LMFDB - Embedded newform 49.10.c.g.18.3

Error: no document with id 225291966 found in table mf_hecke_traces.

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [49,10,Mod(18,49)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("49.18"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(49, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	49.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [10,-18,-161] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$25.2367559720$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
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} - x^{9} + 430 x^{8} + 61 x^{7} + 146753 x^{6} + 23608 x^{5} + 16136944 x^{4} + 30575648 x^{3} + \cdots + 761760000 $ x^10 - x^9 + 430x^8 + 61x^7 + 146753x^6 + 23608x^5 + 16136944x^4 + 30575648x^3 + 1399072384x^2 + 1034227200x + 761760000
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{3}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 7)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			18.3
Root			$-0.371984 + 0.644295i$ of defining polynomial
Character	$\chi$	$=$	49.18
Dual form			49.10.c.g.30.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.74397 - 4.75269i) q^{2} +(1.70307 - 2.94981i) q^{3} +(240.941 - 417.323i) q^{4} +(828.924 + 1435.74i) q^{5} -18.6927 q^{6} -5454.36 q^{8} +(9835.70 + 17035.9i) q^{9} +(4549.08 - 7879.24i) q^{10} +(-16835.7 + 29160.2i) q^{11} +(-820.681 - 1421.46i) q^{12} -47905.5 q^{13} +5646.87 q^{15} +(-108395. - 187746. i) q^{16} +(-172909. + 299487. i) q^{17} +(53977.7 - 93492.1i) q^{18} +(-202522. - 350778. i) q^{19} +798888. q^{20} +184786. q^{22} +(926736. + 1.60515e6i) q^{23} +(-9289.18 + 16089.3i) q^{24} +(-397666. + 688778. i) q^{25} +(131451. + 227680. i) q^{26} +134047. q^{27} +682809. q^{29} +(-15494.8 - 26837.8i) q^{30} +(-4.54839e6 + 7.87804e6i) q^{31} +(-1.99118e6 + 3.44883e6i) q^{32} +(57344.7 + 99324.0i) q^{33} +1.89782e6 q^{34} +9.47930e6 q^{36} +(7.77984e6 + 1.34751e7i) q^{37} +(-1.11143e6 + 1.92505e6i) q^{38} +(-81586.5 + 141312. i) q^{39} +(-4.52125e6 - 7.83104e6i) q^{40} +2.98719e7 q^{41} +6.28733e6 q^{43} +(8.11281e6 + 1.40518e7i) q^{44} +(-1.63061e7 + 2.82430e7i) q^{45} +(5.08587e6 - 8.80898e6i) q^{46} +(5.16042e6 + 8.93811e6i) q^{47} -738421. q^{48} +4.36473e6 q^{50} +(588952. + 1.02010e6i) q^{51} +(-1.15424e7 + 1.99920e7i) q^{52} +(-3.32218e7 + 5.75419e7i) q^{53} +(-367820. - 637083. i) q^{54} -5.58219e7 q^{55} -1.37964e6 q^{57} +(-1.87361e6 - 3.24518e6i) q^{58} +(3.52902e7 - 6.11245e7i) q^{59} +(1.36056e6 - 2.35657e6i) q^{60} +(-4.21696e7 - 7.30399e7i) q^{61} +4.99225e7 q^{62} -8.91419e7 q^{64} +(-3.97100e7 - 6.87797e7i) q^{65} +(314704. - 545084. i) q^{66} +(1.05869e8 - 1.83370e8i) q^{67} +(8.33217e7 + 1.44317e8i) q^{68} +6.31320e6 q^{69} +2.31588e7 q^{71} +(-5.36475e7 - 9.29202e7i) q^{72} +(1.24284e8 - 2.15266e8i) q^{73} +(4.26952e7 - 7.39503e7i) q^{74} +(1.35451e6 + 2.34608e6i) q^{75} -1.95184e8 q^{76} +895483. q^{78} +(-1.33038e8 - 2.30429e8i) q^{79} +(1.79703e8 - 3.11255e8i) q^{80} +(-1.93368e8 + 3.34923e8i) q^{81} +(-8.19675e7 - 1.41972e8i) q^{82} -6.33299e8 q^{83} -5.73312e8 q^{85} +(-1.72522e7 - 2.98817e7i) q^{86} +(1.16287e6 - 2.01416e6i) q^{87} +(9.18278e7 - 1.59050e8i) q^{88} +(3.11190e8 + 5.38997e8i) q^{89} +1.78973e8 q^{90} +8.93156e8 q^{92} +(1.54925e7 + 2.68338e7i) q^{93} +(2.83201e7 - 4.90518e7i) q^{94} +(3.35751e8 - 5.81537e8i) q^{95} +(6.78226e6 + 1.17472e7i) q^{96} +9.94856e8 q^{97} -6.62362e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 18 q^{2} - 161 q^{3} - 940 q^{4} - 1533 q^{5} + 8708 q^{6} + 34272 q^{8} - 35734 q^{9} - 4298 q^{10} + 42213 q^{11} - 135604 q^{12} + 319676 q^{13} + 151394 q^{15} + 322064 q^{16} - 324681 q^{17}+ \cdots - 1900777180 q^{99}+O(q^{100}) $ 10 * q - 18 * q^2 - 161 * q^3 - 940 * q^4 - 1533 * q^5 + 8708 * q^6 + 34272 * q^8 - 35734 * q^9 - 4298 * q^10 + 42213 * q^11 - 135604 * q^12 + 319676 * q^13 + 151394 * q^15 + 322064 * q^16 - 324681 * q^17 - 1012868 * q^18 + 16121 * q^19 + 350616 * q^20 - 62692 * q^22 + 2638863 * q^23 - 8449728 * q^24 - 1304092 * q^25 - 4179252 * q^26 + 18331558 * q^27 + 15292500 * q^29 + 20557942 * q^30 - 19179237 * q^31 - 6263520 * q^32 - 1689359 * q^33 + 62909700 * q^34 + 71476528 * q^36 + 39566985 * q^37 - 67365270 * q^38 - 44299486 * q^39 - 5721744 * q^40 + 53436852 * q^41 + 101835992 * q^43 + 99704916 * q^44 - 85098230 * q^45 - 14489202 * q^46 - 32509659 * q^47 + 185141600 * q^48 + 3328464 * q^50 + 44168403 * q^51 - 103893272 * q^52 - 25714707 * q^53 - 51200926 * q^54 + 144695222 * q^55 - 121710346 * q^57 - 46645516 * q^58 - 46776513 * q^59 + 132391756 * q^60 + 113075039 * q^61 - 467465628 * q^62 - 192008960 * q^64 - 338113566 * q^65 + 836682602 * q^66 - 126707879 * q^67 - 32262636 * q^68 - 1323616182 * q^69 - 1188736032 * q^71 - 950557728 * q^72 + 859257651 * q^73 + 591757530 * q^74 + 169061732 * q^75 - 1101475592 * q^76 + 519432424 * q^78 - 527065417 * q^79 + 1257352656 * q^80 + 551662715 * q^81 + 1341703076 * q^82 + 144863208 * q^83 - 1197360222 * q^85 - 678648216 * q^86 + 340781350 * q^87 + 903700608 * q^88 - 1661554797 * q^89 - 1967758744 * q^90 - 1301840952 * q^92 - 423057489 * q^93 + 272580882 * q^94 - 1197123495 * q^95 + 1441922272 * q^96 - 869770188 * q^97 - 1900777180 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.74397	−	4.75269i	−0.121267	−	0.210041i	0.799000	−	0.601331i	$-0.205363\pi$
$2$	−2.74397	−	4.75269i	−0.121267	−	0.210041i	−0.920268	+	0.391289i	$0.872029\pi$
$3$	1.70307	−	2.94981i	0.0121391	−	0.0210256i	−0.859892	−	0.510476i	$-0.829469\pi$
$3$	1.70307	−	2.94981i	0.0121391	−	0.0210256i	0.872031	+	0.489450i	$0.162803\pi$
$4$	240.941	−	417.323i	0.470588	−	0.815083i
$5$	828.924	+	1435.74i	0.593129	+	1.02733i	0.993808	+	0.111112i	$0.0354411\pi$
$5$	828.924	+	1435.74i	0.593129	+	1.02733i	−0.400679	+	0.916219i	$0.631226\pi$
$6$	−18.6927			−0.00588833
$7$		0			0
$7$		0			0
$8$	−5454.36			−0.470803
$9$	9835.70	+	17035.9i	0.499705	+	0.865515i
$10$	4549.08	−	7879.24i	0.143855	−	0.249163i
$11$	−16835.7	+	29160.2i	−0.346707	+	0.600515i	−0.985662	−	0.168729i	$-0.946034\pi$
$11$	−16835.7	+	29160.2i	−0.346707	+	0.600515i	0.638955	+	0.769244i	$0.279367\pi$
$12$	−820.681	−	1421.46i	−0.0114251	−	0.0197888i
$13$	−47905.5			−0.465200			−0.232600	−	0.972572i	$-0.574723\pi$
$13$	−47905.5			−0.465200			−0.232600	+	0.972572i	$0.574723\pi$
$14$		0			0
$15$	5646.87			0.0288003
$16$	−108395.	−	187746.i	−0.413495	−	0.716195i
$17$	−172909.	+	299487.i	−0.502107	+	0.869676i	0.497890	+	0.867240i	$0.334108\pi$
$17$	−172909.	+	299487.i	−0.502107	+	0.869676i	−0.999997	+	0.00243516i	$0.999225\pi$
$18$	53977.7	−	93492.1i	0.121196	−	0.209917i
$19$	−202522.	−	350778.i	−0.356518	−	0.617507i	0.630859	−	0.775898i	$-0.282703\pi$
$19$	−202522.	−	350778.i	−0.356518	−	0.617507i	−0.987376	+	0.158391i	$0.949369\pi$
$20$	798888.			1.11648
$21$		0			0
$22$	184786.			0.168177
$23$	926736.	+	1.60515e6i	0.690527	+	1.19603i	0.971665	+	0.236361i	$0.0759548\pi$
$23$	926736.	+	1.60515e6i	0.690527	+	1.19603i	−0.281138	+	0.959667i	$0.590712\pi$
$24$	−9289.18	+	16089.3i	−0.00571514	+	0.00989891i
$25$	−397666.	+	688778.i	−0.203605	+	0.352654i
$26$	131451.	+	227680.i	0.0564136	+	0.0977113i
$27$	134047.			0.0485422
$28$		0			0
$29$	682809.			0.179270			0.0896351	−	0.995975i	$-0.471430\pi$
$29$	682809.			0.179270			0.0896351	+	0.995975i	$0.471430\pi$
$30$	−15494.8	−	26837.8i	−0.00349254	−	0.00604925i
$31$	−4.54839e6	+	7.87804e6i	−0.884565	+	1.53211i	−0.0383536	+	0.999264i	$0.512211\pi$
$31$	−4.54839e6	+	7.87804e6i	−0.884565	+	1.53211i	−0.846211	+	0.532847i	$0.821122\pi$
$32$	−1.99118e6	+	3.44883e6i	−0.335688	+	0.581429i
$33$	57344.7	+	99324.0i	0.00841746	+	0.0145795i
$34$	1.89782e6			0.243557
$35$		0			0
$36$	9.47930e6			0.940622
$37$	7.77984e6	+	1.34751e7i	0.682437	+	1.18202i	0.974235	+	0.225536i	$0.0724133\pi$
$37$	7.77984e6	+	1.34751e7i	0.682437	+	1.18202i	−0.291798	+	0.956480i	$0.594253\pi$
$38$	−1.11143e6	+	1.92505e6i	−0.0864679	+	0.149767i
$39$	−81586.5	+	141312.i	−0.00564713	+	0.00978111i
$40$	−4.52125e6	−	7.83104e6i	−0.279247	−	0.483670i
$41$	2.98719e7			1.65095			0.825477	−	0.564435i	$-0.190906\pi$
$41$	2.98719e7			1.65095			0.825477	+	0.564435i	$0.190906\pi$
$42$		0			0
$43$	6.28733e6			0.280452			0.140226	−	0.990120i	$-0.455217\pi$
$43$	6.28733e6			0.280452			0.140226	+	0.990120i	$0.455217\pi$
$44$	8.11281e6	+	1.40518e7i	0.326313	+	0.565191i
$45$	−1.63061e7	+	2.82430e7i	−0.592780	+	1.02672i
$46$	5.08587e6	−	8.80898e6i	0.167477	−	0.290078i
$47$	5.16042e6	+	8.93811e6i	0.154257	+	0.267181i	0.932788	−	0.360425i	$-0.117368\pi$
$47$	5.16042e6	+	8.93811e6i	0.154257	+	0.267181i	−0.778531	+	0.627606i	$0.784035\pi$
$48$	−738421.			−0.0200779
$49$		0			0
$50$	4.36473e6			0.0987626
$51$	588952.	+	1.02010e6i	0.0121903	+	0.0211142i
$52$	−1.15424e7	+	1.99920e7i	−0.218918	+	0.379177i
$53$	−3.32218e7	+	5.75419e7i	−0.578339	+	1.00171i	0.417331	+	0.908754i	$0.362965\pi$
$53$	−3.32218e7	+	5.75419e7i	−0.578339	+	1.00171i	−0.995670	+	0.0929577i	$0.970368\pi$
$54$	−367820.	−	637083.i	−0.00588659	−	0.0101959i
$55$	−5.58219e7			−0.822570
$56$		0			0
$57$	−1.37964e6			−0.0173113
$58$	−1.87361e6	−	3.24518e6i	−0.0217396	−	0.0376541i
$59$	3.52902e7	−	6.11245e7i	0.379158	−	0.656721i	−0.611782	−	0.791027i	$-0.709547\pi$
$59$	3.52902e7	−	6.11245e7i	0.379158	−	0.656721i	0.990940	+	0.134305i	$0.0428803\pi$
$60$	1.36056e6	−	2.35657e6i	0.0135531	−	0.0234746i
$61$	−4.21696e7	−	7.30399e7i	−0.389955	−	0.675423i	0.602488	−	0.798128i	$-0.294176\pi$
$61$	−4.21696e7	−	7.30399e7i	−0.389955	−	0.675423i	−0.992443	+	0.122706i	$0.960843\pi$
$62$	4.99225e7			0.429076
$63$		0			0
$64$	−8.91419e7			−0.664159
$65$	−3.97100e7	−	6.87797e7i	−0.275924	−	0.477914i
$66$	314704.	−	545084.i	0.00204153	−	0.00353603i
$67$	1.05869e8	−	1.83370e8i	0.641846	−	1.11171i	−0.343175	−	0.939272i	$-0.611502\pi$
$67$	1.05869e8	−	1.83370e8i	0.641846	−	1.11171i	0.985020	−	0.172438i	$-0.0551644\pi$
$68$	8.33217e7	+	1.44317e8i	0.472572	+	0.818519i
$69$	6.31320e6			0.0335296
$70$		0			0
$71$	2.31588e7			0.108157			0.0540785	−	0.998537i	$-0.482778\pi$
$71$	2.31588e7			0.108157			0.0540785	+	0.998537i	$0.482778\pi$
$72$	−5.36475e7	−	9.29202e7i	−0.235263	−	0.407487i
$73$	1.24284e8	−	2.15266e8i	0.512226	−	0.887201i	−0.487674	−	0.873026i	$-0.662154\pi$
$73$	1.24284e8	−	2.15266e8i	0.512226	−	0.887201i	0.999900	−	0.0141754i	$-0.00451231\pi$
$74$	4.26952e7	−	7.39503e7i	0.165515	−	0.286680i
$75$	1.35451e6	+	2.34608e6i	0.00494318	+	0.00856184i
$76$	−1.95184e8			−0.671092
$77$		0			0
$78$	895483.			0.00273925
$79$	−1.33038e8	−	2.30429e8i	−0.384287	−	0.665604i	0.607383	−	0.794409i	$-0.292219\pi$
$79$	−1.33038e8	−	2.30429e8i	−0.384287	−	0.665604i	−0.991670	+	0.128805i	$0.958886\pi$
$80$	1.79703e8	−	3.11255e8i	0.490513	−	0.849593i
$81$	−1.93368e8	+	3.34923e8i	−0.499116	+	0.864494i
$82$	−8.19675e7	−	1.41972e8i	−0.200207	−	0.346769i
$83$	−6.33299e8			−1.46473			−0.732365	−	0.680912i	$-0.761583\pi$
$83$	−6.33299e8			−1.46473			−0.732365	+	0.680912i	$0.761583\pi$
$84$		0			0
$85$	−5.73312e8			−1.19126
$86$	−1.72522e7	−	2.98817e7i	−0.0340097	−	0.0589065i
$87$	1.16287e6	−	2.01416e6i	0.00217619	−	0.00376926i
$88$	9.18278e7	−	1.59050e8i	0.163231	−	0.282724i
$89$	3.11190e8	+	5.38997e8i	0.525740	+	0.910608i	0.999550	+	0.0299813i	$0.00954476\pi$
$89$	3.11190e8	+	5.38997e8i	0.525740	+	0.910608i	−0.473811	+	0.880627i	$0.657122\pi$
$90$	1.78973e8			0.287539
$91$		0			0
$92$	8.93156e8			1.29982
$93$	1.54925e7	+	2.68338e7i	0.0214757	+	0.0371970i
$94$	2.83201e7	−	4.90518e7i	0.0374127	−	0.0648007i
$95$	3.35751e8	−	5.81537e8i	0.422922	−	0.732523i
$96$	6.78226e6	+	1.17472e7i	0.00814994	+	0.0141161i
$97$	9.94856e8			1.14100			0.570502	−	0.821296i	$-0.306749\pi$
$97$	9.94856e8			1.14100			0.570502	+	0.821296i	$0.306749\pi$
$98$		0			0
$99$	−6.62362e8			−0.693006
$100$	1.91628e8	+	3.31910e8i	0.191628	+	0.331910i
$101$	−4.19400e8	+	7.26423e8i	−0.401035	+	0.694613i	−0.993851	−	0.110725i	$-0.964683\pi$
$101$	−4.19400e8	+	7.26423e8i	−0.401035	+	0.694613i	0.592816	+	0.805338i	$0.298016\pi$
$102$	3.23213e6	−	5.59822e6i	0.00295657	−	0.00512093i
$103$	−7.67183e8	−	1.32880e9i	−0.671632	−	1.16330i	−0.977441	−	0.211208i	$-0.932260\pi$
$103$	−7.67183e8	−	1.32880e9i	−0.671632	−	1.16330i	0.305809	−	0.952093i	$-0.401073\pi$
$104$	2.61294e8			0.219018
$105$		0			0
$106$	3.64639e8			0.280535
$107$	3.11913e8	+	5.40249e8i	0.230041	+	0.398443i	0.957820	−	0.287369i	$-0.0927805\pi$
$107$	3.11913e8	+	5.40249e8i	0.230041	+	0.398443i	−0.727779	+	0.685812i	$0.759447\pi$
$108$	3.22974e7	−	5.59408e7i	0.0228434	−	0.0395660i
$109$	−1.09462e9	+	1.89593e9i	−0.742749	+	1.28648i	0.208490	+	0.978025i	$0.433145\pi$
$109$	−1.09462e9	+	1.89593e9i	−0.742749	+	1.28648i	−0.951239	+	0.308455i	$0.900188\pi$
$110$	1.53174e8	+	2.65304e8i	0.0997509	+	0.172774i
$111$	5.29985e7			0.0331368
$112$		0			0
$113$	9.14275e8			0.527502			0.263751	−	0.964591i	$-0.415040\pi$
$113$	9.14275e8			0.527502			0.263751	+	0.964591i	$0.415040\pi$
$114$	3.78569e6	+	6.55700e6i	0.00209929	+	0.00363608i
$115$	−1.53639e9	+	2.66110e9i	−0.819144	+	1.41880i
$116$	1.64517e8	−	2.84952e8i	0.0843625	−	0.146120i
$117$	−4.71184e8	−	8.16114e8i	−0.232463	−	0.402638i
$118$	−3.87341e8			−0.183918
$119$		0			0
$120$	−3.08001e7			−0.0135593
$121$	6.12095e8	+	1.06018e9i	0.259588	+	0.449619i
$122$	−2.31424e8	+	4.00838e8i	−0.0945778	+	0.163813i
$123$	5.08740e7	−	8.81163e7i	0.0200412	−	0.0347123i
$124$	2.19179e9	+	3.79629e9i	0.832532	+	1.44199i
$125$	1.91944e9			0.703202
$126$		0			0
$127$	1.00914e9			0.344218			0.172109	−	0.985078i	$-0.444942\pi$
$127$	1.00914e9			0.344218			0.172109	+	0.985078i	$0.444942\pi$
$128$	1.26409e9	+	2.18947e9i	0.416229	+	0.720930i
$129$	1.07078e7	−	1.85464e7i	0.00340444	−	0.00589667i
$130$	−2.17926e8	+	3.77458e8i	−0.0669212	+	0.115911i
$131$	−2.19762e9	−	3.80639e9i	−0.651976	−	1.12926i	−0.982643	−	0.185509i	$-0.940607\pi$
$131$	−2.19762e9	−	3.80639e9i	−0.651976	−	1.12926i	0.330666	−	0.943748i	$-0.392727\pi$
$132$	5.52669e7			0.0158446
$133$		0			0
$134$	−1.16200e9			−0.311340
$135$	1.11115e8	+	1.92456e8i	0.0287918	+	0.0498689i
$136$	9.43107e8	−	1.63351e9i	0.236394	−	0.409446i
$137$	−8.75011e7	+	1.51556e8i	−0.0212212	+	0.0367563i	−0.876441	−	0.481509i	$-0.840089\pi$
$137$	−8.75011e7	+	1.51556e8i	−0.0212212	+	0.0367563i	0.855220	+	0.518266i	$0.173422\pi$
$138$	−1.73232e7	−	3.00047e7i	−0.00406605	−	0.00704260i
$139$	1.87062e9			0.425030			0.212515	−	0.977158i	$-0.431835\pi$
$139$	1.87062e9			0.425030			0.212515	+	0.977158i	$0.431835\pi$
$140$		0			0
$141$	3.51543e7			0.00749018
$142$	−6.35471e7	−	1.10067e8i	−0.0131159	−	0.0227174i
$143$	8.06520e8	−	1.39693e9i	0.161288	−	0.279360i
$144$	2.13229e9	−	3.69323e9i	0.413252	−	0.715773i
$145$	5.65996e8	+	9.80334e8i	0.106330	+	0.184170i
$146$	−1.36412e9			−0.248465
$147$		0			0
$148$	7.49794e9			1.28459
$149$	−5.69185e9	−	9.85857e9i	−0.946053	−	1.63861i	−0.753630	−	0.657299i	$-0.771699\pi$
$149$	−5.69185e9	−	9.85857e9i	−0.946053	−	1.63861i	−0.192423	−	0.981312i	$-0.561634\pi$
$150$	7.43346e6	−	1.28751e7i	0.00119889	−	0.00207654i
$151$	−3.77654e8	+	6.54115e8i	−0.0591149	+	0.102390i	−0.894068	−	0.447931i	$-0.852161\pi$
$151$	−3.77654e8	+	6.54115e8i	−0.0591149	+	0.102390i	0.834953	+	0.550321i	$0.185495\pi$
$152$	1.10463e9	+	1.91327e9i	0.167850	+	0.290724i
$153$	−6.80271e9			−1.00362
$154$		0			0
$155$	−1.50811e10			−2.09865
$156$	3.93151e7	+	6.80958e7i	0.00531495	+	0.00920576i
$157$	−3.52403e8	+	6.10380e8i	−0.0462904	+	0.0801774i	−0.888242	−	0.459375i	$-0.848073\pi$
$157$	−3.52403e8	+	6.10380e8i	−0.0462904	+	0.0801774i	0.841952	+	0.539553i	$0.181407\pi$
$158$	−7.30107e8	+	1.26458e9i	−0.0932029	+	0.161432i
$159$	1.13158e8	+	1.95996e8i	0.0140411	+	0.0243198i
$160$	−6.60216e9			−0.796427
$161$		0			0
$162$	2.12238e9			0.242106
$163$	−3.29346e8	−	5.70444e8i	−0.0365433	−	0.0632949i	0.847175	−	0.531313i	$-0.178301\pi$
$163$	−3.29346e8	−	5.70444e8i	−0.0365433	−	0.0632949i	−0.883719	+	0.468019i	$0.844968\pi$
$164$	7.19737e9	−	1.24662e10i	0.776920	−	1.34567i
$165$	−9.50688e7	+	1.64664e8i	−0.00998528	+	0.0172950i
$166$	1.73775e9	+	3.00988e9i	0.177624	+	0.307654i
$167$	2.62390e9			0.261050			0.130525	−	0.991445i	$-0.458334\pi$
$167$	2.62390e9			0.261050			0.130525	+	0.991445i	$0.458334\pi$
$168$		0			0
$169$	−8.30957e9			−0.783589
$170$	1.57315e9	+	2.72478e9i	0.144461	+	0.250214i
$171$	3.98389e9	−	6.90030e9i	0.356308	−	0.617143i
$172$	1.51488e9	−	2.62384e9i	0.131977	−	0.228592i
$173$	−5.31176e9	−	9.20023e9i	−0.450849	−	0.780893i	0.547590	−	0.836747i	$-0.315545\pi$
$173$	−5.31176e9	−	9.20023e9i	−0.450849	−	0.780893i	−0.998439	+	0.0558539i	$0.982212\pi$
$174$	−1.27636e7			−0.00105560
$175$		0			0
$176$	7.29963e9			0.573448
$177$	−1.20204e8	−	2.08199e8i	−0.00920530	−	0.0159441i
$178$	1.70779e9	−	2.95798e9i	0.127510	−	0.220854i
$179$	2.16215e9	−	3.74496e9i	0.157416	−	0.272652i	−0.776520	−	0.630092i	$-0.783017\pi$
$179$	2.16215e9	−	3.74496e9i	0.157416	−	0.272652i	0.933936	+	0.357440i	$0.116350\pi$
$180$	7.85762e9	+	1.36098e10i	0.557911	+	0.966330i
$181$	−8.10532e8			−0.0561328			−0.0280664	−	0.999606i	$-0.508935\pi$
$181$	−8.10532e8			−0.0561328			−0.0280664	+	0.999606i	$0.508935\pi$
$182$		0			0
$183$	−2.87272e8			−0.0189349
$184$	−5.05476e9	−	8.75509e9i	−0.325102	−	0.563094i
$185$	−1.28978e10	+	2.23396e10i	−0.809547	+	1.40218i
$186$	8.50217e7	−	1.47262e8i	0.00520861	−	0.00902157i
$187$	−5.82206e9	−	1.00841e10i	−0.348169	−	0.603046i
$188$	4.97343e9			0.290366
$189$		0			0
$190$	−3.68516e9			−0.205147
$191$	−6.69665e9	−	1.15989e10i	−0.364089	−	0.630620i	0.624541	−	0.780992i	$-0.285286\pi$
$191$	−6.69665e9	−	1.15989e10i	−0.364089	−	0.630620i	−0.988629	+	0.150372i	$0.951953\pi$
$192$	−1.51815e8	+	2.62952e8i	−0.00806231	+	0.0139643i
$193$	−4.33922e8	+	7.51575e8i	−0.0225115	+	0.0389910i	−0.877062	−	0.480378i	$-0.840500\pi$
$193$	−4.33922e8	+	7.51575e8i	−0.0225115	+	0.0389910i	0.854550	+	0.519369i	$0.173833\pi$
$194$	−2.72985e9	−	4.72824e9i	−0.138367	−	0.239658i
$195$	−2.70516e8			−0.0133979
$196$		0			0
$197$	1.72523e10			0.816112			0.408056	−	0.912957i	$-0.366207\pi$
$197$	1.72523e10			0.816112			0.408056	+	0.912957i	$0.366207\pi$
$198$	1.81750e9	+	3.14800e9i	0.0840390	+	0.145560i
$199$	1.61364e9	−	2.79490e9i	0.0729403	−	0.126336i	−0.827248	−	0.561836i	$-0.810095\pi$
$199$	1.61364e9	−	2.79490e9i	0.0729403	−	0.126336i	0.900189	+	0.435500i	$0.143428\pi$
$200$	2.16902e9	−	3.75684e9i	0.0958578	−	0.166031i
$201$	−3.60604e8	−	6.24585e8i	−0.0155829	−	0.0269904i
$202$	4.60328e9			0.194530
$203$		0			0
$204$	5.67612e8			0.0229465
$205$	2.47615e10	+	4.28882e10i	0.979230	+	1.69608i
$206$	−4.21025e9	+	7.29237e9i	−0.162894	+	0.282141i
$207$	−1.82302e10	+	3.15756e10i	−0.690120	+	1.19532i
$208$	5.19273e9	+	8.99407e9i	0.192358	+	0.333174i
$209$	1.36384e10			0.494429
$210$		0			0
$211$	4.90060e9			0.170207			0.0851036	−	0.996372i	$-0.472878\pi$
$211$	4.90060e9			0.170207			0.0851036	+	0.996372i	$0.472878\pi$
$212$	1.60090e10	+	2.77284e10i	0.544319	+	0.942788i
$213$	3.94412e7	−	6.83142e7i	0.00131293	−	0.00227406i
$214$	1.71176e9	−	2.96485e9i	0.0557931	−	0.0966364i
$215$	5.21172e9	+	9.02696e9i	0.166344	+	0.288117i
$216$	−7.31140e8			−0.0228538
$217$		0			0
$218$	1.20144e10			0.360285
$219$	−4.23329e8	−	7.33227e8i	−0.0124360	−	0.0215397i
$220$	−1.34498e10	+	2.32957e10i	−0.387092	+	0.670463i
$221$	8.28327e9	−	1.43470e10i	0.233581	−	0.404573i
$222$	−1.45426e8	−	2.51886e8i	−0.00401841	−	0.00696009i
$223$	1.61028e10			0.436044			0.218022	−	0.975944i	$-0.430039\pi$
$223$	1.61028e10			0.436044			0.218022	+	0.975944i	$0.430039\pi$
$224$		0			0
$225$	−1.56453e10			−0.406970
$226$	−2.50874e9	−	4.34527e9i	−0.0639688	−	0.110797i
$227$	−2.38627e10	+	4.13315e10i	−0.596491	+	1.03315i	0.396843	+	0.917886i	$0.370106\pi$
$227$	−2.38627e10	+	4.13315e10i	−0.596491	+	1.03315i	−0.993335	+	0.115267i	$0.963228\pi$
$228$	−3.32412e8	+	5.75755e8i	−0.00814648	+	0.0141101i
$229$	−8.48309e9	−	1.46931e10i	−0.203842	−	0.353065i	0.745921	−	0.666035i	$-0.232010\pi$
$229$	−8.48309e9	−	1.46931e10i	−0.203842	−	0.353065i	−0.949763	+	0.312969i	$0.898676\pi$
$230$	1.68632e10			0.397342
$231$		0			0
$232$	−3.72429e9			−0.0844009
$233$	−2.32965e10	−	4.03508e10i	−0.517833	−	0.896912i	−0.999785	−	0.0207152i	$-0.993406\pi$
$233$	−2.32965e10	−	4.03508e10i	−0.517833	−	0.896912i	0.481953	−	0.876197i	$-0.339928\pi$
$234$	−2.58583e9	+	4.47878e9i	−0.0563804	+	0.0976537i
$235$	−8.55519e9	+	1.48180e10i	−0.182989	+	0.316946i
$236$	−1.70057e10	−	2.94548e10i	−0.356855	−	0.618091i
$237$	−9.06297e8			−0.0186596
$238$		0			0
$239$	4.41773e10			0.875808			0.437904	−	0.899022i	$-0.355721\pi$
$239$	4.41773e10			0.875808			0.437904	+	0.899022i	$0.355721\pi$
$240$	−6.12095e8	−	1.06018e9i	−0.0119088	−	0.0206266i
$241$	1.67014e10	−	2.89276e10i	0.318915	−	0.552377i	−0.661347	−	0.750080i	$-0.730015\pi$
$241$	1.67014e10	−	2.89276e10i	0.318915	−	0.552377i	0.980262	+	0.197703i	$0.0633482\pi$
$242$	3.35914e9	−	5.81819e9i	0.0629591	−	0.109048i
$243$	1.97786e9	+	3.42576e9i	0.0363888	+	0.0630272i
$244$	−4.06416e10			−0.734034
$245$		0			0
$246$	−5.58386e8			−0.00972136
$247$	9.70191e9	+	1.68042e10i	0.165852	+	0.287264i
$248$	2.48086e10	−	4.29697e10i	0.416456	−	0.721323i
$249$	−1.07856e9	+	1.86811e9i	−0.0177806	+	0.0307968i
$250$	−5.26689e9	−	9.12252e9i	−0.0852755	−	0.147702i
$251$	3.09851e10			0.492745			0.246372	−	0.969175i	$-0.420761\pi$
$251$	3.09851e10			0.492745			0.246372	+	0.969175i	$0.420761\pi$
$252$		0			0
$253$	−6.24089e10			−0.957644
$254$	−2.76904e9	−	4.79611e9i	−0.0417424	−	0.0722999i
$255$	−9.76393e8	+	1.69116e9i	−0.0144609	+	0.0250469i
$256$	−1.58831e10	+	2.75103e10i	−0.231129	+	0.400328i
$257$	1.44350e10	+	2.50021e10i	0.206404	+	0.357502i	0.950579	−	0.310483i	$-0.100491\pi$
$257$	1.44350e10	+	2.50021e10i	0.206404	+	0.357502i	−0.744175	+	0.667984i	$0.767157\pi$
$258$	−1.17527e8			−0.00165139
$259$		0			0
$260$	−3.82711e10			−0.519387
$261$	6.71590e9	+	1.16323e10i	0.0895823	+	0.155161i
$262$	−1.20604e10	+	2.08892e10i	−0.158127	+	0.273884i
$263$	5.51341e10	−	9.54951e10i	0.710591	−	1.23078i	−0.254044	−	0.967193i	$-0.581761\pi$
$263$	5.51341e10	−	9.54951e10i	0.710591	−	1.23078i	0.964636	−	0.263587i	$-0.0849058\pi$
$264$	−3.12779e8	−	5.41749e8i	−0.00396296	−	0.00686405i
$265$	−1.10153e11			−1.37212
$266$		0			0
$267$	2.11992e9			0.0255281
$268$	−5.10162e10	−	8.83627e10i	−0.604090	−	1.04632i
$269$	7.59021e10	−	1.31466e11i	0.883829	−	1.53084i	0.0367799	−	0.999323i	$-0.488290\pi$
$269$	7.59021e10	−	1.31466e11i	0.883829	−	1.53084i	0.847050	−	0.531514i	$-0.178377\pi$
$270$	6.09790e8	−	1.05619e9i	0.00698302	−	0.0120949i
$271$	6.22958e10	+	1.07899e11i	0.701612	+	1.21523i	0.967900	+	0.251334i	$0.0808692\pi$
$271$	6.22958e10	+	1.07899e11i	0.701612	+	1.21523i	−0.266289	+	0.963893i	$0.585797\pi$
$272$	7.49700e10			0.830476
$273$		0			0
$274$	9.60400e8			0.0102938
$275$	−1.33899e10	−	2.31921e10i	−0.141183	−	0.244536i
$276$	1.52111e9	−	2.63464e9i	0.0157787	−	0.0273294i
$277$	−1.63156e10	+	2.82594e10i	−0.166511	+	0.288405i	−0.937191	−	0.348817i	$-0.886583\pi$
$277$	−1.63156e10	+	2.82594e10i	−0.166511	+	0.288405i	0.770680	+	0.637223i	$0.219917\pi$
$278$	−5.13292e9	−	8.89048e9i	−0.0515422	−	0.0892738i
$279$	−1.78946e11			−1.76809
$280$		0			0
$281$	1.22979e10			0.117666			0.0588331	−	0.998268i	$-0.481262\pi$
$281$	1.22979e10			0.117666			0.0588331	+	0.998268i	$0.481262\pi$
$282$	−9.64623e7	−	1.67078e8i	−0.000908315	−	0.00157325i
$283$	2.97894e10	−	5.15968e10i	0.276072	−	0.478171i	−0.694333	−	0.719654i	$-0.744300\pi$
$283$	2.97894e10	−	5.15968e10i	0.276072	−	0.478171i	0.970405	+	0.241483i	$0.0776337\pi$
$284$	5.57992e9	−	9.66471e9i	0.0508974	−	0.0881569i
$285$	−1.14362e9	−	1.98080e9i	−0.0102678	−	0.0177844i
$286$	−8.85226e9			−0.0782361
$287$		0			0
$288$	−7.83387e10			−0.670981
$289$	−5.00885e8	−	8.67558e8i	−0.00422374	−	0.00731574i
$290$	3.10615e9	−	5.38001e9i	0.0257888	−	0.0446676i
$291$	1.69431e9	−	2.93464e9i	0.0138508	−	0.0239903i
$292$	−5.98902e10	−	1.03733e11i	−0.482095	−	0.835013i
$293$	9.22958e10			0.731606			0.365803	−	0.930692i	$-0.380794\pi$
$293$	9.22958e10			0.731606			0.365803	+	0.930692i	$0.380794\pi$
$294$		0			0
$295$	1.17012e11			0.899559
$296$	−4.24341e10	−	7.34979e10i	−0.321293	−	0.556497i
$297$	−2.25677e9	+	3.90884e9i	−0.0168300	+	0.0291503i
$298$	−3.12365e10	+	5.41032e10i	−0.229451	+	0.397420i
$299$	−4.43957e10	−	7.68957e10i	−0.321233	−	0.556393i
$300$	1.30543e9			0.00930481
$301$		0			0
$302$	4.14508e9			0.0286749
$303$	1.42854e9	+	2.47430e9i	0.00973644	+	0.0168640i
$304$	−4.39049e10	+	7.60455e10i	−0.294837	+	0.510672i
$305$	6.99107e10	−	1.21089e11i	0.462588	−	0.801226i
$306$	1.86664e10	+	3.23312e10i	0.121707	+	0.210802i
$307$	1.38141e11			0.887567			0.443783	−	0.896134i	$-0.353636\pi$
$307$	1.38141e11			0.887567			0.443783	+	0.896134i	$0.353636\pi$
$308$		0			0
$309$	−5.22628e9			−0.0326121
$310$	4.13819e10	+	7.16756e10i	0.254497	+	0.440802i
$311$	−4.44357e10	+	7.69648e10i	−0.269346	+	0.466520i	−0.968693	−	0.248262i	$-0.920141\pi$
$311$	−4.44357e10	+	7.69648e10i	−0.269346	+	0.466520i	0.699347	+	0.714782i	$0.253474\pi$
$312$	4.45003e8	−	7.70767e8i	0.00265868	−	0.00460498i
$313$	1.34313e11	+	2.32637e11i	0.790986	+	1.37003i	0.925357	+	0.379097i	$0.123765\pi$
$313$	1.34313e11	+	2.32637e11i	0.790986	+	1.37003i	−0.134370	+	0.990931i	$0.542901\pi$
$314$	3.86793e9			0.0224541
$315$		0			0
$316$	−1.28218e11			−0.723364
$317$	2.53855e10	+	4.39689e10i	0.141195	+	0.244556i	0.927947	−	0.372713i	$-0.121572\pi$
$317$	2.53855e10	+	4.39689e10i	0.141195	+	0.244556i	−0.786752	+	0.617269i	$0.788239\pi$
$318$	6.21006e8	−	1.07561e9i	0.00340545	−	0.00589841i
$319$	−1.14955e10	+	1.99109e10i	−0.0621543	+	0.107654i
$320$	−7.38918e10	−	1.27984e11i	−0.393932	−	0.682310i
$321$	2.12484e9			0.0111700
$322$		0			0
$323$	1.40071e11			0.716041
$324$	9.31806e10	+	1.61393e11i	0.469756	+	0.813642i
$325$	1.90504e10	−	3.29962e10i	0.0947171	−	0.164055i
$326$	−1.80743e9	+	3.13056e9i	−0.00886302	+	0.0153512i
$327$	3.72842e9	+	6.45781e9i	0.0180327	+	0.0312335i
$328$	−1.62932e11			−0.777274
$329$		0			0
$330$	1.04346e9			0.00484356
$331$	6.58014e10	+	1.13971e11i	0.301307	+	0.521879i	0.976432	−	0.215824i	$-0.0692438\pi$
$331$	6.58014e10	+	1.13971e11i	0.301307	+	0.521879i	−0.675125	+	0.737703i	$0.735911\pi$
$332$	−1.52588e11	+	2.64290e11i	−0.689285	+	1.19388i
$333$	−1.53040e11	+	2.65074e11i	−0.682035	+	1.18132i
$334$	−7.19990e9	−	1.24706e10i	−0.0316568	−	0.0548312i
$335$	3.51028e11			1.52279
$336$		0			0
$337$	1.17560e11			0.496506			0.248253	−	0.968695i	$-0.420144\pi$
$337$	1.17560e11			0.496506			0.248253	+	0.968695i	$0.420144\pi$
$338$	2.28012e10	+	3.94928e10i	0.0950238	+	0.164586i
$339$	1.55708e9	−	2.69694e9i	0.00640341	−	0.0110910i
$340$	−1.38135e11	+	2.39256e11i	−0.560593	+	0.970975i
$341$	−1.53150e11	−	2.65264e11i	−0.613371	−	1.06239i
$342$	−4.37267e10			−0.172834
$343$		0			0
$344$	−3.42934e10			−0.132038
$345$	5.23316e9	+	9.06410e9i	0.0198874	+	0.0344460i
$346$	−2.91506e10	+	5.04903e10i	−0.109346	+	0.189394i
$347$	1.11842e11	−	1.93716e11i	0.414117	−	0.717272i	−0.581218	−	0.813748i	$-0.697424\pi$
$347$	1.11842e11	−	1.93716e11i	0.414117	−	0.717272i	0.995335	+	0.0964758i	$0.0307570\pi$
$348$	−5.60369e8	−	9.70587e8i	−0.00204818	−	0.00354754i
$349$	−1.91861e11			−0.692264			−0.346132	−	0.938186i	$-0.612505\pi$
$349$	−1.91861e11			−0.692264			−0.346132	+	0.938186i	$0.612505\pi$
$350$		0			0
$351$	−6.42158e9			−0.0225819
$352$	−6.70458e10	−	1.16127e11i	−0.232771	−	0.403172i
$353$	−2.23290e11	+	3.86749e11i	−0.765390	+	1.32569i	0.174651	+	0.984630i	$0.444120\pi$
$353$	−2.23290e11	+	3.86749e11i	−0.765390	+	1.32569i	−0.940040	+	0.341063i	$0.889213\pi$
$354$	−6.59670e8	+	1.14258e9i	−0.00223261	+	0.00386699i
$355$	1.91969e10	+	3.32500e10i	0.0641511	+	0.111113i
$356$	2.99914e11			0.989628
$357$		0			0
$358$	−2.37315e10			−0.0763575
$359$	−6.41252e10	−	1.11068e11i	−0.203753	−	0.352910i	0.745982	−	0.665966i	$-0.231981\pi$
$359$	−6.41252e10	−	1.11068e11i	−0.203753	−	0.352910i	−0.949735	+	0.313056i	$0.898647\pi$
$360$	8.89393e10	−	1.54047e11i	0.279082	−	0.483385i
$361$	7.93135e10	−	1.37375e11i	0.245790	−	0.425721i
$362$	2.22407e9	+	3.85221e9i	0.00680708	+	0.0117902i
$363$	4.16977e9			0.0126047
$364$		0			0
$365$	4.12087e11			1.21527
$366$	7.88264e8	+	1.36531e9i	0.00229618	+	0.00397711i
$367$	1.76396e11	−	3.05526e11i	0.507564	−	0.879127i	−0.492397	−	0.870370i	$-0.663879\pi$
$367$	1.76396e11	−	3.05526e11i	0.507564	−	0.879127i	0.999962	−	0.00875648i	$-0.00278731\pi$
$368$	2.00908e11	−	3.47982e11i	0.571060	−	0.989104i
$369$	2.93811e11	+	5.08895e11i	0.824991	+	1.42893i
$370$	1.41564e11			0.392687
$371$		0			0
$372$	1.49311e10			0.0404249
$373$	2.39725e11	+	4.15215e11i	0.641244	+	1.11067i	0.985155	+	0.171665i	$0.0549146\pi$
$373$	2.39725e11	+	4.15215e11i	0.641244	+	1.11067i	−0.343912	+	0.939002i	$0.611752\pi$
$374$	−3.19511e10	+	5.53410e10i	−0.0844430	+	0.146260i
$375$	3.26895e9	−	5.66199e9i	0.00853627	−	0.0147853i
$376$	−2.81468e10	−	4.87517e10i	−0.0726246	−	0.125790i
$377$	−3.27103e10			−0.0833965
$378$		0			0
$379$	−5.82262e11			−1.44958			−0.724790	−	0.688970i	$-0.758063\pi$
$379$	−5.82262e11			−1.44958			−0.724790	+	0.688970i	$0.758063\pi$
$380$	−1.61792e11	−	2.80233e11i	−0.398045	−	0.689434i
$381$	1.71863e9	−	2.97676e9i	0.00417850	−	0.00723738i
$382$	−3.67508e10	+	6.36542e10i	−0.0883042	+	0.152947i
$383$	−2.80765e11	−	4.86300e11i	−0.666729	−	1.15481i	−0.978813	−	0.204754i	$-0.934361\pi$
$383$	−2.80765e11	−	4.86300e11i	−0.666729	−	1.15481i	0.312085	−	0.950054i	$-0.398973\pi$
$384$	8.61134e9			0.0202107
$385$		0			0
$386$	4.76267e9			0.0109196
$387$	6.18403e10	+	1.07111e11i	0.140143	+	0.242735i
$388$	2.39702e11	−	4.15176e11i	0.536944	−	0.930014i
$389$	−2.11258e11	+	3.65909e11i	−0.467778	+	0.810215i	−0.999322	−	0.0368154i	$-0.988279\pi$
$389$	−2.11258e11	+	3.65909e11i	−0.467778	+	0.810215i	0.531544	+	0.847031i	$0.321612\pi$
$390$	7.42287e8	+	1.28568e9i	0.00162473	+	0.00281411i
$391$	−6.40963e11			−1.38688
$392$		0			0
$393$	−1.49708e10			−0.0316577
$394$	−4.73399e10	−	8.19950e10i	−0.0989678	−	0.171417i
$395$	2.20557e11	−	3.82017e11i	0.455864	−	0.789579i
$396$	−1.59590e11	+	2.76419e11i	−0.326121	+	0.564858i
$397$	1.51671e11	+	2.62702e11i	0.306440	+	0.530770i	0.977581	−	0.210560i	$-0.0675287\pi$
$397$	1.51671e11	+	2.62702e11i	0.306440	+	0.530770i	−0.671141	+	0.741330i	$0.734195\pi$
$398$	−1.77111e10			−0.0353811
$399$		0			0
$400$	1.72421e11			0.336759
$401$	−2.98643e11	−	5.17265e11i	−0.576770	−	0.998995i	−0.995847	−	0.0910443i	$-0.970979\pi$
$401$	−2.98643e11	−	5.17265e11i	−0.576770	−	0.998995i	0.419077	−	0.907951i	$-0.362354\pi$
$402$	−1.97897e9	+	3.42768e9i	−0.00377940	+	0.00654611i
$403$	2.17893e11	−	3.77401e11i	0.411500	−	0.712739i
$404$	2.02102e11	+	3.50050e11i	0.377445	+	0.653754i
$405$	−6.41148e11			−1.18416
$406$		0			0
$407$	−5.23915e11			−0.946424
$408$	−3.21236e9	−	5.56397e9i	−0.00573923	−	0.00994064i
$409$	−3.86849e10	+	6.70042e10i	−0.0683575	+	0.118399i	−0.898178	−	0.439631i	$-0.855109\pi$
$409$	−3.86849e10	+	6.70042e10i	−0.0683575	+	0.118399i	0.829821	+	0.558030i	$0.188443\pi$
$410$	1.35890e11	−	2.35368e11i	0.237497	−	0.411357i
$411$	2.98042e8	+	5.16223e8i	0.000515215	+	0.000892379i
$412$	−7.39384e11			−1.26425
$413$		0			0
$414$	2.00092e11			0.334756
$415$	−5.24957e11	−	9.09252e11i	−0.868774	−	1.50476i
$416$	9.53886e10	−	1.65218e11i	0.156162	−	0.270481i
$417$	3.18580e9	−	5.51798e9i	0.00515949	−	0.00893650i
$418$	−3.74233e10	−	6.48190e10i	−0.0599582	−	0.103851i
$419$	1.19811e12			1.89904			0.949521	−	0.313704i	$-0.101570\pi$
$419$	1.19811e12			1.89904			0.949521	+	0.313704i	$0.101570\pi$
$420$		0			0
$421$	−4.34567e11			−0.674198			−0.337099	−	0.941469i	$-0.609446\pi$
$421$	−4.34567e11			−0.674198			−0.337099	+	0.941469i	$0.609446\pi$
$422$	−1.34471e10	−	2.32910e10i	−0.0206406	−	0.0357505i
$423$	−1.01513e11	+	1.75825e11i	−0.154166	+	0.267023i
$424$	1.81204e11	−	3.13855e11i	0.272284	−	0.471609i
$425$	−1.37520e11	−	2.38191e11i	−0.204463	−	0.354141i
$426$	−4.32902e8			−0.000636863
$427$		0			0
$428$	3.00611e11			0.433019
$429$	−2.74713e9	−	4.75816e9i	−0.00391580	−	0.00678237i
$430$	2.86016e10	−	4.95394e10i	0.0403443	−	0.0698783i
$431$	1.35601e11	−	2.34868e11i	0.189284	−	0.327850i	−0.755727	−	0.654886i	$-0.772717\pi$
$431$	1.35601e11	−	2.34868e11i	0.189284	−	0.327850i	0.945012	+	0.327036i	$0.106050\pi$
$432$	−1.45301e10	−	2.51668e10i	−0.0200720	−	0.0347657i
$433$	1.84420e11			0.252123			0.126062	−	0.992022i	$-0.459766\pi$
$433$	1.84420e11			0.252123			0.126062	+	0.992022i	$0.459766\pi$
$434$		0			0
$435$	3.85573e9			0.00516304
$436$	5.27476e11	+	9.13615e11i	0.699058	+	1.21080i
$437$	3.75369e11	−	6.50158e11i	0.492370	−	0.852811i
$438$	−2.32320e9	+	4.02390e9i	−0.00301615	+	0.00522413i
$439$	−3.15142e11	−	5.45842e11i	−0.404963	−	0.701417i	0.589354	−	0.807875i	$-0.299382\pi$
$439$	−3.15142e11	−	5.45842e11i	−0.404963	−	0.701417i	−0.994317	+	0.106458i	$0.966049\pi$
$440$	3.04473e11			0.387268
$441$		0			0
$442$	−9.09161e10			−0.113303
$443$	1.75387e11	+	3.03779e11i	0.216362	+	0.374750i	0.953693	−	0.300782i	$-0.0972476\pi$
$443$	1.75387e11	+	3.03779e11i	0.216362	+	0.374750i	−0.737331	+	0.675531i	$0.763914\pi$
$444$	1.27695e10	−	2.21175e10i	0.0155938	−	0.0270092i
$445$	−5.15906e11	+	8.93575e11i	−0.623663	+	1.08022i
$446$	−4.41857e10	−	7.65319e10i	−0.0528780	−	0.0915873i
$447$	−3.87746e10			−0.0459370
$448$		0			0
$449$	−3.31400e11			−0.384808			−0.192404	−	0.981316i	$-0.561628\pi$
$449$	−3.31400e11			−0.384808			−0.192404	+	0.981316i	$0.561628\pi$
$450$	4.29302e10	+	7.43573e10i	0.0493522	+	0.0854805i
$451$	−5.02913e11	+	8.71071e11i	−0.572398	+	0.991423i
$452$	2.20287e11	−	3.81548e11i	0.248236	−	0.429958i
$453$	1.28634e9	+	2.22801e9i	0.00143521	+	0.00248585i
$454$	2.61914e11			0.289340
$455$		0			0
$456$	7.52506e9			0.00815020
$457$	−1.26740e10	−	2.19519e10i	−0.0135922	−	0.0235424i	0.859149	−	0.511725i	$-0.170993\pi$
$457$	−1.26740e10	−	2.19519e10i	−0.0135922	−	0.0235424i	−0.872741	+	0.488183i	$0.837660\pi$
$458$	−4.65547e10	+	8.06350e10i	−0.0494389	+	0.0856306i
$459$	−2.31779e10	+	4.01452e10i	−0.0243734	+	0.0422160i
$460$	7.40358e11	+	1.28234e12i	0.770960	+	1.33534i
$461$	−4.16101e11			−0.429086			−0.214543	−	0.976715i	$-0.568826\pi$
$461$	−4.16101e11			−0.429086			−0.214543	+	0.976715i	$0.568826\pi$
$462$		0			0
$463$	1.60498e12			1.62313			0.811567	−	0.584259i	$-0.198615\pi$
$463$	1.60498e12			1.62313			0.811567	+	0.584259i	$0.198615\pi$
$464$	−7.40133e10	−	1.28195e11i	−0.0741274	−	0.128392i
$465$	−2.56842e10	+	4.44863e10i	−0.0254757	+	0.0441253i
$466$	−1.27850e11	+	2.21442e11i	−0.125592	+	0.217532i
$467$	−9.14312e10	−	1.58363e11i	−0.0889546	−	0.154074i	0.818115	−	0.575055i	$-0.195019\pi$
$467$	−9.14312e10	−	1.58363e11i	−0.0889546	−	0.154074i	−0.907069	+	0.420981i	$0.861686\pi$
$468$	−4.54110e11			−0.437578
$469$		0			0
$470$	9.39007e10			0.0887622
$471$	1.20034e9	+	2.07904e9i	0.00112385	+	0.00194657i
$472$	−1.92486e11	+	3.33395e11i	−0.178509	+	0.309186i
$473$	−1.05851e11	+	1.83340e11i	−0.0972347	+	0.168415i
$474$	2.48685e9	+	4.30735e9i	0.00226281	+	0.00391929i
$475$	3.22145e11			0.290355
$476$		0			0
$477$	−1.30704e12			−1.15600
$478$	−1.21221e11	−	2.09961e11i	−0.106207	−	0.183956i
$479$	−9.58675e11	+	1.66047e12i	−0.832073	+	1.44119i	0.0643179	+	0.997929i	$0.479513\pi$
$479$	−9.58675e11	+	1.66047e12i	−0.832073	+	1.44119i	−0.896391	+	0.443264i	$0.853821\pi$
$480$	−1.12440e10	+	1.94751e10i	−0.00966793	+	0.0167454i
$481$	−3.72697e11	−	6.45530e11i	−0.317470	−	0.549874i
$482$	−1.83312e11			−0.154696
$483$		0			0
$484$	5.89916e11			0.488636
$485$	8.24660e11	+	1.42835e12i	0.676763	+	1.17219i
$486$	1.08544e10	−	1.88003e10i	0.00882555	−	0.0152863i
$487$	−6.03193e11	+	1.04476e12i	−0.485932	+	0.841660i	−0.999869	−	0.0161683i	$-0.994853\pi$
$487$	−6.03193e11	+	1.04476e12i	−0.485932	+	0.841660i	0.513937	+	0.857828i	$0.328187\pi$
$488$	2.30008e11	+	3.98386e11i	0.183592	+	0.317991i
$489$	−2.24360e9			−0.00177442
$490$		0			0
$491$	1.46000e12			1.13367			0.566835	−	0.823831i	$-0.308168\pi$
$491$	1.46000e12			1.13367			0.566835	+	0.823831i	$0.308168\pi$
$492$	−2.45153e10	−	4.24617e10i	−0.0188623	−	0.0326704i
$493$	−1.18064e11	+	2.04492e11i	−0.0900129	+	0.155907i
$494$	5.32435e10	−	9.22204e10i	0.0402249	−	0.0696716i
$495$	−5.49048e11	−	9.50978e11i	−0.411042	−	0.711946i
$496$	1.97210e12			1.46305
$497$		0			0
$498$	1.18381e10			0.00862481
$499$	6.29177e11	+	1.08977e12i	0.454276	+	0.786830i	0.998646	−	0.0520155i	$-0.0165645\pi$
$499$	6.29177e11	+	1.08977e12i	0.454276	+	0.786830i	−0.544370	+	0.838845i	$0.683231\pi$
$500$	4.62473e11	−	8.01027e11i	0.330919	−	0.573168i
$501$	4.46870e9	−	7.74001e9i	0.00316892	−	0.00548873i
$502$	−8.50222e10	−	1.47263e11i	−0.0597538	−	0.103497i
$503$	1.60066e12			1.11492			0.557458	−	0.830205i	$-0.311777\pi$
$503$	1.60066e12			1.11492			0.557458	+	0.830205i	$0.311777\pi$
$504$		0			0
$505$	−1.39060e12			−0.951463
$506$	1.71248e11	+	2.96610e11i	0.116131	+	0.201145i
$507$	−1.41518e10	+	2.45116e10i	−0.00951209	+	0.0164754i
$508$	2.43143e11	−	4.21135e11i	0.161985	−	0.280566i
$509$	−3.60832e9	−	6.24980e9i	−0.00238273	−	0.00412701i	0.864832	−	0.502062i	$-0.167425\pi$
$509$	−3.60832e9	−	6.24980e9i	−0.00238273	−	0.00412701i	−0.867214	+	0.497935i	$0.834092\pi$
$510$	1.07168e10			0.00701452
$511$		0			0
$512$	1.46876e12			0.944572
$513$	−2.71474e10	−	4.70208e10i	−0.0173062	−	0.0299752i
$514$	7.92183e10	−	1.37210e11i	0.0500601	−	0.0867066i
$515$	1.27187e12	−	2.20295e12i	0.796730	−	1.37998i
$516$	−5.15990e9	−	8.93720e9i	−0.00320418	−	0.00554981i
$517$	−3.47516e11			−0.213928
$518$		0			0
$519$	−3.61852e10			−0.0218916
$520$	2.16593e11	+	3.75149e11i	0.129906	+	0.225003i
$521$	−2.16286e11	+	3.74619e11i	−0.128605	+	0.222751i	−0.923136	−	0.384472i	$-0.874383\pi$
$521$	−2.16286e11	+	3.74619e11i	−0.128605	+	0.222751i	0.794531	+	0.607223i	$0.207717\pi$
$522$	3.68564e10	−	6.38372e10i	0.0217268	−	0.0376319i
$523$	3.75915e11	+	6.51104e11i	0.219701	+	0.380533i	0.954717	−	0.297517i	$-0.0961585\pi$
$523$	3.75915e11	+	6.51104e11i	0.219701	+	0.380533i	−0.735015	+	0.678050i	$0.762825\pi$
$524$	−2.11799e12			−1.22725
$525$		0			0
$526$	−6.05145e11			−0.344686
$527$	−1.57291e12	−	2.72436e12i	−0.888293	−	1.53857i
$528$	1.24318e10	−	2.15325e10i	0.00696116	−	0.0120571i
$529$	−8.17104e11	+	1.41526e12i	−0.453656	+	0.785755i
$530$	3.02258e11	+	5.23525e11i	0.166393	+	0.288202i
$531$	1.38842e12			0.757869
$532$		0			0
$533$	−1.43103e12			−0.768024
$534$	−5.81699e9	−	1.00753e10i	−0.00309573	−	0.00536196i
$535$	−5.17104e11	+	8.95650e11i	−0.272889	+	0.472657i
$536$	−5.77446e11	+	1.00017e12i	−0.302183	+	0.523396i
$537$	−7.36461e9	−	1.27559e10i	−0.00382178	−	0.00661951i
$538$	−8.33091e11			−0.428719
$539$		0			0
$540$	1.07088e11			0.0541964
$541$	−9.04475e11	−	1.56660e12i	−0.453951	−	0.786266i	0.544676	−	0.838646i	$-0.316653\pi$
$541$	−9.04475e11	−	1.56660e12i	−0.453951	−	0.786266i	−0.998627	+	0.0523804i	$0.983319\pi$
$542$	3.41875e11	−	5.92145e11i	0.170165	−	0.294735i
$543$	−1.38040e9	+	2.39092e9i	−0.000681404	+	0.00118023i
$544$	−6.88586e11	−	1.19267e12i	−0.337103	−	0.583880i
$545$	−3.62941e12			−1.76219
$546$		0			0
$547$	−9.94162e11			−0.474804			−0.237402	−	0.971411i	$-0.576296\pi$
$547$	−9.94162e11			−0.474804			−0.237402	+	0.971411i	$0.576296\pi$
$548$	4.21652e10	+	7.30323e10i	0.0199729	+	0.0345942i
$549$	8.29535e11	−	1.43680e12i	0.389726	−	0.675025i
$550$	−7.34831e10	+	1.27277e11i	−0.0342417	+	0.0593084i
$551$	−1.38284e11	−	2.39515e11i	−0.0639130	−	0.110701i
$552$	−3.44345e10			−0.0157858
$553$		0			0
$554$	1.79077e11			0.0807694
$555$	4.39317e10	+	7.60920e10i	0.0196544	+	0.0340424i
$556$	4.50710e11	−	7.80652e11i	0.200014	−	0.346434i
$557$	−2.24919e11	+	3.89571e11i	−0.0990098	+	0.171490i	−0.911275	−	0.411798i	$-0.864901\pi$
$557$	−2.24919e11	+	3.89571e11i	−0.0990098	+	0.171490i	0.812265	+	0.583288i	$0.198234\pi$
$558$	4.91023e11	+	8.50476e11i	0.214411	+	0.371371i
$559$	−3.01198e11			−0.130466
$560$		0			0
$561$	−3.96616e10			−0.0169059
$562$	−3.37450e10	−	5.84480e10i	−0.0142691	−	0.0247148i
$563$	1.65320e12	−	2.86343e12i	0.693487	−	1.20115i	−0.277201	−	0.960812i	$-0.589407\pi$
$563$	1.65320e12	−	2.86343e12i	0.693487	−	1.20115i	0.970688	−	0.240343i	$-0.0772598\pi$
$564$	8.47012e9	−	1.46707e10i	0.00352479	−	0.00610512i
$565$	7.57864e11	+	1.31266e12i	0.312877	+	0.541918i
$566$	−3.26965e11			−0.133914
$567$		0			0
$568$	−1.26317e11			−0.0509206
$569$	9.61760e11	+	1.66582e12i	0.384646	+	0.666227i	0.991720	−	0.128418i	$-0.0409901\pi$
$569$	9.61760e11	+	1.66582e12i	0.384646	+	0.666227i	−0.607074	+	0.794646i	$0.707657\pi$
$570$	−6.27609e9	+	1.08705e10i	−0.00249030	+	0.00431333i
$571$	1.44994e12	−	2.51137e12i	0.570804	−	0.988661i	−0.425680	−	0.904874i	$-0.639965\pi$
$571$	1.44994e12	−	2.51137e12i	0.570804	−	0.988661i	0.996484	−	0.0837874i	$-0.0267017\pi$
$572$	−3.88648e11	−	6.73158e11i	−0.151801	−	0.262927i
$573$	−4.56195e10			−0.0176789
$574$		0			0
$575$	−1.47413e12			−0.562379
$576$	−8.76772e11	−	1.51861e12i	−0.331884	−	0.574839i
$577$	1.38264e12	−	2.39480e12i	0.519299	−	0.899452i	−0.480450	−	0.877022i	$-0.659527\pi$
$577$	1.38264e12	−	2.39480e12i	0.519299	−	0.899452i	0.999748	−	0.0224293i	$-0.00714007\pi$
$578$	−2.74882e9	+	4.76110e9i	−0.00102440	+	0.00177432i
$579$	1.47800e9	+	2.55998e9i	0.000546540	+	0.000946634i
$580$	5.45487e11			0.200151
$581$		0			0
$582$	−1.85966e10			−0.00671861
$583$	−1.11862e12	−	1.93751e12i	−0.401029	−	0.694602i
$584$	−6.77889e11	+	1.17414e12i	−0.241157	+	0.417697i
$585$	7.81151e11	−	1.35299e12i	0.275761	−	0.477633i
$586$	−2.53257e11	−	4.38653e11i	−0.0887200	−	0.153668i
$587$	2.55711e12			0.888950			0.444475	−	0.895791i	$-0.353390\pi$
$587$	2.55711e12			0.888950			0.444475	+	0.895791i	$0.353390\pi$
$588$		0			0
$589$	3.68459e12			1.26145
$590$	−3.21076e11	−	5.56120e11i	−0.109087	−	0.188945i
$591$	2.93820e10	−	5.08911e10i	0.00990690	−	0.0171592i
$592$	1.68660e12	−	2.92127e12i	0.564369	−	0.977516i
$593$	1.90543e12	+	3.30030e12i	0.632771	+	1.09599i	0.986983	+	0.160827i	$0.0514160\pi$
$593$	1.90543e12	+	3.30030e12i	0.632771	+	1.09599i	−0.354211	+	0.935165i	$0.615251\pi$
$594$	2.47700e10			0.00816370
$595$		0			0
$596$	−5.48561e12			−1.78081
$597$	−5.49629e9	−	9.51986e9i	−0.00177086	−	0.00306723i
$598$	−2.43641e11	+	4.21998e11i	−0.0779103	+	0.134945i
$599$	−1.26327e12	+	2.18804e12i	−0.400935	+	0.694441i	−0.993839	−	0.110833i	$-0.964648\pi$
$599$	−1.26327e12	+	2.18804e12i	−0.400935	+	0.694441i	0.592904	+	0.805273i	$0.297981\pi$
$600$	−7.38798e9	−	1.27964e10i	−0.00232726	−	0.00403094i
$601$	−2.55170e12			−0.797802			−0.398901	−	0.916994i	$-0.630608\pi$
$601$	−2.55170e12			−0.797802			−0.398901	+	0.916994i	$0.630608\pi$
$602$		0			0
$603$	4.16517e12			1.28293
$604$	1.81985e11	+	3.15207e11i	0.0556376	+	0.0963672i
$605$	−1.01476e12	+	1.75761e12i	−0.307938	+	0.533365i
$606$	7.83973e9	−	1.35788e10i	0.00236143	−	0.00409011i
$607$	−2.06939e12	−	3.58429e12i	−0.618719	−	1.07165i	−0.989720	−	0.143020i	$-0.954319\pi$
$607$	−2.06939e12	−	3.58429e12i	−0.618719	−	1.07165i	0.371001	−	0.928633i	$-0.379015\pi$
$608$	1.61303e12			0.478716
$609$		0			0
$610$	−7.67331e11			−0.224387
$611$	−2.47212e11	−	4.28184e11i	−0.0717604	−	0.124293i
$612$	−1.63905e12	+	2.83892e12i	−0.472293	+	0.818036i
$613$	7.71066e11	−	1.33553e12i	0.220556	−	0.382015i	−0.734421	−	0.678695i	$-0.762546\pi$
$613$	7.71066e11	−	1.33553e12i	0.220556	−	0.382015i	0.954977	+	0.296680i	$0.0958794\pi$
$614$	−3.79056e11	−	6.56543e11i	−0.107633	−	0.186426i
$615$	1.68683e11			0.0475480
$616$		0			0
$617$	1.47701e12			0.410299			0.205149	−	0.978731i	$-0.434232\pi$
$617$	1.47701e12			0.410299			0.205149	+	0.978731i	$0.434232\pi$
$618$	1.43407e10	+	2.48389e10i	0.00395479	+	0.00684990i
$619$	1.38355e12	−	2.39638e12i	0.378780	−	0.656066i	−0.612105	−	0.790776i	$-0.709677\pi$
$619$	1.38355e12	−	2.39638e12i	0.378780	−	0.656066i	0.990885	+	0.134710i	$0.0430104\pi$
$620$	−3.63365e12	+	6.29367e12i	−0.987599	+	1.71057i
$621$	1.24226e11	+	2.15166e11i	0.0335197	+	0.0580579i
$622$	4.87720e11			0.130651
$623$		0			0
$624$	3.53744e10			0.00934025
$625$	2.36776e12	+	4.10109e12i	0.620695	+	1.07508i
$626$	7.37102e11	−	1.27670e12i	0.191842	−	0.332280i
$627$	2.32272e10	−	4.02306e10i	0.00600195	−	0.0103957i
$628$	1.69817e11	+	2.94132e11i	0.0435675	+	0.0754611i
$629$	−5.38081e12			−1.37063
$630$		0			0
$631$	4.12567e11			0.103601			0.0518004	−	0.998657i	$-0.483504\pi$
$631$	4.12567e11			0.103601			0.0518004	+	0.998657i	$0.483504\pi$
$632$	7.25640e11	+	1.25685e12i	0.180923	+	0.313368i
$633$	8.34608e9	−	1.44558e10i	0.00206617	−	0.00357871i
$634$	1.39314e11	−	2.41299e11i	0.0342446	−	0.0593134i
$635$	8.36497e11	+	1.44886e12i	0.204166	+	0.353625i
$636$	1.09058e11			0.0264303
$637$		0			0
$638$	1.26174e11			0.0301492
$639$	2.27783e11	+	3.94533e11i	0.0540466	+	0.0936114i
$640$	−2.09567e12	+	3.62980e12i	−0.493756	+	0.855210i
$641$	−3.38620e12	+	5.86507e12i	−0.792230	+	1.37218i	0.132353	+	0.991203i	$0.457747\pi$
$641$	−3.38620e12	+	5.86507e12i	−0.792230	+	1.37218i	−0.924583	+	0.380981i	$0.875586\pi$
$642$	−5.83050e9	−	1.00987e10i	−0.00135456	−	0.00234616i
$643$	5.48262e12			1.26485			0.632424	−	0.774622i	$-0.282060\pi$
$643$	5.48262e12			1.26485			0.632424	+	0.774622i	$0.282060\pi$
$644$		0			0
$645$	3.55037e10			0.00807710
$646$	−3.84351e11	−	6.65716e11i	−0.0868324	−	0.150398i
$647$	−2.04205e12	+	3.53693e12i	−0.458139	+	0.793519i	−0.998863	−	0.0476807i	$-0.984817\pi$
$647$	−2.04205e12	+	3.53693e12i	−0.458139	+	0.793519i	0.540724	+	0.841200i	$0.318150\pi$
$648$	1.05470e12	−	1.82679e12i	0.234985	−	0.407006i
$649$	1.18827e12	+	2.05814e12i	0.262914	+	0.455380i
$650$	−2.09094e11			−0.0459444
$651$		0			0
$652$	−3.17412e11			−0.0687874
$653$	2.36249e12	+	4.09196e12i	0.508465	+	0.880688i	0.999952	+	0.00980273i	$0.00312036\pi$
$653$	2.36249e12	+	4.09196e12i	0.508465	+	0.880688i	−0.491487	+	0.870885i	$0.663546\pi$
$654$	2.04613e10	−	3.54401e10i	0.00437355	−	0.00757521i
$655$	3.64332e12	−	6.31041e12i	0.773413	−	1.33959i
$656$	−3.23797e12	−	5.60833e12i	−0.682662	−	1.18241i
$657$	4.88967e12			1.02385
$658$		0			0
$659$	−2.35775e12			−0.486983			−0.243492	−	0.969903i	$-0.578293\pi$
$659$	−2.35775e12			−0.486983			−0.243492	+	0.969903i	$0.578293\pi$
$660$	4.58120e10	+	7.93487e10i	0.00939792	+	0.0162777i
$661$	−3.56976e12	+	6.18301e12i	−0.727332	+	1.25978i	0.230674	+	0.973031i	$0.425907\pi$
$661$	−3.56976e12	+	6.18301e12i	−0.727332	+	1.25978i	−0.958007	+	0.286746i	$0.907427\pi$
$662$	3.61114e11	−	6.25467e11i	0.0730774	−	0.126574i
$663$	−2.82140e10	−	4.88681e10i	−0.00567093	−	0.00982234i
$664$	3.45424e12			0.689599
$665$		0			0
$666$	1.67975e12			0.330834
$667$	6.32784e11	+	1.09601e12i	0.123791	+	0.214412i
$668$	6.32206e11	−	1.09501e12i	0.122847	−	0.212777i
$669$	2.74243e10	−	4.75003e10i	0.00529320	−	0.00916810i
$670$	−9.63209e11	−	1.66833e12i	−0.184665	−	0.319849i
$671$	2.83981e12			0.540802
$672$		0			0
$673$	3.71999e12			0.698994			0.349497	−	0.936937i	$-0.386352\pi$
$673$	3.71999e12			0.698994			0.349497	+	0.936937i	$0.386352\pi$
$674$	−3.22580e11	−	5.58725e11i	−0.0602099	−	0.104287i
$675$	−5.33059e10	+	9.23285e10i	−0.00988344	+	0.0171186i
$676$	−2.00212e12	+	3.46777e12i	−0.368748	+	0.638690i
$677$	3.61937e12	+	6.26893e12i	0.662192	+	1.14695i	0.980038	+	0.198808i	$0.0637071\pi$
$677$	3.61937e12	+	6.26893e12i	0.662192	+	1.14695i	−0.317846	+	0.948142i	$0.602960\pi$
$678$	−1.70903e10			−0.00310610
$679$		0			0
$680$	3.12705e12			0.560848
$681$	8.12800e10	+	1.40781e11i	0.0144818	+	0.0250832i
$682$	−8.40478e11	+	1.45575e12i	−0.148764	+	0.257666i
$683$	1.34575e12	−	2.33091e12i	0.236631	−	0.409857i	−0.723114	−	0.690728i	$-0.757290\pi$
$683$	1.34575e12	−	2.33091e12i	0.236631	−	0.409857i	0.959746	+	0.280871i	$0.0906233\pi$
$684$	−1.91977e12	−	3.32514e12i	−0.335348	−	0.580841i
$685$	−2.90127e11			−0.0503478
$686$		0			0
$687$	−5.77893e10			−0.00989788
$688$	−6.81517e11	−	1.18042e12i	−0.115966	−	0.200858i
$689$	1.59151e12	−	2.75657e12i	0.269043	−	0.465997i
$690$	2.87192e10	−	4.97432e10i	0.00482339	−	0.00835435i
$691$	−2.24362e12	−	3.88606e12i	−0.374367	−	0.648423i	0.615865	−	0.787852i	$-0.288807\pi$
$691$	−2.24362e12	−	3.88606e12i	−0.374367	−	0.648423i	−0.990232	+	0.139429i	$0.955473\pi$
$692$	−5.11929e12			−0.848657
$693$		0			0
$694$	−1.22757e12			−0.200876
$695$	1.55060e12	+	2.68572e12i	0.252098	+	0.436646i
$696$	−6.34274e9	+	1.09859e10i	−0.00102455	+	0.00177458i
$697$	−5.16511e12	+	8.94623e12i	−0.828956	+	1.43579i
$698$	5.26460e11	+	9.11856e11i	0.0839491	+	0.145404i
$699$	−1.58703e11			−0.0251442
$700$		0			0
$701$	−3.40308e12			−0.532280			−0.266140	−	0.963934i	$-0.585748\pi$
$701$	−3.40308e12			−0.532280			−0.266140	+	0.963934i	$0.585748\pi$
$702$	1.76206e10	+	3.05198e10i	0.00273844	+	0.00474312i
$703$	3.15118e12	−	5.45800e12i	0.486602	−	0.842819i
$704$	1.50076e12	−	2.59940e12i	0.230269	−	0.398837i
$705$	2.91402e10	+	5.04724e10i	0.00444265	+	0.00769489i
$706$	2.45080e12			0.371267
$707$		0			0
$708$	−1.15848e11			−0.0173276
$709$	−4.88326e12	−	8.45806e12i	−0.725775	−	1.25708i	−0.958654	−	0.284574i	$-0.908148\pi$
$709$	−4.88326e12	−	8.45806e12i	−0.725775	−	1.25708i	0.232879	−	0.972506i	$-0.425185\pi$
$710$	1.05351e11	−	1.82474e11i	0.0155589	−	0.0269487i
$711$	2.61705e12	−	4.53287e12i	0.384060	−	0.665212i
$712$	−1.69734e12	−	2.93989e12i	−0.247520	−	0.428717i
$713$	−1.68606e13			−2.44327
$714$		0			0
$715$	2.67417e12			0.382660
$716$	−1.04190e12	−	1.80463e12i	−0.148156	−	0.256614i
$717$	7.52373e10	−	1.30315e11i	0.0106316	−	0.0184144i
$718$	−3.51915e11	+	6.09535e11i	−0.0494172	+	0.0855931i
$719$	2.70236e12	+	4.68063e12i	0.377106	+	0.653167i	0.990640	−	0.136502i	$-0.0435859\pi$
$719$	2.70236e12	+	4.68063e12i	0.377106	+	0.653167i	−0.613534	+	0.789668i	$0.710253\pi$
$720$	7.07001e12			0.980447
$721$		0			0
$722$	−8.70535e11			−0.119225
$723$	−5.68873e10	−	9.85317e10i	−0.00774271	−	0.0134108i
$724$	−1.95291e11	+	3.38253e11i	−0.0264155	+	0.0457529i
$725$	−2.71530e11	+	4.70304e11i	−0.0365003	+	0.0632204i
$726$	−1.14417e10	−	1.98176e10i	−0.00152854	−	0.00264751i
$727$	2.66584e11			0.0353939			0.0176970	−	0.999843i	$-0.494367\pi$
$727$	2.66584e11			0.0353939			0.0176970	+	0.999843i	$0.494367\pi$
$728$		0			0
$729$	−7.59864e12			−0.996465
$730$	−1.13075e12	−	1.95852e12i	−0.147372	−	0.255256i
$731$	−1.08713e12	+	1.88297e12i	−0.140817	+	0.243902i
$732$	−6.92156e10	+	1.19885e11i	−0.00891054	+	0.0154335i
$733$	6.89115e12	+	1.19358e13i	0.881706	+	1.52716i	0.849443	+	0.527680i	$0.176938\pi$
$733$	6.89115e12	+	1.19358e13i	0.881706	+	1.52716i	0.0322624	+	0.999479i	$0.489729\pi$
$734$	−1.93610e12			−0.246204
$735$		0			0
$736$	−7.38121e12			−0.927208
$737$	3.56474e12	+	6.17431e12i	0.445065	+	0.770876i
$738$	1.61241e12	−	2.79278e12i	0.200089	−	0.346564i
$739$	5.03261e12	−	8.71674e12i	0.620717	−	1.07511i	−0.368636	−	0.929574i	$-0.620175\pi$
$739$	5.03261e12	−	8.71674e12i	0.620717	−	1.07511i	0.989352	−	0.145539i	$-0.0464917\pi$
$740$	6.21522e12	+	1.07651e13i	0.761927	+	1.31970i
$741$	6.60923e10			0.00805321
$742$		0			0
$743$	1.14809e13			1.38206			0.691029	−	0.722827i	$-0.257158\pi$
$743$	1.14809e13			1.38206			0.691029	+	0.722827i	$0.257158\pi$
$744$	−8.45016e10	−	1.46361e11i	−0.0101108	−	0.0175125i
$745$	9.43622e12	−	1.63440e13i	1.12226	−	1.94382i
$746$	1.31559e12	−	2.27868e12i	0.155524	−	0.269375i
$747$	−6.22894e12	−	1.07888e13i	−0.731933	−	1.26775i
$748$	−5.61110e12			−0.655377
$749$		0			0
$750$	−3.58796e10			−0.00414068
$751$	−2.17453e12	−	3.76639e12i	−0.249451	−	0.432062i	0.713923	−	0.700225i	$-0.246917\pi$
$751$	−2.17453e12	−	3.76639e12i	−0.249451	−	0.432062i	−0.963374	+	0.268163i	$0.913583\pi$
$752$	1.11873e12	−	1.93770e12i	0.127569	−	0.220956i
$753$	5.27700e10	−	9.14003e10i	0.00598149	−	0.0103602i
$754$	8.97559e10	+	1.55462e11i	0.0101133	+	0.0175167i
$755$	−1.25218e12			−0.140251
$756$		0			0
$757$	−2.90851e12			−0.321914			−0.160957	−	0.986961i	$-0.551458\pi$
$757$	−2.90851e12			−0.321914			−0.160957	+	0.986961i	$0.551458\pi$
$758$	1.59771e12	+	2.76731e12i	0.175787	+	0.304472i
$759$	−1.06287e11	+	1.84094e11i	−0.0116250	+	0.0201350i
$760$	−1.83131e12	+	3.17191e12i	−0.199113	+	0.344874i
$761$	−6.22820e12	−	1.07876e13i	−0.673180	−	1.16598i	−0.976997	−	0.213252i	$-0.931594\pi$
$761$	−6.22820e12	−	1.07876e13i	−0.673180	−	1.16598i	0.303817	−	0.952730i	$-0.401739\pi$
$762$	−1.88635e10			−0.00202687
$763$		0			0
$764$	−6.45400e12			−0.685344
$765$	−5.63893e12	−	9.76691e12i	−0.595278	−	1.03105i
$766$	−1.54082e12	+	2.66878e12i	−0.161705	+	0.280081i
$767$	−1.69059e12	+	2.92820e12i	−0.176384	+	0.305507i
$768$	5.41001e10	+	9.37041e10i	0.00561142	+	0.00971926i
$769$	8.52239e12			0.878806			0.439403	−	0.898290i	$-0.355190\pi$
$769$	8.52239e12			0.878806			0.439403	+	0.898290i	$0.355190\pi$
$770$		0			0
$771$	9.83354e10			0.0100222
$772$	2.09100e11	+	3.62171e11i	0.0211873	+	0.0366974i
$773$	4.80341e12	−	8.31975e12i	0.483885	−	0.838113i	−0.515944	−	0.856623i	$-0.672559\pi$
$773$	4.80341e12	−	8.31975e12i	0.483885	−	0.838113i	0.999829	+	0.0185091i	$0.00589196\pi$
$774$	3.39376e11	−	5.87816e11i	0.0339896	−	0.0588717i
$775$	−3.61748e12	−	6.26566e12i	−0.360204	−	0.623891i
$776$	−5.42631e12			−0.537188
$777$		0			0
$778$	2.31874e12			0.226905
$779$	−6.04971e12	−	1.04784e13i	−0.588595	−	1.01948i
$780$	−6.51785e10	+	1.12892e11i	−0.00630490	+	0.0109204i
$781$	−3.89895e11	+	6.75317e11i	−0.0374988	+	0.0649499i
$782$	1.75878e12	+	3.04630e12i	0.168183	+	0.291301i
$783$	9.15284e10			0.00870218
$784$		0			0
$785$	−1.16846e12			−0.109825
$786$	4.10795e10	+	7.11518e10i	0.00383905	+	0.00664943i
$787$	−9.01714e12	+	1.56181e13i	−0.837881	+	1.45125i	0.0537815	+	0.998553i	$0.482873\pi$
$787$	−9.01714e12	+	1.56181e13i	−0.837881	+	1.45125i	−0.891663	+	0.452700i	$0.850461\pi$
$788$	4.15680e12	−	7.19979e12i	0.384053	−	0.665199i
$789$	−1.87795e11	−	3.25271e11i	−0.0172519	−	0.0298812i
$790$	−2.42081e12			−0.221126
$791$		0			0
$792$	3.61276e12			0.326269
$793$	2.02015e12	+	3.49901e12i	0.181407	+	0.314207i
$794$	8.32362e11	−	1.44169e12i	0.0743225	−	0.128730i
$795$	−1.87599e11	+	3.24932e11i	−0.0166563	+	0.0288496i
$796$	−7.77584e11	−	1.34682e12i	−0.0686497	−	0.118905i
$797$	1.36276e12			0.119634			0.0598171	−	0.998209i	$-0.480948\pi$
$797$	1.36276e12			0.119634			0.0598171	+	0.998209i	$0.480948\pi$
$798$		0			0
$799$	−3.56913e12			−0.309814
$800$	−1.58365e12	−	2.74297e12i	−0.136696	−	0.236764i
$801$	−6.12155e12	+	1.06028e13i	−0.525430	+	0.910071i
$802$	−1.63893e12	+	2.83872e12i	−0.139887	+	0.242291i
$803$	4.18480e12	+	7.24829e12i	0.355185	+	0.615199i
$804$	−3.47538e11			−0.0293325
$805$		0			0
$806$	−2.39156e12			−0.199606
$807$	−2.58534e11	−	4.47793e11i	−0.0214578	−	0.0371661i
$808$	2.28756e12	−	3.96217e12i	0.188809	−	0.327026i
$809$	−6.21326e12	+	1.07617e13i	−0.509978	+	0.883308i	0.489955	+	0.871748i	$0.337013\pi$
$809$	−6.21326e12	+	1.07617e13i	−0.509978	+	0.883308i	−0.999933	+	0.0115603i	$0.996320\pi$
$810$	1.75929e12	+	3.04718e12i	0.143600	+	0.248723i
$811$	7.29519e11			0.0592165			0.0296082	−	0.999562i	$-0.490574\pi$
$811$	7.29519e11			0.0592165			0.0296082	+	0.999562i	$0.490574\pi$
$812$		0			0
$813$	4.24377e11			0.0340678
$814$	1.43761e12	+	2.49001e12i	0.114770	+	0.198788i
$815$	5.46005e11	−	9.45708e11i	0.0433498	−	0.0750841i
$816$	1.27679e11	−	2.21147e11i	0.0100813	−	0.0174613i
$817$	−1.27332e12	−	2.20546e12i	−0.0999860	−	0.173181i
$818$	4.24600e11			0.0331582
$819$		0			0
$820$	2.38643e13			1.84326
$821$	1.01494e13	+	1.75792e13i	0.779642	+	1.35038i	0.932148	+	0.362077i	$0.117932\pi$
$821$	1.01494e13	+	1.75792e13i	0.779642	+	1.35038i	−0.152506	+	0.988303i	$0.548734\pi$
$822$	1.63563e9	−	2.83300e9i	0.000124958	−	0.000216433i
$823$	5.23649e12	−	9.06987e12i	0.397870	−	0.689131i	−0.595593	−	0.803286i	$-0.703083\pi$
$823$	5.23649e12	−	9.06987e12i	0.397870	−	0.689131i	0.993463	+	0.114156i	$0.0364162\pi$
$824$	4.18450e12	+	7.24776e12i	0.316206	+	0.547686i
$825$	−9.12162e10			−0.00685535
$826$		0			0
$827$	−1.49862e13			−1.11408			−0.557039	−	0.830486i	$-0.688063\pi$
$827$	−1.49862e13			−1.11408			−0.557039	+	0.830486i	$0.688063\pi$
$828$	8.78481e12	+	1.52157e13i	0.649525	+	1.12501i
$829$	−4.07846e12	+	7.06410e12i	−0.299917	+	0.519471i	−0.976117	−	0.217247i	$-0.930292\pi$
$829$	−4.07846e12	+	7.06410e12i	−0.299917	+	0.519471i	0.676200	+	0.736718i	$0.263626\pi$
$830$	−2.88093e12	+	4.98991e12i	−0.210708	+	0.364957i
$831$	5.55732e10	+	9.62556e10i	0.00404260	+	0.00700199i
$832$	4.27038e12			0.308967
$833$		0			0
$834$	−3.49670e10			−0.00250271
$835$	2.17501e12	+	3.76723e12i	0.154836	+	0.268184i
$836$	3.28605e12	−	5.69160e12i	0.232673	−	0.403001i
$837$	−6.09697e11	+	1.05603e12i	−0.0429388	+	0.0743721i
$838$	−3.28758e12	−	5.69426e12i	−0.230292	−	0.398877i
$839$	1.92668e13			1.34239			0.671197	−	0.741279i	$-0.265780\pi$
$839$	1.92668e13			1.34239			0.671197	+	0.741279i	$0.265780\pi$
$840$		0			0
$841$	−1.40409e13			−0.967862
$842$	1.19244e12	+	2.06536e12i	0.0817582	+	0.141609i
$843$	2.09442e10	−	3.62764e10i	0.00142837	−	0.00247400i
$844$	1.18076e12	−	2.04513e12i	0.0800975	−	0.138733i
$845$	−6.88799e12	−	1.19304e13i	−0.464770	−	0.805004i
$846$	1.11419e12			0.0747813
$847$		0			0
$848$	1.44044e13			0.956562
$849$	−1.01467e11	−	1.75746e11i	−0.00670256	−	0.0116092i
$850$	−7.54700e11	+	1.30718e12i	−0.0495894	+	0.0858914i
$851$	−1.44197e13	+	2.49757e13i	−0.942483	+	1.63243i
$852$	−1.90060e10	−	3.29194e10i	−0.00123570	−	0.00214030i
$853$	−4.93520e12			−0.319179			−0.159589	−	0.987183i	$-0.551017\pi$
$853$	−4.93520e12			−0.319179			−0.159589	+	0.987183i	$0.551017\pi$
$854$		0			0
$855$	1.32094e13			0.845346
$856$	−1.70129e12	−	2.94671e12i	−0.108304	−	0.187588i
$857$	−1.28953e13	+	2.23353e13i	−0.816614	+	1.41442i	0.0915489	+	0.995801i	$0.470818\pi$
$857$	−1.28953e13	+	2.23353e13i	−0.816614	+	1.41442i	−0.908163	+	0.418617i	$0.862515\pi$
$858$	−1.50761e10	+	2.61125e10i	−0.000949719	+	0.00164496i
$859$	−2.82867e12	−	4.89940e12i	−0.177261	−	0.307025i	0.763680	−	0.645595i	$-0.223390\pi$
$859$	−2.82867e12	−	4.89940e12i	−0.177261	−	0.307025i	−0.940941	+	0.338569i	$0.890057\pi$
$860$	5.02287e12			0.313119
$861$		0			0
$862$	−1.48834e12			−0.0918161
$863$	3.14748e11	+	5.45160e11i	0.0193159	+	0.0334561i	0.875522	−	0.483179i	$-0.160518\pi$
$863$	3.14748e11	+	5.45160e11i	0.0193159	+	0.0334561i	−0.856206	+	0.516635i	$0.827185\pi$
$864$	−2.66912e11	+	4.62305e11i	−0.0162951	+	0.0282239i
$865$	8.80608e12	−	1.52526e13i	0.534823	−	0.926341i
$866$	−5.06043e11	−	8.76492e11i	−0.0305743	−	0.0529563i
$867$	−3.41217e9			−0.000205090
$868$		0			0
$869$	8.95917e12			0.532940
$870$	−1.05800e10	−	1.83251e10i	−0.000626108	−	0.00108445i
$871$	−5.07169e12	+	8.78442e12i	−0.298587	+	0.517168i
$872$	5.97043e12	−	1.03411e13i	0.349688	−	0.605678i
$873$	9.78510e12	+	1.69483e13i	0.570166	+	0.987557i
$874$	−4.12000e12			−0.238834
$875$		0			0
$876$	−4.07990e11			−0.0234089
$877$	−1.49229e11	−	2.58471e11i	−0.00851832	−	0.0147542i	0.861735	−	0.507359i	$-0.169378\pi$
$877$	−1.49229e11	−	2.58471e11i	−0.00851832	−	0.0147542i	−0.870253	+	0.492605i	$0.836045\pi$
$878$	−1.72948e12	+	2.99554e12i	−0.0982177	+	0.170118i
$879$	1.57186e11	−	2.72255e11i	0.00888107	−	0.0153825i
$880$	6.05084e12	+	1.04804e13i	0.340129	+	0.589120i
$881$	6.27239e12			0.350785			0.175393	−	0.984499i	$-0.443880\pi$
$881$	6.27239e12			0.350785			0.175393	+	0.984499i	$0.443880\pi$
$882$		0			0
$883$	4.32257e12			0.239287			0.119643	−	0.992817i	$-0.461825\pi$
$883$	4.32257e12			0.239287			0.119643	+	0.992817i	$0.461825\pi$
$884$	−3.99156e12	−	6.91359e12i	−0.219841	−	0.380775i
$885$	1.99279e11	−	3.45162e11i	0.0109199	−	0.0189138i
$886$	9.62512e11	−	1.66712e12i	0.0524753	−	0.0908898i
$887$	−8.10937e12	−	1.40458e13i	−0.439876	−	0.761888i	0.557803	−	0.829973i	$-0.311644\pi$
$887$	−8.10937e12	−	1.40458e13i	−0.439876	−	0.761888i	−0.997680	+	0.0680849i	$0.978311\pi$
$888$	−2.89073e11			−0.0156009
$889$		0			0
$890$	5.66251e12			0.302520
$891$	−6.51095e12	−	1.12773e13i	−0.346094	−	0.599453i
$892$	3.87984e12	−	6.72008e12i	0.205197	−	0.355412i
$893$	2.09020e12	−	3.62033e12i	0.109991	−	0.190509i
$894$	1.06396e11	+	1.84284e11i	0.00557067	+	0.00964868i
$895$	7.16904e12			0.373471
$896$		0			0
$897$	−3.02437e11			−0.0155980
$898$	9.09352e11	+	1.57504e12i	0.0466647	+	0.0808257i
$899$	−3.10568e12	+	5.37919e12i	−0.158576	+	0.274662i
$900$	−3.76960e12	+	6.52913e12i	−0.191515	+	0.331714i
$901$	−1.14887e13	−	1.98990e13i	−0.580776	−	1.00593i
$902$	5.51991e12			0.277653
$903$		0			0
$904$	−4.98679e12			−0.248349
$905$	−6.71869e11	−	1.16371e12i	−0.0332940	−	0.0576669i
$906$	7.05937e9	−	1.22272e10i	0.000348088	−	0.000602906i
$907$	−7.24848e12	+	1.25547e13i	−0.355643	+	0.615992i	−0.987228	−	0.159315i	$-0.949071\pi$
$907$	−7.24848e12	+	1.25547e13i	−0.355643	+	0.615992i	0.631585	+	0.775307i	$0.282405\pi$
$908$	1.14990e13	+	1.99169e13i	0.561404	+	0.972380i
$909$	−1.65004e13			−0.801598
$910$		0			0
$911$	−1.95797e13			−0.941834			−0.470917	−	0.882178i	$-0.656077\pi$
$911$	−1.95797e13			−0.941834			−0.470917	+	0.882178i	$0.656077\pi$
$912$	1.49547e11	+	2.59022e11i	0.00715813	+	0.0123982i
$913$	1.06620e13	−	1.84671e13i	0.507833	−	0.879592i
$914$	−6.95539e10	+	1.20471e11i	−0.00329658	+	0.00570984i
$915$	−2.38126e11	−	4.12447e11i	−0.0112308	−	0.0194524i
$916$	−8.17571e12			−0.383703
$917$		0			0
$918$	2.54397e11			0.0118228
$919$	1.73442e13	+	3.00410e13i	0.802111	+	1.38930i	0.918224	+	0.396061i	$0.129623\pi$
$919$	1.73442e13	+	3.00410e13i	0.802111	+	1.38930i	−0.116113	+	0.993236i	$0.537044\pi$
$920$	8.38001e12	−	1.45146e13i	0.385655	−	0.667975i
$921$	2.35265e11	−	4.07491e11i	0.0107743	−	0.0186616i
$922$	1.14177e12	+	1.97760e12i	0.0520342	+	0.0901258i
$923$	−1.10944e12			−0.0503146
$924$		0			0
$925$	−1.23751e13			−0.555791
$926$	−4.40401e12	−	7.62796e12i	−0.196833	−	0.340925i
$927$	1.50916e13	−	2.61394e13i	0.671236	−	1.16262i
$928$	−1.35960e12	+	2.35489e12i	−0.0601789	+	0.104233i
$929$	−1.44579e13	−	2.50418e13i	−0.636846	−	1.10305i	−0.986121	−	0.166030i	$-0.946905\pi$
$929$	−1.44579e13	−	2.50418e13i	−0.636846	−	1.10305i	0.349274	−	0.937020i	$-0.386428\pi$
$930$	2.81906e11			0.0123575
$931$		0			0
$932$	−2.24524e13			−0.974744
$933$	1.51354e11	+	2.62153e11i	0.00653925	+	0.0113263i
$934$	−5.01768e11	+	8.69088e11i	−0.0215746	+	0.0373683i
$935$	9.65209e12	−	1.67179e13i	0.413018	−	0.715369i
$936$	2.57001e12	+	4.45138e12i	0.109444	+	0.189563i
$937$	−2.01915e13			−0.855737			−0.427869	−	0.903841i	$-0.640735\pi$
$937$	−2.01915e13			−0.855737			−0.427869	+	0.903841i	$0.640735\pi$
$938$		0			0
$939$	9.14981e11			0.0384076
$940$	4.12260e12	+	7.14055e12i	0.172225	+	0.298302i
$941$	−7.80967e12	+	1.35267e13i	−0.324698	+	0.562393i	−0.981451	−	0.191712i	$-0.938596\pi$
$941$	−7.80967e12	+	1.35267e13i	−0.324698	+	0.562393i	0.656753	+	0.754105i	$0.271929\pi$
$942$	6.58737e9	−	1.14097e10i	0.000272573	−	0.000472111i
$943$	2.76833e13	+	4.79490e13i	1.14003	+	1.97459i
$944$	−1.53012e13			−0.627121
$945$		0			0
$946$	1.16181e12			0.0471656
$947$	−2.43439e13	−	4.21649e13i	−0.983592	−	1.70363i	−0.648031	−	0.761614i	$-0.724407\pi$
$947$	−2.43439e13	−	4.21649e13i	−0.983592	−	1.70363i	−0.335561	−	0.942018i	$-0.608926\pi$
$948$	−2.18364e11	+	3.78218e11i	−0.00878101	+	0.0152092i
$949$	−5.95387e12	+	1.03124e13i	−0.238288	+	0.412726i
$950$	−8.83954e11	−	1.53105e12i	−0.0352106	−	0.0609866i
$951$	1.72933e11			0.00685593
$952$		0			0
$953$	2.59691e13			1.01986			0.509928	−	0.860217i	$-0.329672\pi$
$953$	2.59691e13			1.01986			0.509928	+	0.860217i	$0.329672\pi$
$954$	3.58648e12	+	6.21196e12i	0.140185	+	0.242807i
$955$	1.11020e13	−	1.92293e13i	0.431904	−	0.748079i
$956$	1.06441e13	−	1.84362e13i	0.412145	−	0.713857i
$957$	3.91555e10	+	6.78193e10i	0.00150900	+	0.00261366i
$958$	1.05223e13			0.403613
$959$		0			0
$960$	−5.03373e11			−0.0191280
$961$	−2.81558e13	−	4.87673e13i	−1.06491	−	1.84448i
$962$	−2.04534e12	+	3.54262e12i	−0.0769975	+	0.133364i
$963$	−6.13576e12	+	1.06274e13i	−0.229906	+	0.398209i
$964$	−8.04809e12	−	1.39397e13i	−0.300156	−	0.519885i
$965$	−1.43875e12			−0.0534089
$966$		0			0
$967$	−7.34548e12			−0.270148			−0.135074	−	0.990836i	$-0.543127\pi$
$967$	−7.34548e12			−0.270148			−0.135074	+	0.990836i	$0.543127\pi$
$968$	−3.33859e12	−	5.78260e12i	−0.122215	−	0.211682i
$969$	2.38552e11	−	4.13184e11i	0.00869212	−	0.0150552i
$970$	4.52568e12	−	7.83871e12i	0.164139	−	0.284297i
$971$	−1.40101e13	−	2.42662e13i	−0.505771	−	0.876021i	−0.999978	−	0.00667683i	$-0.997875\pi$
$971$	−1.40101e13	−	2.42662e13i	−0.505771	−	0.876021i	0.494207	−	0.869345i	$-0.335459\pi$
$972$	1.90619e12			0.0684966
$973$		0			0
$974$	6.62057e12			0.235711
$975$	−6.48884e10	−	1.12390e11i	−0.00229957	−	0.00398297i
$976$	−9.14197e12	+	1.58344e13i	−0.322490	+	0.558568i
$977$	2.07190e13	−	3.58863e13i	0.727516	−	1.26010i	−0.230413	−	0.973093i	$-0.574008\pi$
$977$	2.07190e13	−	3.58863e13i	0.727516	−	1.26010i	0.957930	−	0.287003i	$-0.0926588\pi$
$978$	6.15637e9	+	1.06631e10i	0.000215179	+	0.000372701i
$979$	−2.09564e13			−0.729112
$980$		0			0
$981$	−4.30652e13			−1.48462
$982$	−4.00620e12	−	6.93894e12i	−0.137477	−	0.238117i
$983$	8.17640e12	−	1.41619e13i	0.279300	−	0.483762i	−0.691911	−	0.721983i	$-0.743231\pi$
$983$	8.17640e12	−	1.41619e13i	0.279300	−	0.483762i	0.971211	+	0.238221i	$0.0765642\pi$
$984$	−2.77485e11	+	4.80619e11i	−0.00943544	+	0.0163427i
$985$	1.43009e13	+	2.47698e13i	0.484060	+	0.838417i
$986$	1.29585e12			0.0436625
$987$		0			0
$988$	9.35037e12			0.312192
$989$	5.82670e12	+	1.00921e13i	0.193660	+	0.335428i
$990$	−3.01314e12	+	5.21891e12i	−0.0996921	+	0.172672i
$991$	−2.21249e13	+	3.83214e13i	−0.728700	+	1.26215i	0.228732	+	0.973489i	$0.426542\pi$
$991$	−2.21249e13	+	3.83214e13i	−0.728700	+	1.26215i	−0.957433	+	0.288657i	$0.906791\pi$
$992$	−1.81133e13	−	3.13732e13i	−0.593877	−	1.02862i
$993$	4.48258e11			0.0146304
$994$		0			0
$995$	5.35033e12			0.173052
$996$	5.19737e11	+	9.00211e11i	0.0167346	+	0.0289853i
$997$	1.72558e13	−	2.98880e13i	0.553105	−	0.958006i	−0.444943	−	0.895559i	$-0.646776\pi$
$997$	1.72558e13	−	2.98880e13i	0.553105	−	0.958006i	0.998048	−	0.0624475i	$-0.0198906\pi$
$998$	3.45288e12	−	5.98057e12i	0.110178	−	0.190834i
$999$	1.04286e12	+	1.80629e12i	0.0331270	+	0.0573777i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.10.c.g.18.3		10
7.2	even	3	inner	49.10.c.g.30.3		10
7.3	odd	6		49.10.a.e.1.3		5
7.4	even	3		49.10.a.f.1.3		5
7.5	odd	6		7.10.c.a.2.3	✓	10
7.6	odd	2		7.10.c.a.4.3	yes	10
21.5	even	6		63.10.e.b.37.3		10
21.20	even	2		63.10.e.b.46.3		10
28.19	even	6		112.10.i.c.65.3		10
28.27	even	2		112.10.i.c.81.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.10.c.a.2.3	✓	10	7.5	odd	6
7.10.c.a.4.3	yes	10	7.6	odd	2
49.10.a.e.1.3		5	7.3	odd	6
49.10.a.f.1.3		5	7.4	even	3
49.10.c.g.18.3		10	1.1	even	1	trivial
49.10.c.g.30.3		10	7.2	even	3	inner
63.10.e.b.37.3		10	21.5	even	6
63.10.e.b.46.3		10	21.20	even	2
112.10.i.c.65.3		10	28.19	even	6
112.10.i.c.81.3		10	28.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	49.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.74397 - 4.75269i) q^{2} +(1.70307 - 2.94981i) q^{3} +(240.941 - 417.323i) q^{4} +(828.924 + 1435.74i) q^{5} -18.6927 q^{6} -5454.36 q^{8} +(9835.70 + 17035.9i) q^{9} +(4549.08 - 7879.24i) q^{10} +(-16835.7 + 29160.2i) q^{11} +(-820.681 - 1421.46i) q^{12} -47905.5 q^{13} +5646.87 q^{15} +(-108395. - 187746. i) q^{16} +(-172909. + 299487. i) q^{17} +(53977.7 - 93492.1i) q^{18} +(-202522. - 350778. i) q^{19} +798888. q^{20} +184786. q^{22} +(926736. + 1.60515e6i) q^{23} +(-9289.18 + 16089.3i) q^{24} +(-397666. + 688778. i) q^{25} +(131451. + 227680. i) q^{26} +134047. q^{27} +682809. q^{29} +(-15494.8 - 26837.8i) q^{30} +(-4.54839e6 + 7.87804e6i) q^{31} +(-1.99118e6 + 3.44883e6i) q^{32} +(57344.7 + 99324.0i) q^{33} +1.89782e6 q^{34} +9.47930e6 q^{36} +(7.77984e6 + 1.34751e7i) q^{37} +(-1.11143e6 + 1.92505e6i) q^{38} +(-81586.5 + 141312. i) q^{39} +(-4.52125e6 - 7.83104e6i) q^{40} +2.98719e7 q^{41} +6.28733e6 q^{43} +(8.11281e6 + 1.40518e7i) q^{44} +(-1.63061e7 + 2.82430e7i) q^{45} +(5.08587e6 - 8.80898e6i) q^{46} +(5.16042e6 + 8.93811e6i) q^{47} -738421. q^{48} +4.36473e6 q^{50} +(588952. + 1.02010e6i) q^{51} +(-1.15424e7 + 1.99920e7i) q^{52} +(-3.32218e7 + 5.75419e7i) q^{53} +(-367820. - 637083. i) q^{54} -5.58219e7 q^{55} -1.37964e6 q^{57} +(-1.87361e6 - 3.24518e6i) q^{58} +(3.52902e7 - 6.11245e7i) q^{59} +(1.36056e6 - 2.35657e6i) q^{60} +(-4.21696e7 - 7.30399e7i) q^{61} +4.99225e7 q^{62} -8.91419e7 q^{64} +(-3.97100e7 - 6.87797e7i) q^{65} +(314704. - 545084. i) q^{66} +(1.05869e8 - 1.83370e8i) q^{67} +(8.33217e7 + 1.44317e8i) q^{68} +6.31320e6 q^{69} +2.31588e7 q^{71} +(-5.36475e7 - 9.29202e7i) q^{72} +(1.24284e8 - 2.15266e8i) q^{73} +(4.26952e7 - 7.39503e7i) q^{74} +(1.35451e6 + 2.34608e6i) q^{75} -1.95184e8 q^{76} +895483. q^{78} +(-1.33038e8 - 2.30429e8i) q^{79} +(1.79703e8 - 3.11255e8i) q^{80} +(-1.93368e8 + 3.34923e8i) q^{81} +(-8.19675e7 - 1.41972e8i) q^{82} -6.33299e8 q^{83} -5.73312e8 q^{85} +(-1.72522e7 - 2.98817e7i) q^{86} +(1.16287e6 - 2.01416e6i) q^{87} +(9.18278e7 - 1.59050e8i) q^{88} +(3.11190e8 + 5.38997e8i) q^{89} +1.78973e8 q^{90} +8.93156e8 q^{92} +(1.54925e7 + 2.68338e7i) q^{93} +(2.83201e7 - 4.90518e7i) q^{94} +(3.35751e8 - 5.81537e8i) q^{95} +(6.78226e6 + 1.17472e7i) q^{96} +9.94856e8 q^{97} -6.62362e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 18 q^{2} - 161 q^{3} - 940 q^{4} - 1533 q^{5} + 8708 q^{6} + 34272 q^{8} - 35734 q^{9} - 4298 q^{10} + 42213 q^{11} - 135604 q^{12} + 319676 q^{13} + 151394 q^{15} + 322064 q^{16} - 324681 q^{17}+ \cdots - 1900777180 q^{99}+O(q^{100}) \) 10 * q - 18 * q^2 - 161 * q^3 - 940 * q^4 - 1533 * q^5 + 8708 * q^6 + 34272 * q^8 - 35734 * q^9 - 4298 * q^10 + 42213 * q^11 - 135604 * q^12 + 319676 * q^13 + 151394 * q^15 + 322064 * q^16 - 324681 * q^17 - 1012868 * q^18 + 16121 * q^19 + 350616 * q^20 - 62692 * q^22 + 2638863 * q^23 - 8449728 * q^24 - 1304092 * q^25 - 4179252 * q^26 + 18331558 * q^27 + 15292500 * q^29 + 20557942 * q^30 - 19179237 * q^31 - 6263520 * q^32 - 1689359 * q^33 + 62909700 * q^34 + 71476528 * q^36 + 39566985 * q^37 - 67365270 * q^38 - 44299486 * q^39 - 5721744 * q^40 + 53436852 * q^41 + 101835992 * q^43 + 99704916 * q^44 - 85098230 * q^45 - 14489202 * q^46 - 32509659 * q^47 + 185141600 * q^48 + 3328464 * q^50 + 44168403 * q^51 - 103893272 * q^52 - 25714707 * q^53 - 51200926 * q^54 + 144695222 * q^55 - 121710346 * q^57 - 46645516 * q^58 - 46776513 * q^59 + 132391756 * q^60 + 113075039 * q^61 - 467465628 * q^62 - 192008960 * q^64 - 338113566 * q^65 + 836682602 * q^66 - 126707879 * q^67 - 32262636 * q^68 - 1323616182 * q^69 - 1188736032 * q^71 - 950557728 * q^72 + 859257651 * q^73 + 591757530 * q^74 + 169061732 * q^75 - 1101475592 * q^76 + 519432424 * q^78 - 527065417 * q^79 + 1257352656 * q^80 + 551662715 * q^81 + 1341703076 * q^82 + 144863208 * q^83 - 1197360222 * q^85 - 678648216 * q^86 + 340781350 * q^87 + 903700608 * q^88 - 1661554797 * q^89 - 1967758744 * q^90 - 1301840952 * q^92 - 423057489 * q^93 + 272580882 * q^94 - 1197123495 * q^95 + 1441922272 * q^96 - 869770188 * q^97 - 1900777180 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more