LMFDB - Embedded newform 22.6.c.b.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,6,Mod(3,22)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("22.3");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	22.c (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52844403589$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 329 x^{10} + 1365 x^{9} + 52729 x^{8} + 242031 x^{7} + 7017903 x^{6} + \cdots + 93740681241 $ x^12 - 2x^11 + 329x^10 + 1365x^9 + 52729x^8 + 242031x^7 + 7017903x^6 + 130221686x^5 + 2541092161x^4 + 14394729912x^3 + 45294850764x^2 + 76920871185*x + 93740681241
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 11^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			5.2
Root			$12.0620 - 8.76353i$ of defining polynomial
Character	$\chi$	$=$	22.5
Dual form			22.6.c.b.9.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.23607 + 3.80423i) q^{2} +(-8.33499 - 6.05573i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(-30.5739 + 94.0969i) q^{5} +(12.7347 - 39.1935i) q^{6} +(-73.6937 + 53.5416i) q^{7} +(-51.7771 - 37.6183i) q^{8} +(-42.2909 - 130.158i) q^{9} -395.757 q^{10} +(372.060 - 150.407i) q^{11} +164.842 q^{12} +(336.858 + 1036.74i) q^{13} +(-294.775 - 214.166i) q^{14} +(824.658 - 599.149i) q^{15} +(79.1084 - 243.470i) q^{16} +(-14.6786 + 45.1762i) q^{17} +(442.876 - 321.768i) q^{18} +(-444.428 - 322.896i) q^{19} +(-489.183 - 1505.55i) q^{20} +938.470 q^{21} +(1032.07 + 1229.49i) q^{22} +1886.68 q^{23} +(203.756 + 627.096i) q^{24} +(-5391.28 - 3916.99i) q^{25} +(-3527.62 + 2562.97i) q^{26} +(-1209.34 + 3721.97i) q^{27} +(450.376 - 1386.11i) q^{28} +(-1170.51 + 850.425i) q^{29} +(3298.63 + 2396.60i) q^{30} +(2441.52 + 7514.22i) q^{31} +1024.00 q^{32} +(-4011.94 - 999.457i) q^{33} -190.004 q^{34} +(-2784.99 - 8571.32i) q^{35} +(1771.50 + 1287.07i) q^{36} +(-2865.77 + 2082.10i) q^{37} +(679.026 - 2089.83i) q^{38} +(3470.52 - 10681.2i) q^{39} +(5122.79 - 3721.92i) q^{40} +(-4989.01 - 3624.73i) q^{41} +(1160.01 + 3570.15i) q^{42} +13732.7 q^{43} +(-3401.54 + 5445.97i) q^{44} +13540.4 q^{45} +(2332.06 + 7177.35i) q^{46} +(-6342.22 - 4607.89i) q^{47} +(-2133.76 + 1550.27i) q^{48} +(-2629.59 + 8093.04i) q^{49} +(8237.14 - 25351.3i) q^{50} +(395.921 - 287.653i) q^{51} +(-14110.5 - 10251.9i) q^{52} +(1150.89 + 3542.09i) q^{53} -15654.0 q^{54} +(2777.45 + 39608.2i) q^{55} +5829.79 q^{56} +(1748.94 + 5382.67i) q^{57} +(-4682.04 - 3401.70i) q^{58} +(26908.1 - 19549.9i) q^{59} +(-5039.86 + 15511.1i) q^{60} +(-888.633 + 2734.93i) q^{61} +(-25567.9 + 18576.2i) q^{62} +(10085.4 + 7327.50i) q^{63} +(1265.73 + 3895.53i) q^{64} -107853. q^{65} +(-1156.87 - 16497.7i) q^{66} +22978.6 q^{67} +(-234.858 - 722.819i) q^{68} +(-15725.4 - 11425.2i) q^{69} +(29164.8 - 21189.5i) q^{70} +(2195.61 - 6757.40i) q^{71} +(-2706.61 + 8330.10i) q^{72} +(70213.6 - 51013.2i) q^{73} +(-11463.1 - 8328.41i) q^{74} +(21216.0 + 65296.2i) q^{75} +8789.50 q^{76} +(-19365.5 + 31004.7i) q^{77} +44923.3 q^{78} +(-4816.20 - 14822.7i) q^{79} +(20491.2 + 14887.7i) q^{80} +(5714.40 - 4151.75i) q^{81} +(7622.53 - 23459.7i) q^{82} +(24311.5 - 74823.1i) q^{83} +(-12147.8 + 8825.90i) q^{84} +(-3802.15 - 2762.43i) q^{85} +(16974.5 + 52242.2i) q^{86} +14906.1 q^{87} +(-24922.2 - 6208.64i) q^{88} -37872.5 q^{89} +(16736.9 + 51510.9i) q^{90} +(-80333.2 - 58365.5i) q^{91} +(-24421.7 + 17743.4i) q^{92} +(25154.0 - 77416.1i) q^{93} +(9690.05 - 29822.9i) q^{94} +(43971.4 - 31947.1i) q^{95} +(-8535.03 - 6201.06i) q^{96} +(54275.9 + 167044. i) q^{97} -34038.1 q^{98} +(-35311.4 - 42065.8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} - 48 q^{4} + 44 q^{5} - 100 q^{6} - 326 q^{7} - 192 q^{8} - 69 q^{9} + 96 q^{10} + 1011 q^{11} + 800 q^{12} - 246 q^{13} - 1304 q^{14} + 112 q^{15} - 768 q^{16} + 400 q^{17} - 1416 q^{18}+ \cdots - 199487 q^{99}+O(q^{100}) $ 12 * q - 12 * q^2 - 48 * q^4 + 44 * q^5 - 100 * q^6 - 326 * q^7 - 192 * q^8 - 69 * q^9 + 96 * q^10 + 1011 * q^11 + 800 * q^12 - 246 * q^13 - 1304 * q^14 + 112 * q^15 - 768 * q^16 + 400 * q^17 - 1416 * q^18 + 7535 * q^19 + 704 * q^20 - 3368 * q^21 + 484 * q^22 + 15732 * q^23 - 1600 * q^24 - 19283 * q^25 - 984 * q^26 - 27411 * q^27 + 3264 * q^28 - 2504 * q^29 + 448 * q^30 + 15336 * q^31 + 12288 * q^32 + 26213 * q^33 + 24600 * q^34 - 33916 * q^35 - 5664 * q^36 - 116 * q^37 - 34880 * q^38 + 4690 * q^39 - 3584 * q^40 - 38836 * q^41 + 19808 * q^42 + 42230 * q^43 - 4704 * q^44 + 139932 * q^45 - 35232 * q^46 - 57840 * q^47 - 125521 * q^49 + 26268 * q^50 + 16467 * q^51 - 3936 * q^52 + 131934 * q^53 + 60176 * q^54 - 53082 * q^55 + 15616 * q^56 - 90021 * q^57 - 10016 * q^58 + 36585 * q^59 - 37248 * q^60 + 43146 * q^61 - 40016 * q^62 - 52922 * q^63 - 12288 * q^64 - 133772 * q^65 - 211008 * q^66 + 325206 * q^67 + 6400 * q^68 - 103894 * q^69 + 68216 * q^70 - 172806 * q^71 - 4416 * q^72 + 49436 * q^73 - 464 * q^74 + 263915 * q^75 + 37920 * q^76 - 207094 * q^77 + 330000 * q^78 + 58364 * q^79 - 14336 * q^80 + 341038 * q^81 + 82836 * q^82 + 82035 * q^83 - 52288 * q^84 - 317604 * q^85 - 104380 * q^86 - 572732 * q^87 - 38336 * q^88 + 97958 * q^89 - 151672 * q^90 - 22162 * q^91 + 15072 * q^92 - 271316 * q^93 + 153720 * q^94 + 549736 * q^95 + 76403 * q^97 + 198656 * q^98 - 199487 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	1.23607	+	3.80423i	0.218508	+	0.672499i
$2$	1.23607	+	3.80423i	0.218508	+	0.672499i
$3$	−8.33499	−	6.05573i	−0.534690	−	0.388475i	0.287419	−	0.957805i	$-0.407203\pi$
$3$	−8.33499	−	6.05573i	−0.534690	−	0.388475i	−0.822109	+	0.569330i	$0.807203\pi$
$4$	−12.9443	+	9.40456i	−0.404508	+	0.293893i
$5$	−30.5739	+	94.0969i	−0.546923	+	1.68326i	0.169451	+	0.985539i	$0.445801\pi$
$5$	−30.5739	+	94.0969i	−0.546923	+	1.68326i	−0.716373	+	0.697717i	$0.754199\pi$
$6$	12.7347	−	39.1935i	0.144415	−	0.444463i
$7$	−73.6937	+	53.5416i	−0.568441	+	0.412997i	−0.834539	−	0.550950i	$-0.814266\pi$
$7$	−73.6937	+	53.5416i	−0.568441	+	0.412997i	0.266098	+	0.963946i	$0.414266\pi$
$8$	−51.7771	−	37.6183i	−0.286031	−	0.207813i
$9$	−42.2909	−	130.158i	−0.174036	−	0.535629i
$10$	−395.757			−1.25149
$11$	372.060	−	150.407i	0.927111	−	0.374788i
$11$	372.060	−	150.407i	0.927111	−	0.374788i
$12$	164.842			0.330457
$13$	336.858	+	1036.74i	0.552826	+	1.70142i	0.701617	+	0.712554i	$0.252462\pi$
$13$	336.858	+	1036.74i	0.552826	+	1.70142i	−0.148791	+	0.988869i	$0.547538\pi$
$14$	−294.775	−	214.166i	−0.401948	−	0.292033i
$15$	824.658	−	599.149i	0.946337	−	0.687554i
$16$	79.1084	−	243.470i	0.0772542	−	0.237764i
$17$	−14.6786	+	45.1762i	−0.0123187	+	0.0379129i	−0.957027	−	0.289999i	$-0.906345\pi$
$17$	−14.6786	+	45.1762i	−0.0123187	+	0.0379129i	0.944708	+	0.327912i	$0.106345\pi$
$18$	442.876	−	321.768i	0.322181	−	0.234079i
$19$	−444.428	−	322.896i	−0.282434	−	0.205201i	0.437544	−	0.899197i	$-0.355848\pi$
$19$	−444.428	−	322.896i	−0.282434	−	0.205201i	−0.719979	+	0.693996i	$0.755848\pi$
$20$	−489.183	−	1505.55i	−0.273461	−	0.841628i
$21$	938.470			0.464379
$22$	1032.07	+	1229.49i	0.454625	+	0.541586i
$23$	1886.68			0.743667			0.371833	−	0.928300i	$-0.378729\pi$
$23$	1886.68			0.743667			0.371833	+	0.928300i	$0.378729\pi$
$24$	203.756	+	627.096i	0.0722074	+	0.222232i
$25$	−5391.28	−	3916.99i	−1.72521	−	1.25344i
$26$	−3527.62	+	2562.97i	−1.02341	+	0.743549i
$27$	−1209.34	+	3721.97i	−0.319256	+	0.982570i
$28$	450.376	−	1386.11i	0.108563	−	0.334121i
$29$	−1170.51	+	850.425i	−0.258452	+	0.187776i	−0.709464	−	0.704741i	$-0.751063\pi$
$29$	−1170.51	+	850.425i	−0.258452	+	0.187776i	0.451012	+	0.892518i	$0.351063\pi$
$30$	3298.63	+	2396.60i	0.669161	+	0.486174i
$31$	2441.52	+	7514.22i	0.456305	+	1.40436i	0.869596	+	0.493764i	$0.164379\pi$
$31$	2441.52	+	7514.22i	0.456305	+	1.40436i	−0.413291	+	0.910599i	$0.635621\pi$
$32$	1024.00			0.176777
$33$	−4011.94	−	999.457i	−0.641312	−	0.159764i
$34$	−190.004			−0.0281881
$35$	−2784.99	−	8571.32i	−0.384285	−	1.18271i
$36$	1771.50	+	1287.07i	0.227817	+	0.165518i
$37$	−2865.77	+	2082.10i	−0.344141	+	0.250033i	−0.746407	−	0.665490i	$-0.768223\pi$
$37$	−2865.77	+	2082.10i	−0.344141	+	0.250033i	0.402266	+	0.915523i	$0.368223\pi$
$38$	679.026	−	2089.83i	0.0762829	−	0.234775i
$39$	3470.52	−	10681.2i	0.365370	−	1.12449i
$40$	5122.79	−	3721.92i	0.506240	−	0.367805i
$41$	−4989.01	−	3624.73i	−0.463505	−	0.336756i	0.331399	−	0.943491i	$-0.392479\pi$
$41$	−4989.01	−	3624.73i	−0.463505	−	0.336756i	−0.794905	+	0.606734i	$0.792479\pi$
$42$	1160.01	+	3570.15i	0.101470	+	0.312294i
$43$	13732.7			1.13262			0.566309	−	0.824193i	$-0.308371\pi$
$43$	13732.7			1.13262			0.566309	+	0.824193i	$0.308371\pi$
$44$	−3401.54	+	5445.97i	−0.264877	+	0.424076i
$45$	13540.4			0.996785
$46$	2332.06	+	7177.35i	0.162497	+	0.500115i
$47$	−6342.22	−	4607.89i	−0.418791	−	0.304269i	0.358360	−	0.933583i	$-0.383336\pi$
$47$	−6342.22	−	4607.89i	−0.418791	−	0.304269i	−0.777151	+	0.629314i	$0.783336\pi$
$48$	−2133.76	+	1550.27i	−0.133672	+	0.0971188i
$49$	−2629.59	+	8093.04i	−0.156458	+	0.481528i
$50$	8237.14	−	25351.3i	0.465963	−	1.43409i
$51$	395.921	−	287.653i	0.0213149	−	0.0154862i
$52$	−14110.5	−	10251.9i	−0.723658	−	0.525769i
$53$	1150.89	+	3542.09i	0.0562789	+	0.173209i	0.975245	−	0.221129i	$-0.0709741\pi$
$53$	1150.89	+	3542.09i	0.0562789	+	0.173209i	−0.918966	+	0.394337i	$0.870974\pi$
$54$	−15654.0			−0.730537
$55$	2777.45	+	39608.2i	0.123805	+	1.76554i
$56$	5829.79			0.248418
$57$	1748.94	+	5382.67i	0.0712996	+	0.219437i
$58$	−4682.04	−	3401.70i	−0.182753	−	0.132778i
$59$	26908.1	−	19549.9i	1.00636	−	0.731163i	0.0429177	−	0.999079i	$-0.486335\pi$
$59$	26908.1	−	19549.9i	1.00636	−	0.731163i	0.963443	+	0.267915i	$0.0863347\pi$
$60$	−5039.86	+	15511.1i	−0.180734	+	0.556243i
$61$	−888.633	+	2734.93i	−0.0305772	+	0.0941070i	−0.965180	−	0.261585i	$-0.915755\pi$
$61$	−888.633	+	2734.93i	−0.0305772	+	0.0941070i	0.934603	+	0.355692i	$0.115755\pi$
$62$	−25567.9	+	18576.2i	−0.844726	+	0.613729i
$63$	10085.4	+	7327.50i	0.320142	+	0.232597i
$64$	1265.73	+	3895.53i	0.0386271	+	0.118882i
$65$	−107853.			−3.16628
$66$	−1156.87	−	16497.7i	−0.0326907	−	0.466191i
$67$	22978.6			0.625368			0.312684	−	0.949857i	$-0.398772\pi$
$67$	22978.6			0.625368			0.312684	+	0.949857i	$0.398772\pi$
$68$	−234.858	−	722.819i	−0.00615933	−	0.0189565i
$69$	−15725.4	−	11425.2i	−0.397631	−	0.288896i
$70$	29164.8	−	21189.5i	0.711400	−	0.516863i
$71$	2195.61	−	6757.40i	0.0516904	−	0.159087i	−0.921879	−	0.387478i	$-0.873346\pi$
$71$	2195.61	−	6757.40i	0.0516904	−	0.159087i	0.973569	+	0.228391i	$0.0733464\pi$
$72$	−2706.61	+	8330.10i	−0.0615312	+	0.189373i
$73$	70213.6	−	51013.2i	1.54211	−	1.12041i	0.593107	−	0.805123i	$-0.297901\pi$
$73$	70213.6	−	51013.2i	1.54211	−	1.12041i	0.948998	−	0.315282i	$-0.102099\pi$
$74$	−11463.1	−	8328.41i	−0.243345	−	0.176800i
$75$	21216.0	+	65296.2i	0.435523	+	1.34040i
$76$	8789.50			0.174554
$77$	−19365.5	+	31004.7i	−0.372222	+	0.595938i
$78$	44923.3			0.836056
$79$	−4816.20	−	14822.7i	−0.0868234	−	0.267215i	0.898213	−	0.439560i	$-0.144866\pi$
$79$	−4816.20	−	14822.7i	−0.0868234	−	0.267215i	−0.985037	+	0.172345i	$0.944866\pi$
$80$	20491.2	+	14887.7i	0.357966	+	0.260077i
$81$	5714.40	−	4151.75i	0.0967738	−	0.0703103i
$82$	7622.53	−	23459.7i	0.125188	−	0.385291i
$83$	24311.5	−	74823.1i	0.387361	−	1.19218i	−0.547391	−	0.836877i	$-0.684379\pi$
$83$	24311.5	−	74823.1i	0.387361	−	1.19218i	0.934753	−	0.355299i	$-0.115621\pi$
$84$	−12147.8	+	8825.90i	−0.187845	+	0.136477i
$85$	−3802.15	−	2762.43i	−0.0570798	−	0.0414709i
$86$	16974.5	+	52242.2i	0.247486	+	0.761684i
$87$	14906.1			0.211138
$88$	−24922.2	−	6208.64i	−0.343068	−	0.0854653i
$89$	−37872.5			−0.506815			−0.253407	−	0.967360i	$-0.581551\pi$
$89$	−37872.5			−0.506815			−0.253407	+	0.967360i	$0.581551\pi$
$90$	16736.9	+	51510.9i	0.217806	+	0.670337i
$91$	−80333.2	−	58365.5i	−1.01693	−	0.738843i
$92$	−24421.7	+	17743.4i	−0.300819	+	0.218558i
$93$	25154.0	−	77416.1i	0.301578	−	0.928162i
$94$	9690.05	−	29822.9i	0.113111	−	0.348121i
$95$	43971.4	−	31947.1i	0.499875	−	0.363181i
$96$	−8535.03	−	6201.06i	−0.0945207	−	0.0686733i
$97$	54275.9	+	167044.i	0.585703	+	1.80261i	0.596428	+	0.802666i	$0.296586\pi$
$97$	54275.9	+	167044.i	0.585703	+	1.80261i	−0.0107252	+	0.999942i	$0.503414\pi$
$98$	−34038.1			−0.358014
$99$	−35311.4	−	42065.8i	−0.362098	−	0.431361i
$100$	106624.			1.06624
$101$	−16411.0	−	50507.8i	−0.160078	−	0.492668i	0.838562	−	0.544806i	$-0.183397\pi$
$101$	−16411.0	−	50507.8i	−0.160078	−	0.492668i	−0.998640	+	0.0521374i	$0.983397\pi$
$102$	1583.68	+	1150.61i	0.0150719	+	0.0109504i
$103$	−151011.	+	109716.i	−1.40254	+	1.01900i	−0.408184	+	0.912900i	$0.633838\pi$
$103$	−151011.	+	109716.i	−1.40254	+	1.01900i	−0.994355	+	0.106104i	$0.966162\pi$
$104$	21558.9	−	66351.5i	0.195453	−	0.601544i
$105$	−28692.7	+	88307.1i	−0.253979	+	0.781668i
$106$	−12052.3	+	8756.52i	−0.104185	+	0.0756950i
$107$	−62635.2	−	45507.1i	−0.528882	−	0.384255i	0.291057	−	0.956706i	$-0.405993\pi$
$107$	−62635.2	−	45507.1i	−0.528882	−	0.384255i	−0.819940	+	0.572450i	$0.805993\pi$
$108$	−19349.5	−	59551.5i	−0.159628	−	0.491285i
$109$	−112381.			−0.905995			−0.452998	−	0.891512i	$-0.649645\pi$
$109$	−112381.			−0.905995			−0.452998	+	0.891512i	$0.649645\pi$
$110$	−147246.	+	59524.5i	−1.16027	+	0.469044i
$111$	36494.8			0.281141
$112$	7206.01	+	22177.8i	0.0542813	+	0.167061i
$113$	173640.	+	126157.i	1.27925	+	0.929428i	0.999530	−	0.0306546i	$-0.00975919\pi$
$113$	173640.	+	126157.i	1.27925	+	0.929428i	0.279718	+	0.960082i	$0.409759\pi$
$114$	−18315.1	+	13306.7i	−0.131992	+	0.0958977i
$115$	−57683.2	+	177530.i	−0.406728	+	1.25178i
$116$	7153.51	−	22016.3i	0.0493599	−	0.151914i
$117$	120694.	−	87689.4i	0.815120	−	0.592219i
$118$	107633.	+	78199.6i	0.711604	+	0.517011i
$119$	−1337.08	−	4115.12i	−0.00865547	−	0.0266388i
$120$	−65237.4			−0.413564
$121$	115807.	−	111921.i	0.719069	−	0.694939i
$122$	−11502.7			−0.0699682
$123$	19633.0	+	60424.1i	0.117010	+	0.360120i
$124$	−102272.	−	74304.7i	−0.597311	−	0.433972i
$125$	283273.	−	205810.i	1.62155	−	1.17812i
$126$	−15409.2	+	47424.6i	−0.0864675	+	0.266120i
$127$	−7545.97	+	23224.1i	−0.0415151	+	0.127770i	−0.969666	−	0.244434i	$-0.921398\pi$
$127$	−7545.97	+	23224.1i	−0.0415151	+	0.127770i	0.928151	+	0.372204i	$0.121398\pi$
$128$	−13254.9	+	9630.27i	−0.0715077	+	0.0519534i
$129$	−114462.	−	83161.3i	−0.605600	−	0.439994i
$130$	−133314.	−	410298.i	−0.691858	−	2.12932i
$131$	274455.			1.39731			0.698656	−	0.715457i	$-0.253782\pi$
$131$	274455.			1.39731			0.698656	+	0.715457i	$0.253782\pi$
$132$	61331.1	−	24793.3i	0.306370	−	0.123851i
$133$	50040.0			0.245294
$134$	28403.1	+	87415.6i	0.136648	+	0.420559i
$135$	−313251.	−	227590.i	−1.47931	−	1.07478i
$136$	2459.47	−	1786.91i	0.0114023	−	0.00828427i
$137$	−33983.6	+	104591.i	−0.154692	+	0.476093i	−0.998130	−	0.0611344i	$-0.980528\pi$
$137$	−33983.6	+	104591.i	−0.154692	+	0.476093i	0.843438	+	0.537227i	$0.180528\pi$
$138$	24026.3	−	73945.5i	0.107396	−	0.330532i
$139$	−84540.6	+	61422.4i	−0.371132	+	0.269643i	−0.757680	−	0.652626i	$-0.773667\pi$
$139$	−84540.6	+	61422.4i	−0.371132	+	0.269643i	0.386548	+	0.922269i	$0.373667\pi$
$140$	116659.	+	84757.9i	0.503036	+	0.365477i
$141$	24958.2	+	76813.5i	0.105722	+	0.325379i
$142$	28420.6			0.118280
$143$	281264.	+	335065.i	1.15020	+	1.37022i
$144$	−35035.2			−0.140798
$145$	−44235.2	−	136142.i	−0.174722	−	0.537740i
$146$	280854.	+	204053.i	1.09043	+	0.792246i
$147$	70926.9	−	51531.4i	0.270718	−	0.196688i
$148$	17514.0	−	53902.6i	0.0657251	−	0.202281i
$149$	−49577.9	+	152585.i	−0.182946	+	0.563049i	−0.999907	−	0.0136435i	$-0.995657\pi$
$149$	−49577.9	+	152585.i	−0.182946	+	0.563049i	0.816961	+	0.576693i	$0.195657\pi$
$150$	−222177.	+	161421.i	−0.806252	+	0.585777i
$151$	−172030.	−	124987.i	−0.613992	−	0.446091i	0.236826	−	0.971552i	$-0.423893\pi$
$151$	−172030.	−	124987.i	−0.613992	−	0.446091i	−0.850818	+	0.525461i	$0.823893\pi$
$152$	10864.4	+	33437.2i	0.0381415	+	0.117387i
$153$	6500.81			0.0224512
$154$	−141886.	−	35346.8i	−0.482101	−	0.120101i
$155$	−781711.			−2.61347
$156$	55528.3	+	170898.i	0.182685	+	0.562246i
$157$	207259.	+	150583.i	0.671066	+	0.487558i	0.870382	−	0.492377i	$-0.163872\pi$
$157$	207259.	+	150583.i	0.671066	+	0.487558i	−0.199316	+	0.979935i	$0.563872\pi$
$158$	50435.9	−	36643.8i	0.160730	−	0.116777i
$159$	11857.2	−	36492.8i	0.0371955	−	0.114476i
$160$	−31307.7	+	96355.2i	−0.0966832	+	0.297560i
$161$	−139036.	+	101016.i	−0.422731	+	0.307132i
$162$	22857.6	+	16607.0i	0.0684294	+	0.0497169i
$163$	−83930.7	−	258312.i	−0.247430	−	0.761510i	−0.995227	−	0.0975834i	$-0.968889\pi$
$163$	−83930.7	−	258312.i	−0.247430	−	0.761510i	0.747798	−	0.663927i	$-0.231111\pi$
$164$	98668.1			0.286462
$165$	216707.	−	346954.i	0.619672	−	0.992114i
$166$	314694.			0.886378
$167$	−162042.	−	498713.i	−0.449610	−	1.38376i	−0.877349	−	0.479854i	$-0.840690\pi$
$167$	−162042.	−	498713.i	−0.449610	−	1.38376i	0.427739	−	0.903902i	$-0.359310\pi$
$168$	−48591.2	−	35303.6i	−0.132827	−	0.0965041i
$169$	−660978.	+	480229.i	−1.78021	+	1.29340i
$170$	5809.17	−	17878.8i	0.0154167	−	0.0474478i
$171$	−23232.2	+	71501.4i	−0.0607576	+	0.186993i
$172$	−177759.	+	129150.i	−0.458154	+	0.332868i
$173$	468258.	+	340210.i	1.18952	+	0.864234i	0.993213	−	0.116309i	$-0.0371064\pi$
$173$	468258.	+	340210.i	1.18952	+	0.864234i	0.196303	+	0.980543i	$0.437106\pi$
$174$	18425.0	+	56706.3i	0.0461354	+	0.141990i
$175$	607025.			1.49834
$176$	−7186.49	−	102484.i	−0.0174878	−	0.249388i
$177$	−342668.			−0.822129
$178$	−46813.0	−	144076.i	−0.110743	−	0.340832i
$179$	127287.	+	92479.6i	0.296929	+	0.215731i	0.726267	−	0.687412i	$-0.241253\pi$
$179$	127287.	+	92479.6i	0.296929	+	0.215731i	−0.429339	+	0.903143i	$0.641253\pi$
$180$	−175271.	+	127342.i	−0.403208	+	0.292948i
$181$	55985.0	−	172304.i	0.127021	−	0.390930i	−0.867243	−	0.497885i	$-0.834110\pi$
$181$	55985.0	−	172304.i	0.127021	−	0.390930i	0.994264	+	0.106955i	$0.0341100\pi$
$182$	122738.	−	377749.i	0.274664	−	0.845328i
$183$	23968.7	−	17414.3i	0.0529075	−	0.0384396i
$184$	−97686.7	−	70973.5i	−0.212711	−	0.154544i
$185$	−108302.	−	333318.i	−0.232651	−	0.716027i
$186$	325600.			0.690085
$187$	1333.46	+	19016.0i	0.00278853	+	0.0397663i
$188$	125431.			0.258827
$189$	−110159.	−	339036.i	−0.224320	−	0.690385i
$190$	175886.	+	127788.i	0.353465	+	0.256807i
$191$	295941.	−	215014.i	0.586978	−	0.426464i	−0.254255	−	0.967137i	$-0.581830\pi$
$191$	295941.	−	215014.i	0.586978	−	0.426464i	0.841233	+	0.540673i	$0.181830\pi$
$192$	13040.4	−	40134.1i	0.0255292	−	0.0785707i
$193$	−70047.6	+	215584.i	−0.135363	+	0.416604i	−0.995646	−	0.0932119i	$-0.970287\pi$
$193$	−70047.6	+	215584.i	−0.135363	+	0.416604i	0.860283	+	0.509816i	$0.170287\pi$
$194$	−568384.	+	412955.i	−1.08427	+	0.787769i
$195$	898956.	+	653130.i	1.69298	+	1.23002i
$196$	−42073.4	−	129489.i	−0.0782290	−	0.240764i
$197$	451713.			0.829273			0.414636	−	0.909987i	$-0.363909\pi$
$197$	451713.			0.829273			0.414636	+	0.909987i	$0.363909\pi$
$198$	116380.	−	186328.i	0.210968	−	0.337766i
$199$	−231140.			−0.413754			−0.206877	−	0.978367i	$-0.566330\pi$
$199$	−231140.			−0.413754			−0.206877	+	0.978367i	$0.566330\pi$
$200$	131794.	+	405621.i	0.232981	+	0.717043i
$201$	−191526.	−	139152.i	−0.334378	−	0.242940i
$202$	171858.	−	124862.i	0.296340	−	0.215304i
$203$	40726.0	−	125342.i	0.0693637	−	0.213479i
$204$	−2419.65	+	7446.92i	−0.00407078	+	0.0125286i
$205$	493609.	−	358628.i	0.820349	−	0.596018i
$206$	−604043.	−	438863.i	−0.991745	−	0.720545i
$207$	−79789.2	−	245566.i	−0.129425	−	0.398329i
$208$	279064.			0.447246
$209$	−213920.	−	53291.9i	−0.338755	−	0.0843908i
$210$	−371406.			−0.581167
$211$	190822.	+	587289.i	0.295068	+	0.908126i	0.983199	+	0.182539i	$0.0584316\pi$
$211$	190822.	+	587289.i	0.295068	+	0.908126i	−0.688131	+	0.725587i	$0.741568\pi$
$212$	−48209.3	−	35026.1i	−0.0736701	−	0.0535244i
$213$	−59221.4	+	43026.8i	−0.0894395	+	0.0649816i
$214$	95698.1	−	294528.i	0.142846	−	0.439635i
$215$	−419862.	+	1.29220e6i	−0.619455	+	1.90649i
$216$	202630.	−	147219.i	0.295508	−	0.214699i
$217$	−582248.	−	423028.i	−0.839380	−	0.609845i
$218$	−138910.	−	427522.i	−0.197967	−	0.609281i
$219$	−894151.			−1.25980
$220$	−408450.	−	486579.i	−0.568961	−	0.677792i
$221$	−51780.6			−0.0713160
$222$	45110.1	+	138834.i	0.0614315	+	0.189067i
$223$	426662.	+	309988.i	0.574542	+	0.417429i	0.836752	−	0.547582i	$-0.184451\pi$
$223$	426662.	+	309988.i	0.574542	+	0.417429i	−0.262210	+	0.965011i	$0.584451\pi$
$224$	−75462.4	+	54826.6i	−0.100487	+	0.0730082i
$225$	−281826.	+	867370.i	−0.371128	+	1.14222i
$226$	−265299.	+	816506.i	−0.345513	+	1.06338i
$227$	597514.	−	434119.i	0.769632	−	0.559171i	−0.132217	−	0.991221i	$-0.542210\pi$
$227$	597514.	−	434119.i	0.769632	−	0.559171i	0.901850	+	0.432050i	$0.142210\pi$
$228$	−73260.4	−	53226.8i	−0.0933323	−	0.0678099i
$229$	1809.70	+	5569.69i	0.00228044	+	0.00701846i	0.952190	−	0.305506i	$-0.0988255\pi$
$229$	1809.70	+	5569.69i	0.00228044	+	0.00701846i	−0.949910	+	0.312524i	$0.898825\pi$
$230$	−746666.			−0.930694
$231$	349167.	−	141152.i	0.430530	−	0.174043i
$232$	92597.0			0.112948
$233$	89833.2	+	276478.i	0.108404	+	0.333635i	0.990514	−	0.137409i	$-0.0438775\pi$
$233$	89833.2	+	276478.i	0.108404	+	0.333635i	−0.882110	+	0.471044i	$0.843877\pi$
$234$	482777.	+	350758.i	0.576377	+	0.418762i
$235$	627495.	−	455902.i	0.741209	−	0.538520i
$236$	−164448.	+	506118.i	−0.192198	+	0.591524i
$237$	−49619.4	+	152713.i	−0.0573827	+	0.176606i
$238$	14002.1	−	10173.1i	0.0160233	−	0.0116416i
$239$	−902308.	−	655565.i	−1.02179	−	0.742371i	−0.0551378	−	0.998479i	$-0.517560\pi$
$239$	−902308.	−	655565.i	−1.02179	−	0.742371i	−0.966648	+	0.256108i	$0.917560\pi$
$240$	−80637.8	−	248178.i	−0.0903671	−	0.278121i
$241$	−450615.			−0.499761			−0.249881	−	0.968277i	$-0.580391\pi$
$241$	−450615.			−0.499761			−0.249881	+	0.968277i	$0.580391\pi$
$242$	568916.	+	302213.i	0.624468	+	0.331723i
$243$	878212.			0.954078
$244$	−14218.1	−	43758.9i	−0.0152886	−	0.0470535i
$245$	−681133.	−	494872.i	−0.724965	−	0.526718i
$246$	−205599.	+	149377.i	−0.216613	+	0.157378i
$247$	185051.	−	569528.i	0.192996	−	0.593981i
$248$	156257.	−	480910.i	0.161328	−	0.496517i
$249$	−655744.	+	476426.i	−0.670249	+	0.486964i
$250$	1.13309e6	+	823239.i	1.14661	+	0.833059i
$251$	−13198.2	−	40619.7i	−0.0132230	−	0.0406961i	0.944227	−	0.329294i	$-0.106811\pi$
$251$	−13198.2	−	40619.7i	−0.0132230	−	0.0406961i	−0.957450	+	0.288598i	$0.906811\pi$
$252$	−199461.			−0.197859
$253$	701958.	−	283769.i	0.689461	−	0.278717i
$254$	−97677.1			−0.0949967
$255$	14962.4	+	46049.6i	0.0144096	+	0.0443481i
$256$	−53019.7	−	38521.1i	−0.0505636	−	0.0367366i
$257$	−408175.	+	296556.i	−0.385490	+	0.280075i	−0.763605	−	0.645684i	$-0.776572\pi$
$257$	−408175.	+	296556.i	−0.385490	+	0.280075i	0.378115	+	0.925759i	$0.376572\pi$
$258$	174882.	−	538231.i	0.163567	−	0.503407i
$259$	99710.0	−	306876.i	0.0923611	−	0.284258i
$260$	1.39608e6	−	1.01431e6i	1.28079	−	0.930547i
$261$	160191.	+	116386.i	0.145559	+	0.105754i
$262$	339246.	+	1.04409e6i	0.305324	+	0.939691i
$263$	695505.			0.620027			0.310014	−	0.950732i	$-0.399666\pi$
$263$	695505.			0.620027			0.310014	+	0.950732i	$0.399666\pi$
$264$	170129.	+	202671.i	0.150234	+	0.178971i
$265$	−368487.			−0.322335
$266$	61852.8	+	190363.i	0.0535988	+	0.164960i
$267$	315667.	+	229346.i	0.270989	+	0.196885i
$268$	−297441.	+	216103.i	−0.252967	+	0.183791i
$269$	170506.	−	524765.i	0.143668	−	0.442165i	−0.853169	−	0.521634i	$-0.825323\pi$
$269$	170506.	−	524765.i	0.143668	−	0.442165i	0.996837	+	0.0794695i	$0.0253226\pi$
$270$	478606.	−	1.47300e6i	0.399547	−	1.22968i
$271$	−396.834	+	288.317i	−0.000328236	+	0.000238477i	−0.587949	−	0.808898i	$-0.700065\pi$
$271$	−396.834	+	288.317i	−0.000328236	+	0.000238477i	0.587621	+	0.809136i	$0.300065\pi$
$272$	9837.86	+	7147.62i	0.00806266	+	0.00585787i
$273$	316131.	+	972951.i	0.256720	+	0.790104i
$274$	−439893.			−0.353973
$275$	−2.59502e6	−	646473.i	−2.06923	−	0.515488i
$276$	311004.			0.245750
$277$	−506033.	−	1.55741e6i	−0.396259	−	1.21956i	−0.927976	−	0.372639i	$-0.878453\pi$
$277$	−506033.	−	1.55741e6i	−0.396259	−	1.21956i	0.531717	−	0.846922i	$-0.321547\pi$
$278$	−338163.	−	245689.i	−0.262430	−	0.190667i
$279$	874781.	−	635565.i	0.672804	−	0.488821i
$280$	−178240.	+	548565.i	−0.135865	+	0.418151i
$281$	563534.	−	1.73438e6i	0.425750	−	1.31032i	−0.476525	−	0.879161i	$-0.658104\pi$
$281$	563534.	−	1.73438e6i	0.425750	−	1.31032i	0.902275	−	0.431162i	$-0.141896\pi$
$282$	−261366.	+	189893.i	−0.195716	+	0.142196i
$283$	−268496.	−	195074.i	−0.199283	−	0.144788i	0.483668	−	0.875251i	$-0.339304\pi$
$283$	−268496.	−	195074.i	−0.199283	−	0.144788i	−0.682952	+	0.730463i	$0.739304\pi$
$284$	35129.8	+	108118.i	0.0258452	+	0.0795433i
$285$	−559964.			−0.408365
$286$	−927001.	+	1.48416e6i	−0.670139	+	1.07291i
$287$	561732.			0.402555
$288$	−43305.8	−	133282.i	−0.0307656	−	0.0946867i
$289$	1.14686e6	+	833245.i	0.807731	+	0.586851i
$290$	463237.	−	336562.i	0.323451	−	0.235001i
$291$	559184.	−	1.72099e6i	0.387099	−	1.19137i
$292$	−429107.	+	1.32066e6i	−0.294516	+	0.906427i
$293$	−1.17547e6	+	854026.i	−0.799910	+	0.581169i	−0.910888	−	0.412654i	$-0.864602\pi$
$293$	−1.17547e6	+	854026.i	−0.799910	+	0.581169i	0.110978	+	0.993823i	$0.464602\pi$
$294$	283707.	+	206126.i	0.191427	+	0.139080i
$295$	1.01690e6	+	3.12969e6i	0.680334	+	2.09385i
$296$	226706.			0.150395
$297$	109861.	+	1.56669e6i	0.0722690	+	1.03060i
$298$	−641750.			−0.418625
$299$	635542.	+	1.95600e6i	0.411118	+	1.26529i
$300$	−888708.	−	645684.i	−0.570106	−	0.414207i
$301$	−1.01201e6	+	735269.i	−0.643827	+	0.467768i
$302$	262839.	−	808936.i	0.165834	−	0.510383i
$303$	−169076.	+	520362.i	−0.105797	+	0.325611i
$304$	−113774.	+	82661.4i	−0.0706086	+	0.0513002i
$305$	−230179.	−	167235.i	−0.141683	−	0.102939i
$306$	8035.44	+	24730.5i	0.00490576	+	0.0150984i
$307$	−1.20965e6			−0.732511			−0.366255	−	0.930514i	$-0.619360\pi$
$307$	−1.20965e6			−0.732511			−0.366255	+	0.930514i	$0.619360\pi$
$308$	−40913.8	−	583458.i	−0.0245750	−	0.350455i
$309$	1.92308e6			1.14578
$310$	−966248.	−	2.97381e6i	−0.571063	−	1.75755i
$311$	−2.25802e6	−	1.64055e6i	−1.32381	−	0.961807i	−0.999876	−	0.0157285i	$-0.994993\pi$
$311$	−2.25802e6	−	1.64055e6i	−1.32381	−	0.961807i	−0.323938	−	0.946078i	$-0.605007\pi$
$312$	−581500.	+	422484.i	−0.338192	+	0.245711i
$313$	−704833.	+	2.16925e6i	−0.406654	+	1.25155i	0.512852	+	0.858477i	$0.328589\pi$
$313$	−704833.	+	2.16925e6i	−0.406654	+	1.25155i	−0.919506	+	0.393076i	$0.871411\pi$
$314$	−316664.	+	974592.i	−0.181249	+	0.557826i
$315$	−997846.	+	724977.i	−0.566614	+	0.411669i
$316$	201744.	+	146575.i	0.113653	+	0.0825739i
$317$	−181583.	−	558856.i	−0.101491	−	0.312357i	0.887400	−	0.461001i	$-0.152509\pi$
$317$	−181583.	−	558856.i	−0.101491	−	0.312357i	−0.988891	+	0.148643i	$0.952509\pi$
$318$	153483.			0.0851124
$319$	−307590.	+	492461.i	−0.169237	+	0.270954i
$320$	−405255.			−0.221235
$321$	246485.	+	758603.i	0.133514	+	0.410915i
$322$	−556145.	−	404063.i	−0.298916	−	0.217175i
$323$	21110.8	−	15337.9i	0.0112590	−	0.00818012i
$324$	−34923.3	+	107483.i	−0.0184822	+	0.0568822i
$325$	2.24482e6	−	6.90883e6i	1.17889	−	3.62824i
$326$	878933.	−	638582.i	0.458049	−	0.332792i
$327$	936693.	+	680548.i	0.484427	+	0.351957i
$328$	121960.	+	375356.i	0.0625942	+	0.192645i
$329$	714096.			0.363720
$330$	1.58775e6	+	395542.i	0.802599	+	0.199944i
$331$	2.61225e6			1.31052			0.655261	−	0.755403i	$-0.272559\pi$
$331$	2.61225e6			1.31052			0.655261	+	0.755403i	$0.272559\pi$
$332$	388984.	+	1.19717e6i	0.193681	+	0.596088i
$333$	392198.	+	284948.i	0.193818	+	0.140817i
$334$	1.69692e6	−	1.23289e6i	0.832330	−	0.604723i
$335$	−702545.	+	2.16221e6i	−0.342028	+	1.05265i
$336$	74240.8	−	228490.i	0.0358752	−	0.110413i
$337$	467790.	−	339869.i	0.224376	−	0.163018i	−0.469918	−	0.882710i	$-0.655717\pi$
$337$	467790.	−	339869.i	0.224376	−	0.163018i	0.694294	+	0.719691i	$0.255717\pi$
$338$	−2.64391e6	−	1.92092e6i	−1.25880	−	0.914569i
$339$	−683318.	−	2.10304e6i	−0.322941	−	0.993911i
$340$	75195.5			0.0352772
$341$	2.03858e6	+	2.42852e6i	0.949383	+	1.13098i
$342$	−300724.			−0.139028
$343$	−712622.	−	2.19323e6i	−0.327057	−	1.00658i
$344$	−711038.	−	516599.i	−0.323964	−	0.235373i
$345$	1.55586e6	−	1.13040e6i	0.703759	−	0.511311i
$346$	−715435.	+	2.20188e6i	−0.321277	+	0.988790i
$347$	−111466.	+	343056.i	−0.0496955	+	0.152947i	−0.972825	−	0.231543i	$-0.925623\pi$
$347$	−111466.	+	343056.i	−0.0496955	+	0.152947i	0.923129	+	0.384490i	$0.125623\pi$
$348$	−192949.	+	140186.i	−0.0854071	+	0.0620519i
$349$	−435481.	−	316395.i	−0.191384	−	0.139049i	0.487967	−	0.872862i	$-0.337739\pi$
$349$	−435481.	−	316395.i	−0.191384	−	0.139049i	−0.679351	+	0.733813i	$0.737739\pi$
$350$	750324.	+	2.30926e6i	0.327400	+	1.00763i
$351$	−4.26610e6			−1.84826
$352$	380990.	−	154016.i	0.163892	−	0.0662537i
$353$	1.39128e6			0.594260			0.297130	−	0.954837i	$-0.403971\pi$
$353$	1.39128e6			0.594260			0.297130	+	0.954837i	$0.403971\pi$
$354$	−423561.	−	1.30359e6i	−0.179642	−	0.552881i
$355$	568722.	+	413200.i	0.239513	+	0.174016i
$356$	490232.	−	356175.i	0.205011	−	0.148949i
$357$	−13775.5	+	42396.5i	−0.00572052	+	0.0176059i
$358$	−194478.	+	598540.i	−0.0801977	+	0.246823i
$359$	3.29416e6	−	2.39335e6i	1.34899	−	0.980098i	0.349928	−	0.936777i	$-0.386206\pi$
$359$	3.29416e6	−	2.39335e6i	1.34899	−	0.980098i	0.999061	−	0.0433212i	$-0.0137939\pi$
$360$	−701085.	−	509368.i	−0.285111	−	0.207145i
$361$	−671902.	−	2.06790e6i	−0.271355	−	0.835145i
$362$	724686.			0.290655
$363$	−1.64301e6	+	231564.i	−0.654445	+	0.0922368i
$364$	1.58876e6			0.628498
$365$	2.65347e6	+	8.16655e6i	1.04252	+	3.20853i
$366$	95875.0	+	69657.3i	0.0374113	+	0.0271809i
$367$	−2.34620e6	+	1.70461e6i	−0.909284	+	0.660634i	−0.940834	−	0.338868i	$-0.889956\pi$
$367$	−2.34620e6	+	1.70461e6i	−0.909284	+	0.660634i	0.0315494	+	0.999502i	$0.489956\pi$
$368$	149252.	−	459350.i	0.0574514	−	0.176817i
$369$	−260797.	+	802652.i	−0.0997097	+	0.306875i
$370$	1.13415e6	−	824007.i	0.430691	−	0.312915i
$371$	−274463.	−	199409.i	−0.103526	−	0.0752159i
$372$	402464.	+	1.23866e6i	0.150789	+	0.464081i
$373$	1.10388e6			0.410820			0.205410	−	0.978676i	$-0.434147\pi$
$373$	1.10388e6			0.410820			0.205410	+	0.978676i	$0.434147\pi$
$374$	−70693.0	+	28577.9i	−0.0261335	+	0.0105645i
$375$	−3.60740e6			−1.32470
$376$	155041.	+	477167.i	0.0565557	+	0.174061i
$377$	−1.27597e6	−	927044.i	−0.462366	−	0.335928i
$378$	1.15360e6	−	838143.i	0.415267	−	0.301709i
$379$	606708.	−	1.86726e6i	0.216961	−	0.667737i	−0.782048	−	0.623219i	$-0.785825\pi$
$379$	606708.	−	1.86726e6i	0.216961	−	0.667737i	0.999009	−	0.0445186i	$-0.0141754\pi$
$380$	−268729.	+	827064.i	−0.0954676	+	0.293819i
$381$	203535.	−	147876.i	0.0718333	−	0.0521899i
$382$	1.18376e6	+	860054.i	0.415056	+	0.301556i
$383$	−644748.	−	1.98433e6i	−0.224591	−	0.691221i	−0.998333	−	0.0577195i	$-0.981617\pi$
$383$	−644748.	−	1.98433e6i	−0.224591	−	0.691221i	0.773742	−	0.633501i	$-0.218383\pi$
$384$	168798.			0.0584170
$385$	−2.32537e6	−	2.77017e6i	−0.799540	−	0.952477i
$386$	−906715.			−0.309744
$387$	−580766.	−	1.78741e6i	−0.197117	−	0.606664i
$388$	−2.27354e6	−	1.65182e6i	−0.766695	−	0.557037i
$389$	−2.07063e6	+	1.50440e6i	−0.693791	+	0.504069i	−0.877904	−	0.478836i	$-0.841059\pi$
$389$	−2.07063e6	+	1.50440e6i	−0.693791	+	0.504069i	0.184113	+	0.982905i	$0.441059\pi$
$390$	−1.37348e6	+	4.22714e6i	−0.457258	+	1.40730i
$391$	−27693.8	+	85232.9i	−0.00916097	+	0.0281946i
$392$	440599.	−	320114.i	0.144820	−	0.105218i
$393$	−2.28758e6	−	1.66203e6i	−0.747129	−	0.542821i
$394$	558348.	+	1.71842e6i	0.181203	+	0.557685i
$395$	1.54202e6			0.497277
$396$	852690.	+	212423.i	0.273246	+	0.0680711i
$397$	−231337.			−0.0736663			−0.0368332	−	0.999321i	$-0.511727\pi$
$397$	−231337.			−0.0736663			−0.0368332	+	0.999321i	$0.511727\pi$
$398$	−285705.	−	879308.i	−0.0904086	−	0.278249i
$399$	−417083.	−	303028.i	−0.131157	−	0.0952908i
$400$	−1.38017e6	+	1.00275e6i	−0.431302	+	0.313359i
$401$	1.12617e6	−	3.46601e6i	0.349739	−	1.07639i	−0.609258	−	0.792972i	$-0.708533\pi$
$401$	1.12617e6	−	3.46601e6i	0.349739	−	1.07639i	0.958997	−	0.283415i	$-0.0914673\pi$
$402$	292626.	−	900610.i	0.0903124	−	0.277953i
$403$	−6.96786e6	+	5.06245e6i	−2.13716	+	1.55274i
$404$	687431.	+	499448.i	0.209544	+	0.152243i
$405$	215955.	+	664642.i	0.0654224	+	0.201349i
$406$	527169.			0.158721
$407$	−753077.	+	1.20570e6i	−0.225348	+	0.360788i
$408$	−31320.6			−0.00931494
$409$	−516709.	−	1.59027e6i	−0.152735	−	0.470070i	0.845190	−	0.534467i	$-0.179488\pi$
$409$	−516709.	−	1.59027e6i	−0.152735	−	0.470070i	−0.997924	+	0.0643972i	$0.979488\pi$
$410$	1.97444e6	+	1.43451e6i	0.580074	+	0.421448i
$411$	916625.	−	665967.i	0.267662	−	0.194468i
$412$	922896.	−	2.84038e6i	0.267861	−	0.824392i
$413$	−936227.	+	2.88141e6i	−0.270088	+	0.831247i
$414$	835564.	−	607073.i	0.239596	−	0.174076i
$415$	6.29732e6	+	4.57527e6i	1.79488	+	1.30406i
$416$	344942.	+	1.06162e6i	0.0977267	+	0.300772i
$417$	1.07660e6			0.303190
$418$	−61685.2	−	879672.i	−0.0172679	−	0.246252i
$419$	7.12923e6			1.98384			0.991922	−	0.126850i	$-0.0404868\pi$
$419$	7.12923e6			1.98384			0.991922	+	0.126850i	$0.0404868\pi$
$420$	−459083.	−	1.41291e6i	−0.126990	−	0.390834i
$421$	1.70799e6	+	1.24093e6i	0.469656	+	0.341225i	0.797307	−	0.603574i	$-0.206257\pi$
$421$	1.70799e6	+	1.24093e6i	0.469656	+	0.341225i	−0.327651	+	0.944799i	$0.606257\pi$
$422$	−1.99831e6	+	1.45186e6i	−0.546238	+	0.396865i
$423$	−331536.	+	1.02036e6i	−0.0900906	+	0.277270i
$424$	73657.2	−	226694.i	0.0198976	−	0.0612385i
$425$	256091.	−	186061.i	0.0687737	−	0.0499670i
$426$	−236885.	−	172107.i	−0.0632433	−	0.0459489i
$427$	−80946.0	−	249126.i	−0.0214845	−	0.0661226i
$428$	1.23874e6			0.326867
$429$	−315274.	−	4.49602e6i	−0.0827076	−	1.17947i
$430$	−5.43480e6			−1.41747
$431$	−1.33935e6	−	4.12211e6i	−0.347298	−	1.06887i	−0.960342	−	0.278825i	$-0.910055\pi$
$431$	−1.33935e6	−	4.12211e6i	−0.347298	−	1.06887i	0.613044	−	0.790049i	$-0.289945\pi$
$432$	810521.	+	588878.i	0.208956	+	0.151815i
$433$	−2.33063e6	+	1.69330e6i	−0.597385	+	0.434025i	−0.844950	−	0.534846i	$-0.820370\pi$
$433$	−2.33063e6	+	1.69330e6i	−0.597385	+	0.434025i	0.247565	+	0.968871i	$0.420370\pi$
$434$	889595.	−	2.73789e6i	0.226709	−	0.697738i
$435$	−455739.	+	1.40262e6i	−0.115476	+	0.355399i
$436$	1.45469e6	−	1.05689e6i	0.366483	−	0.266265i
$437$	−838493.	−	609201.i	−0.210037	−	0.152601i
$438$	−1.10523e6	−	3.40155e6i	−0.275276	−	0.847212i
$439$	6.95333e6			1.72199			0.860997	−	0.508609i	$-0.169840\pi$
$439$	6.95333e6			1.72199			0.860997	+	0.508609i	$0.169840\pi$
$440$	1.34618e6	−	2.15528e6i	0.331492	−	0.530728i
$441$	1.16458e6			0.285150
$442$	−64004.4	−	196985.i	−0.0155831	−	0.0479599i
$443$	1.72672e6	+	1.25454e6i	0.418035	+	0.303721i	0.776847	−	0.629690i	$-0.216818\pi$
$443$	1.72672e6	+	1.25454e6i	0.418035	+	0.303721i	−0.358811	+	0.933410i	$0.616818\pi$
$444$	−472399.	+	343218.i	−0.113724	+	0.0826252i
$445$	1.15791e6	−	3.56368e6i	0.277189	−	0.853099i
$446$	−651881.	+	2.00628e6i	−0.155178	+	0.477590i
$447$	1.33724e6	−	971565.i	0.316550	−	0.229987i
$448$	−301849.	−	219306.i	−0.0710551	−	0.0516246i
$449$	818914.	+	2.52036e6i	0.191700	+	0.589992i	0.999999	+	0.00122025i	$0.000388418\pi$
$449$	818914.	+	2.52036e6i	0.191700	+	0.589992i	−0.808299	+	0.588772i	$0.799612\pi$
$450$	−3.64803e6			−0.849233
$451$	−2.40140e6	−	598237.i	−0.555933	−	0.138494i
$452$	−3.43410e6			−0.790618
$453$	676983.	+	2.08354e6i	0.155000	+	0.477041i
$454$	2.39006e6	+	1.73648e6i	0.544212	+	0.395393i
$455$	7.94811e6	−	5.77464e6i	1.79985	−	1.30766i
$456$	111932.	−	344491.i	0.0252082	−	0.0775829i
$457$	−491387.	+	1.51234e6i	−0.110061	+	0.338733i	−0.990885	−	0.134711i	$-0.956989\pi$
$457$	−491387.	+	1.51234e6i	−0.110061	+	0.338733i	0.880824	+	0.473444i	$0.156989\pi$
$458$	−18951.4	+	13769.0i	−0.00422161	+	0.00306718i
$459$	−150393.	−	109267.i	−0.0333193	−	0.0242079i
$460$	−922930.	−	2.84049e6i	−0.203364	−	0.625891i
$461$	−8.06112e6			−1.76662			−0.883310	−	0.468789i	$-0.844690\pi$
$461$	−8.06112e6			−1.76662			−0.883310	+	0.468789i	$0.844690\pi$
$462$	968569.	+	1.15384e6i	0.211118	+	0.251501i
$463$	−4.95098e6			−1.07334			−0.536671	−	0.843791i	$-0.680319\pi$
$463$	−4.95098e6			−1.07334			−0.536671	+	0.843791i	$0.680319\pi$
$464$	114456.	+	352260.i	0.0246800	+	0.0759571i
$465$	6.51555e6	+	4.73383e6i	1.39739	+	1.01527i
$466$	−940746.	+	683492.i	−0.200682	+	0.145804i
$467$	−196887.	+	605957.i	−0.0417759	+	0.128573i	−0.969769	−	0.244024i	$-0.921532\pi$
$467$	−196887.	+	605957.i	−0.0417759	+	0.128573i	0.927993	+	0.372597i	$0.121532\pi$
$468$	−737617.	+	2.27015e6i	−0.155674	+	0.479115i
$469$	−1.69338e6	+	1.23031e6i	−0.355485	+	0.258275i
$470$	2.50998e6	+	1.82361e6i	0.524114	+	0.380791i
$471$	−815618.	−	2.51021e6i	−0.169408	−	0.521385i
$472$	−2.12866e6			−0.439796
$473$	5.10938e6	−	2.06548e6i	1.05006	−	0.424491i
$474$	−642288.			−0.131306
$475$	1.13125e6	+	3.48164e6i	0.230052	+	0.708028i
$476$	56008.4	+	40692.5i	0.0113302	+	0.00823184i
$477$	412358.	−	299596.i	0.0829810	−	0.0602893i
$478$	1.37860e6	−	4.24291e6i	0.275975	−	0.849364i
$479$	−1.39650e6	+	4.29800e6i	−0.278102	+	0.855909i	0.710281	+	0.703919i	$0.248568\pi$
$479$	−1.39650e6	+	4.29800e6i	−0.278102	+	0.855909i	−0.988382	+	0.151990i	$0.951432\pi$
$480$	844450.	−	613529.i	0.167290	−	0.121544i
$481$	−3.12396e6	−	2.26969e6i	−0.615663	−	0.447305i
$482$	−556990.	−	1.71424e6i	−0.109202	−	0.336089i
$483$	1.77059e6			0.345343
$484$	−446469.	+	2.53784e6i	−0.0866319	+	0.492438i
$485$	−1.73777e7			−3.35459
$486$	1.08553e6	+	3.34092e6i	0.208474	+	0.641616i
$487$	−3.56586e6	−	2.59075e6i	−0.681305	−	0.494997i	0.192485	−	0.981300i	$-0.438345\pi$
$487$	−3.56586e6	−	2.59075e6i	−0.681305	−	0.494997i	−0.873790	+	0.486303i	$0.838345\pi$
$488$	148894.	−	108178.i	0.0283027	−	0.0205631i
$489$	−864705.	+	2.66129e6i	−0.163529	+	0.503292i
$490$	1.04068e6	−	3.20288e6i	0.195806	−	0.602630i
$491$	−6.39185e6	+	4.64395e6i	−1.19653	+	0.869329i	−0.993939	−	0.109935i	$-0.964936\pi$
$491$	−6.39185e6	+	4.64395e6i	−1.19653	+	0.869329i	−0.202590	+	0.979264i	$0.564936\pi$
$492$	−822398.	−	597507.i	−0.153168	−	0.111283i
$493$	−21237.5	−	65362.2i	−0.00393537	−	0.0121118i
$494$	2.39535e6			0.441622
$495$	5.03786e6	−	2.03657e6i	0.924130	−	0.373583i
$496$	2.02263e6			0.369159
$497$	199999.	+	615535.i	0.0363193	+	0.111779i
$498$	−2.62298e6	−	1.90570e6i	−0.473937	−	0.344336i
$499$	−202381.	+	147039.i	−0.0363847	+	0.0264351i	−0.605829	−	0.795595i	$-0.707158\pi$
$499$	−202381.	+	147039.i	−0.0363847	+	0.0264351i	0.569444	+	0.822030i	$0.307158\pi$
$500$	−1.73121e6	+	5.32812e6i	−0.309688	+	0.953122i
$501$	−1.66945e6	+	5.13805e6i	−0.297153	+	0.914542i
$502$	138213.	−	100418.i	0.0244787	−	0.0177848i
$503$	2.53240e6	+	1.83990e6i	0.446285	+	0.324245i	0.788127	−	0.615512i	$-0.211051\pi$
$503$	2.53240e6	+	1.83990e6i	0.446285	+	0.324245i	−0.341842	+	0.939757i	$0.611051\pi$
$504$	−246547.	−	758793.i	−0.0432338	−	0.133060i
$505$	5.25437e6			0.916837
$506$	1.94719e6	+	2.31965e6i	0.338090	+	0.402760i
$507$	8.41738e6			1.45431
$508$	−120736.	−	371586.i	−0.0207575	−	0.0638851i
$509$	4.99920e6	+	3.63213e6i	0.855275	+	0.621393i	0.926595	−	0.376060i	$-0.122721\pi$
$509$	4.99920e6	+	3.63213e6i	0.855275	+	0.621393i	−0.0713206	+	0.997453i	$0.522721\pi$
$510$	−156688.	+	113841.i	−0.0266754	+	0.0193808i
$511$	−2.44297e6	+	7.51870e6i	−0.413872	+	1.27377i
$512$	81007.0	−	249314.i	0.0136568	−	0.0420312i
$513$	1.73928e6	−	1.26366e6i	0.291793	−	0.212000i
$514$	−1.63270e6	−	1.18622e6i	−0.272583	−	0.198043i
$515$	−5.70692e6	−	1.75641e7i	−0.948164	−	2.91815i
$516$	2.26372e6			0.374281
$517$	−3.05275e6	−	760502.i	−0.502301	−	0.125134i
$518$	1.29067e6			0.211345
$519$	−1.84271e6	−	5.67129e6i	−0.300289	−	0.924195i
$520$	5.58433e6	+	4.05725e6i	0.905654	+	0.657996i
$521$	4.76601e6	−	3.46271e6i	0.769238	−	0.558884i	−0.132492	−	0.991184i	$-0.542298\pi$
$521$	4.76601e6	−	3.46271e6i	0.769238	−	0.558884i	0.901730	+	0.432300i	$0.142298\pi$
$522$	−244750.	+	753265.i	−0.0393140	+	0.120996i
$523$	−1.63065e6	+	5.01863e6i	−0.260680	+	0.802290i	0.731977	+	0.681329i	$0.238598\pi$
$523$	−1.63065e6	+	5.01863e6i	−0.260680	+	0.802290i	−0.992657	+	0.120961i	$0.961402\pi$
$524$	−3.55263e6	+	2.58113e6i	−0.565225	+	0.410660i
$525$	−5.05955e6	−	3.67598e6i	−0.801150	−	0.582069i
$526$	859691.	+	2.64586e6i	0.135481	+	0.416967i
$527$	−375302.			−0.0588646
$528$	−560716.	+	897724.i	−0.0875303	+	0.140139i
$529$	−2.87679e6			−0.446960
$530$	−455475.	−	1.40181e6i	−0.0704327	−	0.216770i
$531$	−3.68254e6	−	2.67552e6i	−0.566776	−	0.411787i
$532$	−647731.	+	470604.i	−0.0992237	+	0.0720902i
$533$	2.07732e6	−	6.39333e6i	0.316727	−	0.974786i
$534$	−482296.	+	1.48436e6i	−0.0731915	+	0.225260i
$535$	6.19708e6	−	4.50244e6i	0.936058	−	0.680086i
$536$	−1.18976e6	−	864413.i	−0.178874	−	0.129960i
$537$	−500907.	−	1.54163e6i	−0.0749586	−	0.230699i
$538$	2.20708e6			0.328748
$539$	238881.	+	3.40661e6i	0.0354169	+	0.505068i
$540$	6.19520e6			0.914263
$541$	−1.73545e6	−	5.34118e6i	−0.254929	−	0.784592i	−0.993844	−	0.110792i	$-0.964661\pi$
$541$	−1.73545e6	−	5.34118e6i	−0.254929	−	0.784592i	0.738914	−	0.673799i	$-0.235339\pi$
$542$	−1587.34	−	1153.27i	−0.000232098	−	0.000168629i
$543$	−1.51006e6	+	1.09712e6i	−0.219784	+	0.159682i
$544$	−15030.9	+	46260.4i	−0.00217765	+	0.00670212i
$545$	3.43592e6	−	1.05747e7i	0.495510	−	1.52502i
$546$	−3.31057e6	+	2.40527e6i	−0.475249	+	0.345288i
$547$	1.06434e7	+	7.73288e6i	1.52094	+	1.10503i	0.961019	+	0.276481i	$0.0891682\pi$
$547$	1.06434e7	+	7.73288e6i	1.52094	+	1.10503i	0.559920	+	0.828547i	$0.310832\pi$
$548$	−543737.	−	1.67345e6i	−0.0773459	−	0.238046i
$549$	393554.			0.0557280
$550$	−748291.	−	1.06711e7i	−0.105478	−	1.50419i
$551$	794806.			0.111528
$552$	384422.	+	1.18313e6i	0.0536982	+	0.165266i
$553$	1.14856e6	+	834475.i	0.159713	+	0.116038i
$554$	5.29925e6	−	3.85013e6i	0.733567	−	0.532968i
$555$	−1.11579e6	+	3.43405e6i	−0.153762	+	0.473232i
$556$	516666.	−	1.59014e6i	0.0708799	−	0.218146i
$557$	1.91477e6	−	1.39116e6i	0.261505	−	0.189994i	−0.449305	−	0.893378i	$-0.648329\pi$
$557$	1.91477e6	−	1.39116e6i	0.261505	−	0.189994i	0.710810	+	0.703384i	$0.248329\pi$
$558$	3.49912e6	+	2.54226e6i	0.475744	+	0.345649i
$559$	4.62596e6	+	1.42372e7i	0.626141	+	1.92706i
$560$	−2.30718e6			−0.310893
$561$	104041.	−	166573.i	0.0139572	−	0.0223459i
$562$	7.29454e6			0.974220
$563$	−683849.	−	2.10467e6i	−0.0909262	−	0.279842i	0.895244	−	0.445575i	$-0.147001\pi$
$563$	−683849.	−	2.10467e6i	−0.0909262	−	0.279842i	−0.986171	+	0.165733i	$0.947001\pi$
$564$	−1.04546e6	−	759574.i	−0.138392	−	0.100548i
$565$	−1.71799e7	+	1.24819e7i	−2.26411	+	1.64498i
$566$	410225.	−	1.26254e6i	0.0538246	−	0.165655i
$567$	−198824.	+	611916.i	−0.0259723	+	0.0799345i
$568$	−367884.	+	267283.i	−0.0478454	+	0.0347617i
$569$	−3.01929e6	−	2.19365e6i	−0.390953	−	0.284044i	0.374893	−	0.927068i	$-0.377680\pi$
$569$	−3.01929e6	−	2.19365e6i	−0.390953	−	0.284044i	−0.765846	+	0.643024i	$0.777680\pi$
$570$	−692154.	−	2.13023e6i	−0.0892310	−	0.274625i
$571$	1.15322e7			1.48021			0.740104	−	0.672493i	$-0.234776\pi$
$571$	1.15322e7			1.48021			0.740104	+	0.672493i	$0.234776\pi$
$572$	−6.79190e6	−	1.69200e6i	−0.867963	−	0.216228i
$573$	−3.76873e6			−0.479522
$574$	694339.	+	2.13696e6i	0.0879614	+	0.270717i
$575$	−1.01716e7	−	7.39010e6i	−1.28298	−	0.932139i
$576$	453505.	−	329490.i	0.0569542	−	0.0413796i
$577$	3.30377e6	−	1.01680e7i	0.413114	−	1.27143i	−0.500813	−	0.865556i	$-0.666965\pi$
$577$	3.30377e6	−	1.01680e7i	0.413114	−	1.27143i	0.913927	−	0.405879i	$-0.133035\pi$
$578$	−1.75225e6	+	5.39287e6i	−0.218161	+	0.671430i
$579$	1.88936e6	−	1.37270e6i	0.234218	−	0.170169i
$580$	1.85295e6	+	1.34625e6i	0.228714	+	0.166171i
$581$	2.21454e6	+	6.81567e6i	0.272172	+	0.837660i
$582$	7.23822e6			0.885777
$583$	960956.	+	1.14477e6i	0.117093	+	0.139491i
$584$	−5.55448e6			−0.673925
$585$	4.56121e6	+	1.40379e7i	0.551049	+	1.69595i
$586$	−4.70187e6	−	3.41611e6i	−0.565622	−	0.410948i
$587$	−6.59300e6	+	4.79010e6i	−0.789747	+	0.573785i	−0.907888	−	0.419212i	$-0.862306\pi$
$587$	−6.59300e6	+	4.79010e6i	−0.789747	+	0.573785i	0.118141	+	0.992997i	$0.462306\pi$
$588$	−433466.	+	1.33407e6i	−0.0517026	+	0.159124i
$589$	1.34123e6	−	4.12789e6i	0.159300	−	0.490275i
$590$	−1.06491e7	+	7.73701e6i	−1.25945	+	0.915047i
$591$	−3.76503e6	−	2.73545e6i	−0.443404	−	0.322152i
$592$	280224.	+	862442.i	0.0328626	+	0.101141i
$593$	826423.			0.0965085			0.0482542	−	0.998835i	$-0.484634\pi$
$593$	826423.			0.0965085			0.0482542	+	0.998835i	$0.484634\pi$
$594$	−5.82425e6	+	2.35447e6i	−0.677289	+	0.273796i
$595$	428099.			0.0495738
$596$	−793246.	−	2.44136e6i	−0.0914729	−	0.281525i
$597$	1.92655e6	+	1.39972e6i	0.221230	+	0.160733i
$598$	−6.65549e6	+	4.83549e6i	−0.761074	+	0.552953i
$599$	−3.04294e6	+	9.36522e6i	−0.346519	+	1.06648i	0.614247	+	0.789114i	$0.289460\pi$
$599$	−3.04294e6	+	9.36522e6i	−0.346519	+	1.06648i	−0.960766	+	0.277362i	$0.910540\pi$
$600$	1.35782e6	−	4.17896e6i	0.153980	−	0.473903i
$601$	4.27060e6	−	3.10277e6i	0.482284	−	0.350400i	−0.319925	−	0.947443i	$-0.603658\pi$
$601$	4.27060e6	−	3.10277e6i	0.482284	−	0.350400i	0.802209	+	0.597043i	$0.203658\pi$
$602$	−4.04805e6	−	2.94108e6i	−0.455254	−	0.330762i
$603$	−971783.	−	2.99084e6i	−0.108837	−	0.334965i
$604$	3.40226e6			0.379468
$605$	6.99072e6	+	1.43189e7i	0.776485	+	1.59045i
$606$	−2.18856e6			−0.242090
$607$	−3.99128e6	−	1.22839e7i	−0.439684	−	1.35321i	−0.888210	−	0.459438i	$-0.848051\pi$
$607$	−3.99128e6	−	1.22839e7i	−0.439684	−	1.35321i	0.448526	−	0.893770i	$-0.351949\pi$
$608$	−455095.	−	330646.i	−0.0499278	−	0.0362747i
$609$	−1.09849e6	+	798098.i	−0.120020	+	0.0871993i
$610$	351683.	−	1.08237e6i	0.0382672	−	0.117774i
$611$	2.64077e6	−	8.12745e6i	0.286172	−	0.880748i
$612$	−84148.2	+	61137.2i	−0.00908168	+	0.00659823i
$613$	6.36268e6	+	4.62276e6i	0.683894	+	0.496878i	0.874647	−	0.484760i	$-0.161093\pi$
$613$	6.36268e6	+	4.62276e6i	0.683894	+	0.496878i	−0.190753	+	0.981638i	$0.561093\pi$
$614$	−1.49521e6	−	4.60178e6i	−0.160059	−	0.492612i
$615$	−6.28598e6			−0.670170
$616$	2.16903e6	−	876839.i	0.230311	−	0.0931039i
$617$	1.22405e6			0.129446			0.0647228	−	0.997903i	$-0.479384\pi$
$617$	1.22405e6			0.129446			0.0647228	+	0.997903i	$0.479384\pi$
$618$	2.37706e6	+	7.31584e6i	0.250362	+	0.770536i
$619$	−1.14055e7	−	8.28655e6i	−1.19643	−	0.869254i	−0.202498	−	0.979283i	$-0.564906\pi$
$619$	−1.14055e7	−	8.28655e6i	−1.19643	−	0.869254i	−0.993928	+	0.110028i	$0.964906\pi$
$620$	1.01187e7	−	7.35165e6i	1.05717	−	0.768079i
$621$	−2.28164e6	+	7.02216e6i	−0.237420	+	0.730705i
$622$	3.44995e6	−	1.06178e7i	0.357550	−	1.10043i
$623$	2.79097e6	−	2.02776e6i	0.288094	−	0.209313i
$624$	−2.32600e6	−	1.68994e6i	−0.239138	−	0.173744i
$625$	4.27003e6	+	1.31418e7i	0.437251	+	1.34572i
$626$	−9.12355e6			−0.930525
$627$	1.46030e6	+	1.73963e6i	0.148345	+	0.176721i
$628$	−4.09899e6			−0.414742
$629$	−51995.9	−	160027.i	−0.00524013	−	0.0161275i
$630$	−3.99138e6	−	2.89991e6i	−0.400656	−	0.291094i
$631$	8.27579e6	−	6.01271e6i	0.827439	−	0.601170i	−0.0913947	−	0.995815i	$-0.529132\pi$
$631$	8.27579e6	−	6.01271e6i	0.827439	−	0.601170i	0.918834	+	0.394645i	$0.129132\pi$
$632$	−308237.	+	948655.i	−0.0306967	+	0.0944747i
$633$	1.96596e6	−	6.05062e6i	0.195014	−	0.600192i
$634$	1.90156e6	−	1.38157e6i	0.187883	−	0.136505i
$635$	−1.95461e6	−	1.42010e6i	−0.192365	−	0.139761i
$636$	189716.	+	583884.i	0.0185977	+	0.0572380i
$637$	−9.27620e6			−0.905777
$638$	−2.25364e6	−	561428.i	−0.219196	−	0.0546062i
$639$	−972383.			−0.0942075
$640$	−500923.	−	1.54168e6i	−0.0483416	−	0.148780i
$641$	7.11512e6	+	5.16944e6i	0.683970	+	0.496934i	0.874673	−	0.484714i	$-0.161076\pi$
$641$	7.11512e6	+	5.16944e6i	0.683970	+	0.496934i	−0.190702	+	0.981648i	$0.561076\pi$
$642$	−2.58123e6	+	1.87537e6i	−0.247166	+	0.179577i
$643$	2.54751e6	−	7.84044e6i	0.242990	−	0.747847i	−0.752970	−	0.658055i	$-0.771380\pi$
$643$	2.54751e6	−	7.84044e6i	0.242990	−	0.747847i	0.995960	−	0.0897926i	$-0.0286204\pi$
$644$	849714.	−	2.61515e6i	0.0807343	−	0.248475i
$645$	1.13248e7	−	8.22792e6i	1.07184	−	0.778737i
$646$	84443.2	+	61351.6i	0.00796129	+	0.00578422i
$647$	2.18480e6	+	6.72411e6i	0.205187	+	0.631501i	0.999706	+	0.0242613i	$0.00772337\pi$
$647$	2.18480e6	+	6.72411e6i	0.205187	+	0.631501i	−0.794518	+	0.607240i	$0.792277\pi$
$648$	−452056.			−0.0422917
$649$	7.07101e6	−	1.13209e7i	0.658976	−	1.05504i
$650$	2.90575e7			2.69758
$651$	2.29129e6	+	7.05187e6i	0.211898	+	0.652156i
$652$	3.51573e6	+	2.55433e6i	0.323890	+	0.235320i
$653$	5.47137e6	−	3.97518e6i	0.502126	−	0.364816i	−0.307702	−	0.951483i	$-0.599560\pi$
$653$	5.47137e6	−	3.97518e6i	0.502126	−	0.364816i	0.809829	+	0.586667i	$0.199560\pi$
$654$	−1.43114e6	+	4.40460e6i	−0.130839	+	0.402682i
$655$	−8.39118e6	+	2.58254e7i	−0.764222	+	2.35203i
$656$	−1.27719e6	+	927930.i	−0.115876	+	0.0841891i
$657$	−9.60916e6	−	6.98146e6i	−0.868504	−	0.631005i
$658$	882671.	+	2.71658e6i	0.0794757	+	0.244601i
$659$	−1.84249e7			−1.65269			−0.826344	−	0.563166i	$-0.809583\pi$
$659$	−1.84249e7			−1.65269			−0.826344	+	0.563166i	$0.809583\pi$
$660$	457839.	+	6.52909e6i	0.0409122	+	0.583436i
$661$	1.67737e7			1.49323			0.746614	−	0.665258i	$-0.231678\pi$
$661$	1.67737e7			1.49323			0.746614	+	0.665258i	$0.231678\pi$
$662$	3.22892e6	+	9.93758e6i	0.286360	+	0.881324i
$663$	431591.	+	313569.i	0.0381319	+	0.0277045i
$664$	−4.07349e6	+	2.95956e6i	−0.358547	+	0.260500i
$665$	−1.52992e6	+	4.70860e6i	−0.134157	+	0.412893i
$666$	−599225.	+	1.84423e6i	−0.0523485	+	0.161112i
$667$	−2.20837e6	+	1.60448e6i	−0.192202	+	0.139643i
$668$	6.78769e6	+	4.93154e6i	0.588546	+	0.427604i
$669$	−1.67902e6	−	5.16749e6i	−0.145041	−	0.446390i
$670$	−9.09393e6			−0.782645
$671$	80726.7	+	1.15122e6i	0.00692167	+	0.0987076i
$672$	960993.			0.0820913
$673$	−3.47797e6	−	1.07041e7i	−0.295998	−	0.910988i	−0.982884	−	0.184223i	$-0.941023\pi$
$673$	−3.47797e6	−	1.07041e7i	−0.295998	−	0.910988i	0.686887	−	0.726765i	$-0.258977\pi$
$674$	1.87116e6	+	1.35948e6i	0.158658	+	0.115271i
$675$	2.10988e7	−	1.53292e7i	1.78237	−	1.29497i
$676$	4.03954e6	−	1.24324e7i	0.339989	−	1.04638i
$677$	3.76495e6	−	1.15873e7i	0.315710	−	0.971654i	−0.659752	−	0.751484i	$-0.729339\pi$
$677$	3.76495e6	−	1.15873e7i	0.315710	−	0.971654i	0.975461	−	0.220171i	$-0.0706615\pi$
$678$	7.15580e6	−	5.19899e6i	0.597839	−	0.434355i
$679$	−1.29436e7	−	9.40407e6i	−1.07741	−	0.782783i
$680$	92946.7	+	286061.i	0.00770836	+	0.0237239i
$681$	−7.60918e6			−0.628739
$682$	−6.71882e6	+	1.07570e7i	−0.553136	+	0.885588i
$683$	−7.48955e6			−0.614333			−0.307166	−	0.951656i	$-0.599381\pi$
$683$	−7.48955e6			−0.614333			−0.307166	+	0.951656i	$0.599381\pi$
$684$	−371715.	−	1.14402e6i	−0.0303788	−	0.0934963i
$685$	−8.80264e6	−	6.39549e6i	−0.716781	−	0.520772i
$686$	7.46268e6	−	5.42195e6i	0.605458	−	0.439891i
$687$	18644.7	−	57382.3i	0.00150717	−	0.00463859i
$688$	1.08637e6	−	3.34350e6i	0.0874996	−	0.269296i
$689$	−3.28454e6	+	2.38636e6i	−0.263589	+	0.191509i
$690$	6.22346e6	+	4.52161e6i	0.497633	+	0.361551i
$691$	4.80413e6	+	1.47856e7i	0.382754	+	1.17800i	0.938096	+	0.346374i	$0.112587\pi$
$691$	4.80413e6	+	1.47856e7i	0.382754	+	1.17800i	−0.555342	+	0.831622i	$0.687413\pi$
$692$	−9.26079e6			−0.735161
$693$	4.85449e6	+	1.20935e6i	0.383982	+	0.0956579i
$694$	−1.44284e6			−0.113715
$695$	−3.19491e6	−	9.83293e6i	−0.250898	−	0.772184i
$696$	−771796.	−	560742.i	−0.0603920	−	0.0438773i
$697$	236983.	−	172178.i	0.0184772	−	0.0134244i
$698$	665355.	−	2.04775e6i	0.0516910	−	0.159089i
$699$	925517.	−	2.84845e6i	0.0716459	−	0.220504i
$700$	−7.85750e6	+	5.70881e6i	−0.606093	+	0.440352i
$701$	−1.26916e6	−	922101.i	−0.0975489	−	0.0708734i	0.537942	−	0.842982i	$-0.319202\pi$
$701$	−1.26916e6	−	922101.i	−0.0975489	−	0.0708734i	−0.635491	+	0.772109i	$0.719202\pi$
$702$	−5.27319e6	−	1.62292e7i	−0.403860	−	1.24295i
$703$	1.94593e6			0.148504
$704$	1.05684e6	+	1.25900e6i	0.0803671	+	0.0957399i
$705$	−7.99098e6			−0.605518
$706$	1.71971e6	+	5.29273e6i	0.129851	+	0.399639i
$707$	3.91365e6	+	2.84343e6i	0.294465	+	0.213941i
$708$	4.43559e6	−	3.22264e6i	0.332558	−	0.241618i
$709$	−4.08320e6	+	1.25668e7i	−0.305060	+	0.938878i	0.674595	+	0.738188i	$0.264318\pi$
$709$	−4.08320e6	+	1.25668e7i	−0.305060	+	0.938878i	−0.979655	+	0.200690i	$0.935682\pi$
$710$	−868929.	+	2.67429e6i	−0.0646902	+	0.199096i
$711$	−1.72561e6	+	1.25373e6i	−0.128018	+	0.0930102i
$712$	1.96093e6	+	1.42470e6i	0.144965	+	0.105323i
$713$	4.60636e6	+	1.41769e7i	0.339339	+	1.04438i
$714$	−178313.			−0.0130899
$715$	−4.01279e7	+	1.62218e7i	−2.93550	+	1.18668i
$716$	−2.51737e6			−0.183512
$717$	3.55081e6	+	1.09283e7i	0.257946	+	0.793877i
$718$	1.31766e7	+	9.57339e6i	0.953879	+	0.693034i
$719$	821880.	−	597131.i	0.0592906	−	0.0430772i	−0.557745	−	0.830012i	$-0.688333\pi$
$719$	821880.	−	597131.i	0.0592906	−	0.0430772i	0.617036	+	0.786935i	$0.288333\pi$
$720$	1.07116e6	−	3.29670e6i	0.0770059	−	0.237000i
$721$	5.25419e6	−	1.61707e7i	0.376415	−	1.15849i
$722$	7.03625e6	−	5.11213e6i	0.502341	−	0.364972i
$723$	3.75587e6	+	2.72880e6i	0.267217	+	0.194145i
$724$	895761.	+	2.75687e6i	0.0635105	+	0.195465i
$725$	9.64164e6			0.681249
$726$	−2.91179e6	−	5.96415e6i	−0.205031	−	0.419959i
$727$	1.58130e6			0.110963			0.0554814	−	0.998460i	$-0.482331\pi$
$727$	1.58130e6			0.110963			0.0554814	+	0.998460i	$0.482331\pi$
$728$	1.96381e6	+	6.04399e6i	0.137332	+	0.422664i
$729$	−8.70849e6	−	6.32709e6i	−0.606910	−	0.440946i
$730$	−2.77875e7	+	2.01888e7i	−1.92994	+	1.40218i
$731$	−201577.	+	620389.i	−0.0139523	+	0.0429409i
$732$	−146484.	+	450831.i	−0.0101044	+	0.0310983i
$733$	596037.	−	433046.i	0.0409745	−	0.0297697i	−0.567110	−	0.823642i	$-0.691938\pi$
$733$	596037.	−	433046.i	0.0409745	−	0.0297697i	0.608084	+	0.793873i	$0.291938\pi$
$734$	−9.38480e6	−	6.81845e6i	−0.642961	−	0.467139i
$735$	2.68043e6	+	8.24951e6i	0.183015	+	0.563261i
$736$	1.93196e6			0.131463
$737$	8.54941e6	−	3.45613e6i	0.579786	−	0.234380i
$738$	−3.37583e6			−0.228160
$739$	−3.86219e6	−	1.18866e7i	−0.260150	−	0.800658i	−0.992771	−	0.120022i	$-0.961704\pi$
$739$	−3.86219e6	−	1.18866e7i	−0.260150	−	0.800658i	0.732622	−	0.680636i	$-0.238296\pi$
$740$	4.53659e6	+	3.29603e6i	0.304544	+	0.221264i
$741$	−4.99130e6	+	3.62639e6i	−0.333940	+	0.242621i
$742$	419342.	−	1.29060e6i	0.0279614	−	0.0860563i
$743$	−4.07078e6	+	1.25286e7i	−0.270524	+	0.832588i	0.719845	+	0.694135i	$0.244213\pi$
$743$	−4.07078e6	+	1.25286e7i	−0.270524	+	0.832588i	−0.990369	+	0.138453i	$0.955787\pi$
$744$	−4.21466e6	+	3.06213e6i	−0.279145	+	0.202811i
$745$	−1.28420e7	−	9.33025e6i	−0.847698	−	0.615889i
$746$	1.36448e6	+	4.19943e6i	0.0897675	+	0.276276i
$747$	−1.07670e7			−0.705979
$748$	−196098.	−	233608.i	−0.0128150	−	0.0152663i
$749$	7.05235e6			0.459335
$750$	−4.45900e6	−	1.37234e7i	−0.289457	−	0.890857i
$751$	1.12701e7	+	8.18819e6i	0.729167	+	0.529771i	0.889300	−	0.457325i	$-0.151192\pi$
$751$	1.12701e7	+	8.18819e6i	0.729167	+	0.529771i	−0.160133	+	0.987095i	$0.551192\pi$
$752$	−1.62361e6	+	1.17962e6i	−0.104698	+	0.0760673i
$753$	−135975.	+	418490.i	−0.00873923	+	0.0268966i
$754$	1.94950e6	−	5.99995e6i	0.124881	−	0.384343i
$755$	1.70206e7	−	1.23662e7i	1.08669	−	0.789528i
$756$	4.61442e6	+	3.35257e6i	0.293638	+	0.213341i
$757$	2.03343e6	+	6.25827e6i	0.128971	+	0.396931i	0.994604	−	0.103748i	$-0.0330837\pi$
$757$	2.03343e6	+	6.25827e6i	0.128971	+	0.396931i	−0.865633	+	0.500679i	$0.833084\pi$
$758$	7.85339e6			0.496460
$759$	−7.56924e6	−	1.88565e6i	−0.476923	−	0.118811i
$760$	−3.47851e6			−0.218453
$761$	2.34461e6	+	7.21596e6i	0.146760	+	0.451682i	0.997233	−	0.0743371i	$-0.0236841\pi$
$761$	2.34461e6	+	7.21596e6i	0.146760	+	0.451682i	−0.850473	+	0.526019i	$0.823684\pi$
$762$	814138.	+	591506.i	0.0507938	+	0.0369038i
$763$	8.28176e6	−	6.01705e6i	0.515005	−	0.374173i
$764$	−1.80863e6	+	5.56639e6i	−0.112103	+	0.345017i
$765$	−198755.	+	611705.i	−0.0122790	+	0.0377910i
$766$	6.75189e6	−	4.90553e6i	0.415770	−	0.302075i
$767$	2.93324e7	+	2.13112e7i	1.80036	+	1.30804i
$768$	208646.	+	642146.i	0.0127646	+	0.0392854i
$769$	1.99059e7			1.21385			0.606926	−	0.794758i	$-0.292402\pi$
$769$	1.99059e7			1.21385			0.606926	+	0.794758i	$0.292402\pi$
$770$	7.66403e6	−	1.22703e7i	0.465833	−	0.745813i
$771$	5.19799e6			0.314920
$772$	−1.12076e6	−	3.44935e6i	−0.0676815	−	0.208302i
$773$	4.44560e6	+	3.22992e6i	0.267597	+	0.194421i	0.713490	−	0.700666i	$-0.247114\pi$
$773$	4.44560e6	+	3.22992e6i	0.267597	+	0.194421i	−0.445892	+	0.895087i	$0.647114\pi$
$774$	6.08186e6	−	4.41873e6i	0.364909	−	0.265122i
$775$	1.62702e7	−	5.00746e7i	0.973059	−	2.99477i
$776$	3.47366e6	−	1.06908e7i	0.207077	−	0.637318i
$777$	−2.68944e6	+	1.95399e6i	−0.159812	+	0.116110i
$778$	−8.28252e6	−	6.01761e6i	−0.490584	−	0.356430i
$779$	1.04685e6	+	3.22186e6i	0.0618073	+	0.190223i
$780$	−1.77787e7			−1.04632
$781$	−199457.	−	2.84439e6i	−0.0117010	−	0.166864i
$782$	−358477.			−0.0209625
$783$	−1.74971e6	−	5.38505e6i	−0.101991	−	0.313896i
$784$	1.76239e6	+	1.28045e6i	0.102403	+	0.0744002i
$785$	−2.05061e7	+	1.48986e7i	−1.18771	+	0.862919i
$786$	3.49512e6	−	1.07569e7i	0.201793	−	0.621054i
$787$	−110062.	+	338737.i	−0.00633435	+	0.0194951i	−0.954174	−	0.299253i	$-0.903262\pi$
$787$	−110062.	+	338737.i	−0.00633435	+	0.0194951i	0.947839	+	0.318748i	$0.103262\pi$
$788$	−5.84710e6	+	4.24817e6i	−0.335448	+	0.243717i
$789$	−5.79703e6	−	4.21179e6i	−0.331522	−	0.240865i
$790$	1.90604e6	+	5.86620e6i	0.108659	+	0.334418i
$791$	−1.95509e7			−1.11103
$792$	245879.	+	3.50639e6i	0.0139286	+	0.198631i
$793$	−3.13476e6			−0.177020
$794$	−285948.	−	880058.i	−0.0160967	−	0.0495405i
$795$	3.07133e6	+	2.23145e6i	0.172349	+	0.125219i
$796$	2.99194e6	−	2.17377e6i	0.167367	−	0.121599i
$797$	−5.20538e6	+	1.60205e7i	−0.290273	+	0.893369i	0.694495	+	0.719497i	$0.255628\pi$
$797$	−5.20538e6	+	1.60205e7i	−0.290273	+	0.893369i	−0.984768	+	0.173871i	$0.944372\pi$
$798$	637246.	−	1.96124e6i	0.0354242	−	0.109024i
$799$	301262.	−	218880.i	0.0166947	−	0.0121294i
$800$	−5.52067e6	−	4.01100e6i	−0.304977	−	0.221578i
$801$	1.60166e6	+	4.92941e6i	0.0882042	+	0.271465i
$802$	1.45775e7			0.800289
$803$	1.84510e7	−	2.95406e7i	1.00979	−	1.61670i
$804$	3.78783e6			0.206657
$805$	−5.25438e6	−	1.61713e7i	−0.285780	−	0.879541i
$806$	−2.78714e7	−	2.02498e7i	−1.51120	−	1.09795i
$807$	−4.59900e6	+	3.34137e6i	−0.248588	+	0.180610i
$808$	−1.05030e6	+	3.23250e6i	−0.0565960	+	0.174185i
$809$	−6.81873e6	+	2.09859e7i	−0.366296	+	1.12734i	0.582869	+	0.812566i	$0.301930\pi$
$809$	−6.81873e6	+	2.09859e7i	−0.366296	+	1.12734i	−0.949165	+	0.314778i	$0.898070\pi$
$810$	−2.26151e6	+	1.64309e6i	−0.121112	+	0.0879929i
$811$	1.28641e7	+	9.34633e6i	0.686796	+	0.498987i	0.875605	−	0.483027i	$-0.160463\pi$
$811$	1.28641e7	+	9.34633e6i	0.686796	+	0.498987i	−0.188809	+	0.982014i	$0.560463\pi$
$812$	651617.	+	2.00547e6i	0.0346818	+	0.106740i
$813$	5053.58			0.000268147
$814$	−5.51760e6	−	1.37455e6i	−0.291870	−	0.0727109i
$815$	2.68724e7			1.41714
$816$	−38714.4	−	119151.i	−0.00203539	−	0.00626428i
$817$	−6.10319e6	−	4.43422e6i	−0.319891	−	0.232414i
$818$	5.41105e6	−	3.93136e6i	0.282747	−	0.205428i
$819$	−4.19937e6	+	1.29243e7i	−0.218763	+	0.673283i
$820$	−3.01667e6	+	9.28436e6i	−0.156673	+	0.482189i
$821$	5.93157e6	−	4.30953e6i	0.307122	−	0.223137i	−0.423538	−	0.905878i	$-0.639212\pi$
$821$	5.93157e6	−	4.30953e6i	0.307122	−	0.223137i	0.730661	+	0.682741i	$0.239212\pi$
$822$	3.66650e6	+	2.66387e6i	0.189266	+	0.137510i
$823$	−9.59198e6	−	2.95211e7i	−0.493638	−	1.51926i	−0.819068	−	0.573696i	$-0.805509\pi$
$823$	−9.59198e6	−	2.95211e7i	−0.493638	−	1.51926i	0.325430	−	0.945566i	$-0.394491\pi$
$824$	1.19462e7			0.612932
$825$	1.77146e7	+	2.11031e7i	0.906143	+	1.07947i
$826$	−1.21188e7			−0.618029
$827$	8.89706e6	+	2.73823e7i	0.452358	+	1.39222i	0.874209	+	0.485550i	$0.161381\pi$
$827$	8.89706e6	+	2.73823e7i	0.452358	+	1.39222i	−0.421851	+	0.906665i	$0.638619\pi$
$828$	3.34226e6	+	2.42829e6i	0.169420	+	0.123091i
$829$	−2.44948e6	+	1.77965e6i	−0.123790	+	0.0899390i	−0.647958	−	0.761676i	$-0.724377\pi$
$829$	−2.44948e6	+	1.77965e6i	−0.123790	+	0.0899390i	0.524167	+	0.851615i	$0.324377\pi$
$830$	−9.62144e6	+	2.96118e7i	−0.484780	+	1.49200i
$831$	−5.21346e6	+	1.60454e7i	−0.261893	+	0.806024i
$832$	−3.61228e6	+	2.62448e6i	−0.180915	+	0.131442i
$833$	−327014.	−	237590.i	−0.0163288	−	0.0118636i
$834$	1.33075e6	+	4.09564e6i	0.0662495	+	0.203895i
$835$	5.18816e7			2.57512
$836$	3.27022e6	−	1.32200e6i	0.161831	−	0.0654207i
$837$	−3.09203e7			−1.52556
$838$	8.81221e6	+	2.71212e7i	0.433486	+	1.33413i
$839$	−1.23339e7	−	8.96112e6i	−0.604918	−	0.439498i	0.242703	−	0.970101i	$-0.421966\pi$
$839$	−1.23339e7	−	8.96112e6i	−0.604918	−	0.439498i	−0.847621	+	0.530602i	$0.821966\pi$
$840$	4.80758e6	−	3.49291e6i	0.235087	−	0.170801i
$841$	−5.69142e6	+	1.75164e7i	−0.277480	+	0.853994i
$842$	−2.60957e6	+	8.03144e6i	−0.126850	+	0.390403i
$843$	−1.52000e7	+	1.10434e7i	−0.736672	+	0.535223i
$844$	−7.99325e6	−	5.80744e6i	−0.386249	−	0.280626i
$845$	−2.49793e7	−	7.68785e7i	−1.20348	−	3.70393i
$846$	−4.29149e6			−0.206149
$847$	−2.54181e6	+	1.44483e7i	−0.121741	+	0.692005i
$848$	953439.			0.0455306
$849$	1.05660e6	+	3.25187e6i	0.0503084	+	0.154833i
$850$	1.02436e6	+	744244.i	0.0486303	+	0.0353320i
$851$	−5.40678e6	+	3.92826e6i	−0.255926	+	0.185941i
$852$	361929.	−	1.11390e6i	0.0170814	−	0.0525712i
$853$	6.89010e6	−	2.12056e7i	0.324230	−	0.997877i	−0.647557	−	0.762017i	$-0.724209\pi$
$853$	6.89010e6	−	2.12056e7i	0.324230	−	0.997877i	0.971787	−	0.235860i	$-0.0757907\pi$
$854$	847677.	−	615874.i	0.0397728	−	0.0288966i
$855$	−6.01776e6	−	4.37216e6i	−0.281527	−	0.204541i
$856$	1.53117e6	+	4.71245e6i	0.0714231	+	0.219818i
$857$	−3.59166e7			−1.67048			−0.835242	−	0.549882i	$-0.814673\pi$
$857$	−3.59166e7			−1.67048			−0.835242	+	0.549882i	$0.814673\pi$
$858$	1.67142e7	−	6.75676e6i	0.775117	−	0.313343i
$859$	−2.85896e7			−1.32198			−0.660990	−	0.750395i	$-0.729863\pi$
$859$	−2.85896e7			−1.32198			−0.660990	+	0.750395i	$0.729863\pi$
$860$	−6.71778e6	−	2.06752e7i	−0.309728	−	0.953244i
$861$	−4.68204e6	−	3.40170e6i	−0.215242	−	0.156382i
$862$	1.40259e7	−	1.01904e7i	0.642928	−	0.467115i
$863$	−2.91151e6	+	8.96070e6i	−0.133073	+	0.409557i	−0.995285	−	0.0969900i	$-0.969079\pi$
$863$	−2.91151e6	+	8.96070e6i	−0.133073	+	0.409557i	0.862212	+	0.506547i	$0.169079\pi$
$864$	−1.23837e6	+	3.81130e6i	−0.0564371	+	0.173695i
$865$	−4.63292e7	+	3.36601e7i	−2.10530	+	1.52959i
$866$	−9.32253e6	−	6.77321e6i	−0.422415	−	0.306902i
$867$	−4.51319e6	−	1.38902e7i	−0.203909	−	0.627567i
$868$	1.15152e7			0.518765
$869$	−4.02135e6	−	4.79056e6i	−0.180644	−	0.215197i
$870$	−5.89920e6			−0.264238
$871$	7.74051e6	+	2.38228e7i	0.345720	+	1.06402i
$872$	5.81875e6	+	4.22757e6i	0.259142	+	0.188278i
$873$	1.94467e7	−	1.41289e7i	0.863596	−	0.627439i
$874$	1.28110e6	−	3.94283e6i	0.0567291	−	0.174594i
$875$	−9.85604e6	+	3.03338e7i	−0.435193	+	1.33939i
$876$	1.15741e7	−	8.40911e6i	0.509599	−	0.370245i
$877$	2.36224e7	+	1.71627e7i	1.03711	+	0.753505i	0.969720	−	0.244221i	$-0.0785323\pi$
$877$	2.36224e7	+	1.71627e7i	1.03711	+	0.753505i	0.0673917	+	0.997727i	$0.478532\pi$
$878$	8.59479e6	+	2.64521e7i	0.376270	+	1.15804i
$879$	1.49693e7			0.653474
$880$	9.86315e6	+	2.45712e6i	0.429348	+	0.106959i
$881$	4.93832e6			0.214358			0.107179	−	0.994240i	$-0.465818\pi$
$881$	4.93832e6			0.214358			0.107179	+	0.994240i	$0.465818\pi$
$882$	1.43950e6	+	4.43033e6i	0.0623075	+	0.191763i
$883$	−9.38826e6	−	6.82097e6i	−0.405213	−	0.294405i	0.366448	−	0.930439i	$-0.380574\pi$
$883$	−9.38826e6	−	6.82097e6i	−0.405213	−	0.294405i	−0.771661	+	0.636034i	$0.780574\pi$
$884$	670263.	−	486974.i	0.0288479	−	0.0209592i
$885$	1.04767e7	−	3.22440e7i	0.449641	−	1.38385i
$886$	−2.63820e6	+	8.11953e6i	−0.112908	+	0.347494i
$887$	2.27063e7	−	1.64971e7i	0.969028	−	0.704040i	0.0137983	−	0.999905i	$-0.495608\pi$
$887$	2.27063e7	−	1.64971e7i	0.969028	−	0.704040i	0.955230	+	0.295865i	$0.0956077\pi$
$888$	−1.88959e6	−	1.37287e6i	−0.0804148	−	0.0584248i
$889$	−687366.	−	2.11550e6i	−0.0291698	−	0.0897755i
$890$	1.49883e7			0.634276
$891$	1.50165e6	−	2.40418e6i	0.0633686	−	0.101455i
$892$	−8.43813e6			−0.355086
$893$	1.33079e6	+	4.09576e6i	0.0558447	+	0.171872i
$894$	5.34898e6	+	3.88626e6i	0.223835	+	0.162625i
$895$	−1.25937e7	+	9.14986e6i	−0.525528	+	0.381818i
$896$	461185.	−	1.41938e6i	0.0191913	−	0.0590648i
$897$	6.54775e6	−	2.01519e7i	0.271713	−	0.836248i
$898$	−8.57578e6	+	6.23067e6i	−0.354881	+	0.257836i
$899$	−9.24809e6	−	6.71913e6i	−0.381639	−	0.277277i
$900$	−4.50921e6	−	1.38779e7i	−0.185564	−	0.571108i
$901$	−176912.			−0.00726013
$902$	−692458.	−	9.87491e6i	−0.0283385	−	0.404126i
$903$	1.28877e7			0.525964
$904$	−4.24478e6	−	1.30641e7i	−0.172756	−	0.531690i
$905$	1.45016e7	+	1.05360e7i	0.588565	+	0.427618i
$906$	−7.08945e6	+	5.15079e6i	−0.286941	+	0.208475i
$907$	2.55053e6	−	7.84971e6i	0.102946	−	0.316837i	−0.886297	−	0.463118i	$-0.846731\pi$
$907$	2.55053e6	−	7.84971e6i	0.102946	−	0.316837i	0.989243	+	0.146282i	$0.0467305\pi$
$908$	−3.65168e6	+	1.12387e7i	−0.146987	+	0.452379i
$909$	−5.87995e6	+	4.27203e6i	−0.236028	+	0.171484i
$910$	3.17924e7	+	2.30985e7i	1.27268	+	0.924658i
$911$	−1.01272e7	−	3.11683e7i	−0.404290	−	1.24428i	−0.921486	−	0.388411i	$-0.873024\pi$
$911$	−1.01272e7	−	3.11683e7i	−0.404290	−	1.24428i	0.517196	−	0.855867i	$-0.326976\pi$
$912$	1.44888e6			0.0576826
$913$	−2.20854e6	−	3.14953e7i	−0.0876857	−	1.25046i
$914$	−6.36065e6			−0.251847
$915$	905814.	+	2.78781e6i	0.0357673	+	0.110080i
$916$	−75805.7	−	55076.1i	−0.00298513	−	0.00216882i
$917$	−2.02256e7	+	1.46948e7i	−0.794290	+	0.577085i
$918$	229780.	−	707190.i	0.00899923	−	0.0276968i
$919$	1.18735e7	−	3.65428e7i	0.463756	−	1.42729i	−0.396785	−	0.917912i	$-0.629874\pi$
$919$	1.18735e7	−	3.65428e7i	0.463756	−	1.42729i	0.860540	−	0.509382i	$-0.170126\pi$
$920$	9.66505e6	−	7.02207e6i	0.376474	−	0.273524i
$921$	1.00824e7	+	7.32531e6i	0.391666	+	0.284562i
$922$	−9.96409e6	−	3.06663e7i	−0.386021	−	1.18805i
$923$	7.74529e6			0.299249
$924$	−3.19224e6	+	5.11088e6i	−0.123003	+	0.196932i
$925$	2.36057e7			0.907116
$926$	−6.11975e6	−	1.88346e7i	−0.234534	−	0.721822i
$927$	2.06667e7	+	1.50153e7i	0.789901	+	0.573897i
$928$	−1.19860e6	+	870835.i	−0.0456883	+	0.0331945i
$929$	−7.82062e6	+	2.40694e7i	−0.297305	+	0.915010i	0.685133	+	0.728418i	$0.259744\pi$
$929$	−7.82062e6	+	2.40694e7i	−0.297305	+	0.915010i	−0.982437	+	0.186592i	$0.940256\pi$
$930$	−9.95488e6	+	3.06380e7i	−0.377423	+	1.16159i
$931$	3.78188e6	−	2.74769e6i	0.142999	−	0.103895i
$932$	−3.76298e6	−	2.73397e6i	−0.141903	−	0.103099i
$933$	8.88587e6	+	2.73479e7i	0.334192	+	1.02854i
$934$	−2.54856e6			−0.0955934
$935$	−1.83012e6	−	455920.i	−0.0684620	−	0.0170553i
$936$	−9.54791e6			−0.356220
$937$	−9.68798e6	−	2.98165e7i	−0.360483	−	1.10945i	−0.952762	−	0.303719i	$-0.901772\pi$
$937$	−9.68798e6	−	2.98165e7i	−0.360483	−	1.10945i	0.592279	−	0.805733i	$-0.298228\pi$
$938$	−6.77350e6	−	4.92124e6i	−0.251366	−	0.182628i
$939$	1.90112e7	−	1.38124e7i	0.703631	−	0.511218i
$940$	−3.83491e6	+	1.18026e7i	−0.141558	+	0.435672i
$941$	7.57340e6	−	2.33085e7i	0.278815	−	0.858105i	−0.709369	−	0.704837i	$-0.751020\pi$
$941$	7.57340e6	−	2.33085e7i	0.278815	−	0.858105i	0.988185	−	0.153268i	$-0.0489799\pi$
$942$	8.54126e6	−	6.20559e6i	0.313613	−	0.227853i
$943$	−9.41266e6	−	6.83869e6i	−0.344693	−	0.250434i
$944$	−2.63117e6	−	8.09789e6i	−0.0960988	−	0.295762i
$945$	3.52702e7			1.28478
$946$	1.41731e7	+	1.68842e7i	0.514917	+	0.613411i
$947$	−3.45546e7			−1.25208			−0.626039	−	0.779792i	$-0.715325\pi$
$947$	−3.45546e7			−1.25208			−0.626039	+	0.779792i	$0.715325\pi$
$948$	−793911.	−	2.44341e6i	−0.0286914	−	0.0883029i
$949$	7.65395e7	+	5.56092e7i	2.75880	+	2.00438i
$950$	−1.18467e7	+	8.60710e6i	−0.425879	+	0.309419i
$951$	−1.87078e6	+	5.75768e6i	−0.0670767	+	0.206441i
$952$	−85573.3	+	263368.i	−0.00306017	+	0.00941824i
$953$	−2.77779e7	+	2.01818e7i	−0.990758	+	0.719828i	−0.960087	−	0.279702i	$-0.909764\pi$
$953$	−2.77779e7	+	2.01818e7i	−0.990758	+	0.719828i	−0.0306709	+	0.999530i	$0.509764\pi$
$954$	1.64943e6	+	1.19838e6i	0.0586765	+	0.0426309i
$955$	1.11840e7	+	3.44209e7i	0.396817	+	1.22128i
$956$	1.78450e7			0.631499
$957$	5.54598e6	−	2.24198e6i	0.195748	−	0.0791319i
$958$	−1.80767e7			−0.636365
$959$	−3.09558e6	−	9.52721e6i	−0.108691	−	0.334518i
$960$	3.37780e6	+	2.45412e6i	0.118292	+	0.0859443i
$961$	−2.73410e7	+	1.98644e7i	−0.955005	+	0.693852i
$962$	4.77299e6	−	1.46897e7i	0.166285	−	0.511772i
$963$	−3.27422e6	+	1.00770e7i	−0.113774	+	0.350159i
$964$	5.83288e6	−	4.23783e6i	0.202158	−	0.146876i
$965$	−1.81442e7	−	1.31825e7i	−0.627218	−	0.455701i
$966$	2.18857e6	+	6.73573e6i	0.0754602	+	0.232243i
$967$	2.32311e7			0.798922			0.399461	−	0.916750i	$-0.369197\pi$
$967$	2.32311e7			0.798922			0.399461	+	0.916750i	$0.369197\pi$
$968$	−1.02064e7	+	1.43848e6i	−0.350093	+	0.0493418i
$969$	−268840.			−0.00919783
$970$	−2.14801e7	−	6.61089e7i	−0.733004	−	2.25595i
$971$	−7.59616e6	−	5.51894e6i	−0.258551	−	0.187848i	0.450957	−	0.892546i	$-0.351083\pi$
$971$	−7.59616e6	−	5.51894e6i	−0.258551	−	0.187848i	−0.709508	+	0.704697i	$0.751083\pi$
$972$	−1.13678e7	+	8.25920e6i	−0.385932	+	0.280396i
$973$	2.94146e6	−	9.05289e6i	0.0996050	−	0.306553i
$974$	5.44815e6	−	1.67677e7i	0.184014	−	0.566338i
$975$	−6.05485e7	+	4.39911e7i	−2.03982	+	1.48202i
$976$	595577.	+	432712.i	0.0200130	+	0.0145403i
$977$	−4.84397e6	−	1.49082e7i	−0.162355	−	0.499677i	0.836477	−	0.548002i	$-0.184612\pi$
$977$	−4.84397e6	−	1.49082e7i	−0.162355	−	0.499677i	−0.998832	+	0.0483254i	$0.984612\pi$
$978$	−1.11930e7			−0.374196
$979$	−1.40909e7	+	5.69628e6i	−0.469873	+	0.189948i
$980$	1.34708e7			0.448053
$981$	4.75268e6	+	1.46272e7i	0.157676	+	0.485278i
$982$	−2.55674e7	−	1.85758e7i	−0.846073	−	0.614708i
$983$	334216.	−	242822.i	0.0110317	−	0.00801502i	−0.582256	−	0.813006i	$-0.697830\pi$
$983$	334216.	−	242822.i	0.0110317	−	0.00801502i	0.593287	+	0.804991i	$0.297830\pi$
$984$	1.25651e6	−	3.86715e6i	0.0413694	−	0.127322i
$985$	−1.38106e7	+	4.25048e7i	−0.453548	+	1.39588i
$986$	222402.	−	161584.i	0.00728527	−	0.00529306i
$987$	−5.95199e6	−	4.32437e6i	−0.194477	−	0.141296i
$988$	2.96081e6	+	9.11244e6i	0.0964980	+	0.296990i
$989$	2.59091e7			0.842291
$990$	1.39747e7	+	1.66478e7i	0.453164	+	0.539845i
$991$	−2.22139e7			−0.718522			−0.359261	−	0.933237i	$-0.616971\pi$
$991$	−2.22139e7			−0.718522			−0.359261	+	0.933237i	$0.616971\pi$
$992$	2.50011e6	+	7.69456e6i	0.0806641	+	0.248259i
$993$	−2.17731e7	−	1.58191e7i	−0.700723	−	0.509105i
$994$	−2.09442e6	+	1.52169e6i	−0.0672354	+	0.0488494i
$995$	7.06685e6	−	2.17495e7i	0.226292	−	0.696454i
$996$	4.00755e6	−	1.23340e7i	0.128006	−	0.393962i
$997$	3.23209e7	−	2.34825e7i	1.02978	−	0.748181i	0.0615174	−	0.998106i	$-0.480406\pi$
$997$	3.23209e7	−	2.34825e7i	1.02978	−	0.748181i	0.968265	+	0.249925i	$0.0804060\pi$
$998$	−809526.	−	588155.i	−0.0257279	−	0.0186924i
$999$	−4.28383e6	−	1.31843e7i	−0.135806	−	0.417968i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.6.c.b.5.2	✓	12
3.2	odd	2		198.6.f.e.181.3		12
11.3	even	5		242.6.a.p.1.4		6
11.8	odd	10		242.6.a.o.1.4		6
11.9	even	5	inner	22.6.c.b.9.2	yes	12
33.20	odd	10		198.6.f.e.163.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.6.c.b.5.2	✓	12	1.1	even	1	trivial
22.6.c.b.9.2	yes	12	11.9	even	5	inner
198.6.f.e.163.3		12	33.20	odd	10
198.6.f.e.181.3		12	3.2	odd	2
242.6.a.o.1.4		6	11.8	odd	10
242.6.a.p.1.4		6	11.3	even	5

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:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	22.c (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.23607 + 3.80423i) q^{2} +(-8.33499 - 6.05573i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(-30.5739 + 94.0969i) q^{5} +(12.7347 - 39.1935i) q^{6} +(-73.6937 + 53.5416i) q^{7} +(-51.7771 - 37.6183i) q^{8} +(-42.2909 - 130.158i) q^{9} -395.757 q^{10} +(372.060 - 150.407i) q^{11} +164.842 q^{12} +(336.858 + 1036.74i) q^{13} +(-294.775 - 214.166i) q^{14} +(824.658 - 599.149i) q^{15} +(79.1084 - 243.470i) q^{16} +(-14.6786 + 45.1762i) q^{17} +(442.876 - 321.768i) q^{18} +(-444.428 - 322.896i) q^{19} +(-489.183 - 1505.55i) q^{20} +938.470 q^{21} +(1032.07 + 1229.49i) q^{22} +1886.68 q^{23} +(203.756 + 627.096i) q^{24} +(-5391.28 - 3916.99i) q^{25} +(-3527.62 + 2562.97i) q^{26} +(-1209.34 + 3721.97i) q^{27} +(450.376 - 1386.11i) q^{28} +(-1170.51 + 850.425i) q^{29} +(3298.63 + 2396.60i) q^{30} +(2441.52 + 7514.22i) q^{31} +1024.00 q^{32} +(-4011.94 - 999.457i) q^{33} -190.004 q^{34} +(-2784.99 - 8571.32i) q^{35} +(1771.50 + 1287.07i) q^{36} +(-2865.77 + 2082.10i) q^{37} +(679.026 - 2089.83i) q^{38} +(3470.52 - 10681.2i) q^{39} +(5122.79 - 3721.92i) q^{40} +(-4989.01 - 3624.73i) q^{41} +(1160.01 + 3570.15i) q^{42} +13732.7 q^{43} +(-3401.54 + 5445.97i) q^{44} +13540.4 q^{45} +(2332.06 + 7177.35i) q^{46} +(-6342.22 - 4607.89i) q^{47} +(-2133.76 + 1550.27i) q^{48} +(-2629.59 + 8093.04i) q^{49} +(8237.14 - 25351.3i) q^{50} +(395.921 - 287.653i) q^{51} +(-14110.5 - 10251.9i) q^{52} +(1150.89 + 3542.09i) q^{53} -15654.0 q^{54} +(2777.45 + 39608.2i) q^{55} +5829.79 q^{56} +(1748.94 + 5382.67i) q^{57} +(-4682.04 - 3401.70i) q^{58} +(26908.1 - 19549.9i) q^{59} +(-5039.86 + 15511.1i) q^{60} +(-888.633 + 2734.93i) q^{61} +(-25567.9 + 18576.2i) q^{62} +(10085.4 + 7327.50i) q^{63} +(1265.73 + 3895.53i) q^{64} -107853. q^{65} +(-1156.87 - 16497.7i) q^{66} +22978.6 q^{67} +(-234.858 - 722.819i) q^{68} +(-15725.4 - 11425.2i) q^{69} +(29164.8 - 21189.5i) q^{70} +(2195.61 - 6757.40i) q^{71} +(-2706.61 + 8330.10i) q^{72} +(70213.6 - 51013.2i) q^{73} +(-11463.1 - 8328.41i) q^{74} +(21216.0 + 65296.2i) q^{75} +8789.50 q^{76} +(-19365.5 + 31004.7i) q^{77} +44923.3 q^{78} +(-4816.20 - 14822.7i) q^{79} +(20491.2 + 14887.7i) q^{80} +(5714.40 - 4151.75i) q^{81} +(7622.53 - 23459.7i) q^{82} +(24311.5 - 74823.1i) q^{83} +(-12147.8 + 8825.90i) q^{84} +(-3802.15 - 2762.43i) q^{85} +(16974.5 + 52242.2i) q^{86} +14906.1 q^{87} +(-24922.2 - 6208.64i) q^{88} -37872.5 q^{89} +(16736.9 + 51510.9i) q^{90} +(-80333.2 - 58365.5i) q^{91} +(-24421.7 + 17743.4i) q^{92} +(25154.0 - 77416.1i) q^{93} +(9690.05 - 29822.9i) q^{94} +(43971.4 - 31947.1i) q^{95} +(-8535.03 - 6201.06i) q^{96} +(54275.9 + 167044. i) q^{97} -34038.1 q^{98} +(-35311.4 - 42065.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} - 48 q^{4} + 44 q^{5} - 100 q^{6} - 326 q^{7} - 192 q^{8} - 69 q^{9} + 96 q^{10} + 1011 q^{11} + 800 q^{12} - 246 q^{13} - 1304 q^{14} + 112 q^{15} - 768 q^{16} + 400 q^{17} - 1416 q^{18}+ \cdots - 199487 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 - 48 * q^4 + 44 * q^5 - 100 * q^6 - 326 * q^7 - 192 * q^8 - 69 * q^9 + 96 * q^10 + 1011 * q^11 + 800 * q^12 - 246 * q^13 - 1304 * q^14 + 112 * q^15 - 768 * q^16 + 400 * q^17 - 1416 * q^18 + 7535 * q^19 + 704 * q^20 - 3368 * q^21 + 484 * q^22 + 15732 * q^23 - 1600 * q^24 - 19283 * q^25 - 984 * q^26 - 27411 * q^27 + 3264 * q^28 - 2504 * q^29 + 448 * q^30 + 15336 * q^31 + 12288 * q^32 + 26213 * q^33 + 24600 * q^34 - 33916 * q^35 - 5664 * q^36 - 116 * q^37 - 34880 * q^38 + 4690 * q^39 - 3584 * q^40 - 38836 * q^41 + 19808 * q^42 + 42230 * q^43 - 4704 * q^44 + 139932 * q^45 - 35232 * q^46 - 57840 * q^47 - 125521 * q^49 + 26268 * q^50 + 16467 * q^51 - 3936 * q^52 + 131934 * q^53 + 60176 * q^54 - 53082 * q^55 + 15616 * q^56 - 90021 * q^57 - 10016 * q^58 + 36585 * q^59 - 37248 * q^60 + 43146 * q^61 - 40016 * q^62 - 52922 * q^63 - 12288 * q^64 - 133772 * q^65 - 211008 * q^66 + 325206 * q^67 + 6400 * q^68 - 103894 * q^69 + 68216 * q^70 - 172806 * q^71 - 4416 * q^72 + 49436 * q^73 - 464 * q^74 + 263915 * q^75 + 37920 * q^76 - 207094 * q^77 + 330000 * q^78 + 58364 * q^79 - 14336 * q^80 + 341038 * q^81 + 82836 * q^82 + 82035 * q^83 - 52288 * q^84 - 317604 * q^85 - 104380 * q^86 - 572732 * q^87 - 38336 * q^88 + 97958 * q^89 - 151672 * q^90 - 22162 * q^91 + 15072 * q^92 - 271316 * q^93 + 153720 * q^94 + 549736 * q^95 + 76403 * q^97 + 198656 * q^98 - 199487 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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