67436i
$131$	193424.	−	111674.i	0.0860394	−	0.0496748i	−0.456363	−	0.889794i	$-0.650848\pi$
$131$	193424.	−	111674.i	0.0860394	−	0.0496748i	0.542402	+	0.840119i	$0.317515\pi$
$132$		−	2.27230e6i		−	0.987972i
$133$	−292725.	−	1.32254e6i	−0.124424	−	0.562153i
$134$	−4.05609e6			−1.68575
$135$	361516.	+	626164.i	0.146935	+	0.254499i
$136$	−198699.	−	114719.i	−0.0789912	−	0.0456056i
$137$	1.58525e6	−	2.74573e6i	0.616504	−	1.06782i	−0.373615	−	0.927584i	$-0.621882\pi$
$137$	1.58525e6	−	2.74573e6i	0.616504	−	1.06782i	0.990119	−	0.140232i	$-0.0447849\pi$
$138$	−103583.	+	59803.8i	−0.0394141	+	0.0227558i
$139$			774740.i			0.288477i	0.989543	+	0.144239i	$0.0460733\pi$
$139$			774740.i			0.288477i	−0.989543	+	0.144239i	$0.953927\pi$
$140$	4.42837e6	+	1.39793e6i	1.61384	+	0.509450i
$141$	−2.30105e6			−0.820860
$142$	1.77521e6	+	3.07475e6i	0.619989	+	1.07385i
$143$	5.44604e6	+	3.14427e6i	1.86240	+	1.07526i
$144$	−437942.	+	758538.i	−0.146666	+	0.254033i
$145$	1.53444e6	−	885912.i	0.503323	−	0.290594i
$146$		−	2.74715e6i		−	0.882722i
$147$	773927.	+	1.66267e6i	0.243640	+	0.523424i
$148$	−2.61962e6			−0.808077
$149$	−1.75461e6	−	3.03907e6i	−0.530421	−	0.918716i	−0.999370	−	0.0354908i	$-0.988701\pi$
$149$	−1.75461e6	−	3.03907e6i	−0.530421	−	0.918716i	0.468949	−	0.883225i	$-0.344633\pi$
$150$	−3.26302e6	−	1.88391e6i	−0.966821	−	0.558194i
$151$	−3.22601e6	+	5.58761e6i	−0.936989	+	1.62291i	−0.165940	+	0.986136i	$0.553066\pi$
$151$	−3.22601e6	+	5.58761e6i	−0.936989	+	1.62291i	−0.771049	+	0.636776i	$0.780268\pi$
$152$	275305.	−	158948.i	0.0783942	−	0.0452609i
$153$			692609.i			0.193381i
$154$	−2.46488e6	+	7.80827e6i	−0.674892	+	2.13792i
$155$	−534776.			−0.143607
$156$	1.69168e6	+	2.93008e6i	0.445600	+	0.771802i
$157$	−4.05557e6	−	2.34148e6i	−1.04798	−	0.605051i	−0.125896	−	0.992043i	$-0.540181\pi$
$157$	−4.05557e6	−	2.34148e6i	−1.04798	−	0.605051i	−0.922083	+	0.386992i	$0.873514\pi$
$158$	−3.40600e6	+	5.89937e6i	−0.863523	+	1.49567i
$159$	2.96508e6	−	1.71189e6i	0.737641	−	0.425877i
$160$		−	8.97512e6i		−	2.19119i
$161$	221213.	−	48962.0i	0.0530069	−	0.0117323i
$162$	−685909.			−0.161332
$163$	−2.59116e6	−	4.48803e6i	−0.598318	−	1.03632i	−0.993069	−	0.117529i	$-0.962503\pi$
$163$	−2.59116e6	−	4.48803e6i	−0.598318	−	1.03632i	0.394752	−	0.918788i	$-0.370831\pi$
$164$	4.17344e6	+	2.40953e6i	0.946155	+	0.546263i
$165$	3.05742e6	−	5.29560e6i	0.680617	−	1.17886i
$166$	−1.07012e6	+	617836.i	−0.233943	+	0.135067i
$167$			1.56630e6i			0.336298i	0.985762	+	0.168149i	$0.0537790\pi$
$167$			1.56630e6i			0.336298i	−0.985762	+	0.168149i	$0.946221\pi$
$168$	−317430.	+	290670.i	−0.0669452	+	0.0613017i
$169$	−4.53658e6			−0.939871
$170$	−3.15976e6	−	5.47286e6i	−0.643143	−	1.11396i
$171$	−831071.	−	479819.i	−0.166207	−	0.0959598i
$172$	−437506.	+	757783.i	−0.0859803	+	0.148922i
$173$	−1.07788e6	+	622312.i	−0.208176	+	0.120190i	−0.600463	−	0.799652i	$-0.705017\pi$
$173$	−1.07788e6	+	622312.i	−0.208176	+	0.120190i	0.392287	+	0.919843i	$0.371684\pi$
$174$			1.68085e6i			0.319067i
$175$	4.82000e6	+	5.26373e6i	0.899358	+	0.982154i
$176$	7.40754e6			1.35874
$177$	−1.50053e6	−	2.59899e6i	−0.270597	−	0.468689i
$178$	131359.	+	75839.9i	0.0232916	+	0.0134474i
$179$	−1.12800e6	+	1.95375e6i	−0.196675	+	0.340651i	−0.947448	−	0.319909i	$-0.896348\pi$
$179$	−1.12800e6	+	1.95375e6i	−0.196675	+	0.340651i	0.750773	+	0.660560i	$0.229681\pi$
$180$	2.84914e6	−	1.64495e6i	0.488536	−	0.282057i
$181$			7.97198e6i			1.34441i	0.740367	+	0.672203i	$0.234652\pi$
$181$			7.97198e6i			1.34441i	−0.740367	+	0.672203i	$0.765348\pi$
$182$	−2.63468e6	−	1.19036e7i	−0.437033	−	1.97454i
$183$	−5.18839e6			−0.846603
$184$	26586.1	+	46048.4i	0.00426776	+	0.00739199i
$185$	−6.10502e6	−	3.52473e6i	−0.964210	−	0.556687i
$186$	253660.	−	439351.i	0.0394196	−	0.0682768i
$187$	5.07278e6	−	2.92877e6i	0.775750	−	0.447879i
$188$			1.04701e7i			1.57572i
$189$	1.23901e6	+	391127.i	0.183523	+	0.0579338i
$190$	8.75595e6			1.27656
$191$	−2.13087e6	−	3.69078e6i	−0.305814	−	0.529685i	0.671628	−	0.740888i	$-0.265595\pi$
$191$	−2.13087e6	−	3.69078e6i	−0.305814	−	0.529685i	−0.977442	+	0.211203i	$0.932262\pi$
$192$	4.25935e6	+	2.45914e6i	0.601783	+	0.347440i
$193$	72886.7	−	126243.i	0.0101386	−	0.0175605i	−0.860912	−	0.508755i	$-0.830106\pi$
$193$	72886.7	−	126243.i	0.0101386	−	0.0175605i	0.871050	+	0.491194i	$0.163439\pi$
$194$	−2.06434e6	+	1.19185e6i	−0.282733	+	0.163236i
$195$			9.10474e6i			1.22790i
$196$	7.56541e6	−	3.52149e6i	1.00476	−	0.467690i
$197$	−7.21313e6			−0.943463			−0.471732	−	0.881742i	$-0.656371\pi$
$197$	−7.21313e6			−0.943463			−0.471732	+	0.881742i	$0.656371\pi$
$198$	2.90044e6	+	5.02371e6i	0.373653	+	0.647186i
$199$	1.52836e6	+	882399.i	0.193940	+	0.111971i	0.593826	−	0.804594i	$-0.297617\pi$
$199$	1.52836e6	+	882399.i	0.193940	+	0.111971i	−0.399886	+	0.916565i	$0.630950\pi$
$200$	−837500.	+	1.45059e6i	−0.104687	+	0.181324i
$201$	4.71398e6	−	2.72162e6i	0.580496	−	0.335150i
$202$		−	1.62751e7i		−	1.97455i
$203$	958475.	−	3.03626e6i	0.114576	−	0.362954i
$204$	3.15148e6			0.371214
$205$	6.48413e6	+	1.12308e7i	0.752645	+	1.30362i
$206$	5.20732e6	+	3.00645e6i	0.595680	+	0.343916i
$207$	80256.0	−	139007.i	0.00904829	−	0.0156721i
$208$	−9.55185e6	+	5.51476e6i	−1.06144	+	0.612825i
$209$			8.11587e6i			0.888989i
$210$	−1.15748e7	+	2.56191e6i	−1.24984	+	0.276634i
$211$	1.37033e7			1.45874			0.729369	−	0.684121i	$-0.239814\pi$
$211$	1.37033e7			1.45874			0.729369	+	0.684121i	$0.239814\pi$
$212$	−7.78936e6	−	1.34916e7i	−0.817512	−	1.41597i
$213$	−4.12628e6	−	2.38231e6i	−0.426992	−	0.246524i
$214$	3.75627e6	−	6.50605e6i	0.383279	−	0.663859i
$215$	−2.03922e6	+	1.17734e6i	−0.205186	+	0.118464i
$216$			304924.i			0.0302573i
$217$	−708738.	+	648991.i	−0.0693596	+	0.0635126i
$218$	7.98318e6			0.770560
$219$	1.84332e6	+	3.19273e6i	0.175497	+	0.303969i
$220$	−2.40958e7	−	1.39117e7i	−2.26294	−	1.30651i
$221$	−4.36082e6	+	7.55317e6i	−0.404010	+	0.699765i
$222$	5.79157e6	−	3.34376e6i	0.529343	−	0.305616i
$223$		−	2.15029e7i		−	1.93902i	−0.245055	−	0.969509i	$-0.578806\pi$
$223$		−	2.15029e7i		−	1.93902i	0.245055	−	0.969509i	$-0.421194\pi$
$224$	−1.08920e7	−	1.18947e7i	−0.969087	−	1.05830i
$225$	5.05636e6			0.443906
$226$	1.22936e7	+	2.12932e7i	1.06501	+	1.84465i
$227$	3.40461e6	+	1.96565e6i	0.291065	+	0.168046i	0.638422	−	0.769687i	$-0.279588\pi$
$227$	3.40461e6	+	1.96565e6i	0.291065	+	0.168046i	−0.347357	+	0.937733i	$0.612921\pi$
$228$	−2.18325e6	+	3.78150e6i	−0.184204	+	0.319051i
$229$	486988.	−	281163.i	0.0405520	−	0.0234127i	−0.479587	−	0.877494i	$-0.659213\pi$
$229$	486988.	−	281163.i	0.0405520	−	0.0234127i	0.520139	+	0.854082i	$0.325880\pi$
$230$			1.46455e6i			0.120370i
$231$	−2.37462e6	−	1.07287e7i	−0.192646	−	0.870382i
$232$	747232.			0.0598400
$233$	8.16657e6	+	1.41449e7i	0.645612	+	1.11823i	0.984160	+	0.177284i	$0.0567310\pi$
$233$	8.16657e6	+	1.41449e7i	0.645612	+	1.11823i	−0.338548	+	0.940949i	$0.609936\pi$
$234$	−7.48010e6	−	4.31864e6i	−0.583794	−	0.337054i
$235$	−1.40877e7	+	2.44007e7i	−1.08552	+	1.88018i
$236$	−1.18258e7	+	6.82763e6i	−0.899693	+	0.519438i
$237$		−	9.14164e6i		−	0.686719i
$238$	−1.08294e7	−	3.41857e6i	−0.803289	−	0.253579i
$239$	−1.96132e7			−1.43666			−0.718331	−	0.695702i	$-0.755094\pi$
$239$	−1.96132e7			−1.43666			−0.718331	+	0.695702i	$0.755094\pi$
$240$	5.36243e6	+	9.28800e6i	0.387907	+	0.671875i
$241$	3.11683e6	+	1.79950e6i	0.222670	+	0.128559i	0.607186	−	0.794560i	$-0.292298\pi$
$241$	3.11683e6	+	1.79950e6i	0.222670	+	0.128559i	−0.384516	+	0.923118i	$0.625632\pi$
$242$	1.42405e7	−	2.46653e7i	1.00480	−	1.74036i
$243$	797162.	−	460241.i	0.0555556	−	0.0320750i
$244$			2.36080e7i			1.62514i
$245$	2.23694e7	+	1.97254e6i	1.52109	+	0.134131i
$246$	−1.23024e7			−0.826391
$247$	−6.04210e6	−	1.04652e7i	−0.400956	−	0.694476i
$248$	−195316.	−	112766.i	−0.0128051	−	0.00739302i
$249$	829129.	−	1.43609e6i	0.0537061	−	0.0930218i
$250$	−9.95223e6	+	5.74592e6i	−0.636943	+	0.367739i
$251$		−	6.49855e6i		−	0.410956i	−0.978662	−	0.205478i	$-0.934125\pi$
$251$		−	6.49855e6i		−	0.410956i	0.978662	−	0.205478i	$-0.0658749\pi$
$252$	1.77969e6	−	5.63771e6i	0.111210	−	0.352290i
$253$	−1.35749e6			−0.0838250
$254$	1.91089e7	+	3.30976e7i	1.16610	+	2.01974i
$255$	7.34452e6	+	4.24036e6i	0.442938	+	0.255730i
$256$	−6.28871e6	+	1.08924e7i	−0.374837	+	0.649236i
$257$	2.47506e6	−	1.42897e6i	0.145810	−	0.0841832i	−0.425320	−	0.905043i	$-0.639839\pi$
$257$	2.47506e6	−	1.42897e6i	0.145810	−	0.0841832i	0.571130	+	0.820860i	$0.306505\pi$
$258$		−	2.23379e6i		−	0.130072i
$259$	−1.23685e7	+	2.73758e6i	−0.711898	+	0.157568i
$260$	4.14280e7			2.35708
$261$	−1.12784e6	−	1.95348e6i	−0.0634348	−	0.109872i
$262$	2.24680e6	+	1.29719e6i	0.124928	+	0.0721275i
$263$	2.49913e6	−	4.32862e6i	0.137380	−	0.237948i	−0.789124	−	0.614233i	$-0.789465\pi$
$263$	2.49913e6	−	4.32862e6i	0.137380	−	0.237948i	0.926504	+	0.376285i	$0.122799\pi$
$264$	2.23332e6	−	1.28941e6i	0.121378	−	0.0700774i
$265$		−	4.19228e7i		−	2.25275i
$266$	1.16042e7	−	1.06260e7i	0.616555	−	0.564580i
$267$	−203553.			−0.0106941
$268$	−1.23838e7	−	2.14493e7i	−0.643352	−	1.11432i
$269$	−1.76842e7	−	1.02100e7i	−0.908507	−	0.524527i	−0.0285567	−	0.999592i	$-0.509091\pi$
$269$	−1.76842e7	−	1.02100e7i	−0.908507	−	0.524527i	−0.879951	+	0.475065i	$0.842424\pi$
$270$	−4.19934e6	+	7.27348e6i	−0.213349	+	0.369531i
$271$	1.06885e7	−	6.17102e6i	0.537044	−	0.310062i	−0.206836	−	0.978376i	$-0.566317\pi$
$271$	1.06885e7	−	6.17102e6i	0.537044	−	0.310062i	0.743880	+	0.668313i	$0.232983\pi$
$272$			1.02736e7i			0.510523i
$273$	1.10493e7	+	1.20665e7i	0.543058	+	0.593053i
$274$	3.68283e7			1.79032
$275$	−2.13814e7	−	3.70336e7i	−1.02811	−	1.78073i
$276$	−632506.	−	365177.i	−0.0300841	−	0.0173691i
$277$	1.04151e7	−	1.80395e7i	0.490031	−	0.848758i	−0.509903	−	0.860232i	$-0.670319\pi$
$277$	1.04151e7	−	1.80395e7i	0.490031	−	0.848758i	0.999934	+	0.0114733i	$0.00365216\pi$
$278$	−7.79365e6	+	4.49966e6i	−0.362749	+	0.209433i
$279$			680817.i			0.0313486i
$280$	1.13891e6	+	5.14564e6i	0.0518817	+	0.234404i
$281$	2.10143e7			0.947100			0.473550	−	0.880767i	$-0.342972\pi$
$281$	2.10143e7			0.947100			0.473550	+	0.880767i	$0.342972\pi$
$282$	−1.33644e7	−	2.31479e7i	−0.595941	−	1.03220i
$283$	9.02737e6	+	5.21195e6i	0.398292	+	0.229954i	0.685747	−	0.727840i	$-0.259476\pi$
$283$	9.02737e6	+	5.21195e6i	0.398292	+	0.229954i	−0.287455	+	0.957794i	$0.592809\pi$
$284$	−1.08399e7	+	1.87752e7i	−0.473227	+	0.819653i
$285$	−1.01761e7	+	5.87519e6i	−0.439591	+	0.253798i
$286$			7.30474e7i			3.12253i
$287$	2.22229e7	+	7.01523e6i	0.940058	+	0.296754i
$288$	−1.14261e7			−0.478323
$289$	−8.00684e6	−	1.38683e7i	−0.331717	−	0.574551i
$290$	1.78240e7	+	1.02907e7i	0.730821	+	0.421940i
$291$	1.59945e6	−	2.77033e6i	0.0649070	−	0.112422i
$292$	1.45274e7	−	8.38741e6i	0.583499	−	0.336883i
$293$			2.85328e7i			1.13433i	0.823603	+	0.567167i	$0.191961\pi$
$293$			2.85328e7i			1.13433i	−0.823603	+	0.567167i	$0.808039\pi$
$294$	−1.22310e7	+	1.74422e7i	−0.481305	+	0.686371i
$295$	−3.67467e7			−1.43137
$296$	−1.48649e6	−	2.57467e6i	−0.0573173	−	0.0992765i
$297$	−6.74177e6	−	3.89236e6i	−0.257338	−	0.148574i
$298$	2.03814e7	−	3.53016e7i	0.770167	−	1.33397i
$299$	1.75044e6	−	1.01062e6i	0.0654839	−	0.0378072i
$300$		−	2.30072e7i		−	0.852120i
$301$	−1.27378e6	+	4.03507e6i	−0.0467082	+	0.147963i
$302$	−7.49461e7			−2.72100
$303$	1.09205e7	+	1.89148e7i	0.392567	+	0.679946i
$304$	−1.23274e7	−	7.11724e6i	−0.438785	−	0.253332i
$305$	−3.17649e7	+	5.50185e7i	−1.11956	+	1.93914i
$306$	−6.96744e6	+	4.02265e6i	−0.243169	+	0.140394i
$307$			1.02269e7i			0.353450i	0.984260	+	0.176725i	$0.0565503\pi$
$307$			1.02269e7i			0.353450i	−0.984260	+	0.176725i	$0.943450\pi$
$308$	−4.88171e7	+	1.08049e7i	−1.67078	+	0.369802i
$309$	−8.06925e6			−0.273500
$310$	−3.10596e6	−	5.37968e6i	−0.104258	−	0.180581i
$311$	−1.36331e7	−	7.87108e6i	−0.453225	−	0.261669i	0.255966	−	0.966686i	$-0.417606\pi$
$311$	−1.36331e7	−	7.87108e6i	−0.453225	−	0.261669i	−0.709191	+	0.705016i	$0.750940\pi$
$312$	−1.91987e6	+	3.32532e6i	−0.0632133	+	0.109489i
$313$	4.80881e7	−	2.77637e7i	1.56821	−	0.905408i	0.571834	−	0.820369i	$-0.306232\pi$
$313$	4.80881e7	−	2.77637e7i	1.56821	−	0.905408i	0.996378	−	0.0850387i	$-0.0271014\pi$
$314$		−	5.43970e7i		−	1.75706i
$315$	1.17332e7	−	1.07441e7i	0.375391	−	0.343746i
$316$	−4.15959e7			−1.31822
$317$	3.01539e6	+	5.22282e6i	0.0946600	+	0.163956i	0.909467	−	0.415777i	$-0.136490\pi$
$317$	3.01539e6	+	5.22282e6i	0.0946600	+	0.163956i	−0.814807	+	0.579733i	$0.803157\pi$
$318$	3.44422e7	+	1.98852e7i	1.07105	+	0.618370i
$319$	−9.53842e6	+	1.65210e7i	−0.293836	+	0.508938i
$320$	5.21541e7	−	3.01112e7i	1.59162	−	0.918920i
$321$			1.00817e7i			0.304804i
$322$	1.77734e6	+	1.94096e6i	0.0532357	+	0.0581366i
$323$	−1.12560e7			−0.334022
$324$	−2.09417e6	−	3.62721e6i	−0.0615711	−	0.106644i
$325$	5.51416e7	+	3.18360e7i	1.60631	+	0.927403i
$326$	3.00988e7	−	5.21326e7i	0.868752	−	1.50472i
$327$	−9.27803e6	+	5.35667e6i	−0.265346	+	0.153198i
$328$			5.46910e6i			0.154987i
$329$	1.09416e7	+	4.94347e7i	0.307251	+	1.38818i
$330$	7.10295e7			1.97650
$331$	−4.88277e6	−	8.45720e6i	−0.134643	−	0.233208i	0.790818	−	0.612051i	$-0.209655\pi$
$331$	−4.88277e6	−	8.45720e6i	−0.134643	−	0.233208i	−0.925461	+	0.378843i	$0.876322\pi$
$332$	−6.53445e6	−	3.77267e6i	−0.178564	−	0.103094i
$333$	−4.48729e6	+	7.77222e6i	−0.121521	+	0.210481i
$334$	−1.57564e7	+	9.09699e6i	−0.422882	+	0.244151i
$335$		−	6.66502e7i		−	1.77283i
$336$	1.83785e7	+	5.80165e6i	0.484498	+	0.152945i
$337$	−5.70025e7			−1.48938			−0.744688	−	0.667412i	$-0.767402\pi$
$337$	−5.70025e7			−1.48938			−0.744688	+	0.667412i	$0.767402\pi$
$338$	−2.63483e7	−	4.56366e7i	−0.682343	−	1.18185i
$339$	−2.85752e7	−	1.64979e7i	−0.733483	−	0.423477i
$340$	1.92943e7	−	3.34187e7i	0.490900	−	0.850263i
$341$	4.98642e6	−	2.87891e6i	0.125755	−	0.0726047i
$342$		−	1.11471e7i		−	0.278666i
$343$	3.20399e7	−	2.45327e7i	0.793980	−	0.607944i
$344$	−993041.			−0.0243945
$345$	−982703.	−	1.70209e6i	−0.0239312	−	0.0414501i
$346$	−1.25205e7	−	7.22874e6i	−0.302270	−	0.174516i
$347$	1.83677e7	−	3.18139e7i	0.439610	−	0.761426i	−0.558050	−	0.829808i	$-0.688450\pi$
$347$	1.83677e7	−	3.18139e7i	0.439610	−	0.761426i	0.997659	+	0.0683813i	$0.0217834\pi$
$348$	−8.88865e6	+	5.13187e6i	−0.210910	+	0.121769i
$349$			6.58421e7i			1.54891i	0.632626	+	0.774457i	$0.281977\pi$
$349$			6.58421e7i			1.54891i	−0.632626	+	0.774457i	$0.718023\pi$
$350$	−2.49571e7	+	7.90593e7i	−0.582090	+	1.84395i
$351$	1.15911e7			0.268043
$352$	4.83166e7	+	8.36867e7i	1.10782	+	1.91879i
$353$	2.76008e7	+	1.59353e7i	0.627476	+	0.362273i	0.779774	−	0.626061i	$-0.215334\pi$
$353$	2.76008e7	+	1.59353e7i	0.627476	+	0.362273i	−0.152298	+	0.988335i	$0.548667\pi$
$354$	1.74300e7	−	3.01897e7i	0.392905	−	0.680532i
$355$	−5.05247e7	+	2.91704e7i	−1.12932	+	0.652015i
$356$			926197.i			0.0205283i
$357$	1.48797e7	−	3.29339e6i	0.327031	−	0.0723833i
$358$	−2.62055e7			−0.571141
$359$	1.91128e7	+	3.31044e7i	0.413087	+	0.715488i	0.995226	−	0.0976018i	$-0.0311171\pi$
$359$	1.91128e7	+	3.31044e7i	0.413087	+	0.715488i	−0.582138	+	0.813090i	$0.697784\pi$
$360$	3.23346e6	+	1.86684e6i	0.0693043	+	0.0400128i
$361$	−1.57251e7	+	2.72367e7i	−0.334251	+	0.578940i
$362$	−8.01957e7	+	4.63010e7i	−1.69054	+	0.976033i
$363$			3.82212e7i			0.799070i
$364$	5.49044e7	−	5.02760e7i	1.13842	−	1.04245i
$365$	4.51415e7			0.928320
$366$	−3.01340e7	−	5.21937e7i	−0.614630	−	1.06457i
$367$	8.43371e7	+	4.86920e7i	1.70616	+	0.985053i	0.939206	+	0.343354i	$0.111563\pi$
$367$	8.43371e7	+	4.86920e7i	1.70616	+	0.985053i	0.766956	+	0.641699i	$0.221770\pi$
$368$	1.19045e6	−	2.06192e6i	0.0238874	−	0.0413741i
$369$	1.42978e7	−	8.25486e6i	0.284571	−	0.164297i
$370$		−	8.18861e7i		−	1.61661i
$371$	−5.08765e7	−	5.55602e7i	−0.996312	−	1.08803i
$372$	3.09782e6			0.0601766
$373$	−1.05213e7	−	1.82235e7i	−0.202742	−	0.351160i	0.746669	−	0.665196i	$-0.231652\pi$
$373$	−1.05213e7	−	1.82235e7i	−0.202742	−	0.351160i	−0.949411	+	0.314036i	$0.898319\pi$
$374$	5.89251e7	+	3.40204e7i	1.12638	+	0.650317i
$375$	7.71097e6	−	1.33558e7i	0.146223	−	0.253265i
$376$	−1.02905e7	+	5.94122e6i	−0.193586	+	0.111767i
$377$		−	2.84046e7i		−	0.530109i
$378$	3.26153e6	+	1.47357e7i	0.0603874	+	0.272833i
$379$	−4.11794e7			−0.756418			−0.378209	−	0.925720i	$-0.623460\pi$
$379$	−4.11794e7			−0.756418			−0.378209	+	0.925720i	$0.623460\pi$
$380$	2.67331e7	+	4.63030e7i	0.487189	+	0.843837i
$381$	−4.44166e7	−	2.56440e7i	−0.803102	−	0.463671i
$382$	2.47521e7	−	4.28718e7i	0.444039	−	0.769098i
$383$	−1.31798e7	+	7.60939e6i	−0.234592	+	0.135442i	−0.612689	−	0.790324i	$-0.709912\pi$
$383$	−1.31798e7	+	7.60939e6i	−0.234592	+	0.135442i	0.378096	+	0.925766i	$0.376579\pi$
$384$			1.02193e7i			0.180480i
$385$	−1.28306e8	−	4.05033e7i	−2.24836	−	0.709754i
$386$	1.69329e6			0.0294422
$387$	1.49886e6	+	2.59610e6i	0.0258600	+	0.0447908i
$388$	−1.26054e7	−	7.27774e6i	−0.215805	−	0.124595i
$389$	3.37497e7	−	5.84563e7i	0.573353	−	0.993076i	−0.422866	−	0.906192i	$-0.638976\pi$
$389$	3.37497e7	−	5.84563e7i	0.573353	−	0.993076i	0.996218	−	0.0868835i	$-0.0276908\pi$
$390$	−9.15909e7	+	5.28800e7i	−1.54404	+	0.891452i
$391$		−	1.88271e6i		−	0.0314958i
$392$	7.75401e6	+	5.43735e6i	0.128727	+	0.0902671i
$393$	−3.48164e6			−0.0573596
$394$	−4.18936e7	−	7.25619e7i	−0.684951	−	1.18637i
$395$	−9.69393e7	−	5.59679e7i	−1.57293	−	0.908130i
$396$	−1.77109e7	+	3.06761e7i	−0.285203	+	0.493986i
$397$	8.14198e6	−	4.70078e6i	0.130124	−	0.0751273i	−0.433525	−	0.901142i	$-0.642730\pi$
$397$	8.14198e6	−	4.70078e6i	0.130124	−	0.0751273i	0.563649	+	0.826014i	$0.309397\pi$
$398$			2.04998e7i			0.325162i
$399$	−6.35642e6	+	2.01359e7i	−0.100068	+	0.316995i
$400$	7.50019e7			1.17190
$401$	2.77486e7	+	4.80620e7i	0.430336	+	0.745364i	0.996902	−	0.0786521i	$-0.0250616\pi$
$401$	2.77486e7	+	4.80620e7i	0.430336	+	0.745364i	−0.566566	+	0.824016i	$0.691728\pi$
$402$	5.47573e7	+	3.16141e7i	0.842876	+	0.486635i
$403$	−4.28658e6	+	7.42457e6i	−0.0654931	+	0.113437i
$404$	8.60654e7	−	4.96899e7i	1.30522	−	0.753571i
$405$		−	1.12709e7i		−	0.169666i
$406$	3.61107e7	−	7.99254e6i	0.539582	−	0.119428i
$407$	7.59001e7			1.12579
$408$	1.78829e6	+	3.09741e6i	0.0263304	+	0.0456056i
$409$	1.41570e7	+	8.17357e6i	0.206920	+	0.119465i	0.599879	−	0.800091i	$-0.295215\pi$
$409$	1.41570e7	+	8.17357e6i	0.206920	+	0.119465i	−0.392959	+	0.919556i	$0.628549\pi$
$410$	−7.53192e7	+	1.30457e8i	−1.09283	+	1.89284i
$411$	−4.28017e7	+	2.47116e7i	−0.616504	+	0.355939i
$412$			3.67163e7i			0.525010i
$413$	−4.87003e7	+	4.45949e7i	−0.691324	+	0.633046i
$414$	1.86450e6			0.0262761
$415$	−1.01524e7	−	1.75844e7i	−0.142044	−	0.246027i
$416$	−1.24606e8	−	7.19413e7i	−1.73085	−	0.999306i
$417$	6.03850e6	−	1.04590e7i	0.0832762	−	0.144239i
$418$	−8.16432e7	+	4.71367e7i	−1.11787	+	0.645402i
$419$			3.75022e7i			0.509818i	0.966965	+	0.254909i	$0.0820455\pi$
$419$			3.75022e7i			0.509818i	−0.966965	+	0.254909i	$0.917955\pi$
$420$	−4.88872e7	−	5.33878e7i	−0.659853	−	0.720600i
$421$	9.17501e7			1.22959			0.614795	−	0.788687i	$-0.289239\pi$
$421$	9.17501e7			1.22959			0.614795	+	0.788687i	$0.289239\pi$
$422$	7.95882e7	+	1.37851e8i	1.05904	+	1.83431i
$423$	3.10642e7	+	1.79349e7i	0.410430	+	0.236962i
$424$	8.84006e6	−	1.53114e7i	0.115973	−	0.200871i
$425$	5.13623e7	−	2.96540e7i	0.669080	−	0.386293i
$426$		−	5.53455e7i		−	0.715902i
$427$	2.46711e7	+	1.11465e8i	0.316887	+	1.43171i
$428$	4.58735e7			0.585101
$429$	−4.90144e7	−	8.48954e7i	−0.620800	−	1.07526i
$430$	−2.36874e7	−	1.36759e7i	−0.297928	−	0.172009i
$431$	6.89035e7	−	1.19344e8i	0.860616	−	1.49063i	−0.0107202	−	0.999943i	$-0.503412\pi$
$431$	6.89035e7	−	1.19344e8i	0.860616	−	1.49063i	0.871336	−	0.490687i	$-0.163254\pi$
$432$	1.18244e7	−	6.82684e6i	0.146666	−	0.0846776i
$433$		−	2.00324e7i		−	0.246757i	−0.992360	−	0.123378i	$-0.960627\pi$
$433$		−	2.00324e7i		−	0.246757i	0.992360	−	0.123378i	$-0.0393729\pi$
$434$	−1.06450e7	−	3.36037e6i	−0.130219	−	0.0411071i
$435$	−2.76200e7			−0.335549
$436$	2.43737e7	+	4.22165e7i	0.294078	+	0.509357i
$437$	2.25909e6	+	1.30428e6i	0.0270700	+	0.0156289i
$438$	−2.14119e7	+	3.70865e7i	−0.254820	+	0.441361i
$439$	7.45669e7	−	4.30512e7i	0.881359	−	0.508853i	0.0102525	−	0.999947i	$-0.496736\pi$
$439$	7.45669e7	−	4.30512e7i	0.881359	−	0.508853i	0.871106	+	0.491095i	$0.163403\pi$
$440$		−	3.15765e7i		−	0.370686i
$441$	2.51122e6	−	2.84782e7i	0.0292798	−	0.332045i
$442$	−1.01310e8			−1.17324
$443$	4.03937e6	+	6.99640e6i	0.0464625	+	0.0804754i	0.888321	−	0.459222i	$-0.151872\pi$
$443$	4.03937e6	+	6.99640e6i	0.0464625	+	0.0804754i	−0.841859	+	0.539698i	$0.818539\pi$
$444$	3.53648e7	+	2.04179e7i	0.404038	+	0.233272i
$445$	−1.24621e6	+	2.15850e6i	−0.0141420	+	0.0244947i
$446$	2.16312e8	−	1.24888e8i	2.43824	−	1.40772i
$447$			5.47032e7i			0.612477i
$448$	3.25775e7	−	1.03199e8i	0.362313	−	1.14774i
$449$	−5.16486e7			−0.570584			−0.285292	−	0.958441i	$-0.592091\pi$
$449$	−5.16486e7			−0.570584			−0.285292	+	0.958441i	$0.592091\pi$
$450$	2.93672e7	+	5.08655e7i	0.322274	+	0.558194i
$451$	−1.20920e8	−	6.98132e7i	−1.31816	−	0.761041i
$452$	−7.50680e7	+	1.30022e8i	−0.812904	+	1.40799i
$453$	8.71022e7	−	5.02885e7i	0.936989	−	0.540971i
$454$			4.56657e7i			0.488004i
$455$	1.95602e8	−	4.32935e7i	2.07653	−	0.459609i
$456$	−4.95549e6			−0.0522628
$457$	1.99697e7	+	3.45885e7i	0.209229	+	0.362396i	0.951472	−	0.307735i	$-0.0995711\pi$
$457$	1.99697e7	+	3.45885e7i	0.209229	+	0.362396i	−0.742243	+	0.670131i	$0.766238\pi$
$458$	5.65682e6	+	3.26597e6i	0.0588811	+	0.0339950i
$459$	5.39835e6	−	9.35022e6i	0.0558243	−	0.0966905i
$460$	−7.74478e6	+	4.47145e6i	−0.0795675	+	0.0459383i
$461$			1.40914e7i			0.143831i	0.997411	+	0.0719153i	$0.0229111\pi$
$461$			1.40914e7i			0.143831i	−0.997411	+	0.0719153i	$0.977089\pi$
$462$	9.41353e7	−	8.61997e7i	0.954612	−	0.874138i
$463$	1.25200e8			1.26142			0.630712	−	0.776017i	$-0.282763\pi$
$463$	1.25200e8			1.26142			0.630712	+	0.776017i	$0.282763\pi$
$464$	−1.67295e7	−	2.89763e7i	−0.167467	−	0.290061i
$465$	7.21948e6	+	4.16817e6i	0.0718037	+	0.0414559i
$466$	−9.48623e7	+	1.64306e8i	−0.937423	+	1.62367i
$467$	−8.96567e7	+	5.17633e7i	−0.880303	+	0.508243i	−0.870758	−	0.491711i	$-0.836372\pi$
$467$	−8.96567e7	+	5.17633e7i	−0.880303	+	0.508243i	−0.00954455	+	0.999954i	$0.503038\pi$
$468$		−	5.27415e7i		−	0.514535i
$469$	−8.08851e7	−	8.83315e7i	−0.784061	−	0.856243i
$470$	−3.27284e8			−3.15233
$471$	3.65001e7	+	6.32200e7i	0.349326	+	0.605051i
$472$	−1.34210e7	−	7.74860e6i	−0.127631	−	0.0736880i
$473$	1.26762e7	−	2.19558e7i	0.119786	−	0.207475i
$474$	9.19621e7	−	5.30944e7i	0.863523	−	0.498555i
$475$			8.21738e7i			0.766747i
$476$	−1.49854e7	−	6.77049e7i	−0.138947	−	0.627768i
$477$	−5.33714e7			−0.491760
$478$	−1.13913e8	−	1.97303e8i	−1.04301	−	1.80655i
$479$	−6.75301e7	−	3.89885e7i	−0.614456	−	0.354757i	0.160251	−	0.987076i	$-0.448770\pi$
$479$	−6.75301e7	−	3.89885e7i	−0.614456	−	0.354757i	−0.774708	+	0.632320i	$0.782103\pi$
$480$	−6.99541e7	+	1.21164e8i	−0.632542	+	1.09560i
$481$	−9.78713e7	+	5.65060e7i	−0.879468	+	0.507761i
$482$			4.18058e7i			0.373333i
$483$	−3.36799e6	−	1.06319e6i	−0.0298903	−	0.00943564i
$484$	1.73913e8			1.53389
$485$	−1.95846e7	−	3.39216e7i	−0.171668	−	0.297338i
$486$	9.25978e6	+	5.34613e6i	0.0806662	+	0.0465727i
$487$	−7.13992e7	+	1.23667e8i	−0.618168	+	1.07070i	0.371651	+	0.928372i	$0.378792\pi$
$487$	−7.13992e7	+	1.23667e8i	−0.618168	+	1.07070i	−0.989820	+	0.142327i	$0.954542\pi$
$488$	−2.32029e7	+	1.33962e7i	−0.199657	+	0.115272i
$489$			8.07845e7i			0.690878i
$490$	1.10078e8	+	2.36486e8i	0.935644	+	2.01010i
$491$	5.07818e7			0.429006			0.214503	−	0.976723i	$-0.431187\pi$
$491$	5.07818e7			0.429006			0.214503	+	0.976723i	$0.431187\pi$
$492$	−3.75609e7	−	6.50574e7i	−0.315385	−	0.546263i
$493$	−2.29132e7	−	1.32289e7i	−0.191225	−	0.110404i
$494$	7.01846e7	−	1.21563e8i	0.582185	−	1.00837i
$495$	−8.25503e7	+	4.76604e7i	−0.680617	+	0.392955i
$496$			1.00987e7i			0.0827598i
$497$	−3.15597e7	+	9.99750e7i	−0.257078	+	0.814371i
$498$	1.92622e7			0.155962
$499$	−6.32522e7	−	1.09556e8i	−0.509065	−	0.881727i	−0.999945	−	0.0104998i	$-0.996658\pi$
$499$	−6.32522e7	−	1.09556e8i	−0.509065	−	0.881727i	0.490879	−	0.871228i	$-0.336676\pi$
$500$	−6.07709e7	−	3.50861e7i	−0.486167	−	0.280689i
$501$	1.22081e7	−	2.11450e7i	0.0970808	−	0.168149i
$502$	6.53735e7	−	3.77434e7i	0.516762	−	0.298353i
$503$			7.36652e6i			0.0578840i	0.999581	+	0.0289420i	$0.00921381\pi$
$503$			7.36652e6i			0.0578840i	−0.999581	+	0.0289420i	$0.990786\pi$
$504$	6.55085e6	−	1.44993e6i	0.0511689	−	0.0113254i
$505$	2.67434e8			2.07655
$506$	−7.88423e6	−	1.36559e7i	−0.0608566	−	0.105407i
$507$	6.12438e7	+	3.53591e7i	0.469936	+	0.271317i
$508$	−1.16684e8	+	2.02103e8i	−0.890062	+	1.54163i
$509$	−1.98695e8	+	1.14716e8i	−1.50672	+	0.869906i	−0.506753	+	0.862092i	$0.669154\pi$
$509$	−1.98695e8	+	1.14716e8i	−1.50672	+	0.869906i	−0.999969	+	0.00781491i	$0.997512\pi$
$510$			9.85116e7i			0.742637i
$511$	5.98260e7	−	5.47826e7i	0.448360	−	0.410563i
$512$	−1.88055e8			−1.40112
$513$	7.47964e6	+	1.29551e7i	0.0554024	+	0.0959598i
$514$	2.87501e7	+	1.65989e7i	0.211714	+	0.122233i
$515$	−4.94024e7	+	8.55674e7i	−0.361681	+	0.626450i
$516$	1.18127e7	−	6.82004e6i	0.0859803	−	0.0496407i
$517$		−	3.03359e8i		−	2.19526i
$518$	−9.93750e7	−	1.08524e8i	−0.714970	−	0.780791i
$519$	1.94018e7			0.138784
$520$	2.35081e7	+	4.07172e7i	0.167189	+	0.289579i
$521$	−9.29834e7	−	5.36840e7i	−0.657495	−	0.379605i	0.133827	−	0.991005i	$-0.457273\pi$
$521$	−9.29834e7	−	5.36840e7i	−0.657495	−	0.379605i	−0.791322	+	0.611400i	$0.790607\pi$
$522$	1.31010e7	−	2.26915e7i	0.0921068	−	0.159534i
$523$	1.30357e8	−	7.52614e7i	0.911230	−	0.526099i	0.0304034	−	0.999538i	$-0.490321\pi$
$523$	1.30357e8	−	7.52614e7i	0.911230	−	0.526099i	0.880827	+	0.473439i	$0.156987\pi$
$524$			1.58420e7i			0.110107i
$525$	−2.40432e7	−	1.08628e8i	−0.166156	−	0.750699i
$526$	5.80595e7			0.398948
$527$	3.99279e6	+	6.91571e6i	0.0272800	+	0.0472503i
$528$	−1.00002e8	−	5.77361e7i	−0.679370	−	0.392234i
$529$	7.37998e7	−	1.27825e8i	0.498526	−	0.863473i
$530$	4.21731e8	−	2.43486e8i	2.83275	−	1.63549i
$531$			4.67818e7i			0.312459i
$532$	9.16215e7	+	2.89227e7i	0.608503	+	0.192090i
$533$	2.07898e8			1.37299
$534$	−1.18223e6	−	2.04768e6i	−0.00776385	−	0.0134474i
$535$	1.06908e8	+	6.17235e7i	0.698151	+	0.403078i
$536$	1.40542e7	−	2.43426e7i	0.0912666	−	0.158078i
$537$	3.04560e7	−	1.75838e7i	0.196675	−	0.113550i
$538$		−	2.37197e8i		−	1.52322i
$539$	−2.19198e8	+	1.02031e8i	−1.39981	+	0.651575i
$540$	−5.12846e7			−0.325691
$541$	3.02874e7	+	5.24593e7i	0.191280	+	0.331307i	0.945675	−	0.325114i	$-0.105403\pi$
$541$	3.02874e7	+	5.24593e7i	0.191280	+	0.331307i	−0.754395	+	0.656421i	$0.772069\pi$
$542$	1.24157e8	+	7.16821e7i	0.779783	+	0.450208i
$543$	6.21354e7	−	1.07622e8i	0.388097	−	0.672203i
$544$	−1.16066e8	+	6.70107e7i	−0.720955	+	0.416243i
$545$			1.31181e8i			0.810365i
$546$	−5.72113e7	+	1.81234e8i	−0.351483	+	1.11343i
$547$	−2.68955e8			−1.64330			−0.821651	−	0.569992i	$-0.806946\pi$
$547$	−2.68955e8			−1.64330			−0.821651	+	0.569992i	$0.806946\pi$
$548$	1.12442e8	+	1.94755e8i	0.683259	+	1.18344i
$549$	7.00433e7	+	4.04395e7i	0.423301	+	0.244393i
$550$	2.48365e8	−	4.30180e8i	1.49280	−	2.58561i
$551$	3.17471e7	−	1.83292e7i	0.189780	−	0.109569i
$552$		−	828871.i		−	0.00492799i
$553$	−1.96395e8	+	4.34689e7i	−1.16133	+	0.257042i
$554$	2.41962e8			1.42304
$555$	5.49451e7	+	9.51678e7i	0.321403	+	0.556687i
$556$	−4.75900e7	−	2.74761e7i	−0.276880	−	0.159857i
$557$	−1.00886e8	+	1.74739e8i	−0.583800	+	1.01117i	0.411223	+	0.911535i	$0.365102\pi$
$557$	−1.00886e8	+	1.74739e8i	−0.583800	+	1.01117i	−0.995024	+	0.0996375i	$0.968232\pi$
$558$	−6.84881e6	+	3.95416e6i	−0.0394196	+	0.0227589i
$559$			3.77486e7i			0.216105i
$560$	1.74040e8	−	1.59369e8i	0.991028	−	0.907484i
$561$	−9.13101e7			−0.517166
$562$	1.22050e8	+	2.11397e8i	0.687591	+	1.19094i
$563$	1.52694e8	+	8.81577e7i	0.855650	+	0.494010i	0.862553	−	0.505967i	$-0.168864\pi$
$563$	1.52694e8	+	8.81577e7i	0.855650	+	0.494010i	−0.00690346	+	0.999976i	$0.502197\pi$
$564$	8.16067e7	−	1.41347e8i	0.454871	−	0.787860i
$565$	−3.49892e8	+	2.02010e8i	−1.93994	+	1.12003i
$566$			1.21083e8i			0.667783i
$567$	−1.36781e7	−	1.49374e7i	−0.0750375	−	0.0819455i
$568$	−2.46041e7			−0.134265
$569$	−1.00368e8	−	1.73843e8i	−0.544828	−	0.943669i	−0.998618	−	0.0525605i	$-0.983262\pi$
$569$	−1.00368e8	−	1.73843e8i	−0.544828	−	0.943669i	0.453790	−	0.891109i	$-0.350072\pi$
$570$	−1.18205e8	−	6.82459e7i	−0.638282	−	0.368512i
$571$	2.23204e7	−	3.86600e7i	0.119893	−	0.207660i	−0.799832	−	0.600224i	$-0.795078\pi$
$571$	2.23204e7	−	3.86600e7i	0.119893	−	0.207660i	0.919725	+	0.392563i	$0.128412\pi$
$572$	−3.86287e8	+	2.23023e8i	−2.06406	+	1.19169i
$573$			6.64340e7i			0.353123i
$574$	5.84986e7	+	2.64300e8i	0.309321	+	1.39753i
$575$	−1.37446e7			−0.0722986
$576$	−3.83342e7	−	6.63967e7i	−0.200594	−	0.347440i
$577$	−2.24118e8	−	1.29395e8i	−1.16668	−	0.673581i	−0.213781	−	0.976882i	$-0.568578\pi$
$577$	−2.24118e8	−	1.29395e8i	−1.16668	−	0.673581i	−0.952895	+	0.303301i	$0.901911\pi$
$578$	9.30069e7	−	1.61093e8i	0.481650	−	0.834243i
$579$	−1.96794e6	+	1.13619e6i	−0.0101386	+	0.00585350i
$580$			1.25675e8i			0.644119i
$581$	−3.47949e7	−	1.09839e7i	−0.177414	−	0.0560053i
$582$	3.71582e7			0.188489
$583$	2.25687e8	+	3.90901e8i	1.13894	+	1.97270i
$584$	1.64870e7	+	9.51877e6i	0.0827757	+	0.0477906i
$585$	7.09644e7	−	1.22914e8i	0.354465	−	0.613951i
$586$	−2.87031e8	+	1.65717e8i	−1.42638	+	0.823522i
$587$		−	3.41902e8i		−	1.69039i	−0.534457	−	0.845196i	$-0.679484\pi$
$587$		−	3.41902e8i		−	1.69039i	0.534457	−	0.845196i	$-0.320516\pi$
$588$	−1.29580e8	−	1.14264e7i	−0.637392	−	0.0562055i
$589$	−1.10643e7			−0.0541476
$590$	−2.13424e8	−	3.69661e8i	−1.03917	−	1.79989i
$591$	9.73773e7	+	5.62208e7i	0.471732	+	0.272354i
$592$	−6.65608e7	+	1.15287e8i	−0.320814	+	0.555666i
$593$	1.27791e8	−	7.37803e7i	0.612826	−	0.353815i	−0.161245	−	0.986914i	$-0.551551\pi$
$593$	1.27791e8	−	7.37803e7i	0.612826	−	0.353815i	0.774071	+	0.633099i	$0.218218\pi$
$594$		−	9.04268e7i		−	0.431458i
$595$	5.61744e7	−	1.77949e8i	0.266678	−	0.844784i
$596$	2.48908e8			1.17571
$597$	−1.37552e7	−	2.38248e7i	−0.0646465	−	0.111971i
$598$	2.03331e7	+	1.17393e7i	0.0950822	+	0.0548957i
$599$	3.32461e7	−	5.75840e7i	0.154690	−	0.267930i	−0.778256	−	0.627947i	$-0.783896\pi$
$599$	3.32461e7	−	5.75840e7i	0.154690	−	0.267930i	0.932946	+	0.360017i	$0.117229\pi$
$600$	2.26125e7	−	1.30553e7i	0.104687	−	0.0604413i
$601$		−	3.71302e7i		−	0.171042i	−0.996336	−	0.0855212i	$-0.972744\pi$
$601$		−	3.71302e7i		−	0.171042i	0.996336	−	0.0855212i	$-0.0272555\pi$
$602$	−4.79896e7	+	1.06218e7i	−0.219967	+	0.0486864i
$603$	−8.48516e7			−0.386998
$604$	−2.28820e8	−	3.96328e8i	−1.03845	−	1.79864i
$605$	4.05303e8	+	2.34002e8i	1.83026	+	1.05670i
$606$	−1.26852e8	+	2.19713e8i	−0.570004	+	0.987276i
$607$	1.10132e8	−	6.35850e7i	0.492436	−	0.284308i	−0.233149	−	0.972441i	$-0.574903\pi$
$607$	1.10132e8	−	6.35850e7i	0.492436	−	0.284308i	0.725584	+	0.688133i	$0.241570\pi$
$608$		−	1.85692e8i		−	0.826195i
$609$	−3.66047e7	+	3.35190e7i	−0.162064	+	0.148402i
$610$	−7.37959e8			−3.25119
$611$	2.25845e8	+	3.91174e8i	0.990116	+	1.71493i
$612$	−4.25450e7	−	2.45634e7i	−0.185607	−	0.107160i
$613$	7.14975e7	−	1.23837e8i	0.310391	−	0.537614i	−0.668056	−	0.744111i	$-0.732873\pi$
$613$	7.14975e7	−	1.23837e8i	0.310391	−	0.537614i	0.978447	+	0.206498i	$0.0662066\pi$
$614$	−1.02879e8	+	5.93974e7i	−0.444450	+	0.256603i
$615$		−	2.02155e8i		−	0.869079i
$616$	−3.83205e7	−	4.18483e7i	−0.163942	−	0.179034i
$617$	−2.96115e8			−1.26068			−0.630339	−	0.776320i	$-0.717084\pi$
$617$	−2.96115e8			−1.26068			−0.630339	+	0.776320i	$0.717084\pi$
$618$	−4.68659e7	−	8.11742e7i	−0.198560	−	0.343916i
$619$	2.81343e8	+	1.62433e8i	1.18622	+	0.684862i	0.957444	−	0.288619i	$-0.0931959\pi$
$619$	2.81343e8	+	1.62433e8i	1.18622	+	0.684862i	0.228771	+	0.973480i	$0.426529\pi$
$620$	1.89658e7	−	3.28498e7i	0.0795786	−	0.137834i
$621$	−2.16691e6	+	1.25107e6i	−0.00904829	+	0.00522403i
$622$		−	1.82860e8i		−	0.759884i
$623$	967903.	+	4.37303e6i	0.00400283	+	0.0180850i
$624$	1.71933e8			0.707630
$625$	6.81453e7	+	1.18031e8i	0.279123	+	0.483456i
$626$	5.58588e8	+	3.22501e8i	2.27703	+	1.31464i
$627$	6.32569e7	−	1.09564e8i	0.256629	−	0.444494i
$628$	2.87661e8	−	1.66081e8i	1.16145	−	0.670566i
$629$			1.05267e8i			0.422998i
$630$	1.76228e8	+	5.56310e7i	0.704780	+	0.222482i
$631$	−1.40735e8			−0.560163			−0.280082	−	0.959976i	$-0.590362\pi$
$631$	−1.40735e8			−0.560163			−0.280082	+	0.959976i	$0.590362\pi$
$632$	−2.36034e7	−	4.08822e7i	−0.0935023	−	0.161951i
$633$	−1.84994e8	−	1.06806e8i	−0.729369	−	0.421101i
$634$	−3.50266e7	+	6.06679e7i	−0.137446	+	0.238063i
$635$	−5.43864e8	+	3.14000e8i	−2.12407	+	1.22633i
$636$			2.42848e8i			0.943982i
$637$	2.06691e8	−	2.94754e8i	0.799656	−	1.14036i
$638$	−2.21595e8			−0.853294
$639$	3.71365e7	+	6.43224e7i	0.142331	+	0.246524i
$640$	1.08367e8	+	6.25658e7i	0.413388	+	0.238670i
$641$	1.08339e8	−	1.87648e8i	0.411348	−	0.712476i	−0.583689	−	0.811977i	$-0.698391\pi$
$641$	1.08339e8	−	1.87648e8i	0.411348	−	0.712476i	0.995037	+	0.0995014i	$0.0317248\pi$
$642$	−1.01419e8	+	5.85544e7i	−0.383279	+	0.221286i
$643$			2.61645e8i			0.984192i	0.870541	+	0.492096i	$0.163769\pi$
$643$			2.61645e8i			0.984192i	−0.870541	+	0.492096i	$0.836231\pi$
$644$	−4.83770e6	+	1.53249e7i	−0.0181126	+	0.0573773i
$645$	3.67059e7			0.136791
$646$	−6.53743e7	−	1.13232e8i	−0.242499	−	0.420020i
$647$	−9.29409e7	−	5.36595e7i	−0.343158	−	0.198122i	0.318510	−	0.947920i	$-0.396818\pi$
$647$	−9.29409e7	−	5.36595e7i	−0.343158	−	0.198122i	−0.661668	+	0.749797i	$0.730151\pi$
$648$	2.37665e6	−	4.11648e6i	0.00873454	−	0.0151287i
$649$	3.42637e8	−	1.97822e8i	1.25343	−	0.723669i
$650$			7.39610e8i			2.69316i
$651$	1.46263e7	−	3.23732e6i	0.0530143	−	0.0117339i
$652$	3.67582e8			1.32621
$653$	−2.21977e8	−	3.84475e8i	−0.797200	−	1.38079i	−0.921432	−	0.388539i	$-0.872980\pi$
$653$	−2.21977e8	−	3.84475e8i	−0.797200	−	1.38079i	0.124232	−	0.992253i	$-0.460353\pi$
$654$	−1.07773e8	−	6.22228e7i	−0.385280	−	0.222442i
$655$	−2.13156e7	+	3.69198e7i	−0.0758533	+	0.131382i
$656$	2.12082e8	−	1.22446e8i	0.751265	−	0.433743i
$657$		−	5.74691e7i		−	0.202646i
$658$	−4.33750e8	+	3.97184e8i	−1.52251	+	1.39417i
$659$	−1.87037e7			−0.0653538			−0.0326769	−	0.999466i	$-0.510403\pi$
$659$	−1.87037e7			−0.0653538			−0.0326769	+	0.999466i	$0.510403\pi$
$660$	2.16862e8	+	3.75617e8i	0.754315	+	1.30651i
$661$	−1.85577e7	−	1.07143e7i	−0.0642570	−	0.0370988i	0.467527	−	0.883979i	$-0.345145\pi$
$661$	−1.85577e7	−	1.07143e7i	−0.0642570	−	0.0370988i	−0.531784	+	0.846880i	$0.678478\pi$
$662$	5.67179e7	−	9.82383e7i	0.195500	−	0.338616i
$663$	1.17742e8	−	6.79785e7i	0.404010	−	0.233255i
$664$		−	8.56311e6i		−	0.0292501i
$665$	1.74608e8	+	1.90682e8i	0.593744	+	0.648404i
$666$	−1.04248e8			−0.352895
$667$	3.06580e6	+	5.31012e6i	0.0103316	+	0.0178948i
$668$	−9.62130e7	−	5.55486e7i	−0.322778	−	0.186356i
$669$	−1.67598e8	+	2.90289e8i	−0.559746	+	0.969509i
$670$	6.70481e8	−	3.87102e8i	2.22927	−	1.28707i
$671$		−	6.84012e8i		−	2.26410i
$672$	5.43317e7	+	2.45473e8i	0.179038	+	0.808902i
$673$	2.29593e8			0.753205			0.376603	−	0.926375i	$-0.377092\pi$
$673$	2.29593e8			0.753205			0.376603	+	0.926375i	$0.377092\pi$
$674$	−3.31069e8	−	5.73428e8i	−1.08128	−	1.87283i
$675$	−6.82609e7	−	3.94105e7i	−0.221953	−	0.128145i
$676$	1.60890e8	−	2.78669e8i	0.520820	−	0.902087i
$677$	1.96110e7	−	1.13224e7i	0.0632024	−	0.0364899i	−0.468066	−	0.883694i	$-0.655049\pi$
$677$	1.96110e7	−	1.13224e7i	0.0632024	−	0.0364899i	0.531268	+	0.847204i	$0.321716\pi$
$678$		−	3.83277e8i		−	1.22977i
$679$	−6.71218e7	−	2.11888e7i	−0.214415	−	0.0676856i
$680$	4.37938e7			0.139279
$681$	−3.06415e7	−	5.30726e7i	−0.0970216	−	0.168046i
$682$	5.79219e7	+	3.34412e7i	0.182595	+	0.105421i
$683$	−1.12310e8	+	1.94527e8i	−0.352499	+	0.610546i	−0.986687	−	0.162633i	$-0.948001\pi$
$683$	−1.12310e8	+	1.94527e8i	−0.352499	+	0.610546i	0.634188	+	0.773179i	$0.281335\pi$
$684$	5.89478e7	−	3.40335e7i	0.184204	−	0.106350i
$685$			6.05167e8i			1.88280i
$686$	4.32879e8	+	1.79827e8i	1.34089	+	0.557034i
$687$	−8.76579e6			−0.0270346
$688$	2.22328e7	+	3.85084e7i	0.0682700	+	0.118247i
$689$	−5.82036e8	−	3.36038e8i	−1.77947	−	1.02738i
$690$	1.14150e7	−	1.97714e7i	0.0347480	−	0.0601852i
$691$	2.19279e8	−	1.26601e8i	0.664603	−	0.383709i	−0.129426	−	0.991589i	$-0.541313\pi$
$691$	2.19279e8	−	1.26601e8i	0.664603	−	0.383709i	0.794029	+	0.607880i	$0.207980\pi$
$692$		−	8.82811e7i		−	0.266409i
$693$	−5.15642e7	+	1.63345e8i	−0.154935	+	0.490803i
$694$	4.26717e8			1.27662
$695$	−7.39390e7	−	1.28066e8i	−0.220252	−	0.381487i
$696$	−1.00876e7	−	5.82409e6i	−0.0299200	−	0.0172743i
$697$	9.68246e7	−	1.67705e8i	0.285948	−	0.495277i
$698$	−6.62351e8	+	3.82409e8i	−1.94770	+	1.12451i
$699$		−	2.54608e8i		−	0.745489i
$700$	−4.94277e8	+	1.09401e8i	−1.44104	+	0.318952i
$701$	3.18180e8			0.923674			0.461837	−	0.886965i	$-0.347191\pi$
$701$	3.18180e8			0.923674			0.461837	+	0.886965i	$0.347191\pi$
$702$	6.73209e7	+	1.16603e8i	0.194598	+	0.337054i
$703$	−1.26311e8	−	7.29255e7i	−0.363558	−	0.209900i
$704$	−3.24201e8	+	5.61532e8i	−0.929171	+	1.60937i
$705$	3.80369e8	−	2.19606e8i	1.08552	−	0.626725i
$706$			3.70207e8i			1.05204i
$707$	3.54430e8	−	3.24551e8i	1.00293	−	0.918386i
$708$	2.12864e8			0.599796
$709$	−1.35142e8	−	2.34072e8i	−0.379185	−	0.656767i	0.611759	−	0.791044i	$-0.290462\pi$
$709$	−1.35142e8	−	2.34072e8i	−0.379185	−	0.656767i	−0.990944	+	0.134277i	$0.957129\pi$
$710$	−5.86891e8	−	3.38842e8i	−1.63977	−	0.946721i
$711$	−7.12521e7	+	1.23412e8i	−0.198239	+	0.343360i
$712$	−910305.	+	525565.i	−0.00252201	+	0.00145608i
$713$		−	1.85065e6i		−	0.00510572i
$714$	1.19551e8	+	1.30557e8i	0.328442	+	0.358679i
$715$	−1.20032e9			−3.28383
$716$	−8.00089e7	−	1.38579e8i	−0.217971	−	0.377537i
$717$	2.64778e8	+	1.52870e8i	0.718331	+	0.414728i
$718$	−2.22013e8	+	3.84538e8i	−0.599799	+	1.03888i
$719$	9.13702e7	−	5.27526e7i	0.245820	−	0.141924i	−0.372029	−	0.928221i	$-0.621338\pi$
$719$	9.13702e7	−	5.27526e7i	0.245820	−	0.141924i	0.617849	+	0.786297i	$0.288004\pi$
$720$		−	1.67184e8i		−	0.447916i
$721$	3.83697e7	+	1.73356e8i	0.102372	+	0.462522i
$722$	−3.65324e8			−0.970660
$723$	−2.80515e7	−	4.85866e7i	−0.0742234	−	0.128559i
$724$	−4.89696e8	−	2.82726e8i	−1.29036	−	0.744989i
$725$	−9.65772e7	+	1.67277e8i	−0.253431	+	0.438956i
$726$	−3.84494e8	+	2.21988e8i	−1.00480	+	0.580121i
$727$		−	3.47133e8i		−	0.903425i	−0.892164	−	0.451713i	$-0.850813\pi$
$727$		−	3.47133e8i		−	0.903425i	0.892164	−	0.451713i	$-0.149187\pi$
$728$	8.05686e7	+	2.54336e7i	0.208820	+	0.0659194i
$729$	−1.43489e7			−0.0370370
$730$	2.62180e8	+	4.54110e8i	0.673956	+	1.16733i
$731$	3.04507e7	+	1.75807e7i	0.0779552	+	0.0450074i
$732$	1.84006e8	−	3.18708e8i	0.469137	−	0.812568i
$733$	−4.04599e8	+	2.33596e8i	−1.02734	+	0.593134i	−0.916221	−	0.400673i	$-0.868776\pi$
$733$	−4.04599e8	+	2.33596e8i	−1.02734	+	0.593134i	−0.111117	+	0.993807i	$0.535443\pi$
$734$			1.13121e9i			2.86058i
$735$	−2.86612e8	−	2.00981e8i	−0.721827	−	0.506167i
$736$	3.10594e7			0.0779040
$737$	3.58804e8	+	6.21467e8i	0.896304	+	1.55244i
$738$	1.66083e8	+	9.58879e7i	0.413195	+	0.238558i
$739$	−1.98814e8	+	3.44356e8i	−0.492623	+	0.853247i	−0.999964	−	0.00849788i	$-0.997295\pi$
$739$	−1.98814e8	+	3.44356e8i	−0.492623	+	0.853247i	0.507341	+	0.861745i	$0.330628\pi$
$740$	4.33028e8	−	2.50009e8i	1.06861	−	0.616965i
$741$			1.88374e8i			0.462984i
$742$	2.63430e8	−	8.34494e8i	0.644842	−	2.04273i
$743$	6.88913e8			1.67957			0.839784	−	0.542920i	$-0.182681\pi$
$743$	6.88913e8			1.67957			0.839784	+	0.542920i	$0.182681\pi$
$744$	1.75784e6	+	3.04467e6i	0.00426836	+	0.00739302i
$745$	5.80080e8	+	3.34909e8i	1.40288	+	0.809951i
$746$	1.22215e8	−	2.11683e8i	0.294380	−	0.509881i
$747$	−2.23865e7	+	1.29248e7i	−0.0537061	+	0.0310073i
$748$			4.15475e8i			0.992751i
$749$	2.16591e8	−	4.79392e7i	0.515461	−	0.114089i
$750$	1.79140e8			0.424629
$751$	−1.83282e8	−	3.17453e8i	−0.432712	−	0.749480i	0.564393	−	0.825506i	$-0.309110\pi$
$751$	−1.83282e8	−	3.17453e8i	−0.432712	−	0.749480i	−0.997106	+	0.0760260i	$0.975777\pi$
$752$	4.60781e8	+	2.66032e8i	1.08353	+	0.625576i
$753$	−5.06512e7	+	8.77305e7i	−0.118633	+	0.205478i
$754$	2.85742e8	−	1.64973e8i	0.666592	−	0.384857i
$755$		−	1.23152e9i		−	2.86156i
$756$	−6.79674e7	+	6.22377e7i	−0.157302	+	0.144042i
$757$	−2.07241e8			−0.477735			−0.238868	−	0.971052i	$-0.576776\pi$
$757$	−2.07241e8			−0.477735			−0.238868	+	0.971052i	$0.576776\pi$
$758$	−2.39168e8	−	4.14252e8i	−0.549157	−	0.951167i
$759$	1.83261e7	+	1.05806e7i	0.0419125	+	0.0241982i
$760$	−3.03390e7	+	5.25487e7i	−0.0691132	+	0.119708i
$761$	−5.86021e8	+	3.38339e8i	−1.32972	+	0.767712i	−0.985256	−	0.171088i	$-0.945272\pi$
$761$	−5.86021e8	+	3.38339e8i	−1.32972	+	0.767712i	−0.344461	+	0.938801i	$0.611938\pi$
$762$		−	5.95757e8i		−	1.34649i
$763$	1.59198e8	+	1.73854e8i	0.358396	+	0.391390i
$764$	3.02285e8			0.677854
$765$	−6.61007e7	−	1.14490e8i	−0.147646	−	0.255730i
$766$	−1.53096e8	−	8.83901e7i	−0.340626	−	0.196661i
$767$	−2.94549e8	+	5.10173e8i	−0.652786	+	1.13066i
$768$	1.69795e8	−	9.80314e7i	0.374837	−	0.216412i
$769$			5.58023e8i			1.22708i	0.789663	+	0.613540i	$0.210255\pi$
$769$			5.58023e8i			1.22708i	−0.789663	+	0.613540i	$0.789745\pi$
$770$	−3.37749e8	−	1.52596e9i	−0.739813	−	3.34251i
$771$	−4.45510e7			−0.0972063
$772$	5.16985e6	+	8.95443e6i	0.0112364	+	0.0194619i
$773$	7.17689e7	+	4.14358e7i	0.155381	+	0.0897093i	0.575675	−	0.817679i	$-0.304740\pi$
$773$	7.17689e7	+	4.14358e7i	0.155381	+	0.0897093i	−0.420293	+	0.907388i	$0.638073\pi$
$774$	−1.74107e7	+	3.01561e7i	−0.0375485	+	0.0650358i
$775$	5.04878e7	−	2.91492e7i	0.108463	−	0.0626211i
$776$		−	1.65188e7i		−	0.0353504i
$777$	1.88312e8	+	5.94456e7i	0.401435	+	0.126723i
$778$	7.84070e8			1.66501
$779$	1.34154e8	+	2.32362e8i	0.283787	+	0.491533i
$780$	−5.59278e8	−	3.22899e8i	−1.17854	−	0.680430i
$781$	3.14072e8	−	5.43988e8i	0.659289	−	1.14192i
$782$	1.89395e7	−	1.09347e7i	0.0396048	−	0.0228658i
$783$			3.51627e7i			0.0732482i
$784$	3.72493e7	−	4.22422e8i	0.0772984	−	0.876594i
$785$	8.93859e8			1.84782
$786$	−2.02212e7	−	3.50242e7i	−0.0416428	−	0.0721275i
$787$	−4.59435e8	−	2.65255e8i	−0.942541	−	0.544176i	−0.0517851	−	0.998658i	$-0.516491\pi$
$787$	−4.59435e8	−	2.65255e8i	−0.942541	−	0.544176i	−0.890756	+	0.454482i	$0.849824\pi$
$788$	2.55813e8	−	4.43082e8i	0.522811	−	0.905535i
$789$	−6.74766e7	+	3.89576e7i	−0.137380	+	0.0793161i
$790$		−	1.30024e9i		−	2.63719i
$791$	−2.18556e8	+	6.92344e8i	−0.441605	+	1.39892i
$792$	−4.01997e7			−0.0809184
$793$	5.09233e8	+	8.82017e8i	1.02117	+	1.76871i
$794$	9.45767e7	+	5.46039e7i	0.188939	+	0.109084i
$795$	−3.26756e8	+	5.65958e8i	−0.650313	+	1.12637i
$796$	−1.08406e8	+	6.25885e7i	−0.214939	+	0.124095i
$797$			4.96880e8i			0.981469i	0.871309	+	0.490735i	$0.163272\pi$
$797$			4.96880e8i			0.981469i	−0.871309	+	0.490735i	$0.836728\pi$
$798$	−2.39479e8	+	5.30050e7i	−0.471258	+	0.104306i
$799$	4.20732e8			0.824831
$800$	4.89209e8	+	8.47334e8i	0.955486	+	1.65495i
$801$	2.74796e6	+	1.58654e6i	0.00534703	+	0.00308711i
$802$	−3.22326e8	+	5.58285e8i	−0.624845	+	1.08226i
$803$	−4.20913e8	+	2.43014e8i	−0.812917	+	0.469338i
$804$			3.86088e8i			0.742879i
$805$	−3.18941e7	+	2.92055e7i	−0.0611397	+	0.0559856i
$806$	−9.95852e7			−0.190191
$807$	1.59158e8	+	2.75669e8i	0.302836	+	0.524527i
$808$	9.76747e7	+	5.63925e7i	0.185160	+	0.106902i
$809$	2.10152e8	−	3.63994e8i	0.396906	−	0.687461i	−0.596437	−	0.802660i	$-0.703417\pi$
$809$	2.10152e8	−	3.63994e8i	0.396906	−	0.687461i	0.993342	+	0.115199i	$0.0367506\pi$
$810$	1.13382e8	−	6.54613e7i	0.213349	−	0.123177i
$811$		−	4.27809e8i		−	0.802025i	−0.916073	−	0.401012i	$-0.868658\pi$
$811$		−	4.27809e8i		−	0.802025i	0.916073	−	0.401012i	$-0.131342\pi$
$812$	1.52517e8	+	1.66557e8i	0.284871	+	0.311097i
$813$	−1.92393e8			−0.358029
$814$	4.40825e8	+	7.63531e8i	0.817322	+	1.41564i
$815$	8.56650e8	+	4.94587e8i	1.58245	+	0.913629i
$816$	8.00747e7	−	1.38693e8i	0.147375	−	0.255262i
$817$	−4.21907e7	+	2.43588e7i	−0.0773660	+	0.0446673i
$818$			1.89887e8i			0.346925i
$819$	−5.51164e7	−	2.49018e8i	−0.100330	−	0.453294i
$820$	−9.19837e8			−1.66828
$821$	−4.76401e8	−	8.25152e8i	−0.860882	−	1.49109i	−0.871079	−	0.491143i	$-0.836579\pi$
$821$	−4.76401e8	−	8.25152e8i	−0.860882	−	1.49109i	0.0101968	−	0.999948i	$-0.496754\pi$
$822$	−4.97182e8	−	2.87048e8i	−0.895159	−	0.516820i
$823$	3.70614e8	−	6.41923e8i	0.664848	−	1.15155i	−0.314478	−	0.949265i	$-0.601829\pi$
$823$	3.70614e8	−	6.41923e8i	0.664848	−	1.15155i	0.979326	−	0.202287i	$-0.0648372\pi$
$824$	−3.60864e7	+	2.08345e7i	−0.0645003	+	0.0372392i
$825$			6.66606e8i			1.18715i
$826$	−7.31461e8	−	2.30905e8i	−1.29793	−	0.409725i
$827$	−7.61072e8			−1.34558			−0.672790	−	0.739834i	$-0.734904\pi$
$827$	−7.61072e8			−1.34558			−0.672790	+	0.739834i	$0.734904\pi$
$828$	5.69255e6	+	9.85979e6i	0.0100280	+	0.0173691i
$829$	−7.06469e8	−	4.07880e8i	−1.24002	−	0.715928i	−0.270924	−	0.962601i	$-0.587329\pi$
$829$	−7.06469e8	−	4.07880e8i	−1.24002	−	0.715928i	−0.969099	+	0.246673i	$0.920663\pi$
$830$	1.17929e8	−	2.04259e8i	0.206247	−	0.357230i
$831$	−2.81207e8	+	1.62355e8i	−0.490031	+	0.282919i
$832$		−	9.65442e8i		−	1.67632i
$833$	−1.41507e8	−	3.04008e8i	−0.244818	−	0.525956i
$834$	1.40286e8			0.241833
$835$	−1.49483e8	−	2.58912e8i	−0.256763	−	0.444726i
$836$	−4.98534e8	−	2.87829e8i	−0.853250	−	0.492624i
$837$	5.30644e6	−	9.19103e6i	0.00904955	−	0.0156743i
$838$	−3.77261e8	+	2.17812e8i	−0.641076	+	0.370126i
$839$			1.07654e9i			1.82283i	0.411491	+	0.911414i	$0.365008\pi$
$839$			1.07654e9i			1.82283i	−0.411491	+	0.911414i	$0.634992\pi$
$840$	2.47310e7	−	7.83430e7i	0.0417258	−	0.132179i
$841$	−5.08655e8			−0.855137
$842$	5.32881e8	+	9.22978e8i	0.892677	+	1.54616i
$843$	−2.83693e8	−	1.63790e8i	−0.473550	−	0.273404i
$844$	−4.85986e8	+	8.41753e8i	−0.808345	+	1.40009i
$845$	7.49906e8	−	4.32959e8i	1.24290	−	0.717590i
$846$			4.16662e8i			0.688133i
$847$	8.21126e8	−	1.81744e8i	1.35132	−	0.299095i
$848$	−7.91667e8			−1.29824
$849$	−8.12463e7	−	1.40723e8i	−0.132764	−	0.229954i
$850$	5.96621e8	+	3.44459e8i	0.971498	+	0.560895i
$851$	1.21977e7	−	2.11271e7i	0.0197921	−	0.0342808i
$852$	2.92677e8	−	1.68977e8i	0.473227	−	0.273218i
$853$			9.74565e8i			1.57023i	0.619349	+	0.785116i	$0.287397\pi$
$853$			9.74565e8i			1.57023i	−0.619349	+	0.785116i	$0.712603\pi$
$854$	−9.78015e8	+	8.95568e8i	−1.57026	+	1.43789i
$855$	1.83170e8			0.293060
$856$	2.60307e7	+	4.50864e7i	0.0415015	+	0.0718827i
$857$	−8.31953e8	−	4.80328e8i	−1.32177	−	0.763125i	−0.337760	−	0.941232i	$-0.609669\pi$
$857$	−8.31953e8	−	4.80328e8i	−1.32177	−	0.763125i	−0.984011	+	0.178107i	$0.943003\pi$
$858$	5.69348e8	−	9.86139e8i	0.901396	−	1.56126i
$859$	4.22688e8	−	2.44039e8i	0.666869	−	0.385017i	−0.128020	−	0.991772i	$-0.540862\pi$
$859$	4.22688e8	−	2.44039e8i	0.666869	−	0.385017i	0.794889	+	0.606755i	$0.207529\pi$
$860$		−	1.67018e8i		−	0.262583i
$861$	−2.45330e8	−	2.67916e8i	−0.384363	−	0.419748i
$862$	1.60076e9			2.49921
$863$	−1.61373e8	−	2.79507e8i	−0.251073	−	0.434871i	0.712749	−	0.701420i	$-0.247450\pi$
$863$	−1.61373e8	−	2.79507e8i	−0.251073	−	0.434871i	−0.963821	+	0.266549i	$0.914117\pi$
$864$	1.54252e8	+	8.90577e7i	0.239161	+	0.138080i
$865$	1.18784e8	−	2.05739e8i	0.183530	−	0.317884i
$866$	2.01520e8	−	1.16348e8i	0.310287	−	0.179144i
$867$			2.49629e8i			0.383034i
$868$	−1.47303e7	−	6.65522e7i	−0.0225244	−	0.101766i
$869$	1.20519e9			1.83652
$870$	−1.60416e8	−	2.77849e8i	−0.243607	−	0.421940i
$871$	−9.25339e8	−	5.34245e8i	−1.40038	−	0.808511i
$872$	−2.76614e7	+	4.79110e7i	−0.0417182	+	0.0722580i
$873$	−4.31851e7	+	2.49329e7i	−0.0649070	+	0.0374741i
$874$			3.03010e7i			0.0453860i
$875$	−3.23595e8	−	1.02151e8i	−0.483035	−	0.152482i
$876$	−2.61494e8			−0.388999
$877$	−4.68948e8	−	8.12242e8i	−0.695226	−	1.20417i	−0.970104	−	0.242688i	$-0.921971\pi$
$877$	−4.68948e8	−	8.12242e8i	−0.695226	−	1.20417i	0.274878	−	0.961479i	$-0.411362\pi$
$878$	8.66164e8	+	5.00080e8i	1.27973	+	0.738850i
$879$	2.22391e8	−	3.85192e8i	0.327454	−	0.567167i
$880$	−1.22448e9	+	7.06956e8i	−1.79682	+	1.03739i
$881$		−	9.47337e8i		−	1.38540i	−0.721224	−	0.692702i	$-0.756420\pi$
$881$		−	9.47337e8i		−	1.38540i	0.721224	−	0.692702i	$-0.243580\pi$
$882$	3.01067e8	−	1.40138e8i	0.438791	−	0.204245i
$883$	1.52054e8			0.220860			0.110430	−	0.993884i	$-0.464777\pi$
$883$	1.52054e8			0.220860			0.110430	+	0.993884i	$0.464777\pi$
$884$	−3.09313e8	−	5.35746e8i	−0.447756	−	0.775536i
$885$	4.96080e8	+	2.86412e8i	0.715686	+	0.413201i
$886$	−4.69211e7	+	8.12697e7i	−0.0674632	+	0.116850i
$887$	1.02528e9	−	5.91948e8i	1.46917	−	0.848228i	0.469771	−	0.882788i	$-0.344336\pi$
$887$	1.02528e9	−	5.91948e8i	1.46917	−	0.848228i	0.999403	+	0.0345605i	$0.0110031\pi$
$888$			4.63441e7i			0.0661843i
$889$	−3.39719e8	+	1.07616e9i	−0.483521	+	1.53170i
$890$	−2.89518e7			−0.0410682
$891$	6.06759e7	+	1.05094e8i	0.0857795	+	0.148574i
$892$	1.32086e9	+	7.62599e8i	1.86107	+	1.07449i
$893$	−2.91470e8	+	5.04842e8i	−0.409298	+	0.708926i
$894$	−5.50297e8	+	3.17714e8i	−0.770167	+	0.444656i
$895$		−	4.30612e8i		−	0.600644i
$896$	2.19547e8	−	4.85934e7i	0.305213	−	0.0675543i
$897$	−3.15080e7			−0.0436560
$898$	−2.99974e8	−	5.19569e8i	−0.414242	−	0.717488i
$899$	−2.25231e7	−	1.30037e7i	−0.0309990	−	0.0178973i
$900$	−1.79324e8	+	3.10598e8i	−0.245986	+	0.426060i
$901$	−5.42144e8	+	3.13007e8i	−0.741209	+	0.427937i
$902$		−	1.62189e9i		−	2.21005i
$903$	4.86462e7	−	4.45454e7i	0.0660672	−	0.0604977i
$904$	−1.70388e8			−0.230639
$905$	−7.60824e8	−	1.31779e9i	−1.02645	−	1.77787i
$906$	1.01177e9	+	5.84147e8i	1.36050	+	0.785485i
$907$	−1.69886e8	+	2.94252e8i	−0.227686	+	0.394364i	−0.957122	−	0.289685i	$-0.906449\pi$
$907$	−1.69886e8	+	2.94252e8i	−0.227686	+	0.394364i	0.729436	+	0.684049i	$0.239783\pi$
$908$	−2.41489e8	+	1.39423e8i	−0.322581	+	0.186242i
$909$		−	3.40467e8i		−	0.453297i
$910$	1.57157e9	+	1.71625e9i	2.08549	+	2.27749i
$911$	−9.44286e8			−1.24896			−0.624480	−	0.781041i	$-0.714689\pi$
$911$	−9.44286e8			−1.24896			−0.624480	+	0.781041i	$0.714689\pi$
$912$	1.10947e8	+	1.92165e8i	0.146262	+	0.253332i
$913$	1.89327e8	+	1.09308e8i	0.248772	+	0.143628i
$914$	−2.31967e8	+	4.01778e8i	−0.303799	+	0.526196i
$915$	8.57653e8	−	4.95166e8i	1.11956	−	0.646380i
$916$			3.98857e7i			0.0518956i
$917$	1.65554e7	+	7.47978e7i	0.0214699	+	0.0970021i
$918$	1.25414e8			0.162113
$919$	1.87277e8	+	3.24374e8i	0.241290	+	0.417926i	0.961082	−	0.276264i	$-0.0890963\pi$
$919$	1.87277e8	+	3.24374e8i	0.241290	+	0.417926i	−0.719792	+	0.694189i	$0.755763\pi$
$920$	−8.78947e6	−	5.07460e6i	−0.0112875	−	0.00651686i
$921$	7.97106e7	−	1.38063e8i	0.102032	−	0.176725i
$922$	−1.41755e8	+	8.18424e7i	−0.180862	+	0.104420i
$923$			9.35280e8i			1.18942i
$924$	7.43247e8	+	2.34625e8i	0.942144	+	0.297412i
$925$	7.68494e8			0.970991
$926$	7.27157e8	+	1.25947e9i	0.915788	+	1.58619i
$927$	1.08935e8	+	6.28936e7i	0.136750	+	0.0789527i
$928$	2.18240e8	−	3.78003e8i	0.273081	−	0.472989i
$929$	7.89503e8	−	4.55820e8i	0.984707	−	0.568521i	0.0810189	−	0.996713i	$-0.474183\pi$
$929$	7.89503e8	−	4.55820e8i	0.984707	−	0.568521i	0.903688	+	0.428192i	$0.140849\pi$
$930$			9.68343e7i			0.120387i
$931$	4.62815e8	+	4.08112e7i	0.573533	+	0.0505743i
$932$	−1.15851e9			−1.43104
$933$	1.22698e8	+	2.12519e8i	0.151075	+	0.261669i
$934$	−1.04145e9	−	6.01279e8i	−1.27819	−	0.737965i
$935$	−5.59028e8	+	9.68265e8i	−0.683910	+	1.18457i
$936$	5.18365e7	−	2.99278e7i	0.0632133	−	0.0364962i
$937$			3.76597e8i			0.457781i	0.973452	+	0.228890i	$0.0735097\pi$
$937$			3.76597e8i			0.457781i	−0.973452	+	0.228890i	$0.926490\pi$
$938$	4.18809e8	−	1.32671e9i	0.507467	−	1.60756i
$939$	−8.65586e8			−1.04547
$940$	−9.99242e8	−	1.73074e9i	−1.20306	−	2.08376i
$941$	2.17999e8	+	1.25862e8i	0.261629	+	0.151051i	0.625077	−	0.780563i	$-0.285067\pi$
$941$	2.17999e8	+	1.25862e8i	0.261629	+	0.151051i	−0.363449	+	0.931614i	$0.618401\pi$
$942$	−4.23983e8	+	7.34360e8i	−0.507219	+	0.878529i
$943$	−3.88656e7	+	2.24391e7i	−0.0463479	+	0.0267590i
$944$			6.93922e8i			0.824888i
$945$	−2.42140e8	+	5.35939e7i	−0.286926	+	0.0635068i
$946$	2.94491e8			0.347856
$947$	1.32933e8	+	2.30247e8i	0.156525	+	0.271109i	0.933613	−	0.358282i	$-0.116637\pi$
$947$	1.32933e8	+	2.30247e8i	0.156525	+	0.271109i	−0.777088	+	0.629392i	$0.783304\pi$
$948$	5.61545e8	+	3.24208e8i	0.659112	+	0.380539i
$949$	3.61838e8	−	6.26723e8i	0.423366	−	0.733292i
$950$	−8.26643e8	+	4.77262e8i	−0.964156	+	0.556655i
$951$		−	9.40107e7i		−	0.109304i
$952$	5.80398e7	−	5.31471e7i	0.0672690	−	0.0615983i
$953$	−5.38039e8			−0.621635			−0.310817	−	0.950470i	$-0.600603\pi$
$953$	−5.38039e8			−0.621635			−0.310817	+	0.950470i	$0.600603\pi$
$954$	−3.09979e8	−	5.36900e8i	−0.357016	−	0.618370i
$955$	7.04475e8	+	4.06729e8i	0.808827	+	0.466976i
$956$	6.95581e8	−	1.20478e9i	0.796112	−	1.37891i
$957$	2.57537e8	−	1.48689e8i	0.293836	−	0.169646i
$958$		−	9.05777e8i		−	1.03021i
$959$	7.34416e8	+	8.02027e8i	0.832696	+	0.909355i
$960$	−9.38774e8			−1.06108
$961$	−4.39827e8	−	7.61803e8i	−0.495578	−	0.858366i
$962$	−1.13687e9	−	6.56370e8i	−1.27698	−	0.737265i
$963$	7.85794e7	−	1.36104e8i	0.0879893	−	0.152402i
$964$	−2.21077e8	+	1.27639e8i	−0.246781	+	0.142479i
$965$			2.78244e7i			0.0309631i
$966$	−8.86577e6	−	4.00560e7i	−0.00983525	−	0.0444361i
$967$	−1.16138e9			−1.28439			−0.642194	−	0.766542i	$-0.721976\pi$
$967$	−1.16138e9			−1.28439			−0.642194	+	0.766542i	$0.721976\pi$
$968$	9.86856e7	+	1.70929e8i	0.108800	+	0.188447i
$969$	1.51956e8	+	8.77316e7i	0.167011	+	0.0964240i
$970$	2.27494e8	−	3.94031e8i	0.249261	−	0.431732i
$971$	1.30640e9	−	7.54248e8i	1.42698	−	0.823866i	0.430097	−	0.902783i	$-0.358479\pi$
$971$	1.30640e9	−	7.54248e8i	1.42698	−	0.823866i	0.996881	+	0.0789166i	$0.0251461\pi$
$972$			6.52898e7i			0.0710962i
$973$	−2.53409e8	−	7.99953e7i	−0.275096	−	0.0868412i
$974$	−1.65874e9			−1.79515
$975$	−4.96274e8	−	8.59572e8i	−0.535436	−	0.927403i
$976$	1.03896e9	+	5.99847e8i	1.11751	+	0.645195i
$977$	6.03772e7	−	1.04576e8i	0.0647425	−	0.112137i	−0.831837	−	0.555020i	$-0.812711\pi$
$977$	6.03772e7	−	1.04576e8i	0.0647425	−	0.112137i	0.896580	+	0.442882i	$0.146044\pi$
$978$	−8.12667e8	+	4.69194e8i	−0.868752	+	0.501574i
$979$		−	2.68354e7i		−	0.0285996i
$980$	−9.14497e8	+	1.30413e9i	−0.971637	+	1.38562i
$981$	1.67005e8			0.176897
$982$	2.94939e8	+	5.10849e8i	0.311457	+	0.539459i
$983$	−1.86333e7	−	1.07580e7i	−0.0196169	−	0.0113258i	0.490159	−	0.871633i	$-0.336939\pi$
$983$	−1.86333e7	−	1.07580e7i	−0.0196169	−	0.0113258i	−0.509776	+	0.860307i	$0.670272\pi$
$984$	4.26274e7	−	7.38329e7i	0.0447408	−	0.0774934i
$985$	1.19235e9	−	6.88401e8i	1.24765	−	0.720333i
$986$		−	3.07333e8i		−	0.320611i
$987$	2.37594e8	−	7.52650e8i	0.247106	−	0.782783i
$988$	8.57131e8			0.888743
$989$	−4.07433e6	−	7.05694e6i	−0.00421179	−	0.00729504i
$990$	−9.58899e8	−	5.53621e8i	−0.988251	−	0.570567i
$991$	3.07940e7	−	5.33368e7i	0.0316407	−	0.0548033i	−0.849771	−	0.527151i	$-0.823260\pi$
$991$	3.07940e7	−	5.33368e7i	0.0316407	−	0.0548033i	0.881412	+	0.472348i	$0.156593\pi$
$992$	−1.14090e8	+	6.58698e7i	−0.116872	+	0.0674763i
$993$			1.52230e8i			0.155472i
$994$	−1.18902e9	+	2.63170e8i	−1.21068	+	0.267965i
$995$	−3.36855e8			−0.341959
$996$	5.88100e7	+	1.01862e8i	0.0595215	+	0.103094i
$997$	6.72319e8	+	3.88164e8i	0.678406	+	0.391678i	0.799254	−	0.600993i	$-0.205228\pi$
$997$	6.72319e8	+	3.88164e8i	0.678406	+	0.391678i	−0.120848	+	0.992671i	$0.538561\pi$
$998$	7.34733e8	−	1.27259e9i	0.739159	−	1.28026i
$999$	1.21157e8	−	6.99500e7i	0.121521	−	0.0701603i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.7.f.a.10.4	✓	8
3.2	odd	2		63.7.m.d.10.1		8
4.3	odd	2		336.7.bh.d.241.1		8
7.2	even	3		147.7.f.d.19.4		8
7.3	odd	6		147.7.d.b.97.1		8
7.4	even	3		147.7.d.b.97.2		8
7.5	odd	6	inner	21.7.f.a.19.4	yes	8
7.6	odd	2		147.7.f.d.31.4		8
21.5	even	6		63.7.m.d.19.1		8
21.11	odd	6		441.7.d.c.244.8		8
21.17	even	6		441.7.d.c.244.7		8
28.19	even	6		336.7.bh.d.145.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.f.a.10.4	✓	8	1.1	even	1	trivial
21.7.f.a.19.4	yes	8	7.5	odd	6	inner
63.7.m.d.10.1		8	3.2	odd	2
63.7.m.d.19.1		8	21.5	even	6
147.7.d.b.97.1		8	7.3	odd	6
147.7.d.b.97.2		8	7.4	even	3
147.7.f.d.19.4		8	7.2	even	3
147.7.f.d.31.4		8	7.6	odd	2
336.7.bh.d.145.1		8	28.19	even	6
336.7.bh.d.241.1		8	4.3	odd	2
441.7.d.c.244.7		8	21.17	even	6
441.7.d.c.244.8		8	21.11	odd	6

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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	21.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(5.80797 + 10.0597i) q^{2} +(-13.5000 - 7.79423i) q^{3} +(-35.4650 + 61.4271i) q^{4} +(-165.302 + 95.4373i) q^{5} -181.074i q^{6} +(-103.254 + 327.089i) q^{7} -80.4975 q^{8} +(121.500 + 210.444i) q^{9} +O(q^{10})\)	\(q+(5.80797 + 10.0597i) q^{2} +(-13.5000 - 7.79423i) q^{3} +(-35.4650 + 61.4271i) q^{4} +(-165.302 + 95.4373i) q^{5} -181.074i q^{6} +(-103.254 + 327.089i) q^{7} -80.4975 q^{8} +(121.500 + 210.444i) q^{9} +(-1920.14 - 1108.59i) q^{10} +(1027.55 - 1779.77i) q^{11} +(957.554 - 552.844i) q^{12} +3059.97i q^{13} +(-3890.12 + 861.018i) q^{14} +2975.44 q^{15} +(1802.23 + 3121.55i) q^{16} +(2468.38 + 1425.12i) q^{17} +(-1411.34 + 2444.51i) q^{18} +(-3420.04 + 1974.56i) q^{19} -13538.7i q^{20} +(3943.34 - 3610.92i) q^{21} +23872.0 q^{22} +(-330.272 - 572.047i) q^{23} +(1086.72 + 627.416i) q^{24} +(10404.0 - 18020.3i) q^{25} +(-30782.3 + 17772.2i) q^{26} -3788.00i q^{27} +(-16430.3 - 17942.8i) q^{28} -9282.66 q^{29} +(17281.3 + 29932.0i) q^{30} +(2426.36 + 1400.86i) q^{31} +(-23510.5 + 40721.4i) q^{32} +(-27743.9 + 16018.0i) q^{33} +33108.2i q^{34} +(-14148.4 - 63922.9i) q^{35} -17236.0 q^{36} +(18466.2 + 31984.5i) q^{37} +(-39727.0 - 22936.4i) q^{38} +(23850.1 - 41309.5i) q^{39} +(13306.4 - 7682.46i) q^{40} -67941.3i q^{41} +(59227.6 + 18696.7i) q^{42} +12336.3 q^{43} +(72884.2 + 126239. i) q^{44} +(-40168.4 - 23191.3i) q^{45} +(3836.41 - 6644.86i) q^{46} +(127836. - 73806.3i) q^{47} -56188.0i q^{48} +(-96326.1 - 67546.8i) q^{49} +241705. q^{50} +(-22215.4 - 38478.3i) q^{51} +(-187965. - 108522. i) q^{52} +(-109818. + 190210. i) q^{53} +(38106.1 - 22000.6i) q^{54} +392267. i q^{55} +(8311.72 - 26329.9i) q^{56} +61560.8 q^{57} +(-53913.4 - 93380.8i) q^{58} +(166725. + 96258.8i) q^{59} +(-105524. + 182773. i) q^{60} +(288244. - 166418. i) q^{61} +32544.5i q^{62} +(-81379.5 + 18012.1i) q^{63} -315508. q^{64} +(-292035. - 505819. i) q^{65} +(-322271. - 186063. i) q^{66} +(-174592. + 302402. i) q^{67} +(-175082. + 101084. i) q^{68} +10296.9i q^{69} +(560872. - 513590. i) q^{70} +305650. q^{71} +(-9780.45 - 16940.2i) q^{72} +(-204814. - 118249. i) q^{73} +(-214503. + 371529. i) q^{74} +(-280909. + 162183. i) q^{75} -280111. i q^{76} +(476046. + 519871. i) q^{77} +554082. q^{78} +(293218. + 507869. i) q^{79} +(-595825. - 344000. i) q^{80} +(-29524.5 + 51137.9i) q^{81} +(683468. - 394601. i) q^{82} +106377. i q^{83} +(81957.9 + 370289. i) q^{84} -544039. q^{85} +(71648.8 + 124099. i) q^{86} +(125316. + 72351.2i) q^{87} +(-82715.4 + 143267. i) q^{88} +(11308.5 - 6528.95i) q^{89} -538776. i q^{90} +(-1.00088e6 - 315955. i) q^{91} +46852.3 q^{92} +(-21837.2 - 37823.2i) q^{93} +(1.48494e6 + 857329. i) q^{94} +(376894. - 652799. i) q^{95} +(634784. - 366493. i) q^{96} +205209. i q^{97} +(120042. - 1.36132e6i) q^{98} +499390. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5 q^{2} - 108 q^{3} - 173 q^{4} - 294 q^{5} - 656 q^{7} + 3326 q^{8} + 972 q^{9}+O(q^{10}) \) 8 * q - 5 * q^2 - 108 * q^3 - 173 * q^4 - 294 * q^5 - 656 * q^7 + 3326 * q^8 + 972 * q^9	\( 8 q - 5 q^{2} - 108 q^{3} - 173 q^{4} - 294 q^{5} - 656 q^{7} + 3326 q^{8} + 972 q^{9} - 3411 q^{10} - 314 q^{11} + 4671 q^{12} - 5360 q^{14} + 5292 q^{15} - 12721 q^{16} - 5532 q^{17} + 1215 q^{18} - 18234 q^{19} + 9342 q^{21} + 86106 q^{22} + 3928 q^{23} - 44901 q^{24} - 17038 q^{25} + 12366 q^{26} + 85037 q^{28} - 8300 q^{29} + 30699 q^{30} - 89508 q^{31} - 186207 q^{32} + 8478 q^{33} - 25860 q^{35} - 84078 q^{36} + 64706 q^{37} - 77136 q^{38} + 29106 q^{39} + 221823 q^{40} + 173583 q^{42} + 45740 q^{43} + 92529 q^{44} - 71442 q^{45} - 111504 q^{46} + 483276 q^{47} - 310684 q^{49} + 967216 q^{50} + 49788 q^{51} - 1673988 q^{52} - 540974 q^{53} - 32805 q^{54} - 241885 q^{56} + 328212 q^{57} + 539799 q^{58} - 181770 q^{59} - 146367 q^{60} + 418224 q^{61} - 92826 q^{63} + 2378626 q^{64} - 414204 q^{65} - 1162431 q^{66} - 1158902 q^{67} - 821250 q^{68} + 1087917 q^{70} + 1442344 q^{71} + 404109 q^{72} - 378666 q^{73} - 432940 q^{74} + 460026 q^{75} + 1065994 q^{77} - 222588 q^{78} + 611452 q^{79} - 2094945 q^{80} - 236196 q^{81} - 1561266 q^{82} - 1579716 q^{84} - 275112 q^{85} + 816224 q^{86} + 112050 q^{87} - 366441 q^{88} - 989196 q^{89} + 304446 q^{91} + 678720 q^{92} + 805572 q^{93} - 716148 q^{94} - 591792 q^{95} + 5027589 q^{96} + 3509629 q^{98} - 152604 q^{99}+O(q^{100}) \) 8 * q - 5 * q^2 - 108 * q^3 - 173 * q^4 - 294 * q^5 - 656 * q^7 + 3326 * q^8 + 972 * q^9 - 3411 * q^10 - 314 * q^11 + 4671 * q^12 - 5360 * q^14 + 5292 * q^15 - 12721 * q^16 - 5532 * q^17 + 1215 * q^18 - 18234 * q^19 + 9342 * q^21 + 86106 * q^22 + 3928 * q^23 - 44901 * q^24 - 17038 * q^25 + 12366 * q^26 + 85037 * q^28 - 8300 * q^29 + 30699 * q^30 - 89508 * q^31 - 186207 * q^32 + 8478 * q^33 - 25860 * q^35 - 84078 * q^36 + 64706 * q^37 - 77136 * q^38 + 29106 * q^39 + 221823 * q^40 + 173583 * q^42 + 45740 * q^43 + 92529 * q^44 - 71442 * q^45 - 111504 * q^46 + 483276 * q^47 - 310684 * q^49 + 967216 * q^50 + 49788 * q^51 - 1673988 * q^52 - 540974 * q^53 - 32805 * q^54 - 241885 * q^56 + 328212 * q^57 + 539799 * q^58 - 181770 * q^59 - 146367 * q^60 + 418224 * q^61 - 92826 * q^63 + 2378626 * q^64 - 414204 * q^65 - 1162431 * q^66 - 1158902 * q^67 - 821250 * q^68 + 1087917 * q^70 + 1442344 * q^71 + 404109 * q^72 - 378666 * q^73 - 432940 * q^74 + 460026 * q^75 + 1065994 * q^77 - 222588 * q^78 + 611452 * q^79 - 2094945 * q^80 - 236196 * q^81 - 1561266 * q^82 - 1579716 * q^84 - 275112 * q^85 + 816224 * q^86 + 112050 * q^87 - 366441 * q^88 - 989196 * q^89 + 304446 * q^91 + 678720 * q^92 + 805572 * q^93 - 716148 * q^94 - 591792 * q^95 + 5027589 * q^96 + 3509629 * q^98 - 152604 * q^99

Introduction

L-functions

Modular forms

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