LMFDB - Embedded newform 75.9.c.e.26.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,9,Mod(26,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("75.26");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	75.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$30.5533957546$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 1634x^{8} + 776307x^{6} + 148116566x^{4} + 10575941812x^{2} + 105274575720 $ x^10 + 1634x^8 + 776307x^6 + 148116566x^4 + 10575941812x^2 + 105274575720
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8}\cdot 3^{11}\cdot 5^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			26.3
Root			$-31.4704i$ of defining polynomial
Character	$\chi$	$=$	75.26
Dual form			75.9.c.e.26.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-18.2182i q^{2} +(69.9805 + 40.7889i) q^{3} -75.9021 q^{4} +(743.099 - 1274.92i) q^{6} +4676.68 q^{7} -3281.06i q^{8} +(3233.54 + 5708.85i) q^{9} +O(q^{10})$	\(q-18.2182i q^{2} +(69.9805 + 40.7889i) q^{3} -75.9021 q^{4} +(743.099 - 1274.92i) q^{6} +4676.68 q^{7} -3281.06i q^{8} +(3233.54 + 5708.85i) q^{9} +25315.1i q^{11} +(-5311.66 - 3095.96i) q^{12} -600.138 q^{13} -85200.7i q^{14} -79205.8 q^{16} +73234.6i q^{17} +(104005. - 58909.2i) q^{18} -38440.3 q^{19} +(327277. + 190757. i) q^{21} +461196. q^{22} +196713. i q^{23} +(133831. - 229610. i) q^{24} +10933.4i q^{26} +(-6572.81 + 531400. i) q^{27} -354970. q^{28} -504953. i q^{29} +665132. q^{31} +603035. i q^{32} +(-1.03258e6 + 1.77157e6i) q^{33} +1.33420e6 q^{34} +(-245432. - 433313. i) q^{36} +351425. q^{37} +700312. i q^{38} +(-41997.9 - 24478.9i) q^{39} -2.88219e6i q^{41} +(3.47524e6 - 5.96238e6i) q^{42} -1.17585e6 q^{43} -1.92147e6i q^{44} +3.58375e6 q^{46} -4.20282e6i q^{47} +(-5.54286e6 - 3.23071e6i) q^{48} +1.61066e7 q^{49} +(-2.98715e6 + 5.12499e6i) q^{51} +45551.7 q^{52} -6.57665e6i q^{53} +(9.68115e6 + 119745. i) q^{54} -1.53445e7i q^{56} +(-2.69007e6 - 1.56794e6i) q^{57} -9.19932e6 q^{58} -1.46872e7i q^{59} -1.09139e7 q^{61} -1.21175e7i q^{62} +(1.51222e7 + 2.66985e7i) q^{63} -9.29049e6 q^{64} +(3.22747e7 + 1.88116e7i) q^{66} +1.82376e7 q^{67} -5.55866e6i q^{68} +(-8.02369e6 + 1.37661e7i) q^{69} -1.95691e7i q^{71} +(1.87311e7 - 1.06094e7i) q^{72} -3.13857e7 q^{73} -6.40233e6i q^{74} +2.91770e6 q^{76} +1.18391e8i q^{77} +(-445962. + 765126. i) q^{78} -1.63328e6 q^{79} +(-2.21352e7 + 3.69196e7i) q^{81} -5.25082e7 q^{82} +3.92795e7i q^{83} +(-2.48410e7 - 1.44788e7i) q^{84} +2.14218e7i q^{86} +(2.05965e7 - 3.53369e7i) q^{87} +8.30604e7 q^{88} +1.89625e7i q^{89} -2.80665e6 q^{91} -1.49309e7i q^{92} +(4.65462e7 + 2.71300e7i) q^{93} -7.65678e7 q^{94} +(-2.45971e7 + 4.22007e7i) q^{96} -1.16684e8 q^{97} -2.93432e8i q^{98} +(-1.44520e8 + 8.18574e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 25 q^{3} - 1554 q^{4} + 2257 q^{6} + 1960 q^{7} - 11207 q^{9}+O(q^{10}) $ 10 * q - 25 * q^3 - 1554 * q^4 + 2257 * q^6 + 1960 * q^7 - 11207 * q^9	$ 10 q - 25 q^{3} - 1554 q^{4} + 2257 q^{6} + 1960 q^{7} - 11207 q^{9} - 5915 q^{12} - 16920 q^{13} + 44634 q^{16} - 224875 q^{18} - 143934 q^{19} + 673428 q^{21} + 818990 q^{22} - 1016859 q^{24} - 260830 q^{27} + 3810100 q^{28} - 3014060 q^{31} - 4677515 q^{33} + 4977146 q^{34} + 4500527 q^{36} + 3016760 q^{37} - 7513282 q^{39} - 4001760 q^{42} + 11747340 q^{43} - 13938636 q^{46} - 14748755 q^{48} + 8953546 q^{49} + 6209287 q^{51} - 38918320 q^{52} - 8886272 q^{54} + 14759525 q^{57} - 48407900 q^{58} + 1520220 q^{61} + 74748240 q^{63} - 4536998 q^{64} + 10465295 q^{66} - 16269290 q^{67} + 11394978 q^{69} + 172231185 q^{72} - 52090170 q^{73} - 29529046 q^{76} + 198205810 q^{78} + 8549896 q^{79} + 22612945 q^{81} - 295714190 q^{82} - 136883292 q^{84} + 318901610 q^{87} - 310673250 q^{88} - 107224264 q^{91} + 79679130 q^{93} + 356118596 q^{94} + 525424001 q^{96} - 402167800 q^{97} - 382421335 q^{99}+O(q^{100}) $ 10 * q - 25 * q^3 - 1554 * q^4 + 2257 * q^6 + 1960 * q^7 - 11207 * q^9 - 5915 * q^12 - 16920 * q^13 + 44634 * q^16 - 224875 * q^18 - 143934 * q^19 + 673428 * q^21 + 818990 * q^22 - 1016859 * q^24 - 260830 * q^27 + 3810100 * q^28 - 3014060 * q^31 - 4677515 * q^33 + 4977146 * q^34 + 4500527 * q^36 + 3016760 * q^37 - 7513282 * q^39 - 4001760 * q^42 + 11747340 * q^43 - 13938636 * q^46 - 14748755 * q^48 + 8953546 * q^49 + 6209287 * q^51 - 38918320 * q^52 - 8886272 * q^54 + 14759525 * q^57 - 48407900 * q^58 + 1520220 * q^61 + 74748240 * q^63 - 4536998 * q^64 + 10465295 * q^66 - 16269290 * q^67 + 11394978 * q^69 + 172231185 * q^72 - 52090170 * q^73 - 29529046 * q^76 + 198205810 * q^78 + 8549896 * q^79 + 22612945 * q^81 - 295714190 * q^82 - 136883292 * q^84 + 318901610 * q^87 - 310673250 * q^88 - 107224264 * q^91 + 79679130 * q^93 + 356118596 * q^94 + 525424001 * q^96 - 402167800 * q^97 - 382421335 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	18.2182i		−	1.13864i	−0.822117	−	0.569318i	$-0.807207\pi$
$2$		−	18.2182i		−	1.13864i	0.822117	−	0.569318i	$-0.192793\pi$
$3$	69.9805	+	40.7889i	0.863957	+	0.503566i
$3$	69.9805	+	40.7889i	0.863957	+	0.503566i
$4$	−75.9021			−0.296492
$5$		0			0
$5$		0			0
$6$	743.099	−	1274.92i	0.573379	−	0.983732i
$7$	4676.68			1.94781			0.973903	−	0.226964i	$-0.0728799\pi$
$7$	4676.68			1.94781			0.973903	+	0.226964i	$0.0728799\pi$
$8$		−	3281.06i		−	0.801039i
$9$	3233.54	+	5708.85i	0.492842	+	0.870119i
$10$		0			0
$11$			25315.1i			1.72906i	0.502583	+	0.864529i	$0.332383\pi$
$11$			25315.1i			1.72906i	−0.502583	+	0.864529i	$0.667617\pi$
$12$	−5311.66	−	3095.96i	−0.256157	−	0.149304i
$13$	−600.138			−0.0210125			−0.0105062	−	0.999945i	$-0.503344\pi$
$13$	−600.138			−0.0210125			−0.0105062	+	0.999945i	$0.503344\pi$
$14$		−	85200.7i		−	2.21784i
$15$		0			0
$16$	−79205.8			−1.20858
$17$			73234.6i			0.876840i	0.898770	+	0.438420i	$0.144462\pi$
$17$			73234.6i			0.876840i	−0.898770	+	0.438420i	$0.855538\pi$
$18$	104005.	−	58909.2i	0.990749	−	0.561168i
$19$	−38440.3			−0.294966			−0.147483	−	0.989065i	$-0.547117\pi$
$19$	−38440.3			−0.294966			−0.147483	+	0.989065i	$0.547117\pi$
$20$		0			0
$21$	327277.	+	190757.i	1.68282	+	0.980849i
$22$	461196.			1.96877
$23$			196713.i			0.702945i	0.936198	+	0.351473i	$0.114319\pi$
$23$			196713.i			0.702945i	−0.936198	+	0.351473i	$0.885681\pi$
$24$	133831.	−	229610.i	0.403376	−	0.692063i
$25$		0			0
$26$			10933.4i			0.0239256i
$27$	−6572.81	+	531400.i	−0.0123679	+	0.999924i
$28$	−354970.			−0.577510
$29$		−	504953.i		−	0.713935i	−0.934117	−	0.356968i	$-0.883811\pi$
$29$		−	504953.i		−	0.713935i	0.934117	−	0.356968i	$-0.116189\pi$
$30$		0			0
$31$	665132.			0.720213			0.360106	−	0.932911i	$-0.382740\pi$
$31$	665132.			0.720213			0.360106	+	0.932911i	$0.382740\pi$
$32$			603035.i			0.575099i
$33$	−1.03258e6	+	1.77157e6i	−0.870695	+	1.49383i
$34$	1.33420e6			0.998402
$35$		0			0
$36$	−245432.	−	433313.i	−0.146124	−	0.257984i
$37$	351425.			0.187511			0.0937553	−	0.995595i	$-0.470113\pi$
$37$	351425.			0.187511			0.0937553	+	0.995595i	$0.470113\pi$
$38$			700312.i			0.335859i
$39$	−41997.9	−	24478.9i	−0.0181539	−	0.0105812i
$40$		0			0
$41$		−	2.88219e6i		−	1.01997i	−0.860184	−	0.509984i	$-0.829651\pi$
$41$		−	2.88219e6i		−	1.01997i	0.860184	−	0.509984i	$-0.170349\pi$
$42$	3.47524e6	−	5.96238e6i	1.11683	−	1.91612i
$43$	−1.17585e6			−0.343935			−0.171968	−	0.985103i	$-0.555012\pi$
$43$	−1.17585e6			−0.343935			−0.171968	+	0.985103i	$0.555012\pi$
$44$		−	1.92147e6i		−	0.512652i
$45$		0			0
$46$	3.58375e6			0.800399
$47$		−	4.20282e6i		−	0.861291i	−0.902521	−	0.430645i	$-0.858286\pi$
$47$		−	4.20282e6i		−	0.861291i	0.902521	−	0.430645i	$-0.141714\pi$
$48$	−5.54286e6	−	3.23071e6i	−1.04416	−	0.608602i
$49$	1.61066e7			2.79395
$50$		0			0
$51$	−2.98715e6	+	5.12499e6i	−0.441547	+	0.757552i
$52$	45551.7			0.00623005
$53$		−	6.57665e6i		−	0.833491i	−0.909023	−	0.416746i	$-0.863171\pi$
$53$		−	6.57665e6i		−	0.833491i	0.909023	−	0.416746i	$-0.136829\pi$
$54$	9.68115e6	+	119745.i	1.13855	+	0.0140825i
$55$		0			0
$56$		−	1.53445e7i		−	1.56027i
$57$	−2.69007e6	−	1.56794e6i	−0.254838	−	0.148535i
$58$	−9.19932e6			−0.812913
$59$		−	1.46872e7i		−	1.21208i	−0.795434	−	0.606040i	$-0.792757\pi$
$59$		−	1.46872e7i		−	1.21208i	0.795434	−	0.606040i	$-0.207243\pi$
$60$		0			0
$61$	−1.09139e7			−0.788244			−0.394122	−	0.919058i	$-0.628951\pi$
$61$	−1.09139e7			−0.788244			−0.394122	+	0.919058i	$0.628951\pi$
$62$		−	1.21175e7i		−	0.820060i
$63$	1.51222e7	+	2.66985e7i	0.959961	+	1.69482i
$64$	−9.29049e6			−0.553756
$65$		0			0
$66$	3.22747e7	+	1.88116e7i	1.70093	+	0.991405i
$67$	1.82376e7			0.905041			0.452521	−	0.891754i	$-0.350525\pi$
$67$	1.82376e7			0.905041			0.452521	+	0.891754i	$0.350525\pi$
$68$		−	5.55866e6i		−	0.259977i
$69$	−8.02369e6	+	1.37661e7i	−0.353979	+	0.607314i
$70$		0			0
$71$		−	1.95691e7i		−	0.770084i	−0.922899	−	0.385042i	$-0.874187\pi$
$71$		−	1.95691e7i		−	0.770084i	0.922899	−	0.385042i	$-0.125813\pi$
$72$	1.87311e7	−	1.06094e7i	0.696999	−	0.394786i
$73$	−3.13857e7			−1.10520			−0.552600	−	0.833447i	$-0.686364\pi$
$73$	−3.13857e7			−1.10520			−0.552600	+	0.833447i	$0.686364\pi$
$74$		−	6.40233e6i		−	0.213506i
$75$		0			0
$76$	2.91770e6			0.0874552
$77$			1.18391e8i			3.36787i
$78$	−445962.	+	765126.i	−0.0120481	+	0.0206707i
$79$	−1.63328e6			−0.0419327			−0.0209663	−	0.999780i	$-0.506674\pi$
$79$	−1.63328e6			−0.0419327			−0.0209663	+	0.999780i	$0.506674\pi$
$80$		0			0
$81$	−2.21352e7	+	3.69196e7i	−0.514213	+	0.857663i
$82$	−5.25082e7			−1.16137
$83$			3.92795e7i			0.827663i	0.910353	+	0.413832i	$0.135810\pi$
$83$			3.92795e7i			0.827663i	−0.910353	+	0.413832i	$0.864190\pi$
$84$	−2.48410e7	−	1.44788e7i	−0.498943	−	0.290814i
$85$		0			0
$86$			2.14218e7i			0.391617i
$87$	2.05965e7	−	3.53369e7i	0.359514	−	0.616809i
$88$	8.30604e7			1.38504
$89$			1.89625e7i			0.302229i	0.988516	+	0.151115i	$0.0482862\pi$
$89$			1.89625e7i			0.302229i	−0.988516	+	0.151115i	$0.951714\pi$
$90$		0			0
$91$	−2.80665e6			−0.0409283
$92$		−	1.49309e7i		−	0.208418i
$93$	4.65462e7	+	2.71300e7i	0.622233	+	0.362675i
$94$	−7.65678e7			−0.980697
$95$		0			0
$96$	−2.45971e7	+	4.22007e7i	−0.289600	+	0.496861i
$97$	−1.16684e8			−1.31802			−0.659012	−	0.752133i	$-0.729025\pi$
$97$	−1.16684e8			−1.31802			−0.659012	+	0.752133i	$0.729025\pi$
$98$		−	2.93432e8i		−	3.18129i
$99$	−1.44520e8	+	8.18574e7i	−1.50449	+	0.852153i
$100$		0			0
$101$		−	8.62148e7i		−	0.828507i	−0.910161	−	0.414254i	$-0.864043\pi$
$101$		−	8.62148e7i		−	0.828507i	0.910161	−	0.414254i	$-0.135957\pi$
$102$	9.33680e7	+	5.44205e7i	0.862576	+	0.502762i
$103$	9.28352e7			0.824829			0.412415	−	0.910996i	$-0.364686\pi$
$103$	9.28352e7			0.824829			0.412415	+	0.910996i	$0.364686\pi$
$104$			1.96909e6i			0.0168318i
$105$		0			0
$106$	−1.19815e8			−0.949043
$107$		−	1.95590e8i		−	1.49214i	−0.665865	−	0.746072i	$-0.731937\pi$
$107$		−	1.95590e8i		−	1.49214i	0.665865	−	0.746072i	$-0.268063\pi$
$108$	498889.	−	4.03344e7i	0.00366699	−	0.296470i
$109$	1.62524e8			1.15136			0.575682	−	0.817674i	$-0.304737\pi$
$109$	1.62524e8			1.15136			0.575682	+	0.817674i	$0.304737\pi$
$110$		0			0
$111$	2.45929e7	+	1.43342e7i	0.162001	+	0.0944240i
$112$	−3.70420e8			−2.35409
$113$			1.97203e8i			1.20949i	0.796421	+	0.604743i	$0.206724\pi$
$113$			1.97203e8i			1.20949i	−0.796421	+	0.604743i	$0.793276\pi$
$114$	−2.85649e7	+	4.90082e7i	−0.169127	+	0.290168i
$115$		0			0
$116$			3.83270e7i			0.211676i
$117$	−1.94057e6	−	3.42610e6i	−0.0103558	−	0.0182834i
$118$	−2.67574e8			−1.38012
$119$			3.42495e8i			1.70792i
$120$		0			0
$121$	−4.26497e8			−1.98964
$122$			1.98831e8i			0.897523i
$123$	1.17561e8	−	2.01697e8i	0.513622	−	0.881209i
$124$	−5.04849e7			−0.213538
$125$		0			0
$126$	4.86398e8	−	2.75500e8i	1.92979	−	1.09305i
$127$	2.85596e8			1.09784			0.548918	−	0.835876i	$-0.315040\pi$
$127$	2.85596e8			1.09784			0.548918	+	0.835876i	$0.315040\pi$
$128$			3.23633e8i			1.20563i
$129$	−8.22863e7	−	4.79614e7i	−0.297145	−	0.173194i
$130$		0			0
$131$			9.66770e7i			0.328275i	0.986437	+	0.164138i	$0.0524841\pi$
$131$			9.66770e7i			0.328275i	−0.986437	+	0.164138i	$0.947516\pi$
$132$	7.83746e7	−	1.34465e8i	0.258154	−	0.442909i
$133$	−1.79773e8			−0.574537
$134$		−	3.32256e8i		−	1.03051i
$135$		0			0
$136$	2.40287e8			0.702383
$137$		−	1.84457e8i		−	0.523616i	−0.965120	−	0.261808i	$-0.915681\pi$
$137$		−	1.84457e8i		−	0.523616i	0.965120	−	0.261808i	$-0.0843188\pi$
$138$	2.50793e8	+	1.46177e8i	0.691510	+	0.403054i
$139$	−1.16522e7			−0.0312138			−0.0156069	−	0.999878i	$-0.504968\pi$
$139$	−1.16522e7			−0.0312138			−0.0156069	+	0.999878i	$0.504968\pi$
$140$		0			0
$141$	1.71428e8	−	2.94116e8i	0.433717	−	0.744118i
$142$	−3.56514e8			−0.876845
$143$		−	1.51926e7i		−	0.0363318i
$144$	−2.56115e8	−	4.52174e8i	−0.595642	−	1.05161i
$145$		0			0
$146$			5.71791e8i			1.25842i
$147$	1.12715e9	+	6.56968e8i	2.41385	+	1.40694i
$148$	−2.66739e7			−0.0555955
$149$		−	3.58376e8i		−	0.727099i	−0.931575	−	0.363550i	$-0.881565\pi$
$149$		−	3.58376e8i		−	0.727099i	0.931575	−	0.363550i	$-0.118435\pi$
$150$		0			0
$151$	−1.60549e8			−0.308816			−0.154408	−	0.988007i	$-0.549347\pi$
$151$	−1.60549e8			−0.308816			−0.154408	+	0.988007i	$0.549347\pi$
$152$			1.26125e8i			0.236279i
$153$	−4.18085e8	+	2.36807e8i	−0.762955	+	0.432144i
$154$	2.15687e9			3.83478
$155$		0			0
$156$	3.18773e6	+	1.85800e6i	0.00538249	+	0.00313724i
$157$	−2.60289e8			−0.428408			−0.214204	−	0.976789i	$-0.568716\pi$
$157$	−2.60289e8			−0.428408			−0.214204	+	0.976789i	$0.568716\pi$
$158$			2.97554e7i			0.0477461i
$159$	2.68254e8	−	4.60237e8i	0.419718	−	0.720100i
$160$		0			0
$161$			9.19964e8i			1.36920i
$162$	6.72607e8	+	4.03263e8i	0.976566	+	0.585501i
$163$	−7.22321e8			−1.02325			−0.511623	−	0.859210i	$-0.670955\pi$
$163$	−7.22321e8			−1.02325			−0.511623	+	0.859210i	$0.670955\pi$
$164$			2.18764e8i			0.302413i
$165$		0			0
$166$	7.15601e8			0.942408
$167$		−	1.35239e9i		−	1.73874i	−0.494161	−	0.869370i	$-0.664525\pi$
$167$		−	1.35239e9i		−	1.73874i	0.494161	−	0.869370i	$-0.335475\pi$
$168$	6.25883e8	−	1.07381e9i	0.785699	−	1.34801i
$169$	−8.15371e8			−0.999558
$170$		0			0
$171$	−1.24298e8	−	2.19450e8i	−0.145372	−	0.256656i
$172$	8.92491e7			0.101974
$173$			1.05877e9i			1.18200i	0.806671	+	0.591000i	$0.201267\pi$
$173$			1.05877e9i			1.18200i	−0.806671	+	0.591000i	$0.798733\pi$
$174$	−6.43773e8	−	3.75230e8i	−0.702321	−	0.409355i
$175$		0			0
$176$		−	2.00511e9i		−	2.08971i
$177$	5.99075e8	−	1.02782e9i	0.610363	−	1.04719i
$178$	3.45463e8			0.344129
$179$		−	6.84450e8i		−	0.666699i	−0.942803	−	0.333349i	$-0.891821\pi$
$179$		−	6.84450e8i		−	0.666699i	0.942803	−	0.333349i	$-0.108179\pi$
$180$		0			0
$181$	−8.83562e8			−0.823233			−0.411617	−	0.911357i	$-0.635036\pi$
$181$	−8.83562e8			−0.823233			−0.411617	+	0.911357i	$0.635036\pi$
$182$			5.11321e7i			0.0466024i
$183$	−7.63760e8	−	4.45166e8i	−0.681009	−	0.396933i
$184$	6.45426e8			0.563087
$185$		0			0
$186$	4.94258e8	−	8.47988e8i	0.412955	−	0.708497i
$187$	−1.85394e9			−1.51611
$188$			3.19003e8i			0.255366i
$189$	−3.07389e7	+	2.48519e9i	−0.0240903	+	1.94766i
$190$		0			0
$191$			1.18467e9i			0.890148i	0.895494	+	0.445074i	$0.146823\pi$
$191$			1.18467e9i			0.890148i	−0.895494	+	0.445074i	$0.853177\pi$
$192$	−6.50153e8	−	3.78948e8i	−0.478421	−	0.278853i
$193$	−1.65487e9			−1.19271			−0.596354	−	0.802721i	$-0.703385\pi$
$193$	−1.65487e9			−1.19271			−0.596354	+	0.802721i	$0.703385\pi$
$194$			2.12576e9i			1.50075i
$195$		0			0
$196$	−1.22252e9			−0.828385
$197$			8.60897e8i			0.571592i	0.958290	+	0.285796i	$0.0922580\pi$
$197$			8.60897e8i			0.571592i	−0.958290	+	0.285796i	$0.907742\pi$
$198$	1.49129e9	+	2.63290e9i	0.970292	+	1.71306i
$199$	7.00975e8			0.446982			0.223491	−	0.974706i	$-0.428255\pi$
$199$	7.00975e8			0.446982			0.223491	+	0.974706i	$0.428255\pi$
$200$		0			0
$201$	1.27628e9	+	7.43891e8i	0.781916	+	0.455748i
$202$	−1.57068e9			−0.943369
$203$		−	2.36151e9i		−	1.39061i
$204$	2.26731e8	−	3.88997e8i	0.130915	−	0.224608i
$205$		0			0
$206$		−	1.69129e9i		−	0.939180i
$207$	−1.12300e9	+	6.36079e8i	−0.611646	+	0.346441i
$208$	4.75344e7			0.0253954
$209$		−	9.73121e8i		−	0.510013i
$210$		0			0
$211$	−3.15102e9			−1.58972			−0.794862	−	0.606790i	$-0.792457\pi$
$211$	−3.15102e9			−1.58972			−0.794862	+	0.606790i	$0.792457\pi$
$212$			4.99181e8i			0.247124i
$213$	7.98202e8	−	1.36946e9i	0.387788	−	0.665319i
$214$	−3.56329e9			−1.69901
$215$		0			0
$216$	1.74355e9	+	2.15657e7i	0.800978	+	0.00990717i
$217$	3.11061e9			1.40284
$218$		−	2.96090e9i		−	1.31098i
$219$	−2.19639e9	−	1.28019e9i	−0.954845	−	0.556541i
$220$		0			0
$221$		−	4.39508e7i		−	0.0184246i
$222$	2.61144e8	−	4.48038e8i	0.107515	−	0.184460i
$223$	3.67974e9			1.48798			0.743990	−	0.668191i	$-0.232931\pi$
$223$	3.67974e9			1.48798			0.743990	+	0.668191i	$0.232931\pi$
$224$			2.82020e9i			1.12018i
$225$		0			0
$226$	3.59269e9			1.37716
$227$			5.71593e8i			0.215270i	0.994190	+	0.107635i	$0.0343278\pi$
$227$			5.71593e8i			0.215270i	−0.994190	+	0.107635i	$0.965672\pi$
$228$	2.04182e8	+	1.19009e8i	0.0755575	+	0.0440395i
$229$	−2.94346e9			−1.07033			−0.535164	−	0.844748i	$-0.679750\pi$
$229$	−2.94346e9			−1.07033			−0.535164	+	0.844748i	$0.679750\pi$
$230$		0			0
$231$	−4.82903e9	+	8.28505e9i	−1.69594	+	2.90969i
$232$	−1.65678e9			−0.571890
$233$			2.11678e9i			0.718210i	0.933297	+	0.359105i	$0.116918\pi$
$233$			2.11678e9i			0.718210i	−0.933297	+	0.359105i	$0.883082\pi$
$234$	−6.24172e7	+	3.53536e7i	−0.0208181	+	0.0117915i
$235$		0			0
$236$			1.11479e9i			0.359373i
$237$	−1.14298e8	−	6.66197e7i	−0.0362280	−	0.0211159i
$238$	6.23963e9			1.94469
$239$		−	3.95083e9i		−	1.21087i	−0.795896	−	0.605434i	$-0.793000\pi$
$239$		−	3.95083e9i		−	1.21087i	0.795896	−	0.605434i	$-0.207000\pi$
$240$		0			0
$241$	6.74602e7			0.0199977			0.00999884	−	0.999950i	$-0.496817\pi$
$241$	6.74602e7			0.0199977			0.00999884	+	0.999950i	$0.496817\pi$
$242$			7.77000e9i			2.26548i
$243$	−3.05494e9	+	1.68078e9i	−0.876148	+	0.482043i
$244$	8.28388e8			0.233708
$245$		0			0
$246$	−3.67455e9	−	2.14175e9i	−1.00338	−	0.584828i
$247$	2.30695e7			0.00619797
$248$		−	2.18233e9i		−	0.576919i
$249$	−1.60217e9	+	2.74880e9i	−0.416783	+	0.715065i
$250$		0			0
$251$		−	3.35762e9i		−	0.845934i	−0.906145	−	0.422967i	$-0.860989\pi$
$251$		−	3.35762e9i		−	0.845934i	0.906145	−	0.422967i	$-0.139011\pi$
$252$	−1.14781e9	−	2.02647e9i	−0.284621	−	0.502502i
$253$	−4.97981e9			−1.21543
$254$		−	5.20304e9i		−	1.25004i
$255$		0			0
$256$	3.51763e9			0.819013
$257$			5.89201e8i			0.135061i	0.997717	+	0.0675307i	$0.0215121\pi$
$257$			5.89201e8i			0.135061i	−0.997717	+	0.0675307i	$0.978488\pi$
$258$	−8.73769e8	+	1.49911e9i	−0.197205	+	0.338340i
$259$	1.64350e9			0.365235
$260$		0			0
$261$	2.88270e9	−	1.63278e9i	0.621209	−	0.351858i
$262$	1.76128e9			0.373786
$263$			9.46868e8i			0.197909i	0.995092	+	0.0989547i	$0.0315499\pi$
$263$			9.46868e8i			0.197909i	−0.995092	+	0.0989547i	$0.968450\pi$
$264$	5.81261e9	+	3.38794e9i	1.19662	+	0.697461i
$265$		0			0
$266$			3.27514e9i			0.654189i
$267$	−7.73460e8	+	1.32701e9i	−0.152192	+	0.261113i
$268$	−1.38427e9			−0.268338
$269$			4.99503e9i			0.953958i	0.878915	+	0.476979i	$0.158268\pi$
$269$			4.99503e9i			0.953958i	−0.878915	+	0.476979i	$0.841732\pi$
$270$		0			0
$271$	5.27982e9			0.978908			0.489454	−	0.872029i	$-0.337196\pi$
$271$	5.27982e9			0.978908			0.489454	+	0.872029i	$0.337196\pi$
$272$		−	5.80060e9i		−	1.05974i
$273$	−1.96411e8	−	1.14480e8i	−0.0353603	−	0.0206101i
$274$	−3.36047e9			−0.596208
$275$		0			0
$276$	6.09015e8	−	1.04487e9i	0.104952	−	0.180064i
$277$	9.37450e9			1.59231			0.796157	−	0.605090i	$-0.206863\pi$
$277$	9.37450e9			1.59231			0.796157	+	0.605090i	$0.206863\pi$
$278$			2.12281e8i			0.0355412i
$279$	2.15073e9	+	3.79714e9i	0.354951	+	0.626671i
$280$		0			0
$281$		−	1.16074e10i		−	1.86170i	−0.365396	−	0.930852i	$-0.619066\pi$
$281$		−	1.16074e10i		−	1.86170i	0.365396	−	0.930852i	$-0.380934\pi$
$282$	−5.35825e9	−	3.12311e9i	−0.847280	−	0.493846i
$283$	−1.65370e9			−0.257817			−0.128908	−	0.991656i	$-0.541147\pi$
$283$	−1.65370e9			−0.257817			−0.128908	+	0.991656i	$0.541147\pi$
$284$			1.48534e9i			0.228324i
$285$		0			0
$286$	−2.76781e8			−0.0413687
$287$		−	1.34791e10i		−	1.98670i
$288$	−3.44264e9	+	1.94994e9i	−0.500404	+	0.283433i
$289$	1.61245e9			0.231151
$290$		0			0
$291$	−8.16558e9	−	4.75939e9i	−1.13872	−	0.663712i
$292$	2.38224e9			0.327683
$293$			9.59915e9i			1.30245i	0.758883	+	0.651227i	$0.225745\pi$
$293$			9.59915e9i			1.30245i	−0.758883	+	0.651227i	$0.774255\pi$
$294$	1.19688e10	−	2.05345e10i	1.60199	−	2.74850i
$295$		0			0
$296$		−	1.15305e9i		−	0.150203i
$297$	−1.34525e10	−	1.66391e8i	−1.72893	−	0.0213848i
$298$	−6.52896e9			−0.827901
$299$		−	1.18055e8i		−	0.0147706i
$300$		0			0
$301$	−5.49906e9			−0.669919
$302$			2.92491e9i			0.351629i
$303$	3.51660e9	−	6.03336e9i	0.417208	−	0.715795i
$304$	3.04469e9			0.356492
$305$		0			0
$306$	4.31419e9	+	7.61675e9i	0.492055	+	0.868728i
$307$	8.74107e9			0.984036			0.492018	−	0.870585i	$-0.336259\pi$
$307$	8.74107e9			0.984036			0.492018	+	0.870585i	$0.336259\pi$
$308$		−	8.98611e9i		−	0.998548i
$309$	6.49666e9	+	3.78664e9i	0.712617	+	0.415356i
$310$		0			0
$311$			1.25430e10i			1.34079i	0.742006	+	0.670394i	$0.233875\pi$
$311$			1.25430e10i			1.34079i	−0.742006	+	0.670394i	$0.766125\pi$
$312$	−8.03168e7	+	1.37798e8i	−0.00847594	+	0.0145420i
$313$	3.08002e9			0.320905			0.160452	−	0.987044i	$-0.448705\pi$
$313$	3.08002e9			0.320905			0.160452	+	0.987044i	$0.448705\pi$
$314$			4.74199e9i			0.487801i
$315$		0			0
$316$	1.23969e8			0.0124327
$317$		−	2.81482e9i		−	0.278749i	−0.990240	−	0.139375i	$-0.955491\pi$
$317$		−	2.81482e9i		−	0.278749i	0.990240	−	0.139375i	$-0.0445092\pi$
$318$	−8.38468e9	−	4.88710e9i	−0.819932	−	0.477906i
$319$	1.27830e10			1.23444
$320$		0			0
$321$	7.97788e9	−	1.36875e10i	0.751393	−	1.28915i
$322$	1.67601e10			1.55902
$323$		−	2.81516e9i		−	0.258638i
$324$	1.68011e9	−	2.80227e9i	0.152460	−	0.254290i
$325$		0			0
$326$			1.31594e10i			1.16510i
$327$	1.13735e10	+	6.62918e9i	0.994728	+	0.579788i
$328$	−9.45662e9			−0.817035
$329$		−	1.96553e10i		−	1.67763i
$330$		0			0
$331$	2.09451e10			1.74490			0.872452	−	0.488701i	$-0.162529\pi$
$331$	2.09451e10			1.74490			0.872452	+	0.488701i	$0.162529\pi$
$332$		−	2.98140e9i		−	0.245396i
$333$	1.13635e9	+	2.00623e9i	0.0924132	+	0.163157i
$334$	−2.46380e10			−1.97979
$335$		0			0
$336$	−2.59222e10	−	1.51090e10i	−2.03383	−	1.18544i
$337$	1.91729e7			0.00148651			0.000743255	−	1.00000i	$-0.499763\pi$
$337$	1.91729e7			0.00148651			0.000743255		1.00000i	$0.499763\pi$
$338$			1.48546e10i			1.13813i
$339$	−8.04370e9	+	1.38004e10i	−0.609056	+	1.04494i
$340$		0			0
$341$			1.68379e10i			1.24529i
$342$	−3.99797e9	+	2.26449e9i	−0.292237	+	0.165526i
$343$	4.83652e10			3.49427
$344$			3.85802e9i			0.275506i
$345$		0			0
$346$	1.92889e10			1.34587
$347$			1.16312e10i			0.802247i	0.916024	+	0.401124i	$0.131380\pi$
$347$			1.16312e10i			0.802247i	−0.916024	+	0.401124i	$0.868620\pi$
$348$	−1.56331e9	+	2.68214e9i	−0.106593	+	0.182879i
$349$	−2.89314e9			−0.195015			−0.0975073	−	0.995235i	$-0.531087\pi$
$349$	−2.89314e9			−0.195015			−0.0975073	+	0.995235i	$0.531087\pi$
$350$		0			0
$351$	3.94459e6	−	3.18913e8i	0.000259880	−	0.0210109i
$352$	−1.52659e10			−0.994379
$353$			2.73144e10i			1.75911i	0.475798	+	0.879555i	$0.342159\pi$
$353$			2.73144e10i			1.75911i	−0.475798	+	0.879555i	$0.657841\pi$
$354$	−1.87250e10	−	1.09141e10i	−1.19236	−	0.694981i
$355$		0			0
$356$		−	1.43929e9i		−	0.0896086i
$357$	−1.39700e10	+	2.39680e10i	−0.860048	+	1.47556i
$358$	−1.24694e10			−0.759128
$359$			4.28333e9i			0.257872i	0.991653	+	0.128936i	$0.0411562\pi$
$359$			4.28333e9i			0.257872i	−0.991653	+	0.128936i	$0.958844\pi$
$360$		0			0
$361$	−1.55059e10			−0.912995
$362$			1.60969e10i			0.937363i
$363$	−2.98465e10	−	1.73963e10i	−1.71896	−	1.00192i
$364$	2.13031e8			0.0121349
$365$		0			0
$366$	−8.11011e9	+	1.39143e10i	−0.451962	+	0.775421i
$367$	−1.47834e10			−0.814911			−0.407456	−	0.913225i	$-0.633584\pi$
$367$	−1.47834e10			−0.814911			−0.407456	+	0.913225i	$0.633584\pi$
$368$		−	1.55808e10i		−	0.849569i
$369$	1.64540e10	−	9.31967e9i	0.887494	−	0.502684i
$370$		0			0
$371$		−	3.07569e10i		−	1.62348i
$372$	−3.53296e9	−	2.05922e9i	−0.184487	−	0.107530i
$373$	−9.06733e9			−0.468429			−0.234215	−	0.972185i	$-0.575252\pi$
$373$	−9.06733e9			−0.468429			−0.234215	+	0.972185i	$0.575252\pi$
$374$			3.37755e10i			1.72629i
$375$		0			0
$376$	−1.37897e10			−0.689928
$377$			3.03041e8i			0.0150016i
$378$	4.52757e10	+	5.60007e8i	2.21767	+	0.0274300i
$379$	−3.91064e10			−1.89536			−0.947678	−	0.319227i	$-0.896577\pi$
$379$	−3.91064e10			−1.89536			−0.947678	+	0.319227i	$0.896577\pi$
$380$		0			0
$381$	1.99862e10	+	1.16491e10i	0.948482	+	0.552833i
$382$	2.15824e10			1.01355
$383$		−	1.25913e10i		−	0.585162i	−0.956241	−	0.292581i	$-0.905486\pi$
$383$		−	1.25913e10i		−	0.585162i	0.956241	−	0.292581i	$-0.0945140\pi$
$384$	−1.32006e10	+	2.26480e10i	−0.607112	+	1.04161i
$385$		0			0
$386$			3.01487e10i			1.35806i
$387$	−3.80214e9	−	6.71272e9i	−0.169506	−	0.299264i
$388$	8.85653e9			0.390784
$389$			1.05903e10i			0.462497i	0.972895	+	0.231249i	$0.0742811\pi$
$389$			1.05903e10i			0.462497i	−0.972895	+	0.231249i	$0.925719\pi$
$390$		0			0
$391$	−1.44062e10			−0.616371
$392$		−	5.28466e10i		−	2.23806i
$393$	−3.94334e9	+	6.76550e9i	−0.165308	+	0.283615i
$394$	1.56840e10			0.650836
$395$		0			0
$396$	1.09694e10	−	6.21315e9i	0.446068	−	0.252657i
$397$	−2.97468e10			−1.19751			−0.598753	−	0.800933i	$-0.704337\pi$
$397$	−2.97468e10			−1.19751			−0.598753	+	0.800933i	$0.704337\pi$
$398$		−	1.27705e10i		−	0.508950i
$399$	−1.25806e10	−	7.33274e9i	−0.496375	−	0.289317i
$400$		0			0
$401$		−	2.31791e10i		−	0.896437i	−0.893924	−	0.448219i	$-0.852059\pi$
$401$		−	2.31791e10i		−	0.896437i	0.893924	−	0.448219i	$-0.147941\pi$
$402$	1.35523e10	−	2.32514e10i	0.518931	−	0.890318i
$403$	−3.99171e8			−0.0151335
$404$			6.54388e9i			0.245646i
$405$		0			0
$406$	−4.30223e10			−1.58340
$407$			8.89637e9i			0.324217i
$408$	1.68154e10	+	9.80102e9i	0.606829	+	0.353697i
$409$	2.09807e10			0.749769			0.374885	−	0.927071i	$-0.377682\pi$
$409$	2.09807e10			0.749769			0.374885	+	0.927071i	$0.377682\pi$
$410$		0			0
$411$	7.52379e9	−	1.29084e10i	0.263675	−	0.452382i
$412$	−7.04639e9			−0.244556
$413$		−	6.86875e10i		−	2.36090i
$414$	1.15882e10	+	2.04591e10i	0.394470	+	0.696442i
$415$		0			0
$416$		−	3.61904e8i		−	0.0120843i
$417$	−8.15424e8	−	4.75278e8i	−0.0269674	−	0.0157182i
$418$	−1.77285e10			−0.580720
$419$		−	2.02730e10i		−	0.657752i	−0.944373	−	0.328876i	$-0.893330\pi$
$419$		−	2.02730e10i		−	0.657752i	0.944373	−	0.328876i	$-0.106670\pi$
$420$		0			0
$421$	−3.59575e9			−0.114462			−0.0572310	−	0.998361i	$-0.518227\pi$
$421$	−3.59575e9			−0.114462			−0.0572310	+	0.998361i	$0.518227\pi$
$422$			5.74059e10i			1.81012i
$423$	2.39933e10	−	1.35900e10i	0.749425	−	0.424481i
$424$	−2.15784e10			−0.667659
$425$		0			0
$426$	−2.49490e10	−	1.45418e10i	−0.757556	−	0.441550i
$427$	−5.10409e10			−1.53535
$428$			1.48457e10i			0.442409i
$429$	6.19687e8	−	1.06318e9i	0.0182955	−	0.0313891i
$430$		0			0
$431$			1.22711e10i			0.355610i	0.984066	+	0.177805i	$0.0568996\pi$
$431$			1.22711e10i			0.355610i	−0.984066	+	0.177805i	$0.943100\pi$
$432$	5.20604e8	−	4.20900e10i	0.0149476	−	1.20849i
$433$	5.23052e8			0.0148797			0.00743983	−	0.999972i	$-0.497632\pi$
$433$	5.23052e8			0.0148797			0.00743983	+	0.999972i	$0.497632\pi$
$434$		−	5.66697e10i		−	1.59732i
$435$		0			0
$436$	−1.23359e10			−0.341371
$437$		−	7.56170e9i		−	0.207345i
$438$	−2.33227e10	+	4.00142e10i	−0.633698	+	1.08722i
$439$	5.03940e10			1.35682			0.678408	−	0.734686i	$-0.262670\pi$
$439$	5.03940e10			1.35682			0.678408	+	0.734686i	$0.262670\pi$
$440$		0			0
$441$	5.20812e10	+	9.19499e10i	1.37698	+	2.43107i
$442$	−8.00704e8			−0.0209789
$443$			4.23959e10i			1.10080i	0.834901	+	0.550401i	$0.185525\pi$
$443$			4.23959e10i			1.10080i	−0.834901	+	0.550401i	$0.814475\pi$
$444$	−1.86665e9	−	1.08800e9i	−0.0480321	−	0.0279960i
$445$		0			0
$446$		−	6.70381e10i		−	1.69427i
$447$	1.46177e10	−	2.50793e10i	0.366143	−	0.628182i
$448$	−4.34487e10			−1.07861
$449$			1.38365e9i			0.0340441i	0.999855	+	0.0170221i	$0.00541855\pi$
$449$			1.38365e9i			0.0340441i	−0.999855	+	0.0170221i	$0.994581\pi$
$450$		0			0
$451$	7.29630e10			1.76358
$452$		−	1.49681e10i		−	0.358603i
$453$	−1.12353e10	−	6.54861e9i	−0.266804	−	0.155509i
$454$	1.04134e10			0.245114
$455$		0			0
$456$	−5.14448e9	+	8.82627e9i	−0.118982	+	0.204135i
$457$	6.39577e10			1.46632			0.733159	−	0.680057i	$-0.238045\pi$
$457$	6.39577e10			1.46632			0.733159	+	0.680057i	$0.238045\pi$
$458$			5.36245e10i			1.21871i
$459$	−3.89169e10	−	4.81357e8i	−0.876773	−	0.0108447i
$460$		0			0
$461$		−	4.34582e10i		−	0.962206i	−0.876664	−	0.481103i	$-0.840236\pi$
$461$		−	4.34582e10i		−	0.962206i	0.876664	−	0.481103i	$-0.159764\pi$
$462$	1.50939e11	+	8.79761e10i	3.31308	+	1.93106i
$463$	1.95845e10			0.426175			0.213088	−	0.977033i	$-0.431648\pi$
$463$	1.95845e10			0.426175			0.213088	+	0.977033i	$0.431648\pi$
$464$			3.99952e10i			0.862851i
$465$		0			0
$466$	3.85638e10			0.817780
$467$			6.63498e10i			1.39499i	0.716588	+	0.697497i	$0.245703\pi$
$467$			6.63498e10i			1.39499i	−0.716588	+	0.697497i	$0.754297\pi$
$468$	1.47293e8	+	2.60048e8i	0.00307043	+	0.00542088i
$469$	8.52915e10			1.76285
$470$		0			0
$471$	−1.82152e10	−	1.06169e10i	−0.370126	−	0.215732i
$472$	−4.81896e10			−0.970924
$473$		−	2.97667e10i		−	0.594684i
$474$	−1.21369e9	+	2.08230e9i	−0.0240433	+	0.0412505i
$475$		0			0
$476$		−	2.59961e10i		−	0.506384i
$477$	3.75451e10	−	2.12658e10i	0.725236	−	0.410780i
$478$	−7.19769e10			−1.37874
$479$		−	8.73284e10i		−	1.65887i	−0.558600	−	0.829437i	$-0.688661\pi$
$479$		−	8.73284e10i		−	1.65887i	0.558600	−	0.829437i	$-0.311339\pi$
$480$		0			0
$481$	−2.10904e8			−0.00394007
$482$		−	1.22900e9i		−	0.0227701i
$483$	−3.75243e10	+	6.43795e10i	−0.689483	+	1.18293i
$484$	3.23720e10			0.589913
$485$		0			0
$486$	3.06208e10	+	5.56554e10i	0.548872	+	0.997613i
$487$	−2.65378e10			−0.471790			−0.235895	−	0.971778i	$-0.575802\pi$
$487$	−2.65378e10			−0.471790			−0.235895	+	0.971778i	$0.575802\pi$
$488$			3.58091e10i			0.631414i
$489$	−5.05484e10	−	2.94626e10i	−0.884040	−	0.515272i
$490$		0			0
$491$			6.17958e10i			1.06324i	0.846982	+	0.531622i	$0.178417\pi$
$491$			6.17958e10i			1.06324i	−0.846982	+	0.531622i	$0.821583\pi$
$492$	−8.92313e9	+	1.53092e10i	−0.152285	+	0.261272i
$493$	3.69800e10			0.626007
$494$		−	4.20284e8i		−	0.00705724i
$495$		0			0
$496$	−5.26823e10			−0.870438
$497$		−	9.15186e10i		−	1.49997i
$498$	5.00781e10	+	2.91886e10i	0.814199	+	0.474565i
$499$	−1.22816e10			−0.198086			−0.0990429	−	0.995083i	$-0.531578\pi$
$499$	−1.22816e10			−0.198086			−0.0990429	+	0.995083i	$0.531578\pi$
$500$		0			0
$501$	5.51623e10	−	9.46406e10i	0.875571	−	1.50220i
$502$	−6.11697e10			−0.963211
$503$		−	6.89562e10i		−	1.07721i	−0.842558	−	0.538606i	$-0.818951\pi$
$503$		−	6.89562e10i		−	1.07721i	0.842558	−	0.538606i	$-0.181049\pi$
$504$	8.75992e10	−	4.96169e10i	1.35762	−	0.768967i
$505$		0			0
$506$			9.07231e10i			1.38394i
$507$	−5.70600e10	−	3.32580e10i	−0.863575	−	0.503344i
$508$	−2.16773e10			−0.325500
$509$		−	8.72703e10i		−	1.30016i	−0.759868	−	0.650078i	$-0.774736\pi$
$509$		−	8.72703e10i		−	1.30016i	0.759868	−	0.650078i	$-0.225264\pi$
$510$		0			0
$511$	−1.46781e11			−2.15272
$512$			1.87651e10i			0.273068i
$513$	2.52660e8	−	2.04272e10i	0.00364811	−	0.294944i
$514$	1.07342e10			0.153786
$515$		0			0
$516$	6.24570e9	+	3.64037e9i	0.0881012	+	0.0513507i
$517$	1.06395e11			1.48922
$518$		−	2.99417e10i		−	0.415869i
$519$	−4.31861e10	+	7.40933e10i	−0.595215	+	1.02120i
$520$		0			0
$521$		−	2.40313e10i		−	0.326156i	−0.986613	−	0.163078i	$-0.947858\pi$
$521$		−	2.40313e10i		−	0.326156i	0.986613	−	0.163078i	$-0.0521423\pi$
$522$	−2.97464e10	−	5.25175e10i	−0.400638	−	0.707331i
$523$	−5.40043e10			−0.721808			−0.360904	−	0.932603i	$-0.617532\pi$
$523$	−5.40043e10			−0.721808			−0.360904	+	0.932603i	$0.617532\pi$
$524$		−	7.33798e9i		−	0.0973311i
$525$		0			0
$526$	1.72502e10			0.225347
$527$			4.87106e10i			0.631512i
$528$	8.17859e10	−	1.40318e11i	1.05231	−	1.80542i
$529$	3.96150e10			0.505868
$530$		0			0
$531$	8.38471e10	−	4.74917e10i	1.05465	−	0.597365i
$532$	1.36451e10			0.170346
$533$			1.72971e9i			0.0214321i
$534$	2.41756e10	+	1.40910e10i	0.297312	+	0.173292i
$535$		0			0
$536$		−	5.98386e10i		−	0.724974i
$537$	2.79179e10	−	4.78982e10i	0.335727	−	0.575999i
$538$	9.10004e10			1.08621
$539$			4.07740e11i			4.83090i
$540$		0			0
$541$	8.76711e9			0.102345			0.0511726	−	0.998690i	$-0.483704\pi$
$541$	8.76711e9			0.102345			0.0511726	+	0.998690i	$0.483704\pi$
$542$		−	9.61887e10i		−	1.11462i
$543$	−6.18321e10	−	3.60395e10i	−0.711238	−	0.414552i
$544$	−4.41630e10			−0.504270
$545$		0			0
$546$	−2.08562e9	+	3.57825e9i	−0.0234674	+	0.0402625i
$547$	−7.10847e10			−0.794011			−0.397006	−	0.917816i	$-0.629951\pi$
$547$	−7.10847e10			−0.794011			−0.397006	+	0.917816i	$0.629951\pi$
$548$			1.40007e10i			0.155248i
$549$	−3.52905e10	−	6.23058e10i	−0.388480	−	0.685866i
$550$		0			0
$551$			1.94105e10i			0.210587i
$552$	4.51672e10	+	2.63262e10i	0.486482	+	0.283551i
$553$	−7.63834e9			−0.0816768
$554$		−	1.70786e11i		−	1.81307i
$555$		0			0
$556$	8.84423e8			0.00925467
$557$		−	4.95865e10i		−	0.515161i	−0.966257	−	0.257580i	$-0.917075\pi$
$557$		−	4.95865e10i		−	0.515161i	0.966257	−	0.257580i	$-0.0829252\pi$
$558$	6.91769e10	−	3.91824e10i	0.713550	−	0.404160i
$559$	7.05669e8			0.00722693
$560$		0			0
$561$	−1.29740e11	−	7.56202e10i	−1.30985	−	0.763460i
$562$	−2.11466e11			−2.11980
$563$			1.18225e11i			1.17673i	0.808595	+	0.588366i	$0.200228\pi$
$563$			1.18225e11i			1.17673i	−0.808595	+	0.588366i	$0.799772\pi$
$564$	−1.30118e10	+	2.23240e10i	−0.128594	+	0.220625i
$565$		0			0
$566$			3.01274e10i			0.293560i
$567$	−1.03519e11	+	1.72661e11i	−1.00159	+	1.67056i
$568$	−6.42074e10			−0.616867
$569$			4.39706e10i			0.419482i	0.977757	+	0.209741i	$0.0672620\pi$
$569$			4.39706e10i			0.419482i	−0.977757	+	0.209741i	$0.932738\pi$
$570$		0			0
$571$	−1.48977e11			−1.40144			−0.700722	−	0.713434i	$-0.747139\pi$
$571$	−1.48977e11			−1.40144			−0.700722	+	0.713434i	$0.747139\pi$
$572$			1.15315e9i			0.0107721i
$573$	−4.83211e10	+	8.29035e10i	−0.448248	+	0.769049i
$574$	−2.45564e11			−2.26213
$575$		0			0
$576$	−3.00411e10	−	5.30380e10i	−0.272914	−	0.481833i
$577$	1.29323e10			0.116674			0.0583368	−	0.998297i	$-0.481420\pi$
$577$	1.29323e10			0.116674			0.0583368	+	0.998297i	$0.481420\pi$
$578$		−	2.93760e10i		−	0.263197i
$579$	−1.15809e11	−	6.75002e10i	−1.03045	−	0.600608i
$580$		0			0
$581$			1.83698e11i			1.61213i
$582$	−8.67075e10	+	1.48762e11i	−0.755727	+	1.29658i
$583$	1.66489e11			1.44115
$584$			1.02978e11i			0.885309i
$585$		0			0
$586$	1.74879e11			1.48302
$587$		−	8.37926e10i		−	0.705754i	−0.935670	−	0.352877i	$-0.885203\pi$
$587$		−	8.37926e10i		−	0.705754i	0.935670	−	0.352877i	$-0.114797\pi$
$588$	−8.55527e10	−	4.98653e10i	−0.715689	−	0.417147i
$589$	−2.55678e10			−0.212438
$590$		0			0
$591$	−3.51150e10	+	6.02460e10i	−0.287834	+	0.493831i
$592$	−2.78349e10			−0.226623
$593$			3.46484e10i			0.280198i	0.990138	+	0.140099i	$0.0447421\pi$
$593$			3.46484e10i			0.280198i	−0.990138	+	0.140099i	$0.955258\pi$
$594$	−3.03135e9	+	2.45079e11i	−0.0243495	+	1.96862i
$595$		0			0
$596$			2.72015e10i			0.215579i
$597$	4.90546e10	+	2.85920e10i	0.386173	+	0.225085i
$598$	−2.15074e9			−0.0168184
$599$		−	2.01526e10i		−	0.156539i	−0.996932	−	0.0782696i	$-0.975060\pi$
$599$		−	2.01526e10i		−	0.156539i	0.996932	−	0.0782696i	$-0.0249395\pi$
$600$		0			0
$601$	4.52186e10			0.346593			0.173296	−	0.984870i	$-0.444558\pi$
$601$	4.52186e10			0.346593			0.173296	+	0.984870i	$0.444558\pi$
$602$			1.00183e11i			0.762794i
$603$	5.89720e10	+	1.04116e11i	0.446043	+	0.787493i
$604$	1.21860e10			0.0915616
$605$		0			0
$606$	−1.09917e11	−	6.40661e10i	−0.815030	−	0.475048i
$607$	2.11693e11			1.55938			0.779689	−	0.626167i	$-0.215377\pi$
$607$	2.11693e11			1.55938			0.779689	+	0.626167i	$0.215377\pi$
$608$		−	2.31808e10i		−	0.169635i
$609$	9.63231e10	−	1.65259e11i	0.700263	−	1.20143i
$610$		0			0
$611$			2.52227e9i			0.0180979i
$612$	3.17335e10	−	1.79741e10i	0.226210	−	0.128127i
$613$	1.83429e11			1.29905			0.649527	−	0.760338i	$-0.274967\pi$
$613$	1.83429e11			1.29905			0.649527	+	0.760338i	$0.274967\pi$
$614$		−	1.59246e11i		−	1.12046i
$615$		0			0
$616$	3.88447e11			2.69780
$617$			1.86844e11i			1.28925i	0.764497	+	0.644627i	$0.222988\pi$
$617$			1.86844e11i			1.28925i	−0.764497	+	0.644627i	$0.777012\pi$
$618$	6.89857e10	−	1.18357e11i	0.472939	−	0.811411i
$619$	−2.00363e11			−1.36475			−0.682376	−	0.731001i	$-0.739053\pi$
$619$	−2.00363e11			−1.36475			−0.682376	+	0.731001i	$0.739053\pi$
$620$		0			0
$621$	−1.04533e11	−	1.29296e9i	−0.702891	−	0.00869395i
$622$	2.28511e11			1.52667
$623$			8.86817e10i			0.588684i
$624$	3.32648e9	+	1.93887e9i	0.0219405	+	0.0127883i
$625$		0			0
$626$		−	5.61124e10i		−	0.365394i
$627$	3.96925e10	−	6.80995e10i	0.256825	−	0.440629i
$628$	1.97565e10			0.127020
$629$			2.57365e10i			0.164417i
$630$		0			0
$631$	−1.29595e11			−0.817469			−0.408735	−	0.912653i	$-0.634030\pi$
$631$	−1.29595e11			−0.817469			−0.408735	+	0.912653i	$0.634030\pi$
$632$			5.35889e9i			0.0335897i
$633$	−2.20510e11	−	1.28527e11i	−1.37345	−	0.800531i
$634$	−5.12809e10			−0.317394
$635$		0			0
$636$	−2.03610e10	+	3.49329e10i	−0.124443	+	0.213504i
$637$	−9.66616e9			−0.0587079
$638$		−	2.32882e11i		−	1.40557i
$639$	1.11717e11	−	6.32775e10i	0.670064	−	0.379530i
$640$		0			0
$641$			1.41802e11i			0.839945i	0.907537	+	0.419973i	$0.137960\pi$
$641$			1.41802e11i			0.839945i	−0.907537	+	0.419973i	$0.862040\pi$
$642$	−2.49361e11	−	1.45342e11i	−1.46787	−	0.855563i
$643$	2.74292e10			0.160461			0.0802305	−	0.996776i	$-0.474434\pi$
$643$	2.74292e10			0.160461			0.0802305	+	0.996776i	$0.474434\pi$
$644$		−	6.98271e10i		−	0.405958i
$645$		0			0
$646$	−5.12870e10			−0.294495
$647$			2.68855e11i			1.53427i	0.641486	+	0.767134i	$0.278318\pi$
$647$			2.68855e11i			1.53427i	−0.641486	+	0.767134i	$0.721682\pi$
$648$	1.21135e11	+	7.26268e10i	0.687021	+	0.411905i
$649$	3.71809e11			2.09576
$650$		0			0
$651$	2.17682e11	+	1.26878e11i	1.21199	+	0.706420i
$652$	5.48257e10			0.303385
$653$			1.86797e11i			1.02735i	0.857985	+	0.513674i	$0.171716\pi$
$653$			1.86797e11i			1.02735i	−0.857985	+	0.513674i	$0.828284\pi$
$654$	1.20772e11	−	2.07205e11i	0.660167	−	1.13263i
$655$		0			0
$656$			2.28286e11i			1.23272i
$657$	−1.01487e11	−	1.79176e11i	−0.544689	−	0.961655i
$658$	−3.58083e11			−1.91021
$659$		−	3.39105e10i		−	0.179801i	−0.995951	−	0.0899006i	$-0.971345\pi$
$659$		−	3.39105e10i		−	0.179801i	0.995951	−	0.0899006i	$-0.0286549\pi$
$660$		0			0
$661$	−2.09742e11			−1.09870			−0.549351	−	0.835592i	$-0.685125\pi$
$661$	−2.09742e11			−1.09870			−0.549351	+	0.835592i	$0.685125\pi$
$662$		−	3.81582e11i		−	1.98681i
$663$	1.79270e9	−	3.07570e9i	0.00927801	−	0.0159181i
$664$	1.28878e11			0.662991
$665$		0			0
$666$	3.65499e10	−	2.07022e10i	0.185776	−	0.105225i
$667$	9.93308e10			0.501857
$668$			1.02649e11i			0.515523i
$669$	2.57510e11	+	1.50092e11i	1.28555	+	0.749297i
$670$		0			0
$671$		−	2.76287e11i		−	1.36292i
$672$	−1.15033e11	+	1.97359e11i	−0.564086	+	0.967788i
$673$	−5.94010e10			−0.289557			−0.144778	−	0.989464i	$-0.546247\pi$
$673$	−5.94010e10			−0.289557			−0.144778	+	0.989464i	$0.546247\pi$
$674$		−	3.49295e8i		−	0.00169259i
$675$		0			0
$676$	6.18883e10			0.296362
$677$		−	1.20914e11i		−	0.575602i	−0.957690	−	0.287801i	$-0.907076\pi$
$677$		−	1.20914e11i		−	0.575602i	0.957690	−	0.287801i	$-0.0929242\pi$
$678$	2.51418e11	+	1.46542e11i	1.18981	+	0.693493i
$679$	−5.45693e11			−2.56725
$680$		0			0
$681$	−2.33146e10	+	4.00004e10i	−0.108403	+	0.185984i
$682$	3.06756e11			1.41793
$683$		−	4.27245e11i		−	1.96333i	−0.190605	−	0.981667i	$-0.561045\pi$
$683$		−	4.27245e11i		−	1.96333i	0.190605	−	0.981667i	$-0.438955\pi$
$684$	9.43448e9	+	1.66567e10i	0.0431016	+	0.0760964i
$685$		0			0
$686$		−	8.81125e11i		−	3.97870i
$687$	−2.05985e11	−	1.20060e11i	−0.924716	−	0.538981i
$688$	9.31338e10			0.415675
$689$			3.94689e9i			0.0175137i
$690$		0			0
$691$	−1.15810e11			−0.507964			−0.253982	−	0.967209i	$-0.581740\pi$
$691$	−1.15810e11			−0.507964			−0.253982	+	0.967209i	$0.581740\pi$
$692$		−	8.03629e10i		−	0.350454i
$693$	−6.75875e11	+	3.82821e11i	−2.93045	+	1.65983i
$694$	2.11900e11			0.913468
$695$		0			0
$696$	−1.15942e11	−	6.75781e10i	−0.494088	−	0.287985i
$697$	2.11076e11			0.894350
$698$			5.27077e10i			0.222051i
$699$	−8.63409e10	+	1.48133e11i	−0.361666	+	0.620502i
$700$		0			0
$701$			5.27372e10i			0.218396i	0.994020	+	0.109198i	$0.0348283\pi$
$701$			5.27372e10i			0.218396i	−0.994020	+	0.109198i	$0.965172\pi$
$702$	−5.81002e9	−	7.18632e7i	−0.0239238	−	0.000295909i
$703$	−1.35089e10			−0.0553093
$704$		−	2.35190e11i		−	0.957476i
$705$		0			0
$706$	4.97619e11			2.00299
$707$		−	4.03199e11i		−	1.61377i
$708$	−4.54710e10	+	7.80136e10i	−0.180968	+	0.310482i
$709$	4.17074e11			1.65055			0.825275	−	0.564731i	$-0.191020\pi$
$709$	4.17074e11			1.65055			0.825275	+	0.564731i	$0.191020\pi$
$710$		0			0
$711$	−5.28128e9	−	9.32416e9i	−0.0206662	−	0.0364864i
$712$	6.22171e10			0.242097
$713$			1.30840e11i			0.506270i
$714$	4.36653e11	+	2.54508e11i	1.68013	+	0.979282i
$715$		0			0
$716$			5.19512e10i			0.197671i
$717$	1.61150e11	−	2.76481e11i	0.609752	−	1.04614i
$718$	7.80345e10			0.293622
$719$			2.58351e11i			0.966706i	0.875426	+	0.483353i	$0.160581\pi$
$719$			2.58351e11i			0.966706i	−0.875426	+	0.483353i	$0.839419\pi$
$720$		0			0
$721$	4.34161e11			1.60661
$722$			2.82489e11i			1.03957i
$723$	4.72090e9	+	2.75162e9i	0.0172771	+	0.0100701i
$724$	6.70642e10			0.244082
$725$		0			0
$726$	−3.16929e11	+	5.43748e11i	−1.14082	+	1.95727i
$727$	−1.88297e9			−0.00674072			−0.00337036	−	0.999994i	$-0.501073\pi$
$727$	−1.88297e9			−0.00674072			−0.00337036	+	0.999994i	$0.501073\pi$
$728$			9.20879e9i			0.0327852i
$729$	−2.82343e11	−	6.98558e9i	−0.999694	−	0.0247339i
$730$		0			0
$731$		−	8.61126e10i		−	0.301576i
$732$	5.79710e10	+	3.37890e10i	0.201914	+	0.117688i
$733$	−3.26918e11			−1.13246			−0.566230	−	0.824247i	$-0.691599\pi$
$733$	−3.26918e11			−1.13246			−0.566230	+	0.824247i	$0.691599\pi$
$734$			2.69327e11i			0.927887i
$735$		0			0
$736$	−1.18625e11			−0.404263
$737$			4.61687e11i			1.56487i
$738$	−1.69787e11	−	2.99761e11i	−0.572374	−	1.01053i
$739$	−1.66227e11			−0.557346			−0.278673	−	0.960386i	$-0.589894\pi$
$739$	−1.66227e11			−0.557346			−0.278673	+	0.960386i	$0.589894\pi$
$740$		0			0
$741$	1.61441e9	+	9.40977e8i	0.00535478	+	0.00312109i
$742$	−5.60335e11			−1.84855
$743$		−	2.38178e11i		−	0.781531i	−0.920490	−	0.390766i	$-0.872210\pi$
$743$		−	2.38178e11i		−	0.781531i	0.920490	−	0.390766i	$-0.127790\pi$
$744$	8.90149e10	−	1.52721e11i	0.290517	−	0.498433i
$745$		0			0
$746$			1.65190e11i			0.533370i
$747$	−2.24241e11	+	1.27012e11i	−0.720165	+	0.407908i
$748$	1.40718e11			0.449514
$749$		−	9.14711e11i		−	2.90641i
$750$		0			0
$751$	−2.88947e11			−0.908361			−0.454181	−	0.890910i	$-0.650068\pi$
$751$	−2.88947e11			−0.908361			−0.454181	+	0.890910i	$0.650068\pi$
$752$			3.32888e11i			1.04094i
$753$	1.36953e11	−	2.34968e11i	0.425984	−	0.730850i
$754$	5.52086e9			0.0170813
$755$		0			0
$756$	2.33315e9	−	1.88631e11i	0.00714258	−	0.577466i
$757$	−8.49379e9			−0.0258653			−0.0129327	−	0.999916i	$-0.504117\pi$
$757$	−8.49379e9			−0.0258653			−0.0129327	+	0.999916i	$0.504117\pi$
$758$			7.12447e11i			2.15812i
$759$	−3.48490e11	−	2.03121e11i	−1.05008	−	0.612051i
$760$		0			0
$761$		−	2.86717e11i		−	0.854898i	−0.904039	−	0.427449i	$-0.859412\pi$
$761$		−	2.86717e11i		−	0.854898i	0.904039	−	0.427449i	$-0.140588\pi$
$762$	2.12226e11	−	3.64111e11i	0.629476	−	1.07998i
$763$	7.60075e11			2.24263
$764$		−	8.99185e10i		−	0.263922i
$765$		0			0
$766$	−2.29391e11			−0.666286
$767$			8.81435e9i			0.0254688i
$768$	2.46166e11	+	1.43480e11i	0.707592	+	0.412427i
$769$	1.37170e11			0.392242			0.196121	−	0.980580i	$-0.437166\pi$
$769$	1.37170e11			0.392242			0.196121	+	0.980580i	$0.437166\pi$
$770$		0			0
$771$	−2.40328e10	+	4.12326e10i	−0.0680123	+	0.116687i
$772$	1.25608e11			0.353629
$773$		−	5.00450e11i		−	1.40166i	−0.713328	−	0.700831i	$-0.752813\pi$
$773$		−	5.00450e11i		−	1.40166i	0.713328	−	0.700831i	$-0.247187\pi$
$774$	−1.22294e11	+	6.92681e10i	−0.340753	+	0.193005i
$775$		0			0
$776$			3.82846e11i			1.05579i
$777$	1.15013e11	+	6.70367e10i	0.315547	+	0.183920i
$778$	1.92936e11			0.526616
$779$			1.10792e11i			0.300856i
$780$		0			0
$781$	4.95395e11			1.33152
$782$			2.62454e11i			0.701822i
$783$	2.68332e11	+	3.31896e9i	0.713881	+	0.00882988i
$784$	−1.27573e12			−3.37673
$785$		0			0
$786$	1.23255e11	+	7.18405e10i	0.322935	+	0.188226i
$787$	3.86758e11			1.00818			0.504092	−	0.863650i	$-0.331827\pi$
$787$	3.86758e11			1.00818			0.504092	+	0.863650i	$0.331827\pi$
$788$		−	6.53439e10i		−	0.169473i
$789$	−3.86217e10	+	6.62623e10i	−0.0996605	+	0.170985i
$790$		0			0
$791$			9.22258e11i			2.35584i
$792$	2.68579e11	+	4.74179e11i	0.682608	+	1.20515i
$793$	6.54985e9			0.0165630
$794$			5.41932e11i			1.36352i
$795$		0			0
$796$	−5.32054e10			−0.132527
$797$		−	4.69718e11i		−	1.16414i	−0.813140	−	0.582068i	$-0.802244\pi$
$797$		−	4.69718e11i		−	1.16414i	0.813140	−	0.582068i	$-0.197756\pi$
$798$	−1.33589e11	+	2.29196e11i	−0.329427	+	0.565191i
$799$	3.07792e11			0.755214
$800$		0			0
$801$	−1.08254e11	+	6.13161e10i	−0.262975	+	0.148951i
$802$	−4.22282e11			−1.02072
$803$		−	7.94534e11i		−	1.91095i
$804$	−9.68720e10	−	5.64628e10i	−0.231832	−	0.135126i
$805$		0			0
$806$			7.27216e9i			0.0172315i
$807$	−2.03742e11	+	3.49555e11i	−0.480381	+	0.824178i
$808$	−2.82876e11			−0.663667
$809$			6.02770e11i			1.40721i	0.710594	+	0.703603i	$0.248427\pi$
$809$			6.02770e11i			1.40721i	−0.710594	+	0.703603i	$0.751573\pi$
$810$		0			0
$811$	−2.69496e11			−0.622973			−0.311487	−	0.950251i	$-0.600827\pi$
$811$	−2.69496e11			−0.622973			−0.311487	+	0.950251i	$0.600827\pi$
$812$			1.79243e11i			0.412305i
$813$	3.69484e11	+	2.15358e11i	0.845734	+	0.492945i
$814$	1.62076e11			0.369165
$815$		0			0
$816$	2.36600e11	−	4.05929e11i	0.533647	−	0.915566i
$817$	4.51998e10			0.101449
$818$		−	3.82231e11i		−	0.853715i
$819$	−9.07543e9	−	1.60228e10i	−0.0201712	−	0.0356125i
$820$		0			0
$821$		−	4.19517e11i		−	0.923372i	−0.887044	−	0.461686i	$-0.847245\pi$
$821$		−	4.19517e11i		−	0.923372i	0.887044	−	0.461686i	$-0.152755\pi$
$822$	−2.35168e11	−	1.37070e11i	−0.515098	−	0.300230i
$823$	−6.29847e11			−1.37289			−0.686445	−	0.727182i	$-0.740830\pi$
$823$	−6.29847e11			−1.37289			−0.686445	+	0.727182i	$0.740830\pi$
$824$		−	3.04598e11i		−	0.660720i
$825$		0			0
$826$	−1.25136e12			−2.68820
$827$		−	6.51690e10i		−	0.139322i	−0.997571	−	0.0696609i	$-0.977808\pi$
$827$		−	6.51690e10i		−	0.139322i	0.997571	−	0.0696609i	$-0.0221917\pi$
$828$	8.52383e10	−	4.82797e10i	0.181348	−	0.102717i
$829$	−4.90689e11			−1.03893			−0.519467	−	0.854490i	$-0.673870\pi$
$829$	−4.90689e11			−1.03893			−0.519467	+	0.854490i	$0.673870\pi$
$830$		0			0
$831$	6.56032e11	+	3.82375e11i	1.37569	+	0.801836i
$832$	5.57557e9			0.0116358
$833$			1.17956e12i			2.44985i
$834$	−8.65870e9	+	1.48555e10i	−0.0178973	+	0.0307061i
$835$		0			0
$836$			7.38619e10i			0.151215i
$837$	−4.37178e9	+	3.53451e11i	−0.00890751	+	0.720158i
$838$	−3.69337e11			−0.748940
$839$			7.09436e10i			0.143174i	0.997434	+	0.0715872i	$0.0228064\pi$
$839$			7.09436e10i			0.143174i	−0.997434	+	0.0715872i	$0.977194\pi$
$840$		0			0
$841$	2.45269e11			0.490296
$842$			6.55080e10i			0.130331i
$843$	4.73454e11	−	8.12294e11i	0.937491	−	1.60843i
$844$	2.39169e11			0.471341
$845$		0			0
$846$	−2.47585e11	−	4.37114e11i	−0.483329	−	0.853323i
$847$	−1.99459e12			−3.87543
$848$			5.20909e11i			1.00734i
$849$	−1.15727e11	−	6.74526e10i	−0.222743	−	0.129828i
$850$		0			0
$851$			6.91299e10i			0.131810i
$852$	−6.05852e10	+	1.03945e11i	−0.114976	+	0.197262i
$853$	3.32593e11			0.628227			0.314113	−	0.949385i	$-0.398293\pi$
$853$	3.32593e11			0.628227			0.314113	+	0.949385i	$0.398293\pi$
$854$			9.29872e11i			1.74820i
$855$		0			0
$856$	−6.41741e11			−1.19527
$857$		−	8.20366e11i		−	1.52084i	−0.649430	−	0.760421i	$-0.724992\pi$
$857$		−	8.20366e11i		−	1.52084i	0.649430	−	0.760421i	$-0.275008\pi$
$858$	−1.93693e10	−	1.12896e10i	−0.0357408	−	0.0208319i
$859$	1.94847e11			0.357867			0.178933	−	0.983861i	$-0.442735\pi$
$859$	1.94847e11			0.357867			0.178933	+	0.983861i	$0.442735\pi$
$860$		0			0
$861$	5.49796e11	−	9.43273e11i	1.00044	−	1.71642i
$862$	2.23557e11			0.404910
$863$			8.78219e11i			1.58329i	0.610984	+	0.791643i	$0.290774\pi$
$863$			8.78219e11i			1.58329i	−0.610984	+	0.791643i	$0.709226\pi$
$864$	−3.20453e11	−	3.96363e9i	−0.575055	−	0.00711276i
$865$		0			0
$866$		−	9.52905e9i		−	0.0169425i
$867$	1.12840e11	+	6.57701e10i	0.199704	+	0.116400i
$868$	−2.36102e11			−0.415930
$869$		−	4.13467e10i		−	0.0725040i
$870$		0			0
$871$	−1.09451e10			−0.0190172
$872$		−	5.33252e11i		−	0.922287i
$873$	−3.77301e11	−	6.66129e11i	−0.649578	−	1.14684i
$874$	−1.37760e11			−0.236091
$875$		0			0
$876$	1.66710e11	+	9.71689e10i	0.283104	+	0.165010i
$877$	8.56815e10			0.144840			0.0724201	−	0.997374i	$-0.476928\pi$
$877$	8.56815e10			0.144840			0.0724201	+	0.997374i	$0.476928\pi$
$878$		−	9.18087e11i		−	1.54492i
$879$	−3.91538e11	+	6.71753e11i	−0.655872	+	1.12526i
$880$		0			0
$881$		−	1.01082e12i		−	1.67792i	−0.544192	−	0.838961i	$-0.683164\pi$
$881$		−	1.01082e12i		−	1.67792i	0.544192	−	0.838961i	$-0.316836\pi$
$882$	1.67516e12	−	9.48825e11i	2.76810	−	1.56788i
$883$	6.05032e11			0.995257			0.497629	−	0.867390i	$-0.334204\pi$
$883$	6.05032e11			0.995257			0.497629	+	0.867390i	$0.334204\pi$
$884$			3.33596e9i			0.00546275i
$885$		0			0
$886$	7.72376e11			1.25341
$887$			7.07543e11i			1.14303i	0.820591	+	0.571516i	$0.193645\pi$
$887$			7.07543e11i			1.14303i	−0.820591	+	0.571516i	$0.806355\pi$
$888$	4.70314e10	−	8.06907e10i	0.0756374	−	0.129769i
$889$	1.33564e12			2.13837
$890$		0			0
$891$	−9.34623e11	−	5.60355e11i	−1.48295	−	0.889104i
$892$	−2.79300e11			−0.441175
$893$			1.61558e11i			0.254052i
$894$	−4.56899e11	−	2.66309e11i	−0.715271	−	0.416903i
$895$		0			0
$896$			1.51353e12i			2.34833i
$897$	4.81532e9	−	8.26154e9i	0.00743799	−	0.0127612i
$898$	2.52077e10			0.0387639
$899$		−	3.35860e11i		−	0.514185i
$900$		0			0
$901$	4.81638e11			0.730839
$902$		−	1.32925e12i		−	2.00808i
$903$	−3.84827e11	−	2.24300e11i	−0.578781	−	0.337349i
$904$	6.47035e11			0.968845
$905$		0			0
$906$	−1.19304e11	+	2.04687e11i	−0.177069	+	0.303792i
$907$	2.21446e10			0.0327220			0.0163610	−	0.999866i	$-0.494792\pi$
$907$	2.21446e10			0.0327220			0.0163610	+	0.999866i	$0.494792\pi$
$908$		−	4.33851e10i		−	0.0638259i
$909$	4.92187e11	−	2.78779e11i	0.720900	−	0.408324i
$910$		0			0
$911$			7.59165e11i			1.10221i	0.834437	+	0.551103i	$0.185793\pi$
$911$			7.59165e11i			1.10221i	−0.834437	+	0.551103i	$0.814207\pi$
$912$	2.13069e11	+	1.24190e11i	0.307993	+	0.179517i
$913$	−9.94366e11			−1.43108
$914$		−	1.16519e12i		−	1.66960i
$915$		0			0
$916$	2.23415e11			0.317344
$917$			4.52128e11i			0.639416i
$918$	−8.76944e9	+	7.08995e11i	−0.0123481	+	0.998326i
$919$	2.52389e11			0.353841			0.176921	−	0.984225i	$-0.443386\pi$
$919$	2.52389e11			0.353841			0.176921	+	0.984225i	$0.443386\pi$
$920$		0			0
$921$	6.11704e11	+	3.56538e11i	0.850165	+	0.495527i
$922$	−7.91729e11			−1.09560
$923$			1.17442e10i			0.0161814i
$924$	3.66533e11	−	6.28852e11i	0.502835	−	0.862702i
$925$		0			0
$926$		−	3.56794e11i		−	0.485259i
$927$	3.00186e11	+	5.29982e11i	0.406511	+	0.717699i
$928$	3.04504e11			0.410584
$929$		−	8.46609e11i		−	1.13663i	−0.822810	−	0.568316i	$-0.807595\pi$
$929$		−	8.46609e11i		−	1.13663i	0.822810	−	0.568316i	$-0.192405\pi$
$930$		0			0
$931$	−6.19141e11			−0.824121
$932$		−	1.60668e11i		−	0.212944i
$933$	−5.11615e11	+	8.77765e11i	−0.675175	+	1.15838i
$934$	1.20877e12			1.58839
$935$		0			0
$936$	−1.12412e10	+	6.36712e9i	−0.0146457	+	0.00829544i
$937$	1.26898e12			1.64625			0.823126	−	0.567858i	$-0.192228\pi$
$937$	1.26898e12			1.64625			0.823126	+	0.567858i	$0.192228\pi$
$938$		−	1.55386e12i		−	2.00724i
$939$	2.15541e11	+	1.25631e11i	0.277248	+	0.161597i
$940$		0			0
$941$		−	2.79702e11i		−	0.356728i	−0.983965	−	0.178364i	$-0.942920\pi$
$941$		−	2.79702e11i		−	0.356728i	0.983965	−	0.178364i	$-0.0570804\pi$
$942$	−1.93420e11	+	3.31847e11i	−0.245640	+	0.421439i
$943$	5.66963e11			0.716982
$944$			1.16331e12i			1.46490i
$945$		0			0
$946$	−5.42295e11			−0.677128
$947$			1.01819e12i			1.26599i	0.774158	+	0.632993i	$0.218174\pi$
$947$			1.01819e12i			1.26599i	−0.774158	+	0.632993i	$0.781826\pi$
$948$	8.67544e9	+	5.05657e9i	0.0107413	+	0.00626070i
$949$	1.88358e10			0.0232230
$950$		0			0
$951$	1.14813e11	−	1.96983e11i	0.140369	−	0.240827i
$952$	1.12375e12			1.36811
$953$			7.35745e11i			0.891981i	0.895038	+	0.445990i	$0.147148\pi$
$953$			7.35745e11i			0.891981i	−0.895038	+	0.445990i	$0.852852\pi$
$954$	−3.87425e11	−	6.84003e11i	−0.467729	−	0.825780i
$955$		0			0
$956$			2.99876e11i			0.359013i
$957$	8.94557e11	+	5.21402e11i	1.06650	+	0.621620i
$958$	−1.59096e12			−1.88885
$959$		−	8.62647e11i		−	1.01990i
$960$		0			0
$961$	−4.10491e11			−0.481294
$962$			3.84228e9i			0.00448630i
$963$	1.11659e12	−	6.32447e11i	1.29834	−	0.735392i
$964$	−5.12037e9			−0.00592916
$965$		0			0
$966$	1.17288e12	+	6.83624e11i	1.34693	+	0.785071i
$967$	−1.31775e12			−1.50704			−0.753522	−	0.657422i	$-0.771647\pi$
$967$	−1.31775e12			−1.50704			−0.753522	+	0.657422i	$0.771647\pi$
$968$			1.39936e12i			1.59378i
$969$	1.14827e11	−	1.97006e11i	0.130241	−	0.223452i
$970$		0			0
$971$		−	7.14621e11i		−	0.803895i	−0.915663	−	0.401947i	$-0.868334\pi$
$971$		−	7.14621e11i		−	0.803895i	0.915663	−	0.401947i	$-0.131666\pi$
$972$	2.31876e11	−	1.27575e11i	0.259771	−	0.142922i
$973$	−5.44935e10			−0.0607985
$974$			4.83470e11i			0.537198i
$975$		0			0
$976$	8.64444e11			0.952660
$977$		−	3.39820e11i		−	0.372968i	−0.982458	−	0.186484i	$-0.940291\pi$
$977$		−	3.39820e11i		−	0.372968i	0.982458	−	0.186484i	$-0.0597092\pi$
$978$	−5.36756e11	+	9.20899e11i	−0.586707	+	1.00660i
$979$	−4.80039e11			−0.522571
$980$		0			0
$981$	5.25529e11	+	9.27827e11i	0.567441	+	1.00182i
$982$	1.12581e12			1.21065
$983$			1.00970e12i			1.08138i	0.841220	+	0.540692i	$0.181838\pi$
$983$			1.00970e12i			1.08138i	−0.841220	+	0.540692i	$0.818162\pi$
$984$	−6.61779e11	−	3.85725e11i	−0.705883	−	0.411431i
$985$		0			0
$986$		−	6.73709e11i		−	0.712795i
$987$	8.01716e11	−	1.37549e12i	0.844796	−	1.44940i
$988$	−1.75102e9			−0.00183765
$989$		−	2.31304e11i		−	0.241768i
$990$		0			0
$991$	1.10525e12			1.14595			0.572975	−	0.819573i	$-0.305789\pi$
$991$	1.10525e12			1.14595			0.572975	+	0.819573i	$0.305789\pi$
$992$			4.01098e11i			0.414194i
$993$	1.46575e12	+	8.54328e11i	1.50752	+	0.878674i
$994$	−1.66730e12			−1.70792
$995$		0			0
$996$	1.21608e11	−	2.08640e11i	0.123573	−	0.212011i
$997$	−4.00464e11			−0.405306			−0.202653	−	0.979251i	$-0.564956\pi$
$997$	−4.00464e11			−0.405306			−0.202653	+	0.979251i	$0.564956\pi$
$998$			2.23749e11i			0.225548i
$999$	−2.30985e9	+	1.86747e11i	−0.00231911	+	0.187496i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.9.c.e.26.3	✓	10
3.2	odd	2	inner	75.9.c.e.26.8	yes	10
5.2	odd	4		75.9.d.d.74.15		20
5.3	odd	4		75.9.d.d.74.6		20
5.4	even	2		75.9.c.f.26.8	yes	10
15.2	even	4		75.9.d.d.74.5		20
15.8	even	4		75.9.d.d.74.16		20
15.14	odd	2		75.9.c.f.26.3	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.9.c.e.26.3	✓	10	1.1	even	1	trivial
75.9.c.e.26.8	yes	10	3.2	odd	2	inner
75.9.c.f.26.3	yes	10	15.14	odd	2
75.9.c.f.26.8	yes	10	5.4	even	2
75.9.d.d.74.5		20	15.2	even	4
75.9.d.d.74.6		20	5.3	odd	4
75.9.d.d.74.15		20	5.2	odd	4
75.9.d.d.74.16		20	15.8	even	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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	75.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-18.2182i q^{2} +(69.9805 + 40.7889i) q^{3} -75.9021 q^{4} +(743.099 - 1274.92i) q^{6} +4676.68 q^{7} -3281.06i q^{8} +(3233.54 + 5708.85i) q^{9} +O(q^{10})\)	\(q-18.2182i q^{2} +(69.9805 + 40.7889i) q^{3} -75.9021 q^{4} +(743.099 - 1274.92i) q^{6} +4676.68 q^{7} -3281.06i q^{8} +(3233.54 + 5708.85i) q^{9} +25315.1i q^{11} +(-5311.66 - 3095.96i) q^{12} -600.138 q^{13} -85200.7i q^{14} -79205.8 q^{16} +73234.6i q^{17} +(104005. - 58909.2i) q^{18} -38440.3 q^{19} +(327277. + 190757. i) q^{21} +461196. q^{22} +196713. i q^{23} +(133831. - 229610. i) q^{24} +10933.4i q^{26} +(-6572.81 + 531400. i) q^{27} -354970. q^{28} -504953. i q^{29} +665132. q^{31} +603035. i q^{32} +(-1.03258e6 + 1.77157e6i) q^{33} +1.33420e6 q^{34} +(-245432. - 433313. i) q^{36} +351425. q^{37} +700312. i q^{38} +(-41997.9 - 24478.9i) q^{39} -2.88219e6i q^{41} +(3.47524e6 - 5.96238e6i) q^{42} -1.17585e6 q^{43} -1.92147e6i q^{44} +3.58375e6 q^{46} -4.20282e6i q^{47} +(-5.54286e6 - 3.23071e6i) q^{48} +1.61066e7 q^{49} +(-2.98715e6 + 5.12499e6i) q^{51} +45551.7 q^{52} -6.57665e6i q^{53} +(9.68115e6 + 119745. i) q^{54} -1.53445e7i q^{56} +(-2.69007e6 - 1.56794e6i) q^{57} -9.19932e6 q^{58} -1.46872e7i q^{59} -1.09139e7 q^{61} -1.21175e7i q^{62} +(1.51222e7 + 2.66985e7i) q^{63} -9.29049e6 q^{64} +(3.22747e7 + 1.88116e7i) q^{66} +1.82376e7 q^{67} -5.55866e6i q^{68} +(-8.02369e6 + 1.37661e7i) q^{69} -1.95691e7i q^{71} +(1.87311e7 - 1.06094e7i) q^{72} -3.13857e7 q^{73} -6.40233e6i q^{74} +2.91770e6 q^{76} +1.18391e8i q^{77} +(-445962. + 765126. i) q^{78} -1.63328e6 q^{79} +(-2.21352e7 + 3.69196e7i) q^{81} -5.25082e7 q^{82} +3.92795e7i q^{83} +(-2.48410e7 - 1.44788e7i) q^{84} +2.14218e7i q^{86} +(2.05965e7 - 3.53369e7i) q^{87} +8.30604e7 q^{88} +1.89625e7i q^{89} -2.80665e6 q^{91} -1.49309e7i q^{92} +(4.65462e7 + 2.71300e7i) q^{93} -7.65678e7 q^{94} +(-2.45971e7 + 4.22007e7i) q^{96} -1.16684e8 q^{97} -2.93432e8i q^{98} +(-1.44520e8 + 8.18574e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 25 q^{3} - 1554 q^{4} + 2257 q^{6} + 1960 q^{7} - 11207 q^{9}+O(q^{10}) \) 10 * q - 25 * q^3 - 1554 * q^4 + 2257 * q^6 + 1960 * q^7 - 11207 * q^9	\( 10 q - 25 q^{3} - 1554 q^{4} + 2257 q^{6} + 1960 q^{7} - 11207 q^{9} - 5915 q^{12} - 16920 q^{13} + 44634 q^{16} - 224875 q^{18} - 143934 q^{19} + 673428 q^{21} + 818990 q^{22} - 1016859 q^{24} - 260830 q^{27} + 3810100 q^{28} - 3014060 q^{31} - 4677515 q^{33} + 4977146 q^{34} + 4500527 q^{36} + 3016760 q^{37} - 7513282 q^{39} - 4001760 q^{42} + 11747340 q^{43} - 13938636 q^{46} - 14748755 q^{48} + 8953546 q^{49} + 6209287 q^{51} - 38918320 q^{52} - 8886272 q^{54} + 14759525 q^{57} - 48407900 q^{58} + 1520220 q^{61} + 74748240 q^{63} - 4536998 q^{64} + 10465295 q^{66} - 16269290 q^{67} + 11394978 q^{69} + 172231185 q^{72} - 52090170 q^{73} - 29529046 q^{76} + 198205810 q^{78} + 8549896 q^{79} + 22612945 q^{81} - 295714190 q^{82} - 136883292 q^{84} + 318901610 q^{87} - 310673250 q^{88} - 107224264 q^{91} + 79679130 q^{93} + 356118596 q^{94} + 525424001 q^{96} - 402167800 q^{97} - 382421335 q^{99}+O(q^{100}) \) 10 * q - 25 * q^3 - 1554 * q^4 + 2257 * q^6 + 1960 * q^7 - 11207 * q^9 - 5915 * q^12 - 16920 * q^13 + 44634 * q^16 - 224875 * q^18 - 143934 * q^19 + 673428 * q^21 + 818990 * q^22 - 1016859 * q^24 - 260830 * q^27 + 3810100 * q^28 - 3014060 * q^31 - 4677515 * q^33 + 4977146 * q^34 + 4500527 * q^36 + 3016760 * q^37 - 7513282 * q^39 - 4001760 * q^42 + 11747340 * q^43 - 13938636 * q^46 - 14748755 * q^48 + 8953546 * q^49 + 6209287 * q^51 - 38918320 * q^52 - 8886272 * q^54 + 14759525 * q^57 - 48407900 * q^58 + 1520220 * q^61 + 74748240 * q^63 - 4536998 * q^64 + 10465295 * q^66 - 16269290 * q^67 + 11394978 * q^69 + 172231185 * q^72 - 52090170 * q^73 - 29529046 * q^76 + 198205810 * q^78 + 8549896 * q^79 + 22612945 * q^81 - 295714190 * q^82 - 136883292 * q^84 + 318901610 * q^87 - 310673250 * q^88 - 107224264 * q^91 + 79679130 * q^93 + 356118596 * q^94 + 525424001 * q^96 - 402167800 * q^97 - 382421335 * q^99

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