LMFDB - Embedded newform 37.9.d.a.6.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,9,Mod(6,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

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

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

chi := DirichletCharacter("37.6");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	37.d (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.0730085723$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$25$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			6.5
Character	$\chi$	$=$	37.6
Dual form			37.9.d.a.31.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-15.5660 + 15.5660i) q^{2} -38.2524i q^{3} -228.599i q^{4} +(431.867 + 431.867i) q^{5} +(595.436 + 595.436i) q^{6} -3114.53 q^{7} +(-426.526 - 426.526i) q^{8} +5097.75 q^{9} +O(q^{10})$	\(q+(-15.5660 + 15.5660i) q^{2} -38.2524i q^{3} -228.599i q^{4} +(431.867 + 431.867i) q^{5} +(595.436 + 595.436i) q^{6} -3114.53 q^{7} +(-426.526 - 426.526i) q^{8} +5097.75 q^{9} -13444.9 q^{10} -6134.74i q^{11} -8744.46 q^{12} +(-33981.4 - 33981.4i) q^{13} +(48480.7 - 48480.7i) q^{14} +(16519.9 - 16519.9i) q^{15} +71799.9 q^{16} +(44483.9 + 44483.9i) q^{17} +(-79351.5 + 79351.5i) q^{18} +(-4720.59 - 4720.59i) q^{19} +(98724.2 - 98724.2i) q^{20} +119138. i q^{21} +(95493.2 + 95493.2i) q^{22} +(342621. + 342621. i) q^{23} +(-16315.7 + 16315.7i) q^{24} -17607.1i q^{25} +1.05791e6 q^{26} -445975. i q^{27} +711978. i q^{28} +(931095. - 931095. i) q^{29} +514298. i q^{30} +(545554. - 545554. i) q^{31} +(-1.00844e6 + 1.00844e6i) q^{32} -234669. q^{33} -1.38487e6 q^{34} +(-1.34506e6 - 1.34506e6i) q^{35} -1.16534e6i q^{36} +(1.44401e6 + 1.19470e6i) q^{37} +146961. q^{38} +(-1.29987e6 + 1.29987e6i) q^{39} -368405. i q^{40} -4.15612e6i q^{41} +(-1.85450e6 - 1.85450e6i) q^{42} +(1.63851e6 + 1.63851e6i) q^{43} -1.40240e6 q^{44} +(2.20155e6 + 2.20155e6i) q^{45} -1.06665e7 q^{46} -4.24127e6 q^{47} -2.74652e6i q^{48} +3.93549e6 q^{49} +(274071. + 274071. i) q^{50} +(1.70161e6 - 1.70161e6i) q^{51} +(-7.76811e6 + 7.76811e6i) q^{52} +6.45094e6 q^{53} +(6.94204e6 + 6.94204e6i) q^{54} +(2.64939e6 - 2.64939e6i) q^{55} +(1.32843e6 + 1.32843e6i) q^{56} +(-180574. + 180574. i) q^{57} +2.89868e7i q^{58} +(-1.25594e7 - 1.25594e7i) q^{59} +(-3.77644e6 - 3.77644e6i) q^{60} +(1.05706e7 - 1.05706e7i) q^{61} +1.69842e7i q^{62} -1.58771e7 q^{63} -1.30140e7i q^{64} -2.93509e7i q^{65} +(3.65285e6 - 3.65285e6i) q^{66} +2.69268e7i q^{67} +(1.01690e7 - 1.01690e7i) q^{68} +(1.31061e7 - 1.31061e7i) q^{69} +4.18744e7 q^{70} -1.50849e7 q^{71} +(-2.17433e6 - 2.17433e6i) q^{72} -3.15380e7i q^{73} +(-4.10741e7 + 3.88078e6i) q^{74} -673514. q^{75} +(-1.07912e6 + 1.07912e6i) q^{76} +1.91068e7i q^{77} -4.04675e7i q^{78} +(-1.31503e7 - 1.31503e7i) q^{79} +(3.10080e7 + 3.10080e7i) q^{80} +1.63867e7 q^{81} +(6.46941e7 + 6.46941e7i) q^{82} +2.74975e7 q^{83} +2.72349e7 q^{84} +3.84222e7i q^{85} -5.10100e7 q^{86} +(-3.56166e7 - 3.56166e7i) q^{87} +(-2.61663e6 + 2.61663e6i) q^{88} +(-2.94179e7 + 2.94179e7i) q^{89} -6.85385e7 q^{90} +(1.05836e8 + 1.05836e8i) q^{91} +(7.83228e7 - 7.83228e7i) q^{92} +(-2.08688e7 - 2.08688e7i) q^{93} +(6.60194e7 - 6.60194e7i) q^{94} -4.07734e6i q^{95} +(3.85754e7 + 3.85754e7i) q^{96} +(-3.41860e7 - 3.41860e7i) q^{97} +(-6.12597e7 + 6.12597e7i) q^{98} -3.12734e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 4 q^{2} + 124 q^{5} + 510 q^{6} - 4 q^{7} - 5256 q^{8} - 93534 q^{9}+O(q^{10}) $ 50 * q + 4 * q^2 + 124 * q^5 + 510 * q^6 - 4 * q^7 - 5256 * q^8 - 93534 * q^9	\( 50 q + 4 q^{2} + 124 q^{5} + 510 q^{6} - 4 q^{7} - 5256 q^{8} - 93534 q^{9} - 10756 q^{10} - 45440 q^{12} + 63592 q^{13} - 80206 q^{14} - 124346 q^{15} - 639128 q^{16} - 178796 q^{17} - 45882 q^{18} + 264774 q^{19} + 469204 q^{20} + 714574 q^{22} - 654272 q^{23} - 1573644 q^{24} + 1841660 q^{26} - 1683686 q^{29} + 1766336 q^{31} - 4332632 q^{32} - 1438888 q^{33} - 5838452 q^{34} - 650482 q^{35} - 2870078 q^{37} - 2281528 q^{38} + 11036546 q^{39} - 7453902 q^{42} + 5097830 q^{43} - 14992464 q^{44} - 15078446 q^{45} + 28776464 q^{46} + 13992320 q^{47} + 4370314 q^{49} + 7603288 q^{50} + 19417938 q^{51} + 54318452 q^{52} + 28075952 q^{53} - 19197122 q^{54} - 6104306 q^{55} + 47803128 q^{56} + 17462426 q^{57} - 677072 q^{59} + 24953316 q^{60} + 4206386 q^{61} - 18098032 q^{63} - 56061730 q^{66} - 52579760 q^{68} + 88118984 q^{69} - 295493636 q^{70} - 37172476 q^{71} - 74582504 q^{72} - 224754524 q^{74} - 144364996 q^{75} + 189294548 q^{76} + 271163438 q^{79} - 312998084 q^{80} + 41535626 q^{81} - 177494710 q^{82} - 74250268 q^{83} - 82088924 q^{84} + 112964036 q^{86} - 142771908 q^{87} + 224951860 q^{88} + 84928780 q^{89} + 716592116 q^{90} - 40969098 q^{91} - 701292428 q^{92} - 83761576 q^{93} + 553881406 q^{94} - 7259376 q^{96} + 467792674 q^{97} + 538649310 q^{98}+O(q^{100}) \) 50 * q + 4 * q^2 + 124 * q^5 + 510 * q^6 - 4 * q^7 - 5256 * q^8 - 93534 * q^9 - 10756 * q^10 - 45440 * q^12 + 63592 * q^13 - 80206 * q^14 - 124346 * q^15 - 639128 * q^16 - 178796 * q^17 - 45882 * q^18 + 264774 * q^19 + 469204 * q^20 + 714574 * q^22 - 654272 * q^23 - 1573644 * q^24 + 1841660 * q^26 - 1683686 * q^29 + 1766336 * q^31 - 4332632 * q^32 - 1438888 * q^33 - 5838452 * q^34 - 650482 * q^35 - 2870078 * q^37 - 2281528 * q^38 + 11036546 * q^39 - 7453902 * q^42 + 5097830 * q^43 - 14992464 * q^44 - 15078446 * q^45 + 28776464 * q^46 + 13992320 * q^47 + 4370314 * q^49 + 7603288 * q^50 + 19417938 * q^51 + 54318452 * q^52 + 28075952 * q^53 - 19197122 * q^54 - 6104306 * q^55 + 47803128 * q^56 + 17462426 * q^57 - 677072 * q^59 + 24953316 * q^60 + 4206386 * q^61 - 18098032 * q^63 - 56061730 * q^66 - 52579760 * q^68 + 88118984 * q^69 - 295493636 * q^70 - 37172476 * q^71 - 74582504 * q^72 - 224754524 * q^74 - 144364996 * q^75 + 189294548 * q^76 + 271163438 * q^79 - 312998084 * q^80 + 41535626 * q^81 - 177494710 * q^82 - 74250268 * q^83 - 82088924 * q^84 + 112964036 * q^86 - 142771908 * q^87 + 224951860 * q^88 + 84928780 * q^89 + 716592116 * q^90 - 40969098 * q^91 - 701292428 * q^92 - 83761576 * q^93 + 553881406 * q^94 - 7259376 * q^96 + 467792674 * q^97 + 538649310 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−15.5660	+	15.5660i	−0.972873	+	0.972873i	−0.999642	−	0.0267686i	$-0.991478\pi$
$2$	−15.5660	+	15.5660i	−0.972873	+	0.972873i	0.0267686	+	0.999642i	$0.491478\pi$
$3$		−	38.2524i		−	0.472252i	−0.971722	−	0.236126i	$-0.924122\pi$
$3$		−	38.2524i		−	0.472252i	0.971722	−	0.236126i	$-0.0758778\pi$
$4$		−	228.599i		−	0.892964i
$5$	431.867	+	431.867i	0.690987	+	0.690987i	0.962449	−	0.271462i	$-0.0875072\pi$
$5$	431.867	+	431.867i	0.690987	+	0.690987i	−0.271462	+	0.962449i	$0.587507\pi$
$6$	595.436	+	595.436i	0.459441	+	0.459441i
$7$	−3114.53			−1.29718			−0.648590	−	0.761138i	$-0.724641\pi$
$7$	−3114.53			−1.29718			−0.648590	+	0.761138i	$0.724641\pi$
$8$	−426.526	−	426.526i	−0.104132	−	0.104132i
$9$	5097.75			0.776978
$10$	−13444.9			−1.34449
$11$		−	6134.74i		−	0.419011i	−0.977807	−	0.209506i	$-0.932815\pi$
$11$		−	6134.74i		−	0.419011i	0.977807	−	0.209506i	$-0.0671855\pi$
$12$	−8744.46			−0.421704
$13$	−33981.4	−	33981.4i	−1.18978	−	1.18978i	−0.977127	−	0.212656i	$-0.931789\pi$
$13$	−33981.4	−	33981.4i	−1.18978	−	1.18978i	−0.212656	−	0.977127i	$-0.568211\pi$
$14$	48480.7	−	48480.7i	1.26199	−	1.26199i
$15$	16519.9	−	16519.9i	0.326320	−	0.326320i
$16$	71799.9			1.09558
$17$	44483.9	+	44483.9i	0.532607	+	0.532607i	0.921347	−	0.388740i	$-0.127090\pi$
$17$	44483.9	+	44483.9i	0.532607	+	0.532607i	−0.388740	+	0.921347i	$0.627090\pi$
$18$	−79351.5	+	79351.5i	−0.755901	+	0.755901i
$19$	−4720.59	−	4720.59i	−0.0362228	−	0.0362228i	0.688763	−	0.724986i	$-0.258154\pi$
$19$	−4720.59	−	4720.59i	−0.0362228	−	0.0362228i	−0.724986	+	0.688763i	$0.758154\pi$
$20$	98724.2	−	98724.2i	0.617026	−	0.617026i
$21$			119138.i			0.612596i
$22$	95493.2	+	95493.2i	0.407645	+	0.407645i
$23$	342621.	+	342621.i	1.22434	+	1.22434i	0.966073	+	0.258270i	$0.0831525\pi$
$23$	342621.	+	342621.i	1.22434	+	1.22434i	0.258270	+	0.966073i	$0.416848\pi$
$24$	−16315.7	+	16315.7i	−0.0491767	+	0.0491767i
$25$		−	17607.1i		−	0.0450742i
$26$	1.05791e6			2.31502
$27$		−	445975.i		−	0.839181i
$28$			711978.i			1.15833i
$29$	931095.	−	931095.i	1.31644	−	1.31644i	0.399872	−	0.916571i	$-0.369055\pi$
$29$	931095.	−	931095.i	1.31644	−	1.31644i	0.916571	−	0.399872i	$-0.130945\pi$
$30$			514298.i			0.634936i
$31$	545554.	−	545554.i	0.590733	−	0.590733i	−0.347097	−	0.937829i	$-0.612832\pi$
$31$	545554.	−	545554.i	0.590733	−	0.590733i	0.937829	+	0.347097i	$0.112832\pi$
$32$	−1.00844e6	+	1.00844e6i	−0.961727	+	0.961727i
$33$	−234669.			−0.197879
$34$	−1.38487e6			−1.03632
$35$	−1.34506e6	−	1.34506e6i	−0.896334	−	0.896334i
$36$		−	1.16534e6i		−	0.693813i
$37$	1.44401e6	+	1.19470e6i	0.770485	+	0.637459i
$37$	1.44401e6	+	1.19470e6i	0.770485	+	0.637459i
$38$	146961.			0.0704804
$39$	−1.29987e6	+	1.29987e6i	−0.561878	+	0.561878i
$40$		−	368405.i		−	0.143908i
$41$		−	4.15612e6i		−	1.47080i	−0.677634	−	0.735399i	$-0.736995\pi$
$41$		−	4.15612e6i		−	1.47080i	0.677634	−	0.735399i	$-0.263005\pi$
$42$	−1.85450e6	−	1.85450e6i	−0.595978	−	0.595978i
$43$	1.63851e6	+	1.63851e6i	0.479265	+	0.479265i	0.904897	−	0.425632i	$-0.139948\pi$
$43$	1.63851e6	+	1.63851e6i	0.479265	+	0.479265i	−0.425632	+	0.904897i	$0.639948\pi$
$44$	−1.40240e6			−0.374162
$45$	2.20155e6	+	2.20155e6i	0.536882	+	0.536882i
$46$	−1.06665e7			−2.38226
$47$	−4.24127e6			−0.869169			−0.434584	−	0.900631i	$-0.643105\pi$
$47$	−4.24127e6			−0.869169			−0.434584	+	0.900631i	$0.643105\pi$
$48$		−	2.74652e6i		−	0.517389i
$49$	3.93549e6			0.682676
$50$	274071.	+	274071.i	0.0438514	+	0.0438514i
$51$	1.70161e6	−	1.70161e6i	0.251525	−	0.251525i
$52$	−7.76811e6	+	7.76811e6i	−1.06243	+	1.06243i
$53$	6.45094e6			0.817560			0.408780	−	0.912633i	$-0.365954\pi$
$53$	6.45094e6			0.817560			0.408780	+	0.912633i	$0.365954\pi$
$54$	6.94204e6	+	6.94204e6i	0.816417	+	0.816417i
$55$	2.64939e6	−	2.64939e6i	0.289531	−	0.289531i
$56$	1.32843e6	+	1.32843e6i	0.135078	+	0.135078i
$57$	−180574.	+	180574.i	−0.0171063	+	0.0171063i
$58$			2.89868e7i			2.56146i
$59$	−1.25594e7	−	1.25594e7i	−1.03648	−	1.03648i	−0.999309	−	0.0371678i	$-0.988166\pi$
$59$	−1.25594e7	−	1.25594e7i	−1.03648	−	1.03648i	−0.0371678	−	0.999309i	$-0.511834\pi$
$60$	−3.77644e6	−	3.77644e6i	−0.291392	−	0.291392i
$61$	1.05706e7	−	1.05706e7i	0.763452	−	0.763452i	−0.213493	−	0.976945i	$-0.568484\pi$
$61$	1.05706e7	−	1.05706e7i	0.763452	−	0.763452i	0.976945	+	0.213493i	$0.0684840\pi$
$62$			1.69842e7i			1.14942i
$63$	−1.58771e7			−1.00788
$64$		−	1.30140e7i		−	0.775698i
$65$		−	2.93509e7i		−	1.64425i
$66$	3.65285e6	−	3.65285e6i	0.192511	−	0.192511i
$67$			2.69268e7i			1.33624i	0.744053	+	0.668121i	$0.232901\pi$
$67$			2.69268e7i			1.33624i	−0.744053	+	0.668121i	$0.767099\pi$
$68$	1.01690e7	−	1.01690e7i	0.475599	−	0.475599i
$69$	1.31061e7	−	1.31061e7i	0.578198	−	0.578198i
$70$	4.18744e7			1.74404
$71$	−1.50849e7			−0.593621			−0.296810	−	0.954936i	$-0.595923\pi$
$71$	−1.50849e7			−0.593621			−0.296810	+	0.954936i	$0.595923\pi$
$72$	−2.17433e6	−	2.17433e6i	−0.0809086	−	0.0809086i
$73$		−	3.15380e7i		−	1.11056i	−0.831662	−	0.555282i	$-0.812610\pi$
$73$		−	3.15380e7i		−	1.11056i	0.831662	−	0.555282i	$-0.187390\pi$
$74$	−4.10741e7	+	3.88078e6i	−1.36975	+	0.129417i
$75$	−673514.			−0.0212864
$76$	−1.07912e6	+	1.07912e6i	−0.0323457	+	0.0323457i
$77$			1.91068e7i			0.543533i
$78$		−	4.04675e7i		−	1.09327i
$79$	−1.31503e7	−	1.31503e7i	−0.337620	−	0.337620i	0.517851	−	0.855471i	$-0.326732\pi$
$79$	−1.31503e7	−	1.31503e7i	−0.337620	−	0.337620i	−0.855471	+	0.517851i	$0.826732\pi$
$80$	3.10080e7	+	3.10080e7i	0.757031	+	0.757031i
$81$	1.63867e7			0.380673
$82$	6.46941e7	+	6.46941e7i	1.43090	+	1.43090i
$83$	2.74975e7			0.579402			0.289701	−	0.957117i	$-0.406444\pi$
$83$	2.74975e7			0.579402			0.289701	+	0.957117i	$0.406444\pi$
$84$	2.72349e7			0.547026
$85$			3.84222e7i			0.736049i
$86$	−5.10100e7			−0.932528
$87$	−3.56166e7	−	3.56166e7i	−0.621693	−	0.621693i
$88$	−2.61663e6	+	2.61663e6i	−0.0436326	+	0.0436326i
$89$	−2.94179e7	+	2.94179e7i	−0.468868	+	0.468868i	−0.901548	−	0.432679i	$-0.857568\pi$
$89$	−2.94179e7	+	2.94179e7i	−0.468868	+	0.468868i	0.432679	+	0.901548i	$0.357568\pi$
$90$	−6.85385e7			−1.04464
$91$	1.05836e8	+	1.05836e8i	1.54336	+	1.54336i
$92$	7.83228e7	−	7.83228e7i	1.09329	−	1.09329i
$93$	−2.08688e7	−	2.08688e7i	−0.278975	−	0.278975i
$94$	6.60194e7	−	6.60194e7i	0.845591	−	0.845591i
$95$		−	4.07734e6i		−	0.0500590i
$96$	3.85754e7	+	3.85754e7i	0.454178	+	0.454178i
$97$	−3.41860e7	−	3.41860e7i	−0.386155	−	0.386155i	0.487159	−	0.873313i	$-0.338033\pi$
$97$	−3.41860e7	−	3.41860e7i	−0.386155	−	0.386155i	−0.873313	+	0.487159i	$0.838033\pi$
$98$	−6.12597e7	+	6.12597e7i	−0.664157	+	0.664157i
$99$		−	3.12734e7i		−	0.325563i
$100$	−4.02496e6			−0.0402496
$101$		−	5.68213e7i		−	0.546042i	−0.962008	−	0.273021i	$-0.911977\pi$
$101$		−	5.68213e7i		−	0.546042i	0.962008	−	0.273021i	$-0.0880228\pi$
$102$			5.29746e7i			0.489403i
$103$	1.03163e8	−	1.03163e8i	0.916586	−	0.916586i	−0.0801933	−	0.996779i	$-0.525554\pi$
$103$	1.03163e8	−	1.03163e8i	0.916586	−	0.916586i	0.996779	+	0.0801933i	$0.0255537\pi$
$104$			2.89879e7i			0.247790i
$105$	−5.14519e7	+	5.14519e7i	−0.423296	+	0.423296i
$106$	−1.00415e8	+	1.00415e8i	−0.795382	+	0.795382i
$107$	−1.14025e8			−0.869893			−0.434946	−	0.900456i	$-0.643233\pi$
$107$	−1.14025e8			−0.869893			−0.434946	+	0.900456i	$0.643233\pi$
$108$	−1.01949e8			−0.749359
$109$	−1.28025e8	−	1.28025e8i	−0.906962	−	0.906962i	0.0890643	−	0.996026i	$-0.471612\pi$
$109$	−1.28025e8	−	1.28025e8i	−0.906962	−	0.906962i	−0.996026	+	0.0890643i	$0.971612\pi$
$110$			8.24807e7i			0.563354i
$111$	4.57002e7	−	5.52369e7i	0.301041	−	0.363863i
$112$	−2.23623e8			−1.42116
$113$	−5.78253e7	+	5.78253e7i	−0.354654	+	0.354654i	−0.861838	−	0.507184i	$-0.830686\pi$
$113$	−5.78253e7	+	5.78253e7i	−0.354654	+	0.354654i	0.507184	+	0.861838i	$0.330686\pi$
$114$		−	5.62162e6i		−	0.0332845i
$115$			2.95934e8i			1.69201i
$116$	−2.12847e8	−	2.12847e8i	−1.17554	−	1.17554i
$117$	−1.73229e8	−	1.73229e8i	−0.924436	−	0.924436i
$118$	3.90997e8			2.01672
$119$	−1.38546e8	−	1.38546e8i	−0.690887	−	0.690887i
$120$	−1.40924e7			−0.0679609
$121$	1.76724e8			0.824430
$122$			3.29084e8i			1.48548i
$123$	−1.58982e8			−0.694587
$124$	−1.24713e8	−	1.24713e8i	−0.527503	−	0.527503i
$125$	1.76302e8	−	1.76302e8i	0.722133	−	0.722133i
$126$	2.47142e8	−	2.47142e8i	0.980540	−	0.980540i
$127$	−1.12741e8			−0.433378			−0.216689	−	0.976241i	$-0.569526\pi$
$127$	−1.12741e8			−0.433378			−0.216689	+	0.976241i	$0.569526\pi$
$128$	−5.55854e7	−	5.55854e7i	−0.207072	−	0.207072i
$129$	6.26770e7	−	6.26770e7i	0.226334	−	0.226334i
$130$	4.56875e8	+	4.56875e8i	1.59965	+	1.59965i
$131$	1.71414e8	−	1.71414e8i	0.582050	−	0.582050i	−0.353416	−	0.935466i	$-0.614980\pi$
$131$	1.71414e8	−	1.71414e8i	0.582050	−	0.582050i	0.935466	+	0.353416i	$0.114980\pi$
$132$			5.36450e7i			0.176699i
$133$	1.47024e7	+	1.47024e7i	0.0469875	+	0.0469875i
$134$	−4.19141e8	−	4.19141e8i	−1.29999	−	1.29999i
$135$	1.92602e8	−	1.92602e8i	0.579863	−	0.579863i
$136$		−	3.79471e7i		−	0.110923i
$137$	−2.22995e8			−0.633014			−0.316507	−	0.948590i	$-0.602510\pi$
$137$	−2.22995e8			−0.633014			−0.316507	+	0.948590i	$0.602510\pi$
$138$			4.08018e8i			1.12503i
$139$			4.22839e8i			1.13270i	0.824164	+	0.566351i	$0.191645\pi$
$139$			4.22839e8i			1.13270i	−0.824164	+	0.566351i	$0.808355\pi$
$140$	−3.07479e8	+	3.07479e8i	−0.800394	+	0.800394i
$141$			1.62239e8i			0.410467i
$142$	2.34811e8	−	2.34811e8i	0.577518	−	0.577518i
$143$	−2.08467e8	+	2.08467e8i	−0.498533	+	0.498533i
$144$	3.66018e8			0.851241
$145$	8.04218e8			1.81929
$146$	4.90920e8	+	4.90920e8i	1.08044	+	1.08044i
$147$		−	1.50542e8i		−	0.322395i
$148$	2.73107e8	−	3.30099e8i	0.569228	−	0.688015i
$149$	7.30690e8			1.48248			0.741239	−	0.671241i	$-0.234239\pi$
$149$	7.30690e8			1.48248			0.741239	+	0.671241i	$0.234239\pi$
$150$	1.04839e7	−	1.04839e7i	0.0207089	−	0.0207089i
$151$			4.06999e8i			0.782863i	0.920207	+	0.391432i	$0.128020\pi$
$151$			4.06999e8i			0.782863i	−0.920207	+	0.391432i	$0.871980\pi$
$152$			4.02691e6i			0.00754393i
$153$	2.26768e8	+	2.26768e8i	0.413824	+	0.413824i
$154$	−2.97416e8	−	2.97416e8i	−0.528789	−	0.528789i
$155$	4.71213e8			0.816377
$156$	2.97149e8	+	2.97149e8i	0.501736	+	0.501736i
$157$	−2.79022e8			−0.459240			−0.229620	−	0.973280i	$-0.573748\pi$
$157$	−2.79022e8			−0.459240			−0.229620	+	0.973280i	$0.573748\pi$
$158$	4.09395e8			0.656922
$159$		−	2.46764e8i		−	0.386094i
$160$	−8.71027e8			−1.32908
$161$	−1.06710e9	−	1.06710e9i	−1.58819	−	1.58819i
$162$	−2.55075e8	+	2.55075e8i	−0.370346	+	0.370346i
$163$	5.75899e8	−	5.75899e8i	0.815822	−	0.815822i	−0.169677	−	0.985500i	$-0.554273\pi$
$163$	5.75899e8	−	5.75899e8i	0.815822	−	0.815822i	0.985500	+	0.169677i	$0.0542726\pi$
$164$	−9.50085e8			−1.31337
$165$	−1.01346e8	−	1.01346e8i	−0.136732	−	0.136732i
$166$	−4.28025e8	+	4.28025e8i	−0.563685	+	0.563685i
$167$	−4.89427e8	−	4.89427e8i	−0.629248	−	0.629248i	0.318631	−	0.947879i	$-0.396777\pi$
$167$	−4.89427e8	−	4.89427e8i	−0.629248	−	0.629248i	−0.947879	+	0.318631i	$0.896777\pi$
$168$	5.08156e7	−	5.08156e7i	0.0637911	−	0.0637911i
$169$			1.49374e9i			1.83117i
$170$	−5.98079e8	−	5.98079e8i	−0.716082	−	0.716082i
$171$	−2.40644e7	−	2.40644e7i	−0.0281443	−	0.0281443i
$172$	3.74562e8	−	3.74562e8i	0.427966	−	0.427966i
$173$		−	6.57105e8i		−	0.733585i	−0.930303	−	0.366792i	$-0.880456\pi$
$173$		−	6.57105e8i		−	0.733585i	0.930303	−	0.366792i	$-0.119544\pi$
$174$	1.10881e9			1.20966
$175$			5.48378e7i			0.0584693i
$176$		−	4.40474e8i		−	0.459060i
$177$	−4.80426e8	+	4.80426e8i	−0.489478	+	0.489478i
$178$		−	9.15835e8i		−	0.912299i
$179$	1.46270e8	−	1.46270e8i	0.142477	−	0.142477i	−0.632271	−	0.774747i	$-0.717877\pi$
$179$	1.46270e8	−	1.46270e8i	0.142477	−	0.142477i	0.774747	+	0.632271i	$0.217877\pi$
$180$	5.03272e8	−	5.03272e8i	0.479416	−	0.479416i
$181$	−3.36781e8			−0.313785			−0.156893	−	0.987616i	$-0.550148\pi$
$181$	−3.36781e8			−0.313785			−0.156893	+	0.987616i	$0.550148\pi$
$182$	−3.29488e9			−3.00299
$183$	−4.04352e8	−	4.04352e8i	−0.360542	−	0.360542i
$184$		−	2.92274e8i		−	0.254987i
$185$	1.07669e8	+	1.13957e9i	0.0919191	+	0.972870i
$186$	6.49685e8			0.542814
$187$	2.72897e8	−	2.72897e8i	0.223168	−	0.223168i
$188$			9.69548e8i			0.776136i
$189$			1.38900e9i			1.08857i
$190$	6.34677e7	+	6.34677e7i	0.0487010	+	0.0487010i
$191$	2.39275e8	+	2.39275e8i	0.179789	+	0.179789i	0.791264	−	0.611475i	$-0.209423\pi$
$191$	2.39275e8	+	2.39275e8i	0.179789	+	0.179789i	−0.611475	+	0.791264i	$0.709423\pi$
$192$	−4.97819e8			−0.366325
$193$	8.08823e7	+	8.08823e7i	0.0582940	+	0.0582940i	0.735653	−	0.677359i	$-0.236876\pi$
$193$	8.08823e7	+	8.08823e7i	0.0582940	+	0.0582940i	−0.677359	+	0.735653i	$0.736876\pi$
$194$	1.06428e9			0.751359
$195$	−1.12274e9			−0.776500
$196$		−	8.99648e8i		−	0.609605i
$197$	1.08834e9			0.722604			0.361302	−	0.932449i	$-0.382332\pi$
$197$	1.08834e9			0.722604			0.361302	+	0.932449i	$0.382332\pi$
$198$	4.86801e8	+	4.86801e8i	0.316731	+	0.316731i
$199$	−5.23905e8	+	5.23905e8i	−0.334072	+	0.334072i	−0.854131	−	0.520059i	$-0.825910\pi$
$199$	−5.23905e8	+	5.23905e8i	−0.334072	+	0.334072i	0.520059	+	0.854131i	$0.325910\pi$
$200$	−7.50989e6	+	7.50989e6i	−0.00469368	+	0.00469368i
$201$	1.03001e9			0.631043
$202$	8.84479e8	+	8.84479e8i	0.531229	+	0.531229i
$203$	−2.89992e9	+	2.89992e9i	−1.70766	+	1.70766i
$204$	−3.88987e8	−	3.88987e8i	−0.224602	−	0.224602i
$205$	1.79489e9	−	1.79489e9i	1.01630	−	1.01630i
$206$			3.21165e9i			1.78344i
$207$	1.74660e9	+	1.74660e9i	0.951288	+	0.951288i
$208$	−2.43986e9	−	2.43986e9i	−1.30350	−	1.30350i
$209$	−2.89596e7	+	2.89596e7i	−0.0151778	+	0.0151778i
$210$		−	1.60180e9i		−	0.823626i
$211$	−7.77123e8			−0.392067			−0.196033	−	0.980597i	$-0.562806\pi$
$211$	−7.77123e8			−0.392067			−0.196033	+	0.980597i	$0.562806\pi$
$212$		−	1.47468e9i		−	0.730051i
$213$			5.77034e8i			0.280339i
$214$	1.77491e9	−	1.77491e9i	0.846295	−	0.846295i
$215$			1.41524e9i			0.662332i
$216$	−1.90220e8	+	1.90220e8i	−0.0873860	+	0.0873860i
$217$	−1.69914e9	+	1.69914e9i	−0.766287	+	0.766287i
$218$	3.98567e9			1.76472
$219$	−1.20641e9			−0.524466
$220$	−6.05648e8	−	6.05648e8i	−0.258541	−	0.258541i
$221$		−	3.02325e9i		−	1.26737i
$222$	1.48449e8	+	1.57118e9i	0.0611175	+	0.646867i
$223$	1.84142e9			0.744616			0.372308	−	0.928109i	$-0.378566\pi$
$223$	1.84142e9			0.744616			0.372308	+	0.928109i	$0.378566\pi$
$224$	3.14083e9	−	3.14083e9i	1.24753	−	1.24753i
$225$		−	8.97566e7i		−	0.0350216i
$226$		−	1.80021e9i		−	0.690066i
$227$	−9.86011e8	−	9.86011e8i	−0.371346	−	0.371346i	0.496622	−	0.867967i	$-0.334574\pi$
$227$	−9.86011e8	−	9.86011e8i	−0.371346	−	0.371346i	−0.867967	+	0.496622i	$0.834574\pi$
$228$	4.12790e7	+	4.12790e7i	0.0152753	+	0.0152753i
$229$	−8.65966e8			−0.314890			−0.157445	−	0.987528i	$-0.550326\pi$
$229$	−8.65966e8			−0.314890			−0.157445	+	0.987528i	$0.550326\pi$
$230$	−4.60649e9	−	4.60649e9i	−1.64611	−	1.64611i
$231$	7.30883e8			0.256685
$232$	−7.94273e8			−0.274169
$233$			2.98387e9i			1.01241i	0.862414	+	0.506204i	$0.168952\pi$
$233$			2.98387e9i			1.01241i	−0.862414	+	0.506204i	$0.831048\pi$
$234$	5.39295e9			1.79872
$235$	−1.83166e9	−	1.83166e9i	−0.600584	−	0.600584i
$236$	−2.87106e9	+	2.87106e9i	−0.925537	+	0.925537i
$237$	−5.03031e8	+	5.03031e8i	−0.159442	+	0.159442i
$238$	4.31321e9			1.34429
$239$	2.37986e9	+	2.37986e9i	0.729391	+	0.729391i	0.970498	−	0.241108i	$-0.0775106\pi$
$239$	2.37986e9	+	2.37986e9i	0.729391	+	0.729391i	−0.241108	+	0.970498i	$0.577511\pi$
$240$	1.18613e9	−	1.18613e9i	0.357509	−	0.357509i
$241$	1.73987e9	+	1.73987e9i	0.515762	+	0.515762i	0.916286	−	0.400524i	$-0.131172\pi$
$241$	1.73987e9	+	1.73987e9i	0.515762	+	0.515762i	−0.400524	+	0.916286i	$0.631172\pi$
$242$	−2.75088e9	+	2.75088e9i	−0.802065	+	0.802065i
$243$		−	3.55288e9i		−	1.01895i
$244$	−2.41643e9	−	2.41643e9i	−0.681735	−	0.681735i
$245$	1.69961e9	+	1.69961e9i	0.471720	+	0.471720i
$246$	2.47471e9	−	2.47471e9i	0.675745	−	0.675745i
$247$			3.20825e8i			0.0861946i
$248$	−4.65386e8			−0.123029
$249$		−	1.05184e9i		−	0.273624i
$250$			5.48862e9i			1.40509i
$251$	−5.05500e9	+	5.05500e9i	−1.27358	+	1.27358i	−0.329383	+	0.944197i	$0.606841\pi$
$251$	−5.05500e9	+	5.05500e9i	−1.27358	+	1.27358i	−0.944197	+	0.329383i	$0.893159\pi$
$252$			3.62949e9i			0.900001i
$253$	2.10189e9	−	2.10189e9i	0.513013	−	0.513013i
$254$	1.75492e9	−	1.75492e9i	0.421621	−	0.421621i
$255$	1.46974e9			0.347600
$256$	5.06208e9			1.17861
$257$	−2.35008e9	−	2.35008e9i	−0.538704	−	0.538704i	0.384444	−	0.923148i	$-0.374393\pi$
$257$	−2.35008e9	−	2.35008e9i	−0.538704	−	0.538704i	−0.923148	+	0.384444i	$0.874393\pi$
$258$			1.95126e9i			0.440388i
$259$	−4.49742e9	−	3.72093e9i	−0.999457	−	0.826899i
$260$	−6.70958e9			−1.46826
$261$	4.74649e9	−	4.74649e9i	1.02285	−	1.02285i
$262$			5.33644e9i			1.13252i
$263$		−	1.78979e9i		−	0.374093i	−0.982351	−	0.187047i	$-0.940108\pi$
$263$		−	1.78979e9i		−	0.374093i	0.982351	−	0.187047i	$-0.0598915\pi$
$264$	1.00092e8	+	1.00092e8i	0.0206056	+	0.0206056i
$265$	2.78595e9	+	2.78595e9i	0.564923	+	0.564923i
$266$	−4.57715e8			−0.0914258
$267$	1.12530e9	+	1.12530e9i	0.221424	+	0.221424i
$268$	6.15543e9			1.19322
$269$	−2.29063e8			−0.0437467			−0.0218733	−	0.999761i	$-0.506963\pi$
$269$	−2.29063e8			−0.0437467			−0.0218733	+	0.999761i	$0.506963\pi$
$270$			5.99607e9i			1.12827i
$271$	−7.96034e9			−1.47589			−0.737945	−	0.674860i	$-0.764204\pi$
$271$	−7.96034e9			−1.47589			−0.737945	+	0.674860i	$0.764204\pi$
$272$	3.19394e9	+	3.19394e9i	0.583513	+	0.583513i
$273$	4.04848e9	−	4.04848e9i	0.728856	−	0.728856i
$274$	3.47114e9	−	3.47114e9i	0.615843	−	0.615843i
$275$	−1.08015e8			−0.0188866
$276$	−2.99604e9	−	2.99604e9i	−0.516310	−	0.516310i
$277$	−7.72323e9	+	7.72323e9i	−1.31184	+	1.31184i	−0.391776	+	0.920060i	$0.628139\pi$
$277$	−7.72323e9	+	7.72323e9i	−1.31184	+	1.31184i	−0.920060	+	0.391776i	$0.871861\pi$
$278$	−6.58189e9	−	6.58189e9i	−1.10198	−	1.10198i
$279$	2.78110e9	−	2.78110e9i	0.458986	−	0.458986i
$280$			1.14741e9i			0.186675i
$281$	−7.96438e8	−	7.96438e8i	−0.127740	−	0.127740i	0.640346	−	0.768086i	$-0.278791\pi$
$281$	−7.96438e8	−	7.96438e8i	−0.127740	−	0.127740i	−0.768086	+	0.640346i	$0.778791\pi$
$282$	−2.52540e9	−	2.52540e9i	−0.399332	−	0.399332i
$283$	5.18200e9	−	5.18200e9i	0.807890	−	0.807890i	−0.176425	−	0.984314i	$-0.556453\pi$
$283$	5.18200e9	−	5.18200e9i	0.807890	−	0.807890i	0.984314	+	0.176425i	$0.0564532\pi$
$284$			3.44839e9i			0.530082i
$285$	−1.55968e8			−0.0236405
$286$		−	6.48999e9i		−	0.970018i
$287$			1.29444e10i			1.90789i
$288$	−5.14080e9	+	5.14080e9i	−0.747241	+	0.747241i
$289$		−	3.01813e9i		−	0.432660i
$290$	−1.25184e10	+	1.25184e10i	−1.76994	+	1.76994i
$291$	−1.30770e9	+	1.30770e9i	−0.182362	+	0.182362i
$292$	−7.20956e9			−0.991693
$293$	1.15759e10			1.57067			0.785333	−	0.619074i	$-0.212492\pi$
$293$	1.15759e10			1.57067			0.785333	+	0.619074i	$0.212492\pi$
$294$	2.34333e9	+	2.34333e9i	0.313649	+	0.313649i
$295$		−	1.08479e10i		−	1.43238i
$296$	−1.06338e8	−	1.12548e9i	−0.0138523	−	0.146612i
$297$	−2.73594e9			−0.351626
$298$	−1.13739e10	+	1.13739e10i	−1.44226	+	1.44226i
$299$		−	2.32855e10i		−	2.91341i
$300$			1.53964e8i			0.0190080i
$301$	−5.10319e9	−	5.10319e9i	−0.621693	−	0.621693i
$302$	−6.33534e9	−	6.33534e9i	−0.761627	−	0.761627i
$303$	−2.17355e9			−0.257869
$304$	−3.38938e8	−	3.38938e8i	−0.0396850	−	0.0396850i
$305$	9.13021e9			1.05507
$306$	−7.05972e9			−0.805196
$307$			4.38531e9i			0.493682i	0.969056	+	0.246841i	$0.0793925\pi$
$307$			4.38531e9i			0.493682i	−0.969056	+	0.246841i	$0.920607\pi$
$308$	4.36780e9			0.485355
$309$	−3.94622e9	−	3.94622e9i	−0.432860	−	0.432860i
$310$	−7.33489e9	+	7.33489e9i	−0.794231	+	0.794231i
$311$	5.00031e9	−	5.00031e9i	0.534510	−	0.534510i	−0.387401	−	0.921911i	$-0.626627\pi$
$311$	5.00031e9	−	5.00031e9i	0.534510	−	0.534510i	0.921911	+	0.387401i	$0.126627\pi$
$312$	1.10886e9			0.117019
$313$	8.87820e9	+	8.87820e9i	0.925012	+	0.925012i	0.997378	−	0.0723660i	$-0.0230550\pi$
$313$	8.87820e9	+	8.87820e9i	0.925012	+	0.925012i	−0.0723660	+	0.997378i	$0.523055\pi$
$314$	4.34324e9	−	4.34324e9i	0.446782	−	0.446782i
$315$	−6.85679e9	−	6.85679e9i	−0.696432	−	0.696432i
$316$	−3.00615e9	+	3.00615e9i	−0.301482	+	0.301482i
$317$		−	1.25764e10i		−	1.24543i	−0.782449	−	0.622714i	$-0.786030\pi$
$317$		−	1.25764e10i		−	1.24543i	0.782449	−	0.622714i	$-0.213970\pi$
$318$	3.84112e9	+	3.84112e9i	0.375621	+	0.375621i
$319$	−5.71203e9	−	5.71203e9i	−0.551604	−	0.551604i
$320$	5.62034e9	−	5.62034e9i	0.535997	−	0.535997i
$321$			4.36174e9i			0.410809i
$322$	3.32210e10			3.09022
$323$		−	4.19980e8i		−	0.0385850i
$324$		−	3.74599e9i		−	0.339927i
$325$	−5.98314e8	+	5.98314e8i	−0.0536285	+	0.0536285i
$326$			1.79288e10i			1.58738i
$327$	−4.89727e9	+	4.89727e9i	−0.428314	+	0.428314i
$328$	−1.77270e9	+	1.77270e9i	−0.153158	+	0.153158i
$329$	1.32095e10			1.12747
$330$	3.15509e9			0.266045
$331$	9.12371e9	+	9.12371e9i	0.760080	+	0.760080i	0.976337	−	0.216256i	$-0.0693847\pi$
$331$	9.12371e9	+	9.12371e9i	0.760080	+	0.760080i	−0.216256	+	0.976337i	$0.569385\pi$
$332$		−	6.28589e9i		−	0.517386i
$333$	7.36122e9	+	6.09029e9i	0.598650	+	0.495291i
$334$	1.52368e10			1.22436
$335$	−1.16288e10	+	1.16288e10i	−0.923326	+	0.923326i
$336$			8.55411e9i			0.671147i
$337$			1.09504e10i			0.849006i	0.905427	+	0.424503i	$0.139551\pi$
$337$			1.09504e10i			0.849006i	−0.905427	+	0.424503i	$0.860449\pi$
$338$	−2.32515e10	−	2.32515e10i	−1.78149	−	1.78149i
$339$	2.21196e9	+	2.21196e9i	0.167486	+	0.167486i
$340$	8.78327e9			0.657265
$341$	−3.34683e9	−	3.34683e9i	−0.247524	−	0.247524i
$342$	7.49172e8			0.0547617
$343$	5.69745e9			0.411627
$344$		−	1.39774e9i		−	0.0998140i
$345$	1.13202e10			0.799055
$346$	1.02285e10	+	1.02285e10i	0.713685	+	0.713685i
$347$	−6.19982e9	+	6.19982e9i	−0.427623	+	0.427623i	−0.887818	−	0.460195i	$-0.847779\pi$
$347$	−6.19982e9	+	6.19982e9i	−0.427623	+	0.427623i	0.460195	+	0.887818i	$0.347779\pi$
$348$	−8.14192e9	+	8.14192e9i	−0.555149	+	0.555149i
$349$	1.56699e10			1.05625			0.528123	−	0.849168i	$-0.322896\pi$
$349$	1.56699e10			1.05625			0.528123	+	0.849168i	$0.322896\pi$
$350$	−8.53604e8	−	8.53604e8i	−0.0568832	−	0.0568832i
$351$	−1.51549e10	+	1.51549e10i	−0.998444	+	0.998444i
$352$	6.18655e9	+	6.18655e9i	0.402974	+	0.402974i
$353$	4.23032e9	−	4.23032e9i	0.272442	−	0.272442i	−0.557640	−	0.830083i	$-0.688293\pi$
$353$	4.23032e9	−	4.23032e9i	0.272442	−	0.272442i	0.830083	+	0.557640i	$0.188293\pi$
$354$		−	1.49566e10i		−	0.952400i
$355$	−6.51467e9	−	6.51467e9i	−0.410184	−	0.410184i
$356$	6.72489e9	+	6.72489e9i	0.418683	+	0.418683i
$357$	−5.29973e9	+	5.29973e9i	−0.326273	+	0.326273i
$358$			4.55367e9i			0.277223i
$359$	7.83108e8			0.0471459			0.0235729	−	0.999722i	$-0.492496\pi$
$359$	7.83108e8			0.0471459			0.0235729	+	0.999722i	$0.492496\pi$
$360$		−	1.87804e9i		−	0.111814i
$361$		−	1.69390e10i		−	0.997376i
$362$	5.24231e9	−	5.24231e9i	0.305273	−	0.305273i
$363$		−	6.76011e9i		−	0.389339i
$364$	2.41940e10	−	2.41940e10i	1.37817	−	1.37817i
$365$	1.36202e10	−	1.36202e10i	0.767385	−	0.767385i
$366$	1.25883e10			0.701522
$367$	1.07425e10			0.592163			0.296081	−	0.955163i	$-0.404320\pi$
$367$	1.07425e10			0.592163			0.296081	+	0.955163i	$0.404320\pi$
$368$	2.46002e10	+	2.46002e10i	1.34136	+	1.34136i
$369$		−	2.11869e10i		−	1.14278i
$370$	−1.94145e10	−	1.60626e10i	−1.03590	−	0.857054i
$371$	−2.00916e10			−1.06052
$372$	−4.77057e9	+	4.77057e9i	−0.249114	+	0.249114i
$373$			1.84298e10i			0.952106i	0.879417	+	0.476053i	$0.157933\pi$
$373$			1.84298e10i			0.952106i	−0.879417	+	0.476053i	$0.842067\pi$
$374$			8.49581e9i			0.434229i
$375$	−6.74397e9	−	6.74397e9i	−0.341029	−	0.341029i
$376$	1.80901e9	+	1.80901e9i	0.0905086	+	0.0905086i
$377$	−6.32798e10			−3.13256
$378$	−2.16212e10	−	2.16212e10i	−1.05904	−	1.05904i
$379$	−2.33131e10			−1.12991			−0.564953	−	0.825123i	$-0.691106\pi$
$379$	−2.33131e10			−1.12991			−0.564953	+	0.825123i	$0.691106\pi$
$380$	−9.32074e8			−0.0447009
$381$			4.31261e9i			0.204663i
$382$	−7.44909e9			−0.349824
$383$	−1.62225e10	−	1.62225e10i	−0.753917	−	0.753917i	0.221291	−	0.975208i	$-0.428973\pi$
$383$	−1.62225e10	−	1.62225e10i	−0.753917	−	0.753917i	−0.975208	+	0.221291i	$0.928973\pi$
$384$	−2.12628e9	+	2.12628e9i	−0.0977900	+	0.0977900i
$385$	−8.25161e9	+	8.25161e9i	−0.375574	+	0.375574i
$386$	−2.51802e9			−0.113425
$387$	8.35273e9	+	8.35273e9i	0.372378	+	0.372378i
$388$	−7.81488e9	+	7.81488e9i	−0.344822	+	0.344822i
$389$	1.79988e10	+	1.79988e10i	0.786040	+	0.786040i	0.980842	−	0.194803i	$-0.0624066\pi$
$389$	1.79988e10	+	1.79988e10i	0.786040	+	0.786040i	−0.194803	+	0.980842i	$0.562407\pi$
$390$	1.74766e10	−	1.74766e10i	0.755436	−	0.755436i
$391$			3.04822e10i			1.30419i
$392$	−1.67859e9	−	1.67859e9i	−0.0710886	−	0.0710886i
$393$	−6.55698e9	−	6.55698e9i	−0.274874	−	0.274874i
$394$	−1.69411e10	+	1.69411e10i	−0.703002	+	0.703002i
$395$		−	1.13584e10i		−	0.466582i
$396$	−7.14906e9			−0.290716
$397$			6.48766e9i			0.261172i	0.991437	+	0.130586i	$0.0416858\pi$
$397$			6.48766e9i			0.261172i	−0.991437	+	0.130586i	$0.958314\pi$
$398$		−	1.63102e10i		−	0.650019i
$399$	5.62403e8	−	5.62403e8i	0.0221899	−	0.0221899i
$400$		−	1.26419e9i		−	0.0493823i
$401$	2.15438e10	−	2.15438e10i	0.833191	−	0.833191i	−0.154761	−	0.987952i	$-0.549461\pi$
$401$	2.15438e10	−	2.15438e10i	0.833191	−	0.833191i	0.987952	+	0.154761i	$0.0494607\pi$
$402$	−1.60332e10	+	1.60332e10i	−0.613925	+	0.613925i
$403$	−3.70774e10			−1.40569
$404$	−1.29893e10			−0.487596
$405$	7.07688e9	+	7.07688e9i	0.263040	+	0.263040i
$406$		−	9.02802e10i		−	3.32268i
$407$	7.32918e9	−	8.85864e9i	0.267102	−	0.322842i
$408$	−1.45157e9			−0.0523837
$409$	−3.02395e10	+	3.02395e10i	−1.08064	+	1.08064i	−0.0841898	+	0.996450i	$0.526830\pi$
$409$	−3.02395e10	+	3.02395e10i	−1.08064	+	1.08064i	−0.996450	+	0.0841898i	$0.973170\pi$
$410$			5.58785e10i			1.97747i
$411$			8.53011e9i			0.298942i
$412$	−2.35828e10	−	2.35828e10i	−0.818478	−	0.818478i
$413$	3.91165e10	+	3.91165e10i	1.34450	+	1.34450i
$414$	−5.43750e10			−1.85096
$415$	1.18752e10	+	1.18752e10i	0.400359	+	0.400359i
$416$	6.85367e10			2.28849
$417$	1.61746e10			0.534921
$418$		−	9.01569e8i		−	0.0295321i
$419$	5.64339e10			1.83098			0.915491	−	0.402339i	$-0.131803\pi$
$419$	5.64339e10			1.83098			0.915491	+	0.402339i	$0.131803\pi$
$420$	1.17618e10	+	1.17618e10i	0.377988	+	0.377988i
$421$	−1.15441e8	+	1.15441e8i	−0.00367477	+	0.00367477i	−0.708942	−	0.705267i	$-0.750827\pi$
$421$	−1.15441e8	+	1.15441e8i	−0.00367477	+	0.00367477i	0.705267	+	0.708942i	$0.250827\pi$
$422$	1.20967e10	−	1.20967e10i	0.381431	−	0.381431i
$423$	−2.16209e10			−0.675325
$424$	−2.75149e9	−	2.75149e9i	−0.0851344	−	0.0851344i
$425$	7.83231e8	−	7.83231e8i	0.0240068	−	0.0240068i
$426$	−8.98209e9	−	8.98209e9i	−0.272734	−	0.272734i
$427$	−3.29225e10	+	3.29225e10i	−0.990334	+	0.990334i
$428$			2.60660e10i			0.776783i
$429$	7.97437e9	+	7.97437e9i	0.235433	+	0.235433i
$430$	−2.20295e10	−	2.20295e10i	−0.644365	−	0.644365i
$431$	3.17470e10	−	3.17470e10i	0.920013	−	0.920013i	−0.0770169	−	0.997030i	$-0.524540\pi$
$431$	3.17470e10	−	3.17470e10i	0.920013	−	0.920013i	0.997030	+	0.0770169i	$0.0245395\pi$
$432$		−	3.20210e10i		−	0.919390i
$433$	5.75384e10			1.63684			0.818419	−	0.574622i	$-0.194851\pi$
$433$	5.75384e10			1.63684			0.818419	+	0.574622i	$0.194851\pi$
$434$		−	5.28976e10i		−	1.49100i
$435$		−	3.07633e10i		−	0.859163i
$436$	−2.92664e10	+	2.92664e10i	−0.809884	+	0.809884i
$437$		−	3.23475e9i		−	0.0886983i
$438$	1.87789e10	−	1.87789e10i	0.510239	−	0.510239i
$439$	−1.30971e10	+	1.30971e10i	−0.352628	+	0.352628i	−0.861087	−	0.508458i	$-0.830216\pi$
$439$	−1.30971e10	+	1.30971e10i	−0.352628	+	0.352628i	0.508458	+	0.861087i	$0.330216\pi$
$440$	−2.26007e9			−0.0602992
$441$	2.00621e10			0.530424
$442$	4.70598e10	+	4.70598e10i	1.23299	+	1.23299i
$443$			5.94992e10i			1.54489i	0.635085	+	0.772443i	$0.280965\pi$
$443$			5.94992e10i			1.54489i	−0.635085	+	0.772443i	$0.719035\pi$
$444$	−1.26271e10	−	1.04470e10i	−0.324916	−	0.268819i
$445$	−2.54092e10			−0.647964
$446$	−2.86634e10	+	2.86634e10i	−0.724417	+	0.724417i
$447$		−	2.79507e10i		−	0.700103i
$448$			4.05326e10i			1.00622i
$449$	−2.75365e10	−	2.75365e10i	−0.677522	−	0.677522i	0.281917	−	0.959439i	$-0.409030\pi$
$449$	−2.75365e10	−	2.75365e10i	−0.677522	−	0.677522i	−0.959439	+	0.281917i	$0.909030\pi$
$450$	1.39715e9	+	1.39715e9i	0.0340716	+	0.0340716i
$451$	−2.54968e10			−0.616281
$452$	1.32188e10	+	1.32188e10i	0.316693	+	0.316693i
$453$	1.55687e10			0.369709
$454$	3.06964e10			0.722544
$455$			9.14142e10i			2.13289i
$456$	1.54039e8			0.00356264
$457$	5.38340e9	+	5.38340e9i	0.123422	+	0.123422i	0.766120	−	0.642698i	$-0.222185\pi$
$457$	5.38340e9	+	5.38340e9i	0.123422	+	0.123422i	−0.642698	+	0.766120i	$0.722185\pi$
$458$	1.34796e10	−	1.34796e10i	0.306348	−	0.306348i
$459$	1.98387e10	−	1.98387e10i	0.446954	−	0.446954i
$460$	6.76501e10			1.51090
$461$	4.01003e10	+	4.01003e10i	0.887860	+	0.887860i	0.994317	−	0.106458i	$-0.0339508\pi$
$461$	4.01003e10	+	4.01003e10i	0.887860	+	0.887860i	−0.106458	+	0.994317i	$0.533951\pi$
$462$	−1.13769e10	+	1.13769e10i	−0.249721	+	0.249721i
$463$	−2.20166e10	−	2.20166e10i	−0.479100	−	0.479100i	0.425744	−	0.904844i	$-0.360012\pi$
$463$	−2.20166e10	−	2.20166e10i	−0.479100	−	0.479100i	−0.904844	+	0.425744i	$0.860012\pi$
$464$	6.68525e10	−	6.68525e10i	1.44227	−	1.44227i
$465$		−	1.80250e10i		−	0.385536i
$466$	−4.64468e10	−	4.64468e10i	−0.984945	−	0.984945i
$467$	−3.07835e10	−	3.07835e10i	−0.647218	−	0.647218i	0.305102	−	0.952320i	$-0.401310\pi$
$467$	−3.07835e10	−	3.07835e10i	−0.647218	−	0.647218i	−0.952320	+	0.305102i	$0.901310\pi$
$468$	−3.95999e10	+	3.95999e10i	−0.825488	+	0.825488i
$469$		−	8.38642e10i		−	1.73335i
$470$	5.70232e10			1.16858
$471$			1.06733e10i			0.216877i
$472$			1.07138e10i			0.215862i
$473$	1.00518e10	−	1.00518e10i	0.200817	−	0.200817i
$474$		−	1.56603e10i		−	0.310233i
$475$	−8.31159e7	+	8.31159e7i	−0.00163271	+	0.00163271i
$476$	−3.16715e10	+	3.16715e10i	−0.616937	+	0.616937i
$477$	3.28853e10			0.635226
$478$	−7.40897e10			−1.41921
$479$	3.65511e10	+	3.65511e10i	0.694318	+	0.694318i	0.963179	−	0.268861i	$-0.0866471\pi$
$479$	3.65511e10	+	3.65511e10i	0.694318	+	0.694318i	−0.268861	+	0.963179i	$0.586647\pi$
$480$			3.33189e10i			0.627662i
$481$	−8.47196e9	−	8.96671e10i	−0.158272	−	1.67515i
$482$	−5.41656e10			−1.00354
$483$	−4.08193e10	+	4.08193e10i	−0.750027	+	0.750027i
$484$		−	4.03988e10i		−	0.736186i
$485$		−	2.95276e10i		−	0.533655i
$486$	5.53040e10	+	5.53040e10i	0.991314	+	0.991314i
$487$	−4.31411e10	−	4.31411e10i	−0.766964	−	0.766964i	0.210607	−	0.977571i	$-0.432456\pi$
$487$	−4.31411e10	−	4.31411e10i	−0.766964	−	0.766964i	−0.977571	+	0.210607i	$0.932456\pi$
$488$	−9.01730e9			−0.159000
$489$	−2.20295e10	−	2.20295e10i	−0.385274	−	0.385274i
$490$	−5.29121e10			−0.917847
$491$	5.27698e10			0.907944			0.453972	−	0.891016i	$-0.350007\pi$
$491$	5.27698e10			0.907944			0.453972	+	0.891016i	$0.350007\pi$
$492$			3.63430e10i			0.620242i
$493$	8.28374e10			1.40229
$494$	−4.99395e9	−	4.99395e9i	−0.0838564	−	0.0838564i
$495$	1.35059e10	−	1.35059e10i	0.224959	−	0.224959i
$496$	3.91707e10	−	3.91707e10i	0.647195	−	0.647195i
$497$	4.69823e10			0.770033
$498$	1.63730e10	+	1.63730e10i	0.266201	+	0.266201i
$499$	−7.09078e10	+	7.09078e10i	−1.14365	+	1.14365i	−0.155869	+	0.987778i	$0.549818\pi$
$499$	−7.09078e10	+	7.09078e10i	−1.14365	+	1.14365i	−0.987778	+	0.155869i	$0.950182\pi$
$500$	−4.03024e10	−	4.03024e10i	−0.644838	−	0.644838i
$501$	−1.87218e10	+	1.87218e10i	−0.297164	+	0.297164i
$502$		−	1.57372e11i		−	2.47806i
$503$	−7.99980e10	−	7.99980e10i	−1.24970	−	1.24970i	−0.955850	−	0.293854i	$-0.905062\pi$
$503$	−7.99980e10	−	7.99980e10i	−1.24970	−	1.24970i	−0.293854	−	0.955850i	$-0.594938\pi$
$504$	6.77200e9	+	6.77200e9i	0.104953	+	0.104953i
$505$	2.45393e10	−	2.45393e10i	0.377308	−	0.377308i
$506$			6.54360e10i			0.998194i
$507$	5.71392e10			0.864773
$508$			2.57724e10i			0.386991i
$509$		−	1.56263e10i		−	0.232802i	−0.993202	−	0.116401i	$-0.962864\pi$
$509$		−	1.56263e10i		−	0.232802i	0.993202	−	0.116401i	$-0.0371357\pi$
$510$	−2.28780e10	+	2.28780e10i	−0.338171	+	0.338171i
$511$			9.82262e10i			1.44060i
$512$	−6.45663e10	+	6.45663e10i	−0.939563	+	0.939563i
$513$	−2.10527e9	+	2.10527e9i	−0.0303975	+	0.0303975i
$514$	7.31626e10			1.04818
$515$	8.91050e10			1.26670
$516$	−1.43279e10	−	1.43279e10i	−0.202108	−	0.202108i
$517$			2.60191e10i			0.364191i
$518$	1.27927e11	−	1.20868e10i	1.77681	−	0.167877i
$519$	−2.51359e10			−0.346437
$520$	−1.25189e10	+	1.25189e10i	−0.171220	+	0.171220i
$521$			1.06938e11i			1.45139i	0.688018	+	0.725693i	$0.258481\pi$
$521$			1.06938e11i			1.45139i	−0.688018	+	0.725693i	$0.741519\pi$
$522$			1.47768e11i			1.99020i
$523$	−7.67741e10	−	7.67741e10i	−1.02614	−	1.02614i	−0.999649	−	0.0264948i	$-0.991565\pi$
$523$	−7.67741e10	−	7.67741e10i	−1.02614	−	1.02614i	−0.0264948	−	0.999649i	$-0.508435\pi$
$524$	−3.91849e10	−	3.91849e10i	−0.519749	−	0.519749i
$525$	2.09768e9			0.0276122
$526$	2.78599e10	+	2.78599e10i	0.363945	+	0.363945i
$527$	4.85367e10			0.629257
$528$	−1.68492e10			−0.216792
$529$			1.56468e11i			1.99803i
$530$	−8.67319e10			−1.09920
$531$	−6.40245e10	−	6.40245e10i	−0.805320	−	0.805320i
$532$	3.36096e9	−	3.36096e9i	0.0419582	−	0.0419582i
$533$	−1.41231e11	+	1.41231e11i	−1.74993	+	1.74993i
$534$	−3.50329e10			−0.430835
$535$	−4.92437e10	−	4.92437e10i	−0.601084	−	0.601084i
$536$	1.14850e10	−	1.14850e10i	0.139146	−	0.139146i
$537$	−5.59519e9	−	5.59519e9i	−0.0672849	−	0.0672849i
$538$	3.56558e9	−	3.56558e9i	0.0425600	−	0.0425600i
$539$		−	2.41432e10i		−	0.286049i
$540$	−4.40286e10	−	4.40286e10i	−0.517797	−	0.517797i
$541$	1.13847e10	+	1.13847e10i	0.132903	+	0.132903i	0.770429	−	0.637526i	$-0.220042\pi$
$541$	1.13847e10	+	1.13847e10i	0.132903	+	0.132903i	−0.637526	+	0.770429i	$0.720042\pi$
$542$	1.23910e11	−	1.23910e11i	1.43585	−	1.43585i
$543$			1.28827e10i			0.148186i
$544$	−8.97190e10			−1.02444
$545$		−	1.10580e11i		−	1.25340i
$546$			1.26037e11i			1.41817i
$547$	−9.03219e10	+	9.03219e10i	−1.00889	+	1.00889i	−0.00893027	+	0.999960i	$0.502843\pi$
$547$	−9.03219e10	+	9.03219e10i	−1.00889	+	1.00889i	−0.999960	+	0.00893027i	$0.997157\pi$
$548$			5.09765e10i			0.565259i
$549$	5.38865e10	−	5.38865e10i	0.593185	−	0.593185i
$550$	1.68136e9	−	1.68136e9i	0.0183742	−	0.0183742i
$551$	−8.79064e9			−0.0953705
$552$	−1.11802e10			−0.120418
$553$	4.09570e10	+	4.09570e10i	0.437954	+	0.437954i
$554$		−	2.40439e11i		−	2.55250i
$555$	4.35914e10	−	4.11862e9i	0.459440	−	0.0434090i
$556$	9.66604e10			1.01146
$557$	1.11111e11	−	1.11111e11i	1.15435	−	1.15435i	0.168677	−	0.985671i	$-0.446050\pi$
$557$	1.11111e11	−	1.11111e11i	1.15435	−	1.15435i	0.985671	−	0.168677i	$-0.0539496\pi$
$558$			8.65810e10i			0.893071i
$559$		−	1.11358e11i		−	1.14044i
$560$	−9.65753e10	−	9.65753e10i	−0.982005	−	0.982005i
$561$	−1.04390e10	−	1.04390e10i	−0.105392	−	0.105392i
$562$	2.47947e10			0.248550
$563$	−1.52743e10	−	1.52743e10i	−0.152030	−	0.152030i	0.626994	−	0.779024i	$-0.284285\pi$
$563$	−1.52743e10	−	1.52743e10i	−0.152030	−	0.152030i	−0.779024	+	0.626994i	$0.784285\pi$
$564$	3.70876e10			0.366532
$565$	−4.99457e10			−0.490122
$566$			1.61326e11i			1.57195i
$567$	−5.10369e10			−0.493801
$568$	6.43410e9	+	6.43410e9i	0.0618151	+	0.0618151i
$569$	−9.86387e10	+	9.86387e10i	−0.941019	+	0.941019i	−0.998355	−	0.0573364i	$-0.981739\pi$
$569$	−9.86387e10	+	9.86387e10i	−0.941019	+	0.941019i	0.0573364	+	0.998355i	$0.481739\pi$
$570$	2.42779e9	−	2.42779e9i	0.0229992	−	0.0229992i
$571$	1.16369e11			1.09469			0.547346	−	0.836906i	$-0.315638\pi$
$571$	1.16369e11			1.09469			0.547346	+	0.836906i	$0.315638\pi$
$572$	4.76553e10	+	4.76553e10i	0.445172	+	0.445172i
$573$	9.15284e9	−	9.15284e9i	0.0849058	−	0.0849058i
$574$	−2.01492e11	−	2.01492e11i	−1.85613	−	1.85613i
$575$	6.03257e9	−	6.03257e9i	0.0551862	−	0.0551862i
$576$		−	6.63424e10i		−	0.602700i
$577$	−2.04220e10	−	2.04220e10i	−0.184245	−	0.184245i	0.608958	−	0.793203i	$-0.291588\pi$
$577$	−2.04220e10	−	2.04220e10i	−0.184245	−	0.184245i	−0.793203	+	0.608958i	$0.791588\pi$
$578$	4.69801e10	+	4.69801e10i	0.420923	+	0.420923i
$579$	3.09394e9	−	3.09394e9i	0.0275295	−	0.0275295i
$580$		−	1.83843e11i		−	1.62456i
$581$	−8.56416e10			−0.751589
$582$		−	4.07111e10i		−	0.354831i
$583$		−	3.95748e10i		−	0.342567i
$584$	−1.34518e10	+	1.34518e10i	−0.115646	+	0.115646i
$585$		−	1.49624e11i		−	1.27755i
$586$	−1.80190e11	+	1.80190e11i	−1.52806	+	1.52806i
$587$	−2.30576e10	+	2.30576e10i	−0.194206	+	0.194206i	−0.797511	−	0.603305i	$-0.793850\pi$
$587$	−2.30576e10	+	2.30576e10i	−0.194206	+	0.194206i	0.603305	+	0.797511i	$0.293850\pi$
$588$	−3.44137e10			−0.287887
$589$	−5.15068e9			−0.0427960
$590$	1.68859e11	+	1.68859e11i	1.39353	+	1.39353i
$591$		−	4.16317e10i		−	0.341251i
$592$	1.03680e11	+	8.57793e10i	0.844127	+	0.698387i
$593$	−1.92855e11			−1.55960			−0.779799	−	0.626030i	$-0.784679\pi$
$593$	−1.92855e11			−1.55960			−0.779799	+	0.626030i	$0.784679\pi$
$594$	4.25876e10	−	4.25876e10i	0.342088	−	0.342088i
$595$		−	1.19667e11i		−	0.954787i
$596$		−	1.67035e11i		−	1.32380i
$597$	2.00406e10	+	2.00406e10i	0.157766	+	0.157766i
$598$	3.62461e11	+	3.62461e11i	2.83437	+	2.83437i
$599$	−4.76754e10			−0.370328			−0.185164	−	0.982708i	$-0.559282\pi$
$599$	−4.76754e10			−0.370328			−0.185164	+	0.982708i	$0.559282\pi$
$600$	2.87271e8	+	2.87271e8i	0.00221660	+	0.00221660i
$601$	−5.81789e10			−0.445931			−0.222966	−	0.974826i	$-0.571574\pi$
$601$	−5.81789e10			−0.445931			−0.222966	+	0.974826i	$0.571574\pi$
$602$	1.58872e11			1.20966
$603$			1.37266e11i			1.03823i
$604$	9.30396e10			0.699069
$605$	7.63211e10	+	7.63211e10i	0.569670	+	0.569670i
$606$	3.38335e10	−	3.38335e10i	0.250874	−	0.250874i
$607$	1.16492e11	−	1.16492e11i	0.858109	−	0.858109i	−0.133007	−	0.991115i	$-0.542463\pi$
$607$	1.16492e11	−	1.16492e11i	0.858109	−	0.858109i	0.991115	+	0.133007i	$0.0424632\pi$
$608$	9.52091e9			0.0696729
$609$	1.10929e11	+	1.10929e11i	0.806447	+	0.806447i
$610$	−1.42121e11	+	1.42121e11i	−1.02645	+	1.02645i
$611$	1.44124e11	+	1.44124e11i	1.03412	+	1.03412i
$612$	5.18388e10	−	5.18388e10i	0.369530	−	0.369530i
$613$			7.38830e10i			0.523242i	0.965171	+	0.261621i	$0.0842571\pi$
$613$			7.38830e10i			0.523242i	−0.965171	+	0.261621i	$0.915743\pi$
$614$	−6.82617e10	−	6.82617e10i	−0.480290	−	0.480290i
$615$	−6.86590e10	−	6.86590e10i	−0.479951	−	0.479951i
$616$	8.14957e9	−	8.14957e9i	0.0565994	−	0.0565994i
$617$			1.12673e10i			0.0777459i	0.999244	+	0.0388730i	$0.0123768\pi$
$617$			1.12673e10i			0.0777459i	−0.999244	+	0.0388730i	$0.987623\pi$
$618$	1.22853e11			0.842235
$619$		−	5.27277e10i		−	0.359150i	−0.983744	−	0.179575i	$-0.942528\pi$
$619$		−	5.27277e10i		−	0.359150i	0.983744	−	0.179575i	$-0.0574723\pi$
$620$		−	1.07719e11i		−	0.728995i
$621$	1.52801e11	−	1.52801e11i	1.02745	−	1.02745i
$622$			1.55669e11i			1.04002i
$623$	9.16228e10	−	9.16228e10i	0.608207	−	0.608207i
$624$	−9.33306e10	+	9.33306e10i	−0.615581	+	0.615581i
$625$	1.45400e11			0.952894
$626$	−2.76396e11			−1.79984
$627$	1.10778e9	+	1.10778e9i	0.00716773	+	0.00716773i
$628$			6.37840e10i			0.410085i
$629$	1.10903e10	+	1.17380e11i	0.0708505	+	0.749880i
$630$	2.13465e11			1.35508
$631$	1.22916e11	−	1.22916e11i	0.775338	−	0.775338i	−0.203696	−	0.979034i	$-0.565295\pi$
$631$	1.22916e11	−	1.22916e11i	0.775338	−	0.775338i	0.979034	+	0.203696i	$0.0652954\pi$
$632$			1.12179e10i			0.0703143i
$633$			2.97268e10i			0.185154i
$634$	1.95764e11	+	1.95764e11i	1.21164	+	1.21164i
$635$	−4.86890e10	−	4.86890e10i	−0.299458	−	0.299458i
$636$	−5.64099e10			−0.344768
$637$	−1.33733e11	−	1.33733e11i	−0.812236	−	0.812236i
$638$	1.77827e11			1.07328
$639$	−7.68991e10			−0.461230
$640$		−	4.80110e10i		−	0.286168i
$641$	−1.53028e11			−0.906437			−0.453218	−	0.891399i	$-0.649724\pi$
$641$	−1.53028e11			−0.906437			−0.453218	+	0.891399i	$0.649724\pi$
$642$	−6.78947e10	−	6.78947e10i	−0.399665	−	0.399665i
$643$	−5.05147e10	+	5.05147e10i	−0.295511	+	0.295511i	−0.839253	−	0.543742i	$-0.817007\pi$
$643$	−5.05147e10	+	5.05147e10i	−0.295511	+	0.295511i	0.543742	+	0.839253i	$0.317007\pi$
$644$	−2.43939e11	+	2.43939e11i	−1.41820	+	1.41820i
$645$	5.41363e10			0.312787
$646$	6.53740e9	+	6.53740e9i	0.0375383	+	0.0375383i
$647$	4.87727e10	−	4.87727e10i	0.278330	−	0.278330i	−0.554112	−	0.832442i	$-0.686942\pi$
$647$	4.87727e10	−	4.87727e10i	0.278330	−	0.278330i	0.832442	+	0.554112i	$0.186942\pi$
$648$	−6.98937e9	−	6.98937e9i	−0.0396404	−	0.0396404i
$649$	−7.70485e10	+	7.70485e10i	−0.434295	+	0.434295i
$650$		−	1.86267e10i		−	0.104347i
$651$	6.49964e10	+	6.49964e10i	0.361880	+	0.361880i
$652$	−1.31650e11	−	1.31650e11i	−0.728500	−	0.728500i
$653$	−1.67478e10	+	1.67478e10i	−0.0921095	+	0.0921095i	−0.751660	−	0.659551i	$-0.770747\pi$
$653$	−1.67478e10	+	1.67478e10i	−0.0921095	+	0.0921095i	0.659551	+	0.751660i	$0.270747\pi$
$654$		−	1.52461e11i		−	0.833391i
$655$	1.48056e11			0.804377
$656$		−	2.98409e11i		−	1.61138i
$657$		−	1.60773e11i		−	0.862883i
$658$	−2.05619e11	+	2.05619e11i	−1.09688	+	1.09688i
$659$			6.07816e10i			0.322278i	0.986932	+	0.161139i	$0.0515167\pi$
$659$			6.07816e10i			0.322278i	−0.986932	+	0.161139i	$0.948483\pi$
$660$	−2.31675e10	+	2.31675e10i	−0.122097	+	0.122097i
$661$	−1.80961e11	+	1.80961e11i	−0.947938	+	0.947938i	−0.998710	−	0.0507721i	$-0.983832\pi$
$661$	−1.80961e11	+	1.80961e11i	−0.947938	+	0.947938i	0.0507721	+	0.998710i	$0.483832\pi$
$662$	−2.84039e11			−1.47892
$663$	−1.15647e11			−0.598520
$664$	−1.17284e10	−	1.17284e10i	−0.0603345	−	0.0603345i
$665$			1.26990e10i			0.0649355i
$666$	−2.09386e11	+	1.97833e10i	−1.06427	+	0.100554i
$667$	6.38026e11			3.22356
$668$	−1.11882e11	+	1.11882e11i	−0.561896	+	0.561896i
$669$		−	7.04386e10i		−	0.351646i
$670$		−	3.62026e11i		−	1.79656i
$671$	−6.48481e10	−	6.48481e10i	−0.319895	−	0.319895i
$672$	−1.20144e11	−	1.20144e11i	−0.589150	−	0.589150i
$673$	−8.20775e10			−0.400096			−0.200048	−	0.979786i	$-0.564110\pi$
$673$	−8.20775e10			−0.400096			−0.200048	+	0.979786i	$0.564110\pi$
$674$	−1.70454e11	−	1.70454e11i	−0.825975	−	0.825975i
$675$	−7.85233e9			−0.0378254
$676$	3.41467e11			1.63517
$677$		−	1.10481e10i		−	0.0525937i	−0.999654	−	0.0262969i	$-0.991628\pi$
$677$		−	1.10481e10i		−	0.0525937i	0.999654	−	0.0262969i	$-0.00837152\pi$
$678$	−6.88625e10			−0.325885
$679$	1.06473e11	+	1.06473e11i	0.500912	+	0.500912i
$680$	1.63881e10	−	1.63881e10i	0.0766465	−	0.0766465i
$681$	−3.77173e10	+	3.77173e10i	−0.175369	+	0.175369i
$682$	1.04193e11			0.481618
$683$	−1.44183e11	−	1.44183e11i	−0.662570	−	0.662570i	0.293415	−	0.955985i	$-0.405208\pi$
$683$	−1.44183e11	−	1.44183e11i	−0.662570	−	0.662570i	−0.955985	+	0.293415i	$0.905208\pi$
$684$	−5.50110e9	+	5.50110e9i	−0.0251319	+	0.0251319i
$685$	−9.63043e10	−	9.63043e10i	−0.437405	−	0.437405i
$686$	−8.86863e10	+	8.86863e10i	−0.400461	+	0.400461i
$687$			3.31253e10i			0.148708i
$688$	1.17645e11	+	1.17645e11i	0.525073	+	0.525073i
$689$	−2.19212e11	−	2.19212e11i	−0.972719	−	0.972719i
$690$	−1.76209e11	+	1.76209e11i	−0.777379	+	0.777379i
$691$			3.50391e11i			1.53688i	0.639919	+	0.768442i	$0.278968\pi$
$691$			3.50391e11i			1.53688i	−0.639919	+	0.768442i	$0.721032\pi$
$692$	−1.50213e11			−0.655065
$693$			9.74019e10i			0.422313i
$694$		−	1.93012e11i		−	0.832046i
$695$	−1.82610e11	+	1.82610e11i	−0.782682	+	0.782682i
$696$			3.03829e10i			0.129477i
$697$	1.84880e11	−	1.84880e11i	0.783357	−	0.783357i
$698$	−2.43917e11	+	2.43917e11i	−1.02759	+	1.02759i
$699$	1.14140e11			0.478112
$700$	1.25359e10			0.0522110
$701$	−3.21347e11	−	3.21347e11i	−1.33077	−	1.33077i	−0.904684	−	0.426083i	$-0.859893\pi$
$701$	−3.21347e11	−	3.21347e11i	−1.33077	−	1.33077i	−0.426083	−	0.904684i	$-0.640107\pi$
$702$		−	4.71800e11i		−	1.94272i
$703$	−1.17690e9	−	1.24563e10i	−0.00481857	−	0.0509997i
$704$	−7.98378e10			−0.325026
$705$	−7.00655e10	+	7.00655e10i	−0.283627	+	0.283627i
$706$			1.31698e11i			0.530104i
$707$			1.76972e11i			0.708315i
$708$	1.09825e11	+	1.09825e11i	0.437086	+	0.437086i
$709$	−7.85852e10	−	7.85852e10i	−0.310997	−	0.310997i	0.534299	−	0.845296i	$-0.320576\pi$
$709$	−7.85852e10	−	7.85852e10i	−0.310997	−	0.310997i	−0.845296	+	0.534299i	$0.820576\pi$
$710$	2.02814e11			0.798114
$711$	−6.70371e10	−	6.70371e10i	−0.262323	−	0.262323i
$712$	2.50950e10			0.0976488
$713$	3.73837e11			1.44652
$714$		−	1.64991e11i		−	0.634844i
$715$	−1.80060e11			−0.688959
$716$	−3.34372e10	−	3.34372e10i	−0.127226	−	0.127226i
$717$	9.10355e10	−	9.10355e10i	0.344456	−	0.344456i
$718$	−1.21898e10	+	1.21898e10i	−0.0458670	+	0.0458670i
$719$	7.58777e10			0.283922			0.141961	−	0.989872i	$-0.454659\pi$
$719$	7.58777e10			0.283922			0.141961	+	0.989872i	$0.454659\pi$
$720$	1.58071e11	+	1.58071e11i	0.588196	+	0.588196i
$721$	−3.21303e11	+	3.21303e11i	−1.18898	+	1.18898i
$722$	2.63672e11	+	2.63672e11i	0.970320	+	0.970320i
$723$	6.65543e10	−	6.65543e10i	0.243570	−	0.243570i
$724$			7.69876e10i			0.280199i
$725$	−1.63939e10	−	1.63939e10i	−0.0593376	−	0.0593376i
$726$	1.05228e11	+	1.05228e11i	0.378777	+	0.378777i
$727$	1.69594e11	−	1.69594e11i	0.607119	−	0.607119i	−0.335073	−	0.942192i	$-0.608761\pi$
$727$	1.69594e11	−	1.69594e11i	0.607119	−	0.607119i	0.942192	+	0.335073i	$0.108761\pi$
$728$		−	9.02837e10i		−	0.321428i
$729$	−2.83928e10			−0.100531
$730$			4.24024e11i			1.49314i
$731$			1.45775e11i			0.510520i
$732$	−9.24344e10	+	9.24344e10i	−0.321951	+	0.321951i
$733$		−	2.12088e10i		−	0.0734684i	−0.999325	−	0.0367342i	$-0.988305\pi$
$733$		−	2.12088e10i		−	0.0734684i	0.999325	−	0.0367342i	$-0.0116955\pi$
$734$	−1.67217e11	+	1.67217e11i	−0.576099	+	0.576099i
$735$	6.50141e10	−	6.50141e10i	0.222771	−	0.222771i
$736$	−6.91029e11			−2.35497
$737$	1.65189e11			0.559900
$738$	3.29795e11	+	3.29795e11i	1.11178	+	1.11178i
$739$		−	3.90314e11i		−	1.30869i	−0.756196	−	0.654345i	$-0.772945\pi$
$739$		−	3.90314e11i		−	1.30869i	0.756196	−	0.654345i	$-0.227055\pi$
$740$	2.60505e11	−	2.46131e10i	0.868738	−	0.0820805i
$741$	1.22723e10			0.0407056
$742$	3.12746e11	−	3.12746e11i	1.03175	−	1.03175i
$743$		−	8.46812e10i		−	0.277864i	−0.990302	−	0.138932i	$-0.955633\pi$
$743$		−	8.46812e10i		−	0.277864i	0.990302	−	0.138932i	$-0.0443669\pi$
$744$			1.78021e10i			0.0581006i
$745$	3.15561e11	+	3.15561e11i	1.02437	+	1.02437i
$746$	−2.86878e11	−	2.86878e11i	−0.926279	−	0.926279i
$747$	1.40175e11			0.450183
$748$	−6.23839e10	−	6.23839e10i	−0.199281	−	0.199281i
$749$	3.55135e11			1.12841
$750$	2.09953e11			0.663555
$751$			2.60675e11i			0.819481i	0.912202	+	0.409740i	$0.134381\pi$
$751$			2.60675e11i			0.819481i	−0.912202	+	0.409740i	$0.865619\pi$
$752$	−3.04522e11			−0.952243
$753$	1.93366e11	+	1.93366e11i	0.601450	+	0.601450i
$754$	9.85012e11	−	9.85012e11i	3.04759	−	3.04759i
$755$	−1.75770e11	+	1.75770e11i	−0.540948	+	0.540948i
$756$	3.17524e11			0.972053
$757$	−1.55385e11	−	1.55385e11i	−0.473178	−	0.473178i	0.429763	−	0.902941i	$-0.358597\pi$
$757$	−1.55385e11	−	1.55385e11i	−0.473178	−	0.473178i	−0.902941	+	0.429763i	$0.858597\pi$
$758$	3.62890e11	−	3.62890e11i	1.09926	−	1.09926i
$759$	−8.04025e10	−	8.04025e10i	−0.242272	−	0.242272i
$760$	−1.73909e9	+	1.73909e9i	−0.00521276	+	0.00521276i
$761$			2.11730e11i			0.631311i	0.948874	+	0.315655i	$0.102224\pi$
$761$			2.11730e11i			0.631311i	−0.948874	+	0.315655i	$0.897776\pi$
$762$	−6.71300e10	−	6.71300e10i	−0.199112	−	0.199112i
$763$	3.98738e11	+	3.98738e11i	1.17649	+	1.17649i
$764$	5.46980e10	−	5.46980e10i	0.160545	−	0.160545i
$765$			1.95867e11i			0.571894i
$766$	5.05039e11			1.46693
$767$			8.53570e11i			2.46637i
$768$		−	1.93637e11i		−	0.556599i
$769$	−1.72325e11	+	1.72325e11i	−0.492768	+	0.492768i	−0.909177	−	0.416409i	$-0.863288\pi$
$769$	−1.72325e11	+	1.72325e11i	−0.492768	+	0.492768i	0.416409	+	0.909177i	$0.363288\pi$
$770$		−	2.56889e11i		−	0.730772i
$771$	−8.98963e10	+	8.98963e10i	−0.254404	+	0.254404i
$772$	1.84896e10	−	1.84896e10i	0.0520545	−	0.0520545i
$773$	−3.41075e11			−0.955282			−0.477641	−	0.878555i	$-0.658508\pi$
$773$	−3.41075e11			−0.955282			−0.477641	+	0.878555i	$0.658508\pi$
$774$	−2.60037e11			−0.724554
$775$	−9.60562e9	−	9.60562e9i	−0.0266268	−	0.0266268i
$776$			2.91624e10i			0.0804224i
$777$	−1.42334e11	+	1.72037e11i	−0.390505	+	0.471996i
$778$	−5.60337e11			−1.52943
$779$	−1.96194e10	+	1.96194e10i	−0.0532764	+	0.0532764i
$780$			2.56657e11i			0.693387i
$781$			9.25420e10i			0.248734i
$782$	−4.74486e11	−	4.74486e11i	−1.26881	−	1.26881i
$783$	−4.15246e11	−	4.15246e11i	−1.10473	−	1.10473i
$784$	2.82568e11			0.747925
$785$	−1.20500e11	−	1.20500e11i	−0.317329	−	0.317329i
$786$	2.04132e11			0.534835
$787$	1.89483e10			0.0493937			0.0246968	−	0.999695i	$-0.492138\pi$
$787$	1.89483e10			0.0493937			0.0246968	+	0.999695i	$0.492138\pi$
$788$		−	2.48794e11i		−	0.645260i
$789$	−6.84639e10			−0.176666
$790$	1.76804e11	+	1.76804e11i	0.453925	+	0.453925i
$791$	1.80099e11	−	1.80099e11i	0.460049	−	0.460049i
$792$	−1.33389e10	+	1.33389e10i	−0.0339016	+	0.0339016i
$793$	−7.18410e11			−1.81668
$794$	−1.00987e11	−	1.00987e11i	−0.254087	−	0.254087i
$795$	1.06569e11	−	1.06569e11i	0.266786	−	0.266786i
$796$	1.19764e11	+	1.19764e11i	0.298314	+	0.298314i
$797$	7.94295e10	−	7.94295e10i	0.196856	−	0.196856i	−0.601795	−	0.798651i	$-0.705548\pi$
$797$	7.94295e10	−	7.94295e10i	0.196856	−	0.196856i	0.798651	+	0.601795i	$0.205548\pi$
$798$			1.75087e10i			0.0431760i
$799$	−1.88668e11	−	1.88668e11i	−0.462925	−	0.462925i
$800$	1.77558e10	+	1.77558e10i	0.0433490	+	0.0433490i
$801$	−1.49965e11	+	1.49965e11i	−0.364301	+	0.364301i
$802$			6.70700e11i			1.62118i
$803$	−1.93478e11			−0.465339
$804$		−	2.35460e11i		−	0.563499i
$805$		−	9.21694e11i		−	2.19484i
$806$	5.77145e11	−	5.77145e11i	1.36756	−	1.36756i
$807$			8.76220e9i			0.0206595i
$808$	−2.42358e10	+	2.42358e10i	−0.0568606	+	0.0568606i
$809$	−2.85085e11	+	2.85085e11i	−0.665549	+	0.665549i	−0.956682	−	0.291134i	$-0.905968\pi$
$809$	−2.85085e11	+	2.85085e11i	−0.665549	+	0.665549i	0.291134	+	0.956682i	$0.405968\pi$
$810$	−2.20317e11			−0.511809
$811$	1.57081e11			0.363111			0.181555	−	0.983381i	$-0.441887\pi$
$811$	1.57081e11			0.363111			0.181555	+	0.983381i	$0.441887\pi$
$812$	6.62919e11	+	6.62919e11i	1.52488	+	1.52488i
$813$			3.04502e11i			0.696992i
$814$	2.38076e10	+	2.51979e11i	0.0542273	+	0.573941i
$815$	4.97423e11			1.12745
$816$	1.22176e11	−	1.22176e11i	0.275565	−	0.275565i
$817$		−	1.54695e10i		−	0.0347207i
$818$		−	9.41413e11i		−	2.10265i
$819$	5.39526e11	+	5.39526e11i	1.19916	+	1.19916i
$820$	−4.10310e11	−	4.10310e11i	−0.907521	−	0.907521i
$821$	9.02544e11			1.98653			0.993266	−	0.115852i	$-0.0369600\pi$
$821$	9.02544e11			1.98653			0.993266	+	0.115852i	$0.0369600\pi$
$822$	−1.32779e11	−	1.32779e11i	−0.290833	−	0.290833i
$823$	−3.77194e11			−0.822178			−0.411089	−	0.911595i	$-0.634851\pi$
$823$	−3.77194e11			−0.822178			−0.411089	+	0.911595i	$0.634851\pi$
$824$	−8.80031e10			−0.190893
$825$			4.13183e9i			0.00891923i
$826$	−1.21777e12			−2.61605
$827$	−2.65606e11	−	2.65606e11i	−0.567828	−	0.567828i	0.363692	−	0.931519i	$-0.381516\pi$
$827$	−2.65606e11	−	2.65606e11i	−0.567828	−	0.567828i	−0.931519	+	0.363692i	$0.881516\pi$
$828$	3.99270e11	−	3.99270e11i	0.849466	−	0.849466i
$829$	2.11276e11	−	2.11276e11i	0.447333	−	0.447333i	−0.447134	−	0.894467i	$-0.647555\pi$
$829$	2.11276e11	−	2.11276e11i	0.447333	−	0.447333i	0.894467	+	0.447134i	$0.147555\pi$
$830$	−3.69699e11			−0.778998
$831$	2.95432e11	+	2.95432e11i	0.619518	+	0.619518i
$832$	−4.42236e11	+	4.42236e11i	−0.922912	+	0.922912i
$833$	1.75066e11	+	1.75066e11i	0.363598	+	0.363598i
$834$	−2.51773e11	+	2.51773e11i	−0.520410	+	0.520410i
$835$		−	4.22735e11i		−	0.869605i
$836$	6.62014e9	+	6.62014e9i	0.0135532	+	0.0135532i
$837$	−2.43304e11	−	2.43304e11i	−0.495732	−	0.495732i
$838$	−8.78449e11	+	8.78449e11i	−1.78131	+	1.78131i
$839$			7.45525e11i			1.50458i	0.658834	+	0.752288i	$0.271050\pi$
$839$			7.45525e11i			1.50458i	−0.658834	+	0.752288i	$0.728950\pi$
$840$	4.38911e10			0.0881576
$841$		−	1.23363e12i		−	2.46604i
$842$		−	3.59389e9i		−	0.00715018i
$843$	−3.04657e10	+	3.04657e10i	−0.0603255	+	0.0603255i
$844$			1.77649e11i			0.350101i
$845$	−6.45097e11	+	6.45097e11i	−1.26531	+	1.26531i
$846$	3.36551e11	−	3.36551e11i	0.657006	−	0.657006i
$847$	−5.50411e11			−1.06943
$848$	4.63177e11			0.895701
$849$	−1.98224e11	−	1.98224e11i	−0.381527	−	0.381527i
$850$			2.43835e10i			0.0467111i
$851$	8.54195e10	+	9.04079e11i	0.162869	+	1.72381i
$852$	1.31909e11			0.250332
$853$	−2.02461e11	+	2.02461e11i	−0.382425	+	0.382425i	−0.871975	−	0.489550i	$-0.837161\pi$
$853$	−2.02461e11	+	2.02461e11i	−0.382425	+	0.382425i	0.489550	+	0.871975i	$0.337161\pi$
$854$		−	1.02494e12i		−	1.92694i
$855$		−	2.07852e10i		−	0.0388947i
$856$	4.86347e10	+	4.86347e10i	0.0905840	+	0.0905840i
$857$	2.64637e11	+	2.64637e11i	0.490600	+	0.490600i	0.908495	−	0.417895i	$-0.137232\pi$
$857$	2.64637e11	+	2.64637e11i	0.490600	+	0.490600i	−0.417895	+	0.908495i	$0.637232\pi$
$858$	−2.48258e11			−0.458093
$859$	−2.46428e11	−	2.46428e11i	−0.452602	−	0.452602i	0.443615	−	0.896217i	$-0.353696\pi$
$859$	−2.46428e11	−	2.46428e11i	−0.452602	−	0.452602i	−0.896217	+	0.443615i	$0.853696\pi$
$860$	3.23522e11			0.591438
$861$	4.95153e11			0.901005
$862$			9.88346e11i			1.79011i
$863$	3.46138e11			0.624030			0.312015	−	0.950077i	$-0.398996\pi$
$863$	3.46138e11			0.624030			0.312015	+	0.950077i	$0.398996\pi$
$864$	4.49741e11	+	4.49741e11i	0.807064	+	0.807064i
$865$	2.83782e11	−	2.83782e11i	0.506898	−	0.506898i
$866$	−8.95640e11	+	8.95640e11i	−1.59244	+	1.59244i
$867$	−1.15451e11			−0.204325
$868$	3.88422e11	+	3.88422e11i	0.684266	+	0.684266i
$869$	−8.06738e10	+	8.06738e10i	−0.141466	+	0.141466i
$870$	4.78860e11	+	4.78860e11i	0.835857	+	0.835857i
$871$	9.15010e11	−	9.15010e11i	1.58984	−	1.58984i
$872$			1.09212e11i			0.188888i
$873$	−1.74272e11	−	1.74272e11i	−0.300034	−	0.300034i
$874$	5.03520e10	+	5.03520e10i	0.0862922	+	0.0862922i
$875$	−5.49097e11	+	5.49097e11i	−0.936736	+	0.936736i
$876$			2.75783e11i			0.468329i
$877$	−5.92821e11			−1.00213			−0.501066	−	0.865409i	$-0.667059\pi$
$877$	−5.92821e11			−1.00213			−0.501066	+	0.865409i	$0.667059\pi$
$878$		−	4.07738e11i		−	0.686125i
$879$		−	4.42806e11i		−	0.741750i
$880$	1.90226e11	−	1.90226e11i	0.317204	−	0.317204i
$881$			3.15877e11i			0.524342i	0.965021	+	0.262171i	$0.0844385\pi$
$881$			3.15877e11i			0.524342i	−0.965021	+	0.262171i	$0.915562\pi$
$882$	−3.12287e11	+	3.12287e11i	−0.516035	+	0.516035i
$883$	5.13405e11	−	5.13405e11i	0.844534	−	0.844534i	−0.144911	−	0.989445i	$-0.546290\pi$
$883$	5.13405e11	−	5.13405e11i	0.844534	−	0.844534i	0.989445	+	0.144911i	$0.0462896\pi$
$884$	−6.91111e11			−1.13172
$885$	−4.14960e11			−0.676446
$886$	−9.26163e11	−	9.26163e11i	−1.50298	−	1.50298i
$887$			2.52629e11i			0.408120i	0.978958	+	0.204060i	$0.0654138\pi$
$887$			2.52629e11i			0.408120i	−0.978958	+	0.204060i	$0.934586\pi$
$888$	−4.30523e10	+	4.06769e9i	−0.0692380	+	0.00654177i
$889$	3.51135e11			0.562169
$890$	3.95519e11	−	3.95519e11i	0.630387	−	0.630387i
$891$		−	1.00528e11i		−	0.159506i
$892$		−	4.20945e11i		−	0.664915i
$893$	2.00213e10	+	2.00213e10i	0.0314837	+	0.0314837i
$894$	4.35079e11	+	4.35079e11i	0.681111	+	0.681111i
$895$	1.26338e11			0.196899
$896$	1.73122e11	+	1.73122e11i	0.268609	+	0.268609i
$897$	−8.90727e11			−1.37586
$898$	8.57265e11			1.31829
$899$		−	1.01593e12i		−	1.55533i
$900$	−2.05183e10			−0.0312731
$901$	2.86963e11	+	2.86963e11i	0.435438	+	0.435438i
$902$	3.96882e11	−	3.96882e11i	0.599563	−	0.599563i
$903$	−1.95209e11	+	1.95209e11i	−0.293596	+	0.293596i
$904$	4.93280e10			0.0738618
$905$	−1.45444e11	−	1.45444e11i	−0.216822	−	0.216822i
$906$	−2.42342e11	+	2.42342e11i	−0.359680	+	0.359680i
$907$	8.48839e10	+	8.48839e10i	0.125429	+	0.125429i	0.767034	−	0.641606i	$-0.221732\pi$
$907$	8.48839e10	+	8.48839e10i	0.125429	+	0.125429i	−0.641606	+	0.767034i	$0.721732\pi$
$908$	−2.25401e11	+	2.25401e11i	−0.331598	+	0.331598i
$909$		−	2.89661e11i		−	0.424263i
$910$	−1.42295e12	−	1.42295e12i	−2.07503	−	2.07503i
$911$	2.77380e11	+	2.77380e11i	0.402719	+	0.402719i	0.879190	−	0.476471i	$-0.158084\pi$
$911$	2.77380e11	+	2.77380e11i	0.402719	+	0.402719i	−0.476471	+	0.879190i	$0.658084\pi$
$912$	−1.29652e10	+	1.29652e10i	−0.0187413	+	0.0187413i
$913$		−	1.68690e11i		−	0.242776i
$914$	−1.67596e11			−0.240147
$915$		−	3.49253e11i		−	0.498259i
$916$			1.97959e11i			0.281186i
$917$	−5.33873e11	+	5.33873e11i	−0.755023	+	0.755023i
$918$			6.17617e11i			0.869659i
$919$	7.23983e11	−	7.23983e11i	1.01500	−	1.01500i	0.0151143	−	0.999886i	$-0.495189\pi$
$919$	7.23983e11	−	7.23983e11i	1.01500	−	1.01500i	0.999886	−	0.0151143i	$-0.00481121\pi$
$920$	1.26223e11	−	1.26223e11i	0.176193	−	0.176193i
$921$	1.67749e11			0.233142
$922$	−1.24840e12			−1.72755
$923$	5.12606e11	+	5.12606e11i	0.706280	+	0.706280i
$924$		−	1.67079e11i		−	0.229210i
$925$	2.10352e10	−	2.54249e10i	0.0287329	−	0.0347289i
$926$	6.85419e11			0.932207
$927$	5.25897e11	−	5.25897e11i	0.712167	−	0.712167i
$928$			1.87791e12i			2.53212i
$929$		−	1.17287e12i		−	1.57466i	−0.616531	−	0.787331i	$-0.711462\pi$
$929$		−	1.17287e12i		−	1.57466i	0.616531	−	0.787331i	$-0.288538\pi$
$930$	2.80577e11	+	2.80577e11i	0.375077	+	0.375077i
$931$	−1.85778e10	−	1.85778e10i	−0.0247284	−	0.0247284i
$932$	6.82108e11			0.904044
$933$	−1.91274e11	−	1.91274e11i	−0.252423	−	0.252423i
$934$	9.58350e11			1.25932
$935$	2.35710e11			0.308413
$936$			1.47773e11i			0.192527i
$937$	1.21796e11			0.158006			0.0790030	−	0.996874i	$-0.474826\pi$
$937$	1.21796e11			0.158006			0.0790030	+	0.996874i	$0.474826\pi$
$938$	1.30543e12	+	1.30543e12i	1.68633	+	1.68633i
$939$	3.39612e11	−	3.39612e11i	0.436839	−	0.436839i
$940$	−4.18716e11	+	4.18716e11i	−0.536300	+	0.536300i
$941$	−4.03161e11			−0.514186			−0.257093	−	0.966387i	$-0.582765\pi$
$941$	−4.03161e11			−0.514186			−0.257093	+	0.966387i	$0.582765\pi$
$942$	−1.66140e11	−	1.66140e11i	−0.210994	−	0.210994i
$943$	1.42398e12	−	1.42398e12i	1.80076	−	1.80076i
$944$	−9.01761e11	−	9.01761e11i	−1.13554	−	1.13554i
$945$	−5.99864e11	+	5.99864e11i	−0.752187	+	0.752187i
$946$			3.12934e11i			0.390740i
$947$	−5.32555e11	−	5.32555e11i	−0.662163	−	0.662163i	0.293727	−	0.955889i	$-0.405104\pi$
$947$	−5.32555e11	−	5.32555e11i	−0.662163	−	0.662163i	−0.955889	+	0.293727i	$0.905104\pi$
$948$	1.14992e11	+	1.14992e11i	0.142376	+	0.142376i
$949$	−1.07171e12	+	1.07171e12i	−1.32133	+	1.32133i
$950$		−	2.58756e9i		−	0.00317684i
$951$	−4.81077e11			−0.588156
$952$			1.18187e11i			0.143887i
$953$		−	6.17491e11i		−	0.748616i	−0.927305	−	0.374308i	$-0.877880\pi$
$953$		−	6.17491e11i		−	0.748616i	0.927305	−	0.374308i	$-0.122120\pi$
$954$	−5.11891e11	+	5.11891e11i	−0.617994	+	0.617994i
$955$			2.06670e11i			0.248464i
$956$	5.44034e11	−	5.44034e11i	0.651320	−	0.651320i
$957$	−2.18499e11	+	2.18499e11i	−0.260496	+	0.260496i
$958$	−1.13791e12			−1.35097
$959$	6.94525e11			0.821133
$960$	−2.14991e11	−	2.14991e11i	−0.253126	−	0.253126i
$961$			2.57633e11i			0.302070i
$962$	1.52763e12	+	1.26388e12i	1.78368	+	1.47573i
$963$	−5.81272e11			−0.675888
$964$	3.97733e11	−	3.97733e11i	0.460557	−	0.460557i
$965$			6.98607e10i			0.0805608i
$966$		−	1.27078e12i		−	1.45936i
$967$	6.41760e11	+	6.41760e11i	0.733950	+	0.733950i	0.971400	−	0.237449i	$-0.0763114\pi$
$967$	6.41760e11	+	6.41760e11i	0.733950	+	0.733950i	−0.237449	+	0.971400i	$0.576311\pi$
$968$	−7.53773e10	−	7.53773e10i	−0.0858498	−	0.0858498i
$969$	−1.60653e10			−0.0182219
$970$	4.59625e11	+	4.59625e11i	0.519179	+	0.519179i
$971$	6.96833e11			0.783884			0.391942	−	0.919990i	$-0.371803\pi$
$971$	6.96833e11			0.783884			0.391942	+	0.919990i	$0.371803\pi$
$972$	−8.12183e11			−0.909890
$973$		−	1.31694e12i		−	1.46932i
$974$	1.34307e12			1.49232
$975$	2.28869e10	+	2.28869e10i	0.0253262	+	0.0253262i
$976$	7.58970e11	−	7.58970e11i	0.836422	−	0.836422i
$977$	3.21081e11	−	3.21081e11i	0.352400	−	0.352400i	−0.508602	−	0.861002i	$-0.669837\pi$
$977$	3.21081e11	−	3.21081e11i	0.352400	−	0.352400i	0.861002	+	0.508602i	$0.169837\pi$
$978$	6.85821e11			0.749645
$979$	1.80471e11	+	1.80471e11i	0.196461	+	0.196461i
$980$	3.88528e11	−	3.88528e11i	0.421229	−	0.421229i
$981$	−6.52640e11	−	6.52640e11i	−0.704689	−	0.704689i
$982$	−8.21413e11	+	8.21413e11i	−0.883315	+	0.883315i
$983$		−	3.59477e11i		−	0.384997i	−0.981297	−	0.192499i	$-0.938341\pi$
$983$		−	3.59477e11i		−	0.384997i	0.981297	−	0.192499i	$-0.0616591\pi$
$984$	6.78099e10	+	6.78099e10i	0.0723290	+	0.0723290i
$985$	4.70019e11	+	4.70019e11i	0.499310	+	0.499310i
$986$	−1.28944e12	+	1.28944e12i	−1.36425	+	1.36425i
$987$		−	5.05297e11i		−	0.532449i
$988$	7.33402e10			0.0769687
$989$			1.12278e12i			1.17357i
$990$			4.20466e11i			0.437714i
$991$	−1.15061e11	+	1.15061e11i	−0.119298	+	0.119298i	−0.764236	−	0.644937i	$-0.776884\pi$
$991$	−1.15061e11	+	1.15061e11i	−0.119298	+	0.119298i	0.644937	+	0.764236i	$0.276884\pi$
$992$			1.10032e12i			1.13625i
$993$	3.49004e11	−	3.49004e11i	0.358949	−	0.358949i
$994$	−7.31326e11	+	7.31326e11i	−0.749144	+	0.749144i
$995$	−4.52514e11			−0.461679
$996$	−2.40450e11			−0.244336
$997$	9.29521e11	+	9.29521e11i	0.940760	+	0.940760i	0.998341	−	0.0575810i	$-0.0183387\pi$
$997$	9.29521e11	+	9.29521e11i	0.940760	+	0.940760i	−0.0575810	+	0.998341i	$0.518339\pi$
$998$		−	2.20750e12i		−	2.22525i
$999$	5.32807e11	−	6.43994e11i	0.534944	−	0.646576i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.9.d.a.6.5	✓	50
37.31	odd	4	inner	37.9.d.a.31.5	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.9.d.a.6.5	✓	50	1.1	even	1	trivial
37.9.d.a.31.5	yes	50	37.31	odd	4	inner

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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	37.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-15.5660 + 15.5660i) q^{2} -38.2524i q^{3} -228.599i q^{4} +(431.867 + 431.867i) q^{5} +(595.436 + 595.436i) q^{6} -3114.53 q^{7} +(-426.526 - 426.526i) q^{8} +5097.75 q^{9} +O(q^{10})\)	\(q+(-15.5660 + 15.5660i) q^{2} -38.2524i q^{3} -228.599i q^{4} +(431.867 + 431.867i) q^{5} +(595.436 + 595.436i) q^{6} -3114.53 q^{7} +(-426.526 - 426.526i) q^{8} +5097.75 q^{9} -13444.9 q^{10} -6134.74i q^{11} -8744.46 q^{12} +(-33981.4 - 33981.4i) q^{13} +(48480.7 - 48480.7i) q^{14} +(16519.9 - 16519.9i) q^{15} +71799.9 q^{16} +(44483.9 + 44483.9i) q^{17} +(-79351.5 + 79351.5i) q^{18} +(-4720.59 - 4720.59i) q^{19} +(98724.2 - 98724.2i) q^{20} +119138. i q^{21} +(95493.2 + 95493.2i) q^{22} +(342621. + 342621. i) q^{23} +(-16315.7 + 16315.7i) q^{24} -17607.1i q^{25} +1.05791e6 q^{26} -445975. i q^{27} +711978. i q^{28} +(931095. - 931095. i) q^{29} +514298. i q^{30} +(545554. - 545554. i) q^{31} +(-1.00844e6 + 1.00844e6i) q^{32} -234669. q^{33} -1.38487e6 q^{34} +(-1.34506e6 - 1.34506e6i) q^{35} -1.16534e6i q^{36} +(1.44401e6 + 1.19470e6i) q^{37} +146961. q^{38} +(-1.29987e6 + 1.29987e6i) q^{39} -368405. i q^{40} -4.15612e6i q^{41} +(-1.85450e6 - 1.85450e6i) q^{42} +(1.63851e6 + 1.63851e6i) q^{43} -1.40240e6 q^{44} +(2.20155e6 + 2.20155e6i) q^{45} -1.06665e7 q^{46} -4.24127e6 q^{47} -2.74652e6i q^{48} +3.93549e6 q^{49} +(274071. + 274071. i) q^{50} +(1.70161e6 - 1.70161e6i) q^{51} +(-7.76811e6 + 7.76811e6i) q^{52} +6.45094e6 q^{53} +(6.94204e6 + 6.94204e6i) q^{54} +(2.64939e6 - 2.64939e6i) q^{55} +(1.32843e6 + 1.32843e6i) q^{56} +(-180574. + 180574. i) q^{57} +2.89868e7i q^{58} +(-1.25594e7 - 1.25594e7i) q^{59} +(-3.77644e6 - 3.77644e6i) q^{60} +(1.05706e7 - 1.05706e7i) q^{61} +1.69842e7i q^{62} -1.58771e7 q^{63} -1.30140e7i q^{64} -2.93509e7i q^{65} +(3.65285e6 - 3.65285e6i) q^{66} +2.69268e7i q^{67} +(1.01690e7 - 1.01690e7i) q^{68} +(1.31061e7 - 1.31061e7i) q^{69} +4.18744e7 q^{70} -1.50849e7 q^{71} +(-2.17433e6 - 2.17433e6i) q^{72} -3.15380e7i q^{73} +(-4.10741e7 + 3.88078e6i) q^{74} -673514. q^{75} +(-1.07912e6 + 1.07912e6i) q^{76} +1.91068e7i q^{77} -4.04675e7i q^{78} +(-1.31503e7 - 1.31503e7i) q^{79} +(3.10080e7 + 3.10080e7i) q^{80} +1.63867e7 q^{81} +(6.46941e7 + 6.46941e7i) q^{82} +2.74975e7 q^{83} +2.72349e7 q^{84} +3.84222e7i q^{85} -5.10100e7 q^{86} +(-3.56166e7 - 3.56166e7i) q^{87} +(-2.61663e6 + 2.61663e6i) q^{88} +(-2.94179e7 + 2.94179e7i) q^{89} -6.85385e7 q^{90} +(1.05836e8 + 1.05836e8i) q^{91} +(7.83228e7 - 7.83228e7i) q^{92} +(-2.08688e7 - 2.08688e7i) q^{93} +(6.60194e7 - 6.60194e7i) q^{94} -4.07734e6i q^{95} +(3.85754e7 + 3.85754e7i) q^{96} +(-3.41860e7 - 3.41860e7i) q^{97} +(-6.12597e7 + 6.12597e7i) q^{98} -3.12734e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 4 q^{2} + 124 q^{5} + 510 q^{6} - 4 q^{7} - 5256 q^{8} - 93534 q^{9}+O(q^{10}) \) 50 * q + 4 * q^2 + 124 * q^5 + 510 * q^6 - 4 * q^7 - 5256 * q^8 - 93534 * q^9	\( 50 q + 4 q^{2} + 124 q^{5} + 510 q^{6} - 4 q^{7} - 5256 q^{8} - 93534 q^{9} - 10756 q^{10} - 45440 q^{12} + 63592 q^{13} - 80206 q^{14} - 124346 q^{15} - 639128 q^{16} - 178796 q^{17} - 45882 q^{18} + 264774 q^{19} + 469204 q^{20} + 714574 q^{22} - 654272 q^{23} - 1573644 q^{24} + 1841660 q^{26} - 1683686 q^{29} + 1766336 q^{31} - 4332632 q^{32} - 1438888 q^{33} - 5838452 q^{34} - 650482 q^{35} - 2870078 q^{37} - 2281528 q^{38} + 11036546 q^{39} - 7453902 q^{42} + 5097830 q^{43} - 14992464 q^{44} - 15078446 q^{45} + 28776464 q^{46} + 13992320 q^{47} + 4370314 q^{49} + 7603288 q^{50} + 19417938 q^{51} + 54318452 q^{52} + 28075952 q^{53} - 19197122 q^{54} - 6104306 q^{55} + 47803128 q^{56} + 17462426 q^{57} - 677072 q^{59} + 24953316 q^{60} + 4206386 q^{61} - 18098032 q^{63} - 56061730 q^{66} - 52579760 q^{68} + 88118984 q^{69} - 295493636 q^{70} - 37172476 q^{71} - 74582504 q^{72} - 224754524 q^{74} - 144364996 q^{75} + 189294548 q^{76} + 271163438 q^{79} - 312998084 q^{80} + 41535626 q^{81} - 177494710 q^{82} - 74250268 q^{83} - 82088924 q^{84} + 112964036 q^{86} - 142771908 q^{87} + 224951860 q^{88} + 84928780 q^{89} + 716592116 q^{90} - 40969098 q^{91} - 701292428 q^{92} - 83761576 q^{93} + 553881406 q^{94} - 7259376 q^{96} + 467792674 q^{97} + 538649310 q^{98}+O(q^{100}) \) 50 * q + 4 * q^2 + 124 * q^5 + 510 * q^6 - 4 * q^7 - 5256 * q^8 - 93534 * q^9 - 10756 * q^10 - 45440 * q^12 + 63592 * q^13 - 80206 * q^14 - 124346 * q^15 - 639128 * q^16 - 178796 * q^17 - 45882 * q^18 + 264774 * q^19 + 469204 * q^20 + 714574 * q^22 - 654272 * q^23 - 1573644 * q^24 + 1841660 * q^26 - 1683686 * q^29 + 1766336 * q^31 - 4332632 * q^32 - 1438888 * q^33 - 5838452 * q^34 - 650482 * q^35 - 2870078 * q^37 - 2281528 * q^38 + 11036546 * q^39 - 7453902 * q^42 + 5097830 * q^43 - 14992464 * q^44 - 15078446 * q^45 + 28776464 * q^46 + 13992320 * q^47 + 4370314 * q^49 + 7603288 * q^50 + 19417938 * q^51 + 54318452 * q^52 + 28075952 * q^53 - 19197122 * q^54 - 6104306 * q^55 + 47803128 * q^56 + 17462426 * q^57 - 677072 * q^59 + 24953316 * q^60 + 4206386 * q^61 - 18098032 * q^63 - 56061730 * q^66 - 52579760 * q^68 + 88118984 * q^69 - 295493636 * q^70 - 37172476 * q^71 - 74582504 * q^72 - 224754524 * q^74 - 144364996 * q^75 + 189294548 * q^76 + 271163438 * q^79 - 312998084 * q^80 + 41535626 * q^81 - 177494710 * q^82 - 74250268 * q^83 - 82088924 * q^84 + 112964036 * q^86 - 142771908 * q^87 + 224951860 * q^88 + 84928780 * q^89 + 716592116 * q^90 - 40969098 * q^91 - 701292428 * q^92 - 83761576 * q^93 + 553881406 * q^94 - 7259376 * q^96 + 467792674 * q^97 + 538649310 * q^98

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