LMFDB - Embedded newform 38.5.d.a.27.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,5,Mod(27,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("38.27");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	38.d (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.92805859719$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 1024 x^{14} - 7028 x^{13} + 404698 x^{12} - 2337188 x^{11} + 77836288 x^{10} + \cdots + 23840536514409 $ x^16 - 8x^15 + 1024x^14 - 7028x^13 + 404698x^12 - 2337188x^11 + 77836288x^10 - 367923764x^9 + 7565874847x^8 - 28081380444x^7 + 352870494000x^6 - 961846520868x^5 + 6856327325898x^4 - 12141615583188x^3 + 32749209391860x^2 - 26834137576128*x + 23840536514409
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			27.4
Root			$0.500000 - 15.9560i$ of defining polynomial
Character	$\chi$	$=$	38.27
Dual form			38.5.d.a.31.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.44949 - 1.41421i) q^{2} +(14.2931 + 8.25212i) q^{3} +(4.00000 + 6.92820i) q^{4} +(-13.5555 + 23.4789i) q^{5} +(-23.3405 - 40.4270i) q^{6} -45.5687 q^{7} -22.6274i q^{8} +(95.6949 + 165.748i) q^{9} +O(q^{10})$	\(q+(-2.44949 - 1.41421i) q^{2} +(14.2931 + 8.25212i) q^{3} +(4.00000 + 6.92820i) q^{4} +(-13.5555 + 23.4789i) q^{5} +(-23.3405 - 40.4270i) q^{6} -45.5687 q^{7} -22.6274i q^{8} +(95.6949 + 165.748i) q^{9} +(66.4083 - 38.3408i) q^{10} +108.933 q^{11} +132.034i q^{12} +(38.0933 - 21.9932i) q^{13} +(111.620 + 64.4439i) q^{14} +(-387.501 + 223.724i) q^{15} +(-32.0000 + 55.4256i) q^{16} +(248.218 - 429.926i) q^{17} -541.332i q^{18} +(168.123 + 319.462i) q^{19} -216.888 q^{20} +(-651.317 - 376.038i) q^{21} +(-266.830 - 154.054i) q^{22} +(-360.199 - 623.882i) q^{23} +(186.724 - 323.416i) q^{24} +(-55.0047 - 95.2709i) q^{25} -124.412 q^{26} +1821.90i q^{27} +(-182.275 - 315.709i) q^{28} +(542.493 - 313.209i) q^{29} +1265.57 q^{30} -383.335i q^{31} +(156.767 - 90.5097i) q^{32} +(1556.99 + 898.926i) q^{33} +(-1216.01 + 702.067i) q^{34} +(617.708 - 1069.90i) q^{35} +(-765.559 + 1325.99i) q^{36} +1271.63i q^{37} +(39.9727 - 1020.28i) q^{38} +725.962 q^{39} +(531.266 + 306.727i) q^{40} +(-2510.24 - 1449.29i) q^{41} +(1063.60 + 1842.20i) q^{42} +(896.735 - 1553.19i) q^{43} +(435.731 + 754.708i) q^{44} -5188.78 q^{45} +2037.59i q^{46} +(59.5867 + 103.207i) q^{47} +(-914.758 + 528.136i) q^{48} -324.494 q^{49} +311.153i q^{50} +(7095.60 - 4096.65i) q^{51} +(304.747 + 175.945i) q^{52} +(760.310 - 438.965i) q^{53} +(2576.56 - 4462.73i) q^{54} +(-1476.64 + 2557.62i) q^{55} +1031.10i q^{56} +(-233.246 + 5953.46i) q^{57} -1771.78 q^{58} +(733.885 + 423.708i) q^{59} +(-3100.01 - 1789.79i) q^{60} +(1523.85 + 2639.38i) q^{61} +(-542.117 + 938.974i) q^{62} +(-4360.69 - 7552.94i) q^{63} -512.000 q^{64} +1192.52i q^{65} +(-2542.55 - 4403.82i) q^{66} +(-740.319 + 427.423i) q^{67} +3971.49 q^{68} -11889.6i q^{69} +(-3026.14 + 1747.14i) q^{70} +(4849.36 + 2799.78i) q^{71} +(3750.46 - 2165.33i) q^{72} +(-2747.54 + 4758.89i) q^{73} +(1798.35 - 3114.84i) q^{74} -1815.62i q^{75} +(-1540.81 + 2442.63i) q^{76} -4963.93 q^{77} +(-1778.24 - 1026.66i) q^{78} +(-8841.44 - 5104.61i) q^{79} +(-867.554 - 1502.65i) q^{80} +(-7283.25 + 12615.0i) q^{81} +(4099.21 + 7100.04i) q^{82} +12014.3 q^{83} -6016.61i q^{84} +(6729.45 + 11655.8i) q^{85} +(-4393.09 + 2536.35i) q^{86} +10338.5 q^{87} -2464.87i q^{88} +(-2610.25 + 1507.03i) q^{89} +(12709.9 + 7338.04i) q^{90} +(-1735.86 + 1002.20i) q^{91} +(2881.59 - 4991.06i) q^{92} +(3163.32 - 5479.04i) q^{93} -337.073i q^{94} +(-9779.59 - 383.146i) q^{95} +2987.59 q^{96} +(-7644.86 - 4413.76i) q^{97} +(794.844 + 458.904i) q^{98} +(10424.3 + 18055.4i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{3} + 64 q^{4} - 18 q^{5} - 16 q^{6} + 72 q^{7} + 352 q^{9}+O(q^{10}) $ 16 * q - 12 * q^3 + 64 * q^4 - 18 * q^5 - 16 * q^6 + 72 * q^7 + 352 * q^9	\( 16 q - 12 q^{3} + 64 q^{4} - 18 q^{5} - 16 q^{6} + 72 q^{7} + 352 q^{9} - 84 q^{11} + 450 q^{13} + 288 q^{14} - 390 q^{15} - 512 q^{16} + 606 q^{17} - 306 q^{19} - 288 q^{20} - 2160 q^{21} - 1680 q^{22} - 54 q^{23} + 128 q^{24} - 434 q^{25} + 1344 q^{26} + 288 q^{28} - 4914 q^{29} + 2752 q^{30} + 7890 q^{33} - 1536 q^{34} + 2328 q^{35} - 2816 q^{36} + 1344 q^{38} + 7620 q^{39} - 1692 q^{41} + 2080 q^{42} - 7402 q^{43} - 336 q^{44} - 16720 q^{45} + 3198 q^{47} + 768 q^{48} + 24816 q^{49} + 10710 q^{51} + 3600 q^{52} + 3870 q^{53} - 16 q^{54} - 13588 q^{55} + 3702 q^{57} - 1728 q^{58} - 18288 q^{59} - 3120 q^{60} - 6522 q^{61} - 6144 q^{62} - 15676 q^{63} - 8192 q^{64} + 4960 q^{66} - 30168 q^{67} + 9696 q^{68} + 15360 q^{70} + 35874 q^{71} + 5376 q^{72} - 8080 q^{73} - 9120 q^{74} + 480 q^{76} + 34560 q^{77} - 46560 q^{78} - 30738 q^{79} - 1152 q^{80} - 30920 q^{81} + 6720 q^{82} - 1476 q^{83} + 33626 q^{85} + 288 q^{86} + 113100 q^{87} + 19782 q^{89} + 44256 q^{90} - 34260 q^{91} + 432 q^{92} - 4272 q^{93} - 23706 q^{95} + 2048 q^{96} - 9936 q^{97} + 12672 q^{98} + 3848 q^{99}+O(q^{100}) \) 16 * q - 12 * q^3 + 64 * q^4 - 18 * q^5 - 16 * q^6 + 72 * q^7 + 352 * q^9 - 84 * q^11 + 450 * q^13 + 288 * q^14 - 390 * q^15 - 512 * q^16 + 606 * q^17 - 306 * q^19 - 288 * q^20 - 2160 * q^21 - 1680 * q^22 - 54 * q^23 + 128 * q^24 - 434 * q^25 + 1344 * q^26 + 288 * q^28 - 4914 * q^29 + 2752 * q^30 + 7890 * q^33 - 1536 * q^34 + 2328 * q^35 - 2816 * q^36 + 1344 * q^38 + 7620 * q^39 - 1692 * q^41 + 2080 * q^42 - 7402 * q^43 - 336 * q^44 - 16720 * q^45 + 3198 * q^47 + 768 * q^48 + 24816 * q^49 + 10710 * q^51 + 3600 * q^52 + 3870 * q^53 - 16 * q^54 - 13588 * q^55 + 3702 * q^57 - 1728 * q^58 - 18288 * q^59 - 3120 * q^60 - 6522 * q^61 - 6144 * q^62 - 15676 * q^63 - 8192 * q^64 + 4960 * q^66 - 30168 * q^67 + 9696 * q^68 + 15360 * q^70 + 35874 * q^71 + 5376 * q^72 - 8080 * q^73 - 9120 * q^74 + 480 * q^76 + 34560 * q^77 - 46560 * q^78 - 30738 * q^79 - 1152 * q^80 - 30920 * q^81 + 6720 * q^82 - 1476 * q^83 + 33626 * q^85 + 288 * q^86 + 113100 * q^87 + 19782 * q^89 + 44256 * q^90 - 34260 * q^91 + 432 * q^92 - 4272 * q^93 - 23706 * q^95 + 2048 * q^96 - 9936 * q^97 + 12672 * q^98 + 3848 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−2.44949	−	1.41421i	−0.612372	−	0.353553i
$2$	−2.44949	−	1.41421i	−0.612372	−	0.353553i
$3$	14.2931	+	8.25212i	1.58812	+	0.916902i	0.993617	+	0.112810i	$0.0359851\pi$
$3$	14.2931	+	8.25212i	1.58812	+	0.916902i	0.594504	+	0.804092i	$0.297348\pi$
$4$	4.00000	+	6.92820i	0.250000	+	0.433013i
$5$	−13.5555	+	23.4789i	−0.542221	+	0.939155i	0.456555	+	0.889695i	$0.349083\pi$
$5$	−13.5555	+	23.4789i	−0.542221	+	0.939155i	−0.998776	+	0.0494593i	$0.984250\pi$
$6$	−23.3405	−	40.4270i	−0.648348	−	1.12297i
$7$	−45.5687			−0.929973			−0.464987	−	0.885318i	$-0.653941\pi$
$7$	−45.5687			−0.929973			−0.464987	+	0.885318i	$0.653941\pi$
$8$		−	22.6274i		−	0.353553i
$9$	95.6949	+	165.748i	1.18142	+	2.04628i
$10$	66.4083	−	38.3408i	0.664083	−	0.383408i
$11$	108.933			0.900271			0.450135	−	0.892960i	$-0.351376\pi$
$11$	108.933			0.900271			0.450135	+	0.892960i	$0.351376\pi$
$12$			132.034i			0.916902i
$13$	38.0933	−	21.9932i	0.225404	−	0.130137i	−0.383046	−	0.923729i	$-0.625125\pi$
$13$	38.0933	−	21.9932i	0.225404	−	0.130137i	0.608450	+	0.793592i	$0.291792\pi$
$14$	111.620	+	64.4439i	0.569490	+	0.328795i
$15$	−387.501	+	223.724i	−1.72223	+	0.994327i
$16$	−32.0000	+	55.4256i	−0.125000	+	0.216506i
$17$	248.218	−	429.926i	0.858886	−	1.48763i	−0.0141067	−	0.999900i	$-0.504490\pi$
$17$	248.218	−	429.926i	0.858886	−	1.48763i	0.872993	−	0.487733i	$-0.162176\pi$
$18$		−	541.332i		−	1.67078i
$19$	168.123	+	319.462i	0.465713	+	0.884936i
$19$	168.123	+	319.462i	0.465713	+	0.884936i
$20$	−216.888			−0.542221
$21$	−651.317	−	376.038i	−1.47691	−	0.852695i
$22$	−266.830	−	154.054i	−0.551301	−	0.318294i
$23$	−360.199	−	623.882i	−0.680905	−	1.17936i	−0.974705	−	0.223495i	$-0.928253\pi$
$23$	−360.199	−	623.882i	−0.680905	−	1.17936i	0.293800	−	0.955867i	$-0.405080\pi$
$24$	186.724	−	323.416i	0.324174	−	0.561486i
$25$	−55.0047	−	95.2709i	−0.0880075	−	0.152433i
$26$	−124.412			−0.184042
$27$			1821.90i			2.49918i
$28$	−182.275	−	315.709i	−0.232493	−	0.402690i
$29$	542.493	−	313.209i	0.645058	−	0.372424i	−0.141503	−	0.989938i	$-0.545193\pi$
$29$	542.493	−	313.209i	0.645058	−	0.372424i	0.786560	+	0.617514i	$0.211860\pi$
$30$	1265.57			1.40619
$31$		−	383.335i		−	0.398891i	−0.979909	−	0.199446i	$-0.936086\pi$
$31$		−	383.335i		−	0.398891i	0.979909	−	0.199446i	$-0.0639142\pi$
$32$	156.767	−	90.5097i	0.153093	−	0.0883883i
$33$	1556.99	+	898.926i	1.42974	+	0.825460i
$34$	−1216.01	+	702.067i	−1.05192	+	0.607324i
$35$	617.708	−	1069.90i	0.504251	−	0.873389i
$36$	−765.559	+	1325.99i	−0.590709	+	1.02314i
$37$			1271.63i			0.928873i	0.885607	+	0.464436i	$0.153743\pi$
$37$			1271.63i			0.928873i	−0.885607	+	0.464436i	$0.846257\pi$
$38$	39.9727	−	1020.28i	0.0276819	−	0.706565i
$39$	725.962			0.477292
$40$	531.266	+	306.727i	0.332041	+	0.191704i
$41$	−2510.24	−	1449.29i	−1.49330	−	0.862159i	−0.493333	−	0.869841i	$-0.664222\pi$
$41$	−2510.24	−	1449.29i	−1.49330	−	0.862159i	−0.999970	+	0.00768156i	$0.997555\pi$
$42$	1063.60	+	1842.20i	0.602946	+	1.04433i
$43$	896.735	−	1553.19i	0.484984	−	0.840017i	−0.514867	−	0.857270i	$-0.672159\pi$
$43$	896.735	−	1553.19i	0.484984	−	0.840017i	0.999851	+	0.0172532i	$0.00549212\pi$
$44$	435.731	+	754.708i	0.225068	+	0.389829i
$45$	−5188.78			−2.56236
$46$			2037.59i			0.962945i
$47$	59.5867	+	103.207i	0.0269745	+	0.0467213i	0.879198	−	0.476457i	$-0.158079\pi$
$47$	59.5867	+	103.207i	0.0269745	+	0.0467213i	−0.852223	+	0.523179i	$0.824746\pi$
$48$	−914.758	+	528.136i	−0.397030	+	0.229226i
$49$	−324.494			−0.135149
$50$			311.153i			0.124461i
$51$	7095.60	−	4096.65i	2.72803	−	1.57503i
$52$	304.747	+	175.945i	0.112702	+	0.0650686i
$53$	760.310	−	438.965i	0.270669	−	0.156271i	−0.358523	−	0.933521i	$-0.616719\pi$
$53$	760.310	−	438.965i	0.270669	−	0.156271i	0.629192	+	0.777250i	$0.283386\pi$
$54$	2576.56	−	4462.73i	0.883593	−	1.53043i
$55$	−1476.64	+	2557.62i	−0.488146	+	0.845494i
$56$			1031.10i			0.328795i
$57$	−233.246	+	5953.46i	−0.0717900	+	1.83240i
$58$	−1771.78			−0.526687
$59$	733.885	+	423.708i	0.210826	+	0.121720i	0.601695	−	0.798726i	$-0.294492\pi$
$59$	733.885	+	423.708i	0.210826	+	0.121720i	−0.390869	+	0.920446i	$0.627826\pi$
$60$	−3100.01	−	1789.79i	−0.861113	−	0.497164i
$61$	1523.85	+	2639.38i	0.409527	+	0.709321i	0.994837	−	0.101489i	$-0.0323606\pi$
$61$	1523.85	+	2639.38i	0.409527	+	0.709321i	−0.585310	+	0.810809i	$0.699027\pi$
$62$	−542.117	+	938.974i	−0.141029	+	0.244270i
$63$	−4360.69	−	7552.94i	−1.09869	−	1.90298i
$64$	−512.000			−0.125000
$65$			1192.52i			0.282253i
$66$	−2542.55	−	4403.82i	−0.583689	−	1.01098i
$67$	−740.319	+	427.423i	−0.164918	+	0.0952157i	−0.580188	−	0.814483i	$-0.697021\pi$
$67$	−740.319	+	427.423i	−0.164918	+	0.0952157i	0.415269	+	0.909699i	$0.363687\pi$
$68$	3971.49			0.858886
$69$		−	11889.6i		−	2.49729i
$70$	−3026.14	+	1747.14i	−0.617579	+	0.356559i
$71$	4849.36	+	2799.78i	0.961984	+	0.555401i	0.896783	−	0.442471i	$-0.145898\pi$
$71$	4849.36	+	2799.78i	0.961984	+	0.555401i	0.0652006	+	0.997872i	$0.479231\pi$
$72$	3750.46	−	2165.33i	0.723468	−	0.417695i
$73$	−2747.54	+	4758.89i	−0.515584	+	0.893017i	0.484253	+	0.874928i	$0.339091\pi$
$73$	−2747.54	+	4758.89i	−0.515584	+	0.893017i	−0.999836	+	0.0180887i	$0.994242\pi$
$74$	1798.35	−	3114.84i	0.328406	−	0.568816i
$75$		−	1815.62i		−	0.322777i
$76$	−1540.81	+	2442.63i	−0.266760	+	0.422894i
$77$	−4963.93			−0.837228
$78$	−1778.24	−	1026.66i	−0.292281	−	0.168748i
$79$	−8841.44	−	5104.61i	−1.41667	−	0.817915i	−0.420666	−	0.907216i	$-0.638203\pi$
$79$	−8841.44	−	5104.61i	−1.41667	−	0.817915i	−0.996005	+	0.0893006i	$0.971537\pi$
$80$	−867.554	−	1502.65i	−0.135555	−	0.234789i
$81$	−7283.25	+	12615.0i	−1.11008	+	1.92272i
$82$	4099.21	+	7100.04i	0.609639	+	1.05592i
$83$	12014.3			1.74398			0.871992	−	0.489520i	$-0.162828\pi$
$83$	12014.3			1.74398			0.871992	+	0.489520i	$0.162828\pi$
$84$		−	6016.61i		−	0.852695i
$85$	6729.45	+	11655.8i	0.931412	+	1.61325i
$86$	−4393.09	+	2536.35i	−0.593982	+	0.342935i
$87$	10338.5			1.36591
$88$		−	2464.87i		−	0.318294i
$89$	−2610.25	+	1507.03i	−0.329535	+	0.190257i	−0.655635	−	0.755078i	$-0.727599\pi$
$89$	−2610.25	+	1507.03i	−0.329535	+	0.190257i	0.326100	+	0.945335i	$0.394265\pi$
$90$	12709.9	+	7338.04i	1.56912	+	0.905931i
$91$	−1735.86	+	1002.20i	−0.209620	+	0.121024i
$92$	2881.59	−	4991.06i	0.340452	−	0.589681i
$93$	3163.32	−	5479.04i	0.365744	−	0.633488i
$94$		−	337.073i		−	0.0381477i
$95$	−9779.59	−	383.146i	−1.08361	−	0.0424539i
$96$	2987.59			0.324174
$97$	−7644.86	−	4413.76i	−0.812505	−	0.469100i	0.0353202	−	0.999376i	$-0.488755\pi$
$97$	−7644.86	−	4413.76i	−0.812505	−	0.469100i	−0.847825	+	0.530276i	$0.822088\pi$
$98$	794.844	+	458.904i	0.0827618	+	0.0477825i
$99$	10424.3	+	18055.4i	1.06360	+	1.84220i
$100$	440.037	−	762.167i	0.0440037	−	0.0762167i
$101$	−2093.45	−	3625.97i	−0.205220	−	0.355452i	0.744983	−	0.667084i	$-0.232458\pi$
$101$	−2093.45	−	3625.97i	−0.205220	−	0.355452i	−0.950203	+	0.311632i	$0.899124\pi$
$102$	−23174.1			−2.22743
$103$		−	1131.66i		−	0.106669i	−0.998577	−	0.0533347i	$-0.983015\pi$
$103$		−	1131.66i		−	0.106669i	0.998577	−	0.0533347i	$-0.0169850\pi$
$104$	−497.649	−	861.953i	−0.0460104	−	0.0796924i
$105$	17657.9	−	10194.8i	1.60162	−	0.924698i
$106$	−2483.16			−0.221000
$107$			7895.65i			0.689636i	0.938669	+	0.344818i	$0.112059\pi$
$107$			7895.65i			0.689636i	−0.938669	+	0.344818i	$0.887941\pi$
$108$	−12622.5	+	7287.60i	−1.08218	+	0.624794i
$109$	−6676.28	−	3854.55i	−0.561929	−	0.324430i	0.191990	−	0.981397i	$-0.438506\pi$
$109$	−6676.28	−	3854.55i	−0.561929	−	0.324430i	−0.753919	+	0.656967i	$0.771839\pi$
$110$	7234.04	−	4176.57i	0.597854	−	0.345171i
$111$	−10493.6	+	18175.5i	−0.851685	+	1.47516i
$112$	1458.20	−	2525.67i	0.116247	−	0.201345i
$113$		−	16731.4i		−	1.31031i	−0.755494	−	0.655156i	$-0.772603\pi$
$113$		−	16731.4i		−	1.31031i	0.755494	−	0.655156i	$-0.227397\pi$
$114$	8990.80	−	14253.1i	0.691813	−	1.09673i
$115$	19530.7			1.47680
$116$	4339.95	+	2505.67i	0.322529	+	0.186212i
$117$	7290.67	+	4209.27i	0.532594	+	0.307493i
$118$	−1198.43	−	2075.74i	−0.0860693	−	0.149076i
$119$	−11311.0	+	19591.2i	−0.798741	+	1.38346i
$120$	5062.29	+	8768.14i	0.351548	+	0.608899i
$121$	−2774.65			−0.189512
$122$		−	8620.19i		−	0.579158i
$123$	−23919.4	−	41429.6i	−1.58103	−	2.73843i
$124$	2655.82	−	1533.34i	0.172725	−	0.0997229i
$125$	−13961.9			−0.893564
$126$			24667.8i			1.55378i
$127$	19553.2	−	11289.1i	1.21230	−	0.699924i	0.249043	−	0.968493i	$-0.419884\pi$
$127$	19553.2	−	11289.1i	1.21230	−	0.699924i	0.963260	+	0.268569i	$0.0865507\pi$
$128$	1254.14	+	724.077i	0.0765466	+	0.0441942i
$129$	25634.2	−	14799.9i	1.54043	−	0.889365i
$130$	1686.47	−	2921.06i	0.0997913	−	0.172844i
$131$	−1319.50	+	2285.44i	−0.0768895	+	0.133176i	−0.901906	−	0.431932i	$-0.857832\pi$
$131$	−1319.50	+	2285.44i	−0.0768895	+	0.133176i	0.825017	+	0.565108i	$0.191166\pi$
$132$			14382.8i			0.825460i
$133$	−7661.13	−	14557.5i	−0.433101	−	0.822967i
$134$	2417.87			0.134655
$135$	−42776.2	−	24696.8i	−2.34711	−	1.35511i
$136$	−9728.12	−	5616.53i	−0.525958	−	0.303662i
$137$	−10850.7	−	18794.0i	−0.578118	−	1.00133i	−0.995695	−	0.0926888i	$-0.970454\pi$
$137$	−10850.7	−	18794.0i	−0.578118	−	1.00133i	0.417577	−	0.908642i	$-0.362879\pi$
$138$	−16814.4	+	29123.5i	−0.882926	+	1.52927i
$139$	1417.08	+	2454.45i	0.0733440	+	0.127036i	0.900365	−	0.435136i	$-0.143300\pi$
$139$	1417.08	+	2454.45i	0.0733440	+	0.127036i	−0.827021	+	0.562171i	$0.809966\pi$
$140$	9883.32			0.504251
$141$			1966.87i			0.0989320i
$142$	−7918.97	−	13716.1i	−0.392728	−	0.680225i
$143$	4149.61	−	2395.78i	0.202925	−	0.117159i
$144$	−12249.0			−0.590709
$145$			16982.8i			0.807745i
$146$	13460.2	−	7771.23i	0.631458	−	0.364573i
$147$	−4638.02	−	2677.76i	−0.214634	−	0.123919i
$148$	−8810.09	+	5086.51i	−0.402214	+	0.232218i
$149$	−19366.3	+	33543.4i	−0.872315	+	1.51089i	−0.0127203	+	0.999919i	$0.504049\pi$
$149$	−19366.3	+	33543.4i	−0.872315	+	1.51089i	−0.859595	+	0.510976i	$0.829284\pi$
$150$	−2567.67	+	4447.34i	−0.114119	+	0.197660i
$151$			3211.72i			0.140859i	0.997517	+	0.0704293i	$0.0224369\pi$
$151$			3211.72i			0.140859i	−0.997517	+	0.0704293i	$0.977563\pi$
$152$	7228.59	−	3804.18i	0.312872	−	0.164655i
$153$	95012.8			4.05882
$154$	12159.1	+	7020.05i	0.512695	+	0.296005i
$155$	9000.26	+	5196.30i	0.374621	+	0.216287i
$156$	2903.85	+	5029.61i	0.119323	+	0.206674i
$157$	−1918.57	+	3323.07i	−0.0778357	+	0.134815i	−0.902316	−	0.431075i	$-0.858134\pi$
$157$	−1918.57	+	3323.07i	−0.0778357	+	0.134815i	0.824480	+	0.565891i	$0.191468\pi$
$158$	14438.0	+	25007.4i	0.578353	+	1.00174i
$159$	14489.6			0.573140
$160$			4907.63i			0.191704i
$161$	16413.8	+	28429.5i	0.633223	+	1.09678i
$162$	35680.5	−	20600.1i	1.35957	−	0.784947i
$163$	3719.78			0.140005			0.0700023	−	0.997547i	$-0.477699\pi$
$163$	3719.78			0.140005			0.0700023	+	0.997547i	$0.477699\pi$
$164$		−	23188.6i		−	0.862159i
$165$	−42211.5	+	24370.8i	−1.55047	+	0.895164i
$166$	−29428.9	−	16990.8i	−1.06797	−	0.616592i
$167$	16952.2	−	9787.38i	0.607847	−	0.350940i	−0.164276	−	0.986414i	$-0.552529\pi$
$167$	16952.2	−	9787.38i	0.607847	−	0.350940i	0.772122	+	0.635474i	$0.219195\pi$
$168$	−8508.78	+	14737.6i	−0.301473	+	0.522167i
$169$	−13313.1	+	23059.0i	−0.466129	+	0.807358i
$170$		−	38067.5i		−	1.31722i
$171$	−36861.8	+	58436.9i	−1.26062	+	1.99846i
$172$	14347.8			0.484984
$173$	6314.53	+	3645.69i	0.210984	+	0.121811i	0.601768	−	0.798671i	$-0.294463\pi$
$173$	6314.53	+	3645.69i	0.210984	+	0.121811i	−0.390785	+	0.920482i	$0.627796\pi$
$174$	−25324.2	−	14620.9i	−0.836443	−	0.482921i
$175$	2506.49	+	4341.37i	0.0818446	+	0.141759i
$176$	−3485.85	+	6037.67i	−0.112534	+	0.194914i
$177$	6992.99	+	12112.2i	0.223211	+	0.386613i
$178$	8525.03			0.269064
$179$		−	16666.6i		−	0.520164i	−0.965587	−	0.260082i	$-0.916250\pi$
$179$		−	16666.6i		−	0.520164i	0.965587	−	0.260082i	$-0.0837496\pi$
$180$	−20755.1	−	35948.9i	−0.640590	−	1.10953i
$181$	27509.3	−	15882.5i	0.839696	−	0.484799i	−0.0174648	−	0.999847i	$-0.505559\pi$
$181$	27509.3	−	15882.5i	0.839696	−	0.484799i	0.857161	+	0.515049i	$0.172226\pi$
$182$	5669.30			0.171154
$183$			50299.9i			1.50198i
$184$	−14116.8	+	8150.37i	−0.416967	+	0.240736i
$185$	−29856.3	−	17237.6i	−0.872355	−	0.503654i
$186$	−15497.1	+	8947.23i	−0.447944	+	0.258620i
$187$	27039.1	−	46833.1i	0.773230	−	1.33927i
$188$	−476.694	+	825.658i	−0.0134873	+	0.0233606i
$189$		−	83021.6i		−	2.32417i
$190$	23413.2	+	14768.9i	0.648564	+	0.409112i
$191$	−50709.9			−1.39004			−0.695018	−	0.718993i	$-0.744603\pi$
$191$	−50709.9			−1.39004			−0.695018	+	0.718993i	$0.744603\pi$
$192$	−7318.06	−	4225.08i	−0.198515	−	0.114613i
$193$	−28922.8	−	16698.6i	−0.776471	−	0.448295i	0.0587074	−	0.998275i	$-0.481302\pi$
$193$	−28922.8	−	16698.6i	−0.776471	−	0.448295i	−0.835178	+	0.549980i	$0.814635\pi$
$194$	12484.0	+	21622.9i	0.331704	+	0.574528i
$195$	−9840.79	+	17044.8i	−0.258798	+	0.448251i
$196$	−1297.98	−	2248.16i	−0.0337874	−	0.0585214i
$197$	−57376.1			−1.47842			−0.739211	−	0.673473i	$-0.764802\pi$
$197$	−57376.1			−1.47842			−0.739211	+	0.673473i	$0.764802\pi$
$198$		−	58968.8i		−	1.50415i
$199$	11030.4	+	19105.3i	0.278539	+	0.482444i	0.971022	−	0.238990i	$-0.0768164\pi$
$199$	11030.4	+	19105.3i	0.278539	+	0.482444i	−0.692483	+	0.721435i	$0.743483\pi$
$200$	−2155.73	+	1244.61i	−0.0538934	+	0.0311153i
$201$	−14108.6			−0.349214
$202$			11842.4i			0.290225i
$203$	−24720.7	+	14272.5i	−0.599886	+	0.346345i
$204$	56764.8	+	32773.2i	1.36401	+	0.787514i
$205$	68055.3	−	39291.8i	1.61940	−	0.934962i
$206$	−1600.40	+	2771.98i	−0.0377134	+	0.0653215i
$207$	68938.4	−	119405.i	1.60887	−	2.78664i
$208$			2815.13i			0.0650686i
$209$	18314.1	+	34799.9i	0.419268	+	0.796682i
$210$	−57670.5			−1.30772
$211$	−5501.42	−	3176.25i	−0.123569	−	0.0713427i	0.436941	−	0.899490i	$-0.356062\pi$
$211$	−5501.42	−	3176.25i	−0.123569	−	0.0713427i	−0.560511	+	0.828147i	$0.689395\pi$
$212$	6082.48	+	3511.72i	0.135335	+	0.0781354i
$213$	46208.2	+	80035.0i	1.01850	+	1.76409i
$214$	11166.1	−	19340.3i	0.243823	−	0.422314i
$215$	24311.4	+	42108.6i	0.525937	+	0.910950i
$216$	41224.9			0.883593
$217$			17468.1i			0.370958i
$218$	10902.3	+	18883.4i	0.229407	+	0.397344i
$219$	−78541.8	+	45346.1i	−1.63762	+	0.945479i
$220$	−23626.3			−0.488146
$221$		−	21836.4i		−	0.447092i
$222$	51408.0	−	29680.4i	1.04310	−	0.602232i
$223$	4247.34	+	2452.20i	0.0854096	+	0.0493113i	0.542097	−	0.840316i	$-0.317631\pi$
$223$	4247.34	+	2452.20i	0.0854096	+	0.0493113i	−0.456687	+	0.889627i	$0.650964\pi$
$224$	−7143.68	+	4124.41i	−0.142373	+	0.0821988i
$225$	10527.3	−	18233.9i	0.207947	−	0.360175i
$226$	−23661.7	+	40983.3i	−0.463265	+	0.802398i
$227$		−	13029.5i		−	0.252858i	−0.991976	−	0.126429i	$-0.959648\pi$
$227$		−	13029.5i		−	0.252858i	0.991976	−	0.126429i	$-0.0403515\pi$
$228$	−42179.8	+	22197.9i	−0.811399	+	0.427014i
$229$	3538.98			0.0674849			0.0337425	−	0.999431i	$-0.489257\pi$
$229$	3538.98			0.0674849			0.0337425	+	0.999431i	$0.489257\pi$
$230$	−47840.3	−	27620.6i	−0.904354	−	0.522129i
$231$	−70949.8	−	40962.9i	−1.32962	−	0.767656i
$232$	−7087.10	−	12275.2i	−0.131672	−	0.228062i
$233$	−8283.86	+	14348.1i	−0.152588	+	0.264290i	−0.932178	−	0.362000i	$-0.882094\pi$
$233$	−8283.86	+	14348.1i	−0.152588	+	0.264290i	0.779590	+	0.626290i	$0.215427\pi$
$234$	−11905.6	−	20621.1i	−0.217430	−	0.376601i
$235$	−3230.92			−0.0585046
$236$			6779.34i			0.121720i
$237$	−84247.7	−	145921.i	−1.49990	−	2.59790i
$238$	55412.2	−	31992.3i	0.978254	−	0.564795i
$239$	50399.8			0.882334			0.441167	−	0.897425i	$-0.354565\pi$
$239$	50399.8			0.882334			0.441167	+	0.897425i	$0.354565\pi$
$240$		−	28636.6i		−	0.497164i
$241$	28633.8	−	16531.7i	0.492997	−	0.284632i	−0.232820	−	0.972520i	$-0.574795\pi$
$241$	28633.8	−	16531.7i	0.492997	−	0.284632i	0.725817	+	0.687888i	$0.241462\pi$
$242$	6796.47	+	3923.94i	0.116052	+	0.0670027i
$243$	−80397.5	+	46417.5i	−1.36154	+	0.786085i
$244$	−12190.8	+	21115.1i	−0.204763	+	0.354660i
$245$	4398.69	−	7618.75i	0.0732809	−	0.126926i
$246$			135309.i			2.23592i
$247$	13430.3	+	8471.81i	0.220137	+	0.138862i
$248$	−8673.87			−0.141029
$249$	171722.	+	99143.5i	2.76966	+	1.59906i
$250$	34199.6	+	19745.2i	0.547194	+	0.315923i
$251$	6219.69	+	10772.8i	0.0987237	+	0.170994i	0.911157	−	0.412060i	$-0.135191\pi$
$251$	6219.69	+	10772.8i	0.0987237	+	0.170994i	−0.812433	+	0.583055i	$0.801857\pi$
$252$	34885.5	−	60423.5i	0.549344	−	0.951492i
$253$	−39237.4	−	67961.3i	−0.612999	−	1.06175i
$254$	−63860.6			−0.989841
$255$			222129.i			3.41605i
$256$	−2048.00	−	3547.24i	−0.0312500	−	0.0541266i
$257$	39832.7	−	22997.4i	0.603077	−	0.348187i	−0.167174	−	0.985927i	$-0.553464\pi$
$257$	39832.7	−	22997.4i	0.603077	−	0.348187i	0.770251	+	0.637741i	$0.220131\pi$
$258$	−83721.1			−1.25775
$259$		−	57946.4i		−	0.863827i
$260$	−8262.00	+	4770.07i	−0.122219	+	0.0705631i
$261$	103828.	+	59945.0i	1.52417	+	0.879978i
$262$	6464.20	−	3732.11i	0.0941700	−	0.0543691i
$263$	26246.1	−	45459.6i	0.379449	−	0.657225i	−0.611533	−	0.791219i	$-0.709447\pi$
$263$	26246.1	−	45459.6i	0.379449	−	0.657225i	0.990982	+	0.133994i	$0.0427803\pi$
$264$	20340.4	−	35230.6i	0.291844	−	0.505489i
$265$			23801.6i			0.338934i
$266$	−1821.50	+	46492.8i	−0.0257434	+	0.657086i
$267$	−49744.6			−0.697788
$268$	−5922.55	−	3419.39i	−0.0824592	−	0.0476078i
$269$	−27562.0	−	15913.0i	−0.380896	−	0.219911i	0.297312	−	0.954780i	$-0.403910\pi$
$269$	−27562.0	−	15913.0i	−0.380896	−	0.219911i	−0.678208	+	0.734870i	$0.737243\pi$
$270$	69853.2	+	120989.i	0.958205	+	1.65966i
$271$	23483.6	−	40674.8i	0.319761	−	0.553843i	−0.660677	−	0.750670i	$-0.729731\pi$
$271$	23483.6	−	40674.8i	0.319761	−	0.553843i	0.980438	+	0.196828i	$0.0630640\pi$
$272$	15886.0	+	27515.3i	0.214721	+	0.371908i
$273$	−33081.1			−0.443869
$274$			61380.9i			0.817583i
$275$	−5991.81	−	10378.1i	−0.0792306	−	0.137231i
$276$	82373.6	−	47558.4i	1.08136	−	0.624323i
$277$	−15561.0			−0.202805			−0.101402	−	0.994845i	$-0.532333\pi$
$277$	−15561.0			−0.202805			−0.101402	+	0.994845i	$0.532333\pi$
$278$		−	8016.21i		−	0.103724i
$279$	63537.1	−	36683.2i	0.816243	−	0.471258i
$280$	−24209.1	−	13977.1i	−0.308790	−	0.178280i
$281$	−9448.74	+	5455.23i	−0.119663	+	0.0690877i	−0.558637	−	0.829412i	$-0.688675\pi$
$281$	−9448.74	+	5455.23i	−0.119663	+	0.0690877i	0.438974	+	0.898500i	$0.355342\pi$
$282$	2781.57	−	4817.82i	0.0349777	−	0.0605832i
$283$	6280.81	−	10878.7i	0.0784229	−	0.135832i	−0.824147	−	0.566376i	$-0.808345\pi$
$283$	6280.81	−	10878.7i	0.0784229	−	0.135832i	0.902570	+	0.430544i	$0.141678\pi$
$284$			44796.5i			0.555401i
$285$	−136619.	−	86178.7i	−1.68198	−	1.06099i
$286$	−13552.6			−0.165687
$287$	114388.	+	66042.2i	1.38873	+	0.801785i
$288$	30003.7	+	17322.6i	0.361734	+	0.208847i
$289$	−81463.9	−	141100.i	−0.975370	−	1.68939i
$290$	24017.4	−	41599.3i	0.285581	−	0.494641i
$291$	−72845.7	−	126173.i	−0.860237	−	1.48997i
$292$	−43960.7			−0.515584
$293$		−	76489.5i		−	0.890977i	−0.895288	−	0.445488i	$-0.853030\pi$
$293$		−	76489.5i		−	0.890977i	0.895288	−	0.445488i	$-0.146970\pi$
$294$	7573.85	+	13118.3i	0.0876238	+	0.151769i
$295$	−19896.4	+	11487.2i	−0.228628	+	0.131999i
$296$	28773.6			0.328406
$297$			198465.i			2.24994i
$298$	94875.0	−	54776.1i	1.06836	−	0.616820i
$299$	−27442.3	−	15843.8i	−0.306958	−	0.177222i
$300$	12579.0	−	7262.48i	0.139767	−	0.0806942i
$301$	−40863.1	+	70776.9i	−0.451022	+	0.781193i
$302$	4542.06	−	7867.07i	0.0498011	−	0.0862580i
$303$		−	69101.7i		−	0.752668i
$304$	−23086.3	−	904.478i	−0.249808	−	0.00978703i
$305$	−82626.3			−0.888216
$306$	−232733.	−	134368.i	−2.48551	−	1.43501i
$307$	−89839.1	−	51868.7i	−0.953211	−	0.550336i	−0.0591338	−	0.998250i	$-0.518834\pi$
$307$	−89839.1	−	51868.7i	−0.953211	−	0.550336i	−0.894077	+	0.447914i	$0.852167\pi$
$308$	−19855.7	−	34391.1i	−0.209307	−	0.362530i
$309$	9338.56	−	16174.9i	0.0978055	−	0.169404i
$310$	−14697.4	−	25456.6i	−0.152938	−	0.264897i
$311$	4690.48			0.0484950			0.0242475	−	0.999706i	$-0.492281\pi$
$311$	4690.48			0.0484950			0.0242475	+	0.999706i	$0.492281\pi$
$312$		−	16426.6i		−	0.168748i
$313$	68490.1	+	118628.i	0.699100	+	1.21088i	0.968779	+	0.247927i	$0.0797492\pi$
$313$	68490.1	+	118628.i	0.699100	+	1.21088i	−0.269679	+	0.962950i	$0.586917\pi$
$314$	9399.05	−	5426.54i	0.0953289	−	0.0550382i
$315$	236446.			2.38293
$316$		−	81673.7i		−	0.817915i
$317$	−106114.	+	61264.8i	−1.05597	+	0.609667i	−0.924316	−	0.381629i	$-0.875363\pi$
$317$	−106114.	+	61264.8i	−1.05597	+	0.609667i	−0.131658	+	0.991295i	$0.542030\pi$
$318$	−35492.0	−	20491.3i	−0.350975	−	0.202636i
$319$	59095.3	−	34118.7i	0.580727	−	0.335283i
$320$	6940.43	−	12021.2i	0.0677776	−	0.117394i
$321$	−65155.8	+	112853.i	−0.632329	+	1.09523i
$322$		−	92850.4i		−	0.895513i
$323$	179076.	+	7015.87i	1.71645	+	0.0672475i
$324$	−116532.			−1.11008
$325$	−4190.62	−	2419.46i	−0.0396745	−	0.0229061i
$326$	−9111.57	−	5260.57i	−0.0857350	−	0.0494991i
$327$	−63616.4	−	110187.i	−0.594941	−	1.03047i
$328$	−32793.7	+	56800.3i	−0.304819	+	0.527962i
$329$	−2715.29	−	4703.02i	−0.0250856	−	0.0434495i
$330$	137862.			1.26595
$331$			154898.i			1.41381i	0.707310	+	0.706904i	$0.249909\pi$
$331$			154898.i			1.41381i	−0.707310	+	0.706904i	$0.750091\pi$
$332$	48057.2	+	83237.6i	0.435996	+	0.755167i
$333$	−210770.	+	121688.i	−1.90073	+	1.09739i
$334$	−55365.8			−0.496305
$335$		−	23175.8i		−	0.206512i
$336$	41684.3	−	24066.5i	0.369228	−	0.213174i
$337$	56988.9	+	32902.6i	0.501800	+	0.289714i	0.729457	−	0.684027i	$-0.239773\pi$
$337$	56988.9	+	32902.6i	0.501800	+	0.289714i	−0.227657	+	0.973741i	$0.573106\pi$
$338$	65220.6	−	37655.1i	0.570889	−	0.329603i
$339$	138069.	−	239143.i	1.20143	−	2.08093i
$340$	−53835.6	+	93246.0i	−0.465706	+	0.806627i
$341$		−	41757.7i		−	0.359110i
$342$	172935.	−	91010.2i	1.47853	−	0.778104i
$343$	124197.			1.05566
$344$	−35144.7	−	20290.8i	−0.296991	−	0.171468i
$345$	279155.	+	161170.i	2.34534	+	1.35408i
$346$	−10311.6	−	17860.2i	−0.0861337	−	0.149188i
$347$	−105358.	+	182486.i	−0.875004	+	1.51555i	−0.0182458	+	0.999834i	$0.505808\pi$
$347$	−105358.	+	182486.i	−0.875004	+	1.51555i	−0.856758	+	0.515718i	$0.827525\pi$
$348$	41354.2	+	71627.5i	0.341476	+	0.591455i
$349$	−73325.4			−0.602010			−0.301005	−	0.953623i	$-0.597322\pi$
$349$	−73325.4			−0.602010			−0.301005	+	0.953623i	$0.597322\pi$
$350$		−	14178.9i		−	0.115746i
$351$	40069.4	+	69402.2i	0.325236	+	0.563325i
$352$	17077.1	−	9859.47i	0.137825	−	0.0795735i
$353$	101182.			0.811996			0.405998	−	0.913874i	$-0.366924\pi$
$353$	101182.			0.811996			0.405998	+	0.913874i	$0.366924\pi$
$354$		−	39558.3i		−	0.315668i
$355$	−131471.	+	75905.0i	−1.04322	+	0.602301i
$356$	−20882.0	−	12056.2i	−0.164767	−	0.0951285i
$357$	−323337.	+	186679.i	−2.53699	+	1.46473i
$358$	−23570.1	+	40824.6i	−0.183906	+	0.318534i
$359$	80870.7	−	140072.i	0.627484	−	1.08683i	−0.360571	−	0.932732i	$-0.617418\pi$
$359$	80870.7	−	140072.i	0.627484	−	1.08683i	0.988055	−	0.154102i	$-0.0492484\pi$
$360$			117409.i			0.905931i
$361$	−73790.6	+	107417.i	−0.566222	+	0.824253i
$362$	−89845.0			−0.685609
$363$	−39658.3	−	22896.7i	−0.300968	−	0.173764i
$364$	−13886.9	−	8017.61i	−0.104810	−	0.0605121i
$365$	−74488.8	−	129018.i	−0.559121	−	0.968425i
$366$	71134.8	−	123209.i	0.531031	−	0.919773i
$367$	128969.	+	223380.i	0.957530	+	1.65849i	0.728470	+	0.685078i	$0.240232\pi$
$367$	128969.	+	223380.i	0.957530	+	1.65849i	0.229060	+	0.973412i	$0.426435\pi$
$368$	46105.4			0.340452
$369$		−	554759.i		−	4.07428i
$370$	48755.2	+	84446.5i	0.356137	+	0.616848i
$371$	−34646.3	+	20003.1i	−0.251715	+	0.145328i
$372$	50613.2			0.365744
$373$			70024.0i			0.503303i	0.967818	+	0.251651i	$0.0809736\pi$
$373$			70024.0i			0.503303i	−0.967818	+	0.251651i	$0.919026\pi$
$374$	−132464.	+	76478.1i	−0.947009	+	0.546756i
$375$	−199559.	−	115216.i	−1.41909	−	0.819311i
$376$	2335.31	−	1348.29i	0.0165185	−	0.00953694i
$377$	13776.9	−	23862.3i	0.0969325	−	0.167892i
$378$	−117410.	+	203361.i	−0.821718	+	1.42326i
$379$			201137.i			1.40027i	0.714008	+	0.700137i	$0.246878\pi$
$379$			201137.i			1.40027i	−0.714008	+	0.700137i	$0.753122\pi$
$380$	−36463.8	−	69287.6i	−0.252520	−	0.479831i
$381$	372635.			2.56705
$382$	124213.	+	71714.6i	0.851219	+	0.491452i
$383$	−121519.	−	70158.9i	−0.828411	−	0.478284i	0.0248971	−	0.999690i	$-0.492074\pi$
$383$	−121519.	−	70158.9i	−0.828411	−	0.478284i	−0.853308	+	0.521407i	$0.825408\pi$
$384$	11950.3	+	20698.6i	0.0810435	+	0.140371i
$385$	67288.6	−	116547.i	0.453963	−	0.786287i
$386$	47230.7	+	81805.9i	0.316993	+	0.549048i
$387$	343252.			2.29188
$388$		−	70620.2i		−	0.469100i
$389$	138944.	+	240658.i	0.918207	+	1.59038i	0.802137	+	0.597140i	$0.203696\pi$
$389$	138944.	+	240658.i	0.918207	+	1.59038i	0.116069	+	0.993241i	$0.462971\pi$
$390$	48209.8	−	27834.0i	0.316961	−	0.182998i
$391$	−357631.			−2.33928
$392$			7342.46i			0.0477825i
$393$	−37719.5	+	21777.3i	−0.244220	+	0.141000i
$394$	140542.	+	81142.1i	0.905345	+	0.522701i
$395$	239701.	−	138391.i	1.53630	−	0.886982i
$396$	−83394.5	+	144444.i	−0.531799	+	0.921102i
$397$	−23155.0	+	40105.6i	−0.146914	+	0.254463i	−0.930085	−	0.367343i	$-0.880267\pi$
$397$	−23155.0	+	40105.6i	−0.146914	+	0.254463i	0.783171	+	0.621806i	$0.213601\pi$
$398$		−	62397.6i		−	0.393914i
$399$	10628.7	−	271292.i	0.0667628	−	1.70408i
$400$	7040.60			0.0440037
$401$	−78330.8	−	45224.3i	−0.487129	−	0.281244i	0.236254	−	0.971691i	$-0.424080\pi$
$401$	−78330.8	−	45224.3i	−0.487129	−	0.281244i	−0.723383	+	0.690447i	$0.757414\pi$
$402$	34558.8	+	19952.6i	0.213849	+	0.123466i
$403$	−8430.75	−	14602.5i	−0.0519106	−	0.0899118i
$404$	16747.6	−	29007.7i	0.102610	−	0.177726i
$405$	−197457.	−	342005.i	−1.20382	−	2.08508i
$406$	80737.5			0.489805
$407$			138522.i			0.836237i
$408$	−92696.6	−	160555.i	−0.556857	−	0.964504i
$409$	−214163.	+	123647.i	−1.28026	+	0.739159i	−0.976896	−	0.213715i	$-0.931444\pi$
$409$	−214163.	+	123647.i	−1.28026	+	0.739159i	−0.303365	+	0.952874i	$0.598110\pi$
$410$	−222268.			−1.32224
$411$		−	358165.i		−	2.12031i
$412$	7840.35	−	4526.63i	0.0461892	−	0.0266674i
$413$	−33442.2	−	19307.8i	−0.196062	−	0.113197i
$414$	−337728.	+	194987.i	−1.97045	+	1.13764i
$415$	−162860.	+	282082.i	−0.945625	+	1.63787i
$416$	3981.19	−	6895.63i	0.0230052	−	0.0398462i
$417$			46775.6i			0.268997i
$418$	4354.33	−	111142.i	0.0249212	−	0.636100i
$419$	59130.4			0.336809			0.168404	−	0.985718i	$-0.446139\pi$
$419$	59130.4			0.336809			0.168404	+	0.985718i	$0.446139\pi$
$420$	141263.	+	81558.4i	0.800812	+	0.462349i
$421$	224490.	+	129609.i	1.26658	+	0.731259i	0.974339	−	0.225086i	$-0.0722662\pi$
$421$	224490.	+	129609.i	1.26658	+	0.731259i	0.292240	+	0.956345i	$0.405600\pi$
$422$	8983.79	+	15560.4i	0.0504469	+	0.0873766i
$423$	−11404.3	+	19752.8i	−0.0637364	+	0.110395i
$424$	−9932.64	−	17203.8i	−0.0552501	−	0.0956960i
$425$	−54612.6			−0.302354
$426$		−	261393.i		−	1.44037i
$427$	−69439.8	−	120273.i	−0.380849	−	0.659649i
$428$	−54702.7	+	31582.6i	−0.298621	+	0.172409i
$429$	79081.0			0.429692
$430$		−	137526.i		−	0.743787i
$431$	254454.	−	146909.i	1.36979	−	0.790851i	0.378893	−	0.925441i	$-0.376305\pi$
$431$	254454.	−	146909.i	1.36979	−	0.790851i	0.990901	+	0.134589i	$0.0429715\pi$
$432$	−100980.	−	58300.8i	−0.541088	−	0.312397i
$433$	168884.	−	97505.3i	0.900768	−	0.520059i	0.0233190	−	0.999728i	$-0.492577\pi$
$433$	168884.	−	97505.3i	0.900768	−	0.520059i	0.877449	+	0.479669i	$0.159243\pi$
$434$	24703.6	−	42787.8i	0.131154	−	0.227165i
$435$	−140144.	+	242737.i	−0.740623	+	1.28280i
$436$		−	61672.8i		−	0.324430i
$437$	138749.	−	219958.i	0.726553	−	1.15180i
$438$	256516.			1.33711
$439$	−116261.	−	67123.5i	−0.603263	−	0.348294i	0.167061	−	0.985946i	$-0.446572\pi$
$439$	−116261.	−	67123.5i	−0.603263	−	0.348294i	−0.770324	+	0.637653i	$0.779906\pi$
$440$	57872.3	+	33412.6i	0.298927	+	0.172586i
$441$	−31052.4	−	53784.4i	−0.159668	−	0.276553i
$442$	−30881.4	+	53488.1i	−0.158071	+	0.273787i
$443$	−69342.5	−	120105.i	−0.353339	−	0.612002i	0.633493	−	0.773748i	$-0.281621\pi$
$443$	−69342.5	−	120105.i	−0.353339	−	0.612002i	−0.986832	+	0.161747i	$0.948287\pi$
$444$	−167898.			−0.851685
$445$		−	81714.1i		−	0.412646i
$446$	−6935.87	−	12013.3i	−0.0348683	−	0.0603937i
$447$	−553608.	+	319626.i	−2.77069	+	1.59966i
$448$	23331.2			0.116247
$449$			34968.8i			0.173455i	0.996232	+	0.0867276i	$0.0276410\pi$
$449$			34968.8i			0.173455i	−0.996232	+	0.0867276i	$0.972359\pi$
$450$	−51573.2	+	29775.8i	−0.254682	+	0.147041i
$451$	−273448.	−	157875.i	−1.34438	−	0.776177i
$452$	115918.	−	66925.5i	0.567381	−	0.327578i
$453$	−26503.5	+	45905.4i	−0.129154	+	0.223701i
$454$	−18426.5	+	31915.6i	−0.0893987	+	0.154843i
$455$		−	54341.4i		−	0.262487i
$456$	134711.	+	5277.75i	0.647851	+	0.0253816i
$457$	−15045.4			−0.0720396			−0.0360198	−	0.999351i	$-0.511468\pi$
$457$	−15045.4			−0.0720396			−0.0360198	+	0.999351i	$0.511468\pi$
$458$	−8668.69	−	5004.87i	−0.0413259	−	0.0238595i
$459$	783283.	+	452229.i	3.71786	+	2.14651i
$460$	78122.9	+	135313.i	0.369201	+	0.639475i
$461$	87640.3	−	151797.i	0.412384	−	0.714270i	−0.582766	−	0.812640i	$-0.698030\pi$
$461$	87640.3	−	151797.i	0.412384	−	0.714270i	0.995150	+	0.0983700i	$0.0313629\pi$
$462$	115861.	+	200676.i	0.542815	+	0.940183i
$463$	−124266.			−0.579683			−0.289842	−	0.957075i	$-0.593603\pi$
$463$	−124266.			−0.579683			−0.289842	+	0.957075i	$0.593603\pi$
$464$			40090.7i			0.186212i
$465$	85761.0	+	148542.i	0.396629	+	0.686981i
$466$	40582.5	−	23430.3i	0.186882	−	0.107896i
$467$	25117.0			0.115169			0.0575843	−	0.998341i	$-0.481660\pi$
$467$	25117.0			0.115169			0.0575843	+	0.998341i	$0.481660\pi$
$468$			67348.4i			0.307493i
$469$	33735.4	−	19477.1i	0.153370	−	0.0885481i
$470$	7914.10	+	4569.21i	0.0358266	+	0.0206845i
$471$	−54844.7	+	31664.6i	−0.247225	+	0.142736i
$472$	9587.43	−	16605.9i	0.0430346	−	0.0745382i
$473$	97683.9	−	169193.i	0.436617	−	0.756243i
$474$			476577.i			2.12117i
$475$	21187.9	−	33589.1i	0.0939075	−	0.148871i
$476$	−180976.			−0.798741
$477$	145516.	+	84013.4i	0.639547	+	0.369243i
$478$	−123454.	−	71276.1i	−0.540317	−	0.311952i
$479$	89441.7	+	154918.i	0.389824	+	0.675196i	0.992426	−	0.122847i	$-0.0392024\pi$
$479$	89441.7	+	154918.i	0.389824	+	0.675196i	−0.602601	+	0.798042i	$0.705869\pi$
$480$	−40498.3	+	70145.1i	−0.175774	+	0.304449i
$481$	27967.1	+	48440.5i	0.120881	+	0.209372i
$482$	−93517.5			−0.402530
$483$			541794.i			2.32242i
$484$	−11098.6	−	19223.3i	−0.0473780	−	0.0820612i
$485$	207260.	−	119662.i	0.881114	−	0.508712i
$486$	262577.			1.11169
$487$		−	233565.i		−	0.984806i	−0.870367	−	0.492403i	$-0.836119\pi$
$487$		−	233565.i		−	0.984806i	0.870367	−	0.492403i	$-0.163881\pi$
$488$	59722.4	−	34480.7i	0.250783	−	0.144789i
$489$	53167.2	+	30696.1i	0.222344	+	0.128371i
$490$	−21549.1	+	12441.4i	−0.0897504	+	0.0518174i
$491$	−161537.	+	279791.i	−0.670055	+	1.16057i	0.307833	+	0.951440i	$0.400396\pi$
$491$	−161537.	+	279791.i	−0.670055	+	1.16057i	−0.977888	+	0.209129i	$0.932937\pi$
$492$	191355.	−	331437.i	0.790515	−	1.36921i
$493$		−	310976.i		−	1.27948i
$494$	−20916.5	−	39745.0i	−0.0857107	−	0.162865i
$495$	−565228.			−2.30682
$496$	21246.6	+	12266.7i	0.0863625	+	0.0498614i
$497$	−220979.	−	127582.i	−0.894619	−	0.516509i
$498$	−280420.	−	485702.i	−1.13071	−	1.95844i
$499$	165726.	−	287046.i	0.665565	−	1.15279i	−0.313567	−	0.949566i	$-0.601524\pi$
$499$	165726.	−	287046.i	0.665565	−	1.15279i	0.979132	−	0.203226i	$-0.0651427\pi$
$500$	−55847.8	−	96731.2i	−0.223391	−	0.386925i
$501$	323066.			1.28711
$502$		−	35183.9i		−	0.139616i
$503$	181571.	+	314490.i	0.717647	+	1.24300i	0.961930	+	0.273297i	$0.0881142\pi$
$503$	181571.	+	314490.i	0.717647	+	1.24300i	−0.244283	+	0.969704i	$0.578552\pi$
$504$	−170904.	+	98671.2i	−0.672806	+	0.388445i
$505$	113511.			0.445099
$506$			221961.i			0.866911i
$507$	−380571.	+	219723.i	−1.48054	+	0.854789i
$508$	156426.	+	90312.5i	0.606152	+	0.349962i
$509$	−342217.	+	197579.i	−1.32089	+	0.762614i	−0.983870	−	0.178885i	$-0.942751\pi$
$509$	−342217.	+	197579.i	−1.32089	+	0.762614i	−0.337016	+	0.941499i	$0.609418\pi$
$510$	314138.	−	544103.i	1.20776	−	2.09190i
$511$	125202.	−	216856.i	0.479479	−	0.830482i
$512$			11585.2i			0.0441942i
$513$	−582027.	+	306303.i	−2.21161	+	1.16390i
$514$	−130093.			−0.492411
$515$	26570.0	+	15340.2i	0.100179	+	0.0578384i
$516$	205074.	+	118399.i	0.770213	+	0.444683i
$517$	6490.95	+	11242.7i	0.0242844	+	0.0420618i
$518$	−81948.5	+	141939.i	−0.305409	+	0.528984i
$519$	60169.4	+	104216.i	0.223378	+	0.386902i
$520$	26983.6			0.0997913
$521$			76241.3i			0.280876i	0.990089	+	0.140438i	$0.0448511\pi$
$521$			76241.3i			0.280876i	−0.990089	+	0.140438i	$0.955149\pi$
$522$	−169550.	−	293669.i	−0.622238	−	1.07775i
$523$	427334.	−	246722.i	1.56230	−	0.901994i	0.565276	−	0.824902i	$-0.308770\pi$
$523$	427334.	−	246722.i	1.56230	−	0.901994i	0.997024	−	0.0770925i	$-0.0245637\pi$
$524$	−21112.0			−0.0768895
$525$			82735.5i			0.300174i
$526$	−128579.	+	74235.2i	−0.464728	+	0.268311i
$527$	−164806.	−	95150.6i	−0.593404	−	0.342602i
$528$	−99647.1	+	57531.3i	−0.357435	+	0.206365i
$529$	−119566.	+	207094.i	−0.427263	+	0.740041i
$530$	33660.6	−	58301.8i	0.119831	−	0.207554i
$531$			162187.i			0.575211i
$532$	70212.5	−	111308.i	0.248080	−	0.393280i
$533$	−127498.			−0.448796
$534$	121849.	+	70349.5i	0.427306	+	0.246705i
$535$	−185381.	−	107030.i	−0.647675	−	0.373935i
$536$	9671.48	+	16751.5i	0.0336638	+	0.0583075i
$537$	137535.	−	238217.i	0.476939	−	0.826083i
$538$	45008.6	+	77957.2i	0.155500	+	0.269334i
$539$	−35348.0			−0.121671
$540$		−	395149.i		−	1.35511i
$541$	246855.	+	427565.i	0.843427	+	1.46086i	0.886980	+	0.461807i	$0.152799\pi$
$541$	246855.	+	427565.i	0.843427	+	1.46086i	−0.0435535	+	0.999051i	$0.513868\pi$
$542$	−115046.	+	66421.6i	−0.391626	+	0.226105i
$543$	524257.			1.77805
$544$		−	89864.5i		−	0.303662i
$545$	181001.	−	104501.i	0.609379	−	0.351825i
$546$	81031.9	+	46783.8i	0.271813	+	0.156931i
$547$	96558.3	−	55748.0i	0.322712	−	0.186318i	−0.329889	−	0.944020i	$-0.607011\pi$
$547$	96558.3	−	55748.0i	0.322712	−	0.186318i	0.652601	+	0.757702i	$0.273678\pi$
$548$	86805.6	−	150352.i	0.289059	−	0.500665i
$549$	−291649.	+	505151.i	−0.967645	+	1.67601i
$550$			33894.8i			0.112049i
$551$	191264.	+	120648.i	0.629983	+	0.397391i
$552$	−269031.			−0.882926
$553$	402893.	+	232610.i	1.31747	+	0.760639i
$554$	38116.5	+	22006.6i	0.124192	+	0.0717023i
$555$	−284493.	−	492756.i	−0.923603	−	1.59973i
$556$	−11336.6	+	19635.6i	−0.0366720	+	0.0635178i
$557$	−63821.5	−	110542.i	−0.205711	−	0.356301i	0.744648	−	0.667457i	$-0.232617\pi$
$557$	−63821.5	−	110542.i	−0.205711	−	0.356301i	−0.950359	+	0.311156i	$0.899284\pi$
$558$	−207511.			−0.666459
$559$		−	78888.3i		−	0.252458i
$560$	39533.3	+	68473.7i	0.126063	+	0.218347i
$561$	772944.	−	446259.i	2.45597	−	1.41795i
$562$	30859.5			0.0977048
$563$		−	31713.1i		−	0.100051i	−0.998748	−	0.0500256i	$-0.984070\pi$
$563$		−	31713.1i		−	0.100051i	0.998748	−	0.0500256i	$-0.0159303\pi$
$564$	−13626.9	+	7867.47i	−0.0428388	+	0.0247330i
$565$	392833.	+	226802.i	1.23058	+	0.710478i
$566$	−30769.5	+	17764.8i	−0.0960480	+	0.0554533i
$567$	331888.	−	574847.i	1.03235	−	1.78808i
$568$	63351.8	−	109728.i	0.196364	−	0.340113i
$569$		−	196675.i		−	0.607470i	−0.952757	−	0.303735i	$-0.901766\pi$
$569$		−	196675.i		−	0.607470i	0.952757	−	0.303735i	$-0.0982337\pi$
$570$	212771.	+	404302.i	0.654882	+	1.24439i
$571$	−286009.			−0.877218			−0.438609	−	0.898678i	$-0.644529\pi$
$571$	−286009.			−0.877218			−0.438609	+	0.898678i	$0.644529\pi$
$572$	33196.9	+	19166.2i	0.101462	+	0.0585794i
$573$	−724801.	−	418464.i	−2.20754	−	1.27453i
$574$	−186796.	−	323540.i	−0.566948	−	0.981982i
$575$	−39625.2	+	68632.9i	−0.119849	+	0.207585i
$576$	−48995.8	−	84863.2i	−0.147677	−	0.255785i
$577$	−345646.			−1.03820			−0.519099	−	0.854714i	$-0.673732\pi$
$577$	−345646.			−1.03820			−0.519099	+	0.854714i	$0.673732\pi$
$578$			460829.i			1.37938i
$579$	−275597.	−	477348.i	−0.822086	−	1.42389i
$580$	−117661.	+	67931.3i	−0.349764	+	0.201936i
$581$	−547476.			−1.62186
$582$			412078.i			1.21656i
$583$	82822.6	−	47817.7i	0.243676	−	0.140686i
$584$	107681.	+	62169.8i	0.315729	+	0.182286i
$585$	−197658.	+	114118.i	−0.577567	+	0.333458i
$586$	−108172.	+	187360.i	−0.315008	+	0.545610i
$587$	−82643.2	+	143142.i	−0.239845	+	0.415424i	−0.960670	−	0.277694i	$-0.910430\pi$
$587$	−82643.2	+	143142.i	−0.239845	+	0.415424i	0.720825	+	0.693117i	$0.243763\pi$
$588$		−	42844.2i		−	0.123919i
$589$	122461.	−	64447.2i	0.352993	−	0.185769i
$590$	64981.3			0.186674
$591$	−820082.	−	473474.i	−2.34791	−	1.35557i
$592$	−70480.7	−	40692.1i	−0.201107	−	0.116109i
$593$	202726.	+	351131.i	0.576500	+	0.998527i	0.995877	+	0.0907151i	$0.0289153\pi$
$593$	202726.	+	351131.i	0.576500	+	0.998527i	−0.419377	+	0.907812i	$0.637751\pi$
$594$	280671.	−	486137.i	0.795473	−	1.37780i
$595$	−306652.	−	531138.i	−0.866189	−	1.50028i
$596$	−309860.			−0.872315
$597$			364098.i			1.02157i
$598$	44813.1	+	77618.6i	0.125315	+	0.217052i
$599$	−499284.	+	288262.i	−1.39153	+	0.803403i	−0.993485	−	0.113962i	$-0.963646\pi$
$599$	−499284.	+	288262.i	−1.39153	+	0.803403i	−0.398049	+	0.917364i	$0.630313\pi$
$600$	−41082.8			−0.114119
$601$		−	274026.i		−	0.758651i	−0.925263	−	0.379326i	$-0.876156\pi$
$601$		−	274026.i		−	0.758651i	0.925263	−	0.379326i	$-0.123844\pi$
$602$	200187.	−	115578.i	0.552387	−	0.318921i
$603$	−141690.	−	81804.5i	−0.389675	−	0.224979i
$604$	−22251.4	+	12846.9i	−0.0609936	+	0.0352147i
$605$	37611.8	−	65145.6i	0.102758	−	0.177981i
$606$	−97724.5	+	169264.i	−0.266108	+	0.460913i
$607$			309970.i			0.841283i	0.907227	+	0.420642i	$0.138195\pi$
$607$			309970.i			0.841283i	−0.907227	+	0.420642i	$0.861805\pi$
$608$	55270.5	+	34864.5i	0.149516	+	0.0943139i
$609$	−471114.			−1.27026
$610$	202392.	+	116851.i	0.543919	+	0.314032i
$611$	4539.71	+	2621.00i	0.0121603	+	0.00702078i
$612$	380051.	+	658268.i	1.01470	+	1.75752i
$613$	242475.	−	419980.i	0.645278	−	1.11765i	−0.338959	−	0.940801i	$-0.610075\pi$
$613$	242475.	−	419980.i	0.645278	−	1.11765i	0.984237	−	0.176853i	$-0.0565917\pi$
$614$	146707.	+	254103.i	0.389147	+	0.674022i
$615$	1.29696e6			3.42907
$616$			112321.i			0.296005i
$617$	−45677.1	−	79115.1i	−0.119985	−	0.207821i	0.799776	−	0.600298i	$-0.204951\pi$
$617$	−45677.1	−	79115.1i	−0.119985	−	0.207821i	−0.919762	+	0.392477i	$0.871618\pi$
$618$	−45749.4	+	26413.4i	−0.119787	+	0.0691589i
$619$	−143028.			−0.373284			−0.186642	−	0.982428i	$-0.559760\pi$
$619$	−143028.			−0.373284			−0.186642	+	0.982428i	$0.559760\pi$
$620$			83140.9i			0.216287i
$621$	1.13665e6	−	656246.i	2.94743	−	1.70170i
$622$	−11489.3	−	6633.34i	−0.0296970	−	0.0171456i
$623$	118946.	−	68673.2i	0.306459	−	0.176934i
$624$	−23230.8	+	40236.9i	−0.0596615	+	0.103337i
$625$	223639.	−	387355.i	0.572517	−	0.991628i
$626$		−	387439.i		−	0.988677i
$627$	−25408.1	+	648527.i	−0.0646304	+	1.64966i
$628$	−30697.2			−0.0778357
$629$	546706.	+	315641.i	1.38182	+	0.797796i
$630$	−579172.	−	334385.i	−1.45924	−	0.842492i
$631$	340340.	+	589486.i	0.854780	+	1.48052i	0.876849	+	0.480766i	$0.159641\pi$
$631$	340340.	+	589486.i	0.854780	+	1.48052i	−0.0220686	+	0.999756i	$0.507025\pi$
$632$	−115504.	+	200059.i	−0.289177	+	0.500869i
$633$	−52421.6	−	90796.8i	−0.130829	−	0.226602i
$634$	346566.			0.862199
$635$			612117.i			1.51805i
$636$	57958.3	+	100387.i	0.143285	+	0.248177i
$637$	−12361.0	+	7136.65i	−0.0304633	+	0.0175880i
$638$	−193004.			−0.474161
$639$			1.07170e6i			2.62465i
$640$	−34001.0	+	19630.5i	−0.0830103	+	0.0479260i
$641$	−254038.	−	146669.i	−0.618276	−	0.356962i	0.157921	−	0.987452i	$-0.449521\pi$
$641$	−254038.	−	146669.i	−0.618276	−	0.356962i	−0.776198	+	0.630490i	$0.782854\pi$
$642$	319197.	−	184288.i	0.774442	−	0.447124i
$643$	202790.	−	351243.i	0.490484	−	0.849543i	−0.509456	−	0.860497i	$-0.670153\pi$
$643$	202790.	−	351243.i	0.490484	−	0.849543i	0.999940	+	0.0109537i	$0.00348673\pi$
$644$	−131310.	+	227436.i	−0.316612	+	0.548388i
$645$			802484.i			1.92893i
$646$	−428723.	−	270437.i	−1.02733	−	0.648039i
$647$	567578.			1.35587			0.677933	−	0.735124i	$-0.262876\pi$
$647$	567578.			1.35587			0.677933	+	0.735124i	$0.262876\pi$
$648$	285444.	+	164801.i	0.679784	+	0.392473i
$649$	79944.1	+	46155.7i	0.189800	+	0.109581i
$650$	6843.25	+	11852.9i	0.0161971	+	0.0280541i
$651$	−144149.	+	249673.i	−0.340133	+	0.589127i
$652$	14879.1	+	25771.4i	0.0350012	+	0.0606238i
$653$	−708081.			−1.66057			−0.830284	−	0.557340i	$-0.811822\pi$
$653$	−708081.			−1.66057			−0.830284	+	0.557340i	$0.811822\pi$
$654$			359869.i			0.841373i
$655$	−35773.0	−	61960.7i	−0.0833822	−	0.144422i
$656$	160656.	−	92754.5i	0.373326	−	0.215540i
$657$	−1.05170e6			−2.43648
$658$			15360.0i			0.0354764i
$659$	−174814.	+	100929.i	−0.402537	+	0.232405i	−0.687578	−	0.726110i	$-0.741326\pi$
$659$	−174814.	+	100929.i	−0.402537	+	0.232405i	0.285041	+	0.958515i	$0.407993\pi$
$660$	−337692.	−	194967.i	−0.775235	−	0.447582i
$661$	385678.	−	222671.i	0.882718	−	0.509638i	0.0111647	−	0.999938i	$-0.496446\pi$
$661$	385678.	−	222671.i	0.882718	−	0.509638i	0.871554	+	0.490300i	$0.163113\pi$
$662$	219059.	−	379421.i	0.499856	−	0.865777i
$663$	180197.	−	312110.i	0.409940	−	0.710036i
$664$		−	271853.i		−	0.616592i
$665$	445643.	+	17459.5i	1.00773	+	0.0394810i
$666$	688373.			1.55194
$667$	−390811.	−	225635.i	−0.878446	−	0.507171i
$668$	135618.	+	78299.0i	0.303923	+	0.175470i
$669$	40471.7	+	70099.0i	0.0904272	+	0.156625i
$670$	−32775.5	+	56768.9i	−0.0730130	+	0.126462i
$671$	165997.	+	287515.i	0.368685	+	0.638581i
$672$	−136140.			−0.301473
$673$			99055.7i			0.218700i	0.994003	+	0.109350i	$0.0348770\pi$
$673$			99055.7i			0.218700i	−0.994003	+	0.109350i	$0.965123\pi$
$674$	−93062.5	−	161189.i	−0.204859	−	0.354826i
$675$	173574.	−	100213.i	0.380958	−	0.219946i
$676$	−213010.			−0.466129
$677$		−	348874.i		−	0.761187i	−0.924743	−	0.380593i	$-0.875720\pi$
$677$		−	348874.i		−	0.761187i	0.924743	−	0.380593i	$-0.124280\pi$
$678$	−676398.	+	390519.i	−1.47144	+	0.849537i
$679$	348366.	+	201129.i	0.755608	+	0.436250i
$680$	263740.	−	152270.i	0.570371	−	0.329304i
$681$	107521.	−	186232.i	0.231846	−	0.401568i
$682$	−59054.3	+	102285.i	−0.126965	+	0.219909i
$683$		−	505774.i		−	1.08421i	−0.840309	−	0.542107i	$-0.817627\pi$
$683$		−	505774.i		−	1.08421i	0.840309	−	0.542107i	$-0.182373\pi$
$684$	−552310.	−	21638.5i	−1.18051	−	0.0462503i
$685$	588348.			1.25387
$686$	−304220.	−	175641.i	−0.646456	−	0.373232i
$687$	50582.9	+	29204.1i	0.107174	+	0.0618771i
$688$	57391.1	+	99404.2i	0.121246	+	0.210004i
$689$	19308.5	−	33443.3i	0.0406733	−	0.0704482i
$690$	−455857.	−	789568.i	−0.957483	−	1.65841i
$691$	−617230.			−1.29268			−0.646340	−	0.763049i	$-0.723701\pi$
$691$	−617230.			−1.29268			−0.646340	+	0.763049i	$0.723701\pi$
$692$			58331.1i			0.121811i
$693$	−475022.	−	822763.i	−0.989117	−	1.71320i
$694$	516149.	−	297998.i	1.07166	−	0.618721i
$695$	−76837.0			−0.159075
$696$		−	233934.i		−	0.482921i
$697$	−1.24618e6	+	719479.i	−2.56515	+	1.48099i
$698$	179610.	+	103698.i	0.368654	+	0.212843i
$699$	−236804.	+	136719.i	−0.484657	+	0.279817i
$700$	−20051.9	+	34731.0i	−0.0409223	+	0.0708795i
$701$	−56004.4	+	97002.5i	−0.113969	+	0.197400i	−0.917367	−	0.398042i	$-0.869690\pi$
$701$	−56004.4	+	97002.5i	−0.113969	+	0.197400i	0.803398	+	0.595442i	$0.203023\pi$
$702$		−	226667.i		−	0.459953i
$703$	−406236.	+	213789.i	−0.821992	+	0.432588i
$704$	−55773.6			−0.112534
$705$	−46179.8	−	26661.9i	−0.0929124	−	0.0536430i
$706$	−247844.	−	143093.i	−0.497244	−	0.287084i
$707$	95395.9	+	165231.i	0.190849	+	0.330561i
$708$	−55943.9	+	96897.7i	−0.111606	+	0.193307i
$709$	−68549.6	−	118731.i	−0.136368	−	0.236196i	0.789751	−	0.613427i	$-0.210210\pi$
$709$	−68549.6	−	118731.i	−0.136368	−	0.236196i	−0.926119	+	0.377231i	$0.876876\pi$
$710$	429383.			0.851782
$711$		−	1.95394e6i		−	3.86520i
$712$	34100.1	+	59063.1i	0.0672660	+	0.116508i
$713$	−239156.	+	138077.i	−0.470437	+	0.271607i
$714$	1.05602e6			2.07145
$715$			129904.i			0.254104i
$716$	115469.	−	66666.3i	0.225238	−	0.130041i
$717$	720369.	+	415905.i	1.40125	+	0.809014i
$718$	−396184.	+	228737.i	−0.768507	+	0.443698i
$719$	−125747.	+	217800.i	−0.243242	+	0.421308i	−0.961636	−	0.274329i	$-0.911544\pi$
$719$	−125747.	+	217800.i	−0.243242	+	0.421308i	0.718394	+	0.695637i	$0.244878\pi$
$720$	166041.	−	287591.i	0.320295	−	0.554767i
$721$			51568.1i			0.0991998i
$722$	332661.	−	158762.i	0.638156	−	0.304560i
$723$	545687.			1.04392
$724$	220074.	+	127060.i	0.419848	+	0.242399i
$725$	−59679.3	−	34455.9i	−0.113540	−	0.0655522i
$726$	64761.7	+	112171.i	0.122870	+	0.212817i
$727$	−130268.	+	225631.i	−0.246473	+	0.426903i	−0.962545	−	0.271123i	$-0.912605\pi$
$727$	−130268.	+	225631.i	−0.246473	+	0.426903i	0.716072	+	0.698027i	$0.245938\pi$
$728$	22677.2	+	39278.1i	0.0427885	+	0.0741118i
$729$	−352285.			−0.662886
$730$			421372.i			0.790716i
$731$	−445172.	−	771060.i	−0.833092	−	1.44296i
$732$	−348488.	+	201200.i	−0.650378	+	0.375496i
$733$	533519.			0.992982			0.496491	−	0.868042i	$-0.334621\pi$
$733$	533519.			0.992982			0.496491	+	0.868042i	$0.334621\pi$
$734$		−	729557.i		−	1.35415i
$735$	125742.	−	72596.9i	0.232758	−	0.134383i
$736$	−112935.	−	65202.9i	−0.208484	−	0.120368i
$737$	−80645.0	+	46560.4i	−0.148471	+	0.0857199i
$738$	−784547.	+	1.35888e6i	−1.44048	+	2.49498i
$739$	−53933.3	+	93415.2i	−0.0987571	+	0.171052i	−0.911170	−	0.412030i	$-0.864820\pi$
$739$	−53933.3	+	93415.2i	−0.0987571	+	0.171052i	0.812413	+	0.583082i	$0.198153\pi$
$740$		−	275801.i		−	0.503654i
$741$	122051.	+	231917.i	0.222281	+	0.422373i
$742$	113154.			0.205525
$743$	−187525.	−	108268.i	−0.339690	−	0.196120i	0.320445	−	0.947267i	$-0.396168\pi$
$743$	−187525.	−	108268.i	−0.339690	−	0.196120i	−0.660135	+	0.751147i	$0.729501\pi$
$744$	−123976.	−	71577.8i	−0.223972	−	0.129310i
$745$	−525040.	−	909396.i	−0.945976	−	1.63848i
$746$	99028.9	−	171523.i	0.177944	−	0.308209i
$747$	1.14971e6	+	1.99135e6i	2.06038	+	3.56868i
$748$	432625.			0.773230
$749$		−	359794.i		−	0.641344i
$750$	325879.	+	564439.i	0.579340	+	1.00345i
$751$	800664.	−	462264.i	1.41961	−	0.819615i	0.423350	−	0.905966i	$-0.360854\pi$
$751$	800664.	−	462264.i	1.41961	−	0.819615i	0.996265	+	0.0863516i	$0.0275208\pi$
$752$	−7627.10			−0.0134873
$753$			205303.i			0.362080i
$754$	−67492.8	+	38967.0i	−0.118718	+	0.0685416i
$755$	−75407.5	−	43536.5i	−0.132288	−	0.0763766i
$756$	575191.	−	332087.i	1.00639	−	0.581042i
$757$	−470899.	+	815622.i	−0.821744	+	1.42330i	0.0826389	+	0.996580i	$0.473665\pi$
$757$	−470899.	+	815622.i	−0.821744	+	1.42330i	−0.904383	+	0.426722i	$0.859668\pi$
$758$	284450.	−	492683.i	0.495072	−	0.857490i
$759$		−	1.29517e6i		−	2.24824i
$760$	−8669.61	+	221287.i	−0.0150097	+	0.383114i
$761$	−873322.			−1.50801			−0.754007	−	0.656867i	$-0.771881\pi$
$761$	−873322.			−1.50801			−0.754007	+	0.656867i	$0.771881\pi$
$762$	−912765.	−	526985.i	−1.57199	−	0.907588i
$763$	304229.	+	175647.i	0.522579	+	0.301711i
$764$	−202840.	−	351328.i	−0.347509	−	0.601903i
$765$	−1.28795e6	+	2.23079e6i	−2.20078	+	3.81186i
$766$	198439.	+	343707.i	0.338198	+	0.585775i
$767$	37274.8			0.0633614
$768$		−	67601.4i		−	0.114613i
$769$	339911.	+	588744.i	0.574795	+	0.995575i	0.996064	+	0.0886386i	$0.0282516\pi$
$769$	339911.	+	588744.i	0.574795	+	0.995575i	−0.421269	+	0.906936i	$0.638415\pi$
$770$	−329646.	+	190321.i	−0.555989	+	0.321000i
$771$	759109.			1.27701
$772$		−	267177.i		−	0.448295i
$773$	382639.	−	220917.i	0.640369	−	0.369717i	−0.144388	−	0.989521i	$-0.546121\pi$
$773$	382639.	−	220917.i	0.640369	−	0.369717i	0.784756	+	0.619804i	$0.212788\pi$
$774$	−840792.	−	485432.i	−1.40348	−	0.810301i
$775$	−36520.6	+	21085.2i	−0.0608044	+	0.0351054i
$776$	−99872.0	+	172983.i	−0.165852	+	0.287264i
$777$	478180.	−	828233.i	0.792045	−	1.37186i
$778$		−	785986.i		−	1.29854i
$779$	40964.1	−	1.04558e6i	0.0675038	−	1.72300i
$780$	−157453.			−0.258798
$781$	528254.	+	304988.i	0.866046	+	0.500012i
$782$	876014.	+	505767.i	1.43251	+	0.827060i
$783$	570635.	+	988369.i	0.930754	+	1.61211i
$784$	10383.8	−	17985.3i	0.0168937	−	0.0292607i
$785$	−52014.5	−	90091.8i	−0.0844084	−	0.146200i
$786$	123191.			0.199404
$787$		−	1.09729e6i		−	1.77163i	−0.464040	−	0.885814i	$-0.653600\pi$
$787$		−	1.09729e6i		−	1.77163i	0.464040	−	0.885814i	$-0.346400\pi$
$788$	−229504.	−	397513.i	−0.369606	−	0.640176i
$789$	750276.	−	433172.i	1.20522	−	0.695835i
$790$	−782860.			−1.25438
$791$			762426.i			1.21855i
$792$	408548.	−	235875.i	0.651318	−	0.376038i
$793$	116097.	+	67028.6i	0.184618	+	0.106589i
$794$	113436.	−	65492.2i	0.179932	−	0.103884i
$795$	−196414.	+	340198.i	−0.310769	+	0.538267i
$796$	−88243.5	+	152842.i	−0.139270	+	0.241222i
$797$			989170.i			1.55724i	0.627499	+	0.778618i	$0.284079\pi$
$797$			989170.i			1.55724i	−0.627499	+	0.778618i	$0.715921\pi$
$798$	−409699.	+	649495.i	−0.643368	+	1.01993i
$799$	59162.0			0.0926722
$800$	−17245.9	−	9956.91i	−0.0269467	−	0.0155577i
$801$	−499575.	−	288430.i	−0.778638	−	0.449547i
$802$	127914.	+	221553.i	0.198870	+	0.344452i
$803$	−299298.	+	518399.i	−0.464165	+	0.803957i
$804$	−56434.4	−	97747.2i	−0.0873035	−	0.151214i
$805$	−889990.			−1.37339
$806$			47691.5i			0.0734127i
$807$	−262631.	−	454891.i	−0.403273	−	0.698489i
$808$	−82046.3	+	47369.4i	−0.125671	+	0.0725564i
$809$	−234442.			−0.358210			−0.179105	−	0.983830i	$-0.557320\pi$
$809$	−234442.			−0.358210			−0.179105	+	0.983830i	$0.557320\pi$
$810$			1.11698e6i			1.70246i
$811$	−897875.	+	518388.i	−1.36513	+	0.788159i	−0.990301	−	0.138935i	$-0.955632\pi$
$811$	−897875.	+	518388.i	−1.36513	+	0.788159i	−0.374829	+	0.927094i	$0.622299\pi$
$812$	−197766.	−	114180.i	−0.299943	−	0.173172i
$813$	671306.	−	387579.i	1.01564	−	0.586380i
$814$	195899.	−	339308.i	0.295654	−	0.512089i
$815$	−50423.6	+	87336.3i	−0.0759135	+	0.131486i
$816$			524371.i			0.787514i
$817$	646947.	+	25346.2i	0.969224	+	0.0379724i
$818$	699455.			1.04533
$819$	−332227.	−	191811.i	−0.495298	−	0.285960i
$820$	544443.	+	314334.i	0.809701	+	0.467481i
$821$	163032.	+	282380.i	0.241873	+	0.418937i	0.961248	−	0.275686i	$-0.0889049\pi$
$821$	163032.	+	282380.i	0.241873	+	0.418937i	−0.719375	+	0.694622i	$0.755572\pi$
$822$	−506522.	+	877322.i	−0.749643	+	1.29842i
$823$	160326.	+	277693.i	0.236703	+	0.409982i	0.959766	−	0.280800i	$-0.0905997\pi$
$823$	160326.	+	277693.i	0.236703	+	0.409982i	−0.723063	+	0.690782i	$0.757266\pi$
$824$	−25606.5			−0.0377134
$825$		−	197781.i		−	0.290587i
$826$	54610.8	+	94588.7i	0.0800421	+	0.138637i
$827$	830053.	−	479231.i	1.21365	−	0.700703i	0.250100	−	0.968220i	$-0.419536\pi$
$827$	830053.	−	479231.i	1.21365	−	0.700703i	0.963553	+	0.267517i	$0.0862031\pi$
$828$	1.10301e6			1.60887
$829$		−	311615.i		−	0.453429i	−0.973961	−	0.226715i	$-0.927202\pi$
$829$		−	311615.i		−	0.453429i	0.973961	−	0.226715i	$-0.0727985\pi$
$830$	797849.	−	460638.i	1.15815	−	0.668658i
$831$	−222415.	−	128411.i	−0.322079	−	0.185952i
$832$	−19503.8	+	11260.5i	−0.0281755	+	0.0162671i
$833$	−80545.2	+	139508.i	−0.116078	+	0.201053i
$834$	66150.7	−	114576.i	0.0951048	−	0.164726i
$835$			530692.i			0.761149i
$836$	−167844.	+	266083.i	−0.240156	+	0.380719i
$837$	698398.			0.996901
$838$	−144839.	−	83623.1i	−0.206252	−	0.119080i
$839$	46665.7	+	26942.4i	0.0662939	+	0.0382748i	0.532781	−	0.846253i	$-0.321147\pi$
$839$	46665.7	+	26942.4i	0.0662939	+	0.0382748i	−0.466487	+	0.884528i	$0.654480\pi$
$840$	−230682.	−	399553.i	−0.326930	−	0.566260i
$841$	−157441.	+	272696.i	−0.222601	+	0.385555i
$842$	−366590.	−	634953.i	−0.517079	−	0.895606i
$843$	−180069.			−0.253387
$844$		−	50820.0i		−	0.0713427i
$845$	−360932.	−	625153.i	−0.505490	−	0.875534i
$846$	55869.4	−	32256.2i	0.0780609	−	0.0450685i
$847$	126437.			0.176241
$848$			56187.5i			0.0781354i
$849$	179544.	−	103660.i	0.249090	−	0.143812i
$850$	133773.	+	77233.9i	0.185153	+	0.106898i
$851$	793346.	−	458038.i	1.09548	−	0.632474i
$852$	−369666.	+	640280.i	−0.509249	+	0.882045i
$853$	−437680.	+	758084.i	−0.601532	+	1.04188i	0.391057	+	0.920366i	$0.372109\pi$
$853$	−437680.	+	758084.i	−0.601532	+	1.04188i	−0.992589	+	0.121518i	$0.961224\pi$
$854$			392811.i			0.538601i
$855$	−872351.	−	1.65762e6i	−1.19333	−	2.26752i
$856$	178658.			0.243823
$857$	−925783.	−	534501.i	−1.26051	−	0.727758i	−0.287340	−	0.957829i	$-0.592771\pi$
$857$	−925783.	−	534501.i	−1.26051	−	0.727758i	−0.973174	+	0.230071i	$0.926104\pi$
$858$	−193708.	−	111837.i	−0.263132	−	0.151919i
$859$	−94002.2	−	162817.i	−0.127395	−	0.220654i	0.795272	−	0.606253i	$-0.207328\pi$
$859$	−94002.2	−	162817.i	−0.127395	−	0.220654i	−0.922666	+	0.385599i	$0.873995\pi$
$860$	−194492.	+	336869.i	−0.262969	+	0.455475i
$861$	1.08998e6	+	1.88789e6i	1.47032	+	2.54666i
$862$	−831044.			−1.11843
$863$			347316.i			0.466341i	0.972436	+	0.233170i	$0.0749100\pi$
$863$			347316.i			0.466341i	−0.972436	+	0.233170i	$0.925090\pi$
$864$	164900.	+	285614.i	0.220898	+	0.382607i
$865$	−171193.	+	98838.6i	−0.228799	+	0.132097i
$866$	−551573.			−0.735474
$867$		−	2.68900e6i		−	3.57727i
$868$	−121022.	+	69872.2i	−0.160630	+	0.0927396i
$869$	−963123.	−	556059.i	−1.27539	−	0.736345i
$870$	686564.	−	396388.i	0.907074	−	0.523700i
$871$	−18800.8	+	32563.9i	−0.0247822	+	0.0429240i
$872$	−87218.5	+	151067.i	−0.114703	+	0.198672i
$873$		−	1.68950e6i		−	2.21681i
$874$	−650933.	+	342565.i	−0.852144	+	0.448456i
$875$	636227.			0.830991
$876$	−628334.	−	362769.i	−0.818809	−	0.472740i
$877$	−915730.	−	528697.i	−1.19061	−	0.687397i	−0.232162	−	0.972677i	$-0.574580\pi$
$877$	−915730.	−	528697.i	−1.19061	−	0.687397i	−0.958444	+	0.285280i	$0.907913\pi$
$878$	189854.	+	328837.i	0.246281	+	0.426571i
$879$	631200.	−	1.09327e6i	0.816939	−	1.41498i
$880$	−94505.1	−	163688.i	−0.122036	−	0.211373i
$881$	841534.			1.08423			0.542113	−	0.840305i	$-0.317624\pi$
$881$	841534.			1.08423			0.542113	+	0.840305i	$0.317624\pi$
$882$			175659.i			0.225805i
$883$	−98242.9	−	170162.i	−0.126003	−	0.218243i	0.796122	−	0.605136i	$-0.206881\pi$
$883$	−98242.9	−	170162.i	−0.126003	−	0.218243i	−0.922124	+	0.386893i	$0.873548\pi$
$884$	151287.	−	87345.7i	0.193597	−	0.111773i
$885$	−379174.			−0.484119
$886$			392260.i			0.499697i
$887$	571698.	−	330070.i	0.726640	−	0.419526i	−0.0905515	−	0.995892i	$-0.528863\pi$
$887$	571698.	−	330070.i	0.726640	−	0.419526i	0.817192	+	0.576366i	$0.195530\pi$
$888$	411264.	+	237443.i	0.521549	+	0.301116i
$889$	−891016.	+	514428.i	−1.12741	+	0.650910i
$890$	−115561.	+	200158.i	−0.145892	+	0.252693i
$891$	−793385.	+	1.37418e6i	−0.999375	+	1.73097i
$892$			39235.2i			0.0493113i
$893$	−22952.9	+	36387.1i	−0.0287829	+	0.0456294i
$894$	1.80808e6			2.26225
$895$	391312.	+	225924.i	0.488514	+	0.282044i
$896$	−57149.5	−	32995.3i	−0.0711863	−	0.0410994i
$897$	−261490.	−	452915.i	−0.324991	−	0.562900i
$898$	49453.3	−	85655.6i	0.0613257	−	0.106219i
$899$	−120064.	−	207957.i	−0.148557	−	0.257308i
$900$	168437.			0.207947
$901$		−	435836.i		−	0.536875i
$902$	446538.	+	773427.i	0.548840	+	0.950619i
$903$	−1.16812e6	+	674414.i	−1.43256	+	0.827086i
$904$	−378588.			−0.463265
$905$			861182.i			1.05147i
$906$	129840.	−	74963.2i	0.158180	−	0.0913254i
$907$	1.28352e6	+	741042.i	1.56023	+	0.900800i	0.997233	+	0.0743424i	$0.0236858\pi$
$907$	1.28352e6	+	741042.i	1.56023	+	0.900800i	0.562999	+	0.826458i	$0.309648\pi$
$908$	90271.0	−	52118.0i	0.109491	−	0.0632144i
$909$	400666.	−	693973.i	0.484902	−	0.839876i
$910$	−76850.4	+	133109.i	−0.0928033	+	0.160740i
$911$			1.35079e6i			1.62761i	0.581139	+	0.813804i	$0.302607\pi$
$911$			1.35079e6i			1.62761i	−0.581139	+	0.813804i	$0.697393\pi$
$912$	−322511.	−	203439.i	−0.387752	−	0.244593i
$913$	1.30875e6			1.57006
$914$	36853.5	+	21277.4i	0.0441150	+	0.0254698i
$915$	−1.18098e6	−	681842.i	−1.41059	−	0.814407i
$916$	14155.9	+	24518.8i	0.0168712	+	0.0292218i
$917$	60127.9	−	104145.i	0.0715051	−	0.123851i
$918$	−1.27910e6	−	2.21546e6i	−1.51781	−	2.62893i
$919$	−554201.			−0.656200			−0.328100	−	0.944643i	$-0.606408\pi$
$919$	−554201.			−0.656200			−0.328100	+	0.944643i	$0.606408\pi$
$920$		−	441930.i		−	0.522129i
$921$	−856053.	−	1.48273e6i	−1.00921	−	1.74800i
$922$	−429348.	+	247884.i	−0.505065	+	0.291600i
$923$	246304.			0.289114
$924$		−	655406.i		−	0.767656i
$925$	121149.	−	69945.4i	0.141591	−	0.0817477i
$926$	304389.	+	175739.i	0.354982	+	0.204949i
$927$	187570.	−	108294.i	0.218275	−	0.126021i
$928$	56696.8	−	98201.8i	0.0658359	−	0.114031i
$929$	255965.	−	443344.i	0.296584	−	0.513699i	−0.678768	−	0.734353i	$-0.737486\pi$
$929$	255965.	−	443344.i	0.296584	−	0.513699i	0.975352	+	0.220654i	$0.0708190\pi$
$930$		−	485138.i		−	0.560918i
$931$	−54554.7	−	103663.i	−0.0629409	−	0.119599i
$932$	−132542.			−0.152588
$933$	67041.5	+	38706.4i	0.0770159	+	0.0444651i
$934$	−61523.9	−	35520.8i	−0.0705261	−	0.0407183i
$935$	733058.	+	1.26969e6i	0.838523	+	1.45236i
$936$	95245.0	−	164969.i	0.108715	−	0.188300i
$937$	−371185.	−	642912.i	−0.422777	−	0.732271i	0.573433	−	0.819253i	$-0.305611\pi$
$937$	−371185.	−	642912.i	−0.422777	−	0.732271i	−0.996210	+	0.0869812i	$0.972278\pi$
$938$	−110179.			−0.125226
$939$			2.26076e6i			2.56403i
$940$	−12923.7	−	22384.5i	−0.0146262	−	0.0253333i
$941$	−592306.	+	341968.i	−0.668909	+	0.386195i	−0.795663	−	0.605739i	$-0.792877\pi$
$941$	−592306.	+	341968.i	−0.668909	+	0.386195i	0.126754	+	0.991934i	$0.459544\pi$
$942$	179122.			0.201858
$943$			2.08813e6i			2.34819i
$944$	−46968.6	+	27117.3i	−0.0527065	+	0.0304301i
$945$	1.94925e6	+	1.12540e6i	2.18275	+	1.26021i
$946$	−478551.	+	276292.i	−0.534744	+	0.308735i
$947$	100459.	−	173999.i	0.112018	−	0.194021i	−0.804566	−	0.593863i	$-0.797602\pi$
$947$	100459.	−	173999.i	0.112018	−	0.194021i	0.916584	+	0.399843i	$0.130935\pi$
$948$	673981.	−	1.16737e6i	0.749948	−	1.29895i
$949$			241709.i			0.268386i
$950$	−99401.6	+	52311.9i	−0.110140	+	0.0579633i
$951$	−2.02226e6			−2.23602
$952$	443298.	+	255938.i	0.489127	+	0.282398i
$953$	−103420.	−	59709.6i	−0.113872	−	0.0657443i	0.441982	−	0.897024i	$-0.354276\pi$
$953$	−103420.	−	59709.6i	−0.113872	−	0.0657443i	−0.555854	+	0.831280i	$0.687609\pi$
$954$	−237626.	−	411580.i	−0.261094	−	0.452228i
$955$	687399.	−	1.19061e6i	0.753707	−	1.30546i
$956$	201599.	+	349180.i	0.220584	+	0.382062i
$957$	1.12621e6			1.22969
$958$		−	505959.i		−	0.551295i
$959$	494452.	+	856417.i	0.537635	+	0.931211i
$960$	198400.	−	114547.i	0.215278	−	0.124291i
$961$	776576.			0.840886
$962$		−	158206.i		−	0.170951i
$963$	−1.30869e6	+	755573.i	−1.41119	+	0.814749i
$964$	229070.	+	132254.i	0.246499	+	0.142316i
$965$	784126.	−	452716.i	0.842037	−	0.486151i
$966$	766212.	−	1.32712e6i	0.821098	−	1.42218i
$967$	−530380.	+	918645.i	−0.567197	+	0.982415i	0.429644	+	0.902998i	$0.358639\pi$
$967$	−530380.	+	918645.i	−0.567197	+	0.982415i	−0.996842	+	0.0794163i	$0.974694\pi$
$968$			62783.1i			0.0670027i
$969$	2.50165e6	+	1.57804e6i	2.66428	+	1.68062i
$970$	−676909.			−0.719427
$971$	−5827.53	−	3364.53i	−0.00618082	−	0.00356850i	0.496906	−	0.867804i	$-0.334469\pi$
$971$	−5827.53	−	3364.53i	−0.00618082	−	0.00356850i	−0.503087	+	0.864236i	$0.667803\pi$
$972$	−643180.	−	371340.i	−0.680769	−	0.393042i
$973$	−64574.5	−	111846.i	−0.0682080	−	0.118140i
$974$	−330311.	+	572116.i	−0.348181	+	0.603068i
$975$	−39931.3	−	69163.0i	−0.0420053	−	0.0727553i
$976$	−195053.			−0.204763
$977$			326810.i			0.342379i	0.985238	+	0.171189i	$0.0547610\pi$
$977$			326810.i			0.342379i	−0.985238	+	0.171189i	$0.945239\pi$
$978$	−86821.7	−	150380.i	−0.0907717	−	0.157221i
$979$	−284341.	+	164165.i	−0.296671	+	0.171283i
$980$	70379.0			0.0732809
$981$		−	1.47544e6i		−	1.53315i
$982$	791369.	−	456897.i	0.820646	−	0.473800i
$983$	−859172.	−	496043.i	−0.889146	−	0.513349i	−0.0154828	−	0.999880i	$-0.504929\pi$
$983$	−859172.	−	496043.i	−0.889146	−	0.513349i	−0.873663	+	0.486532i	$0.838262\pi$
$984$	−937446.	+	541235.i	−0.968180	+	0.558979i
$985$	777763.	−	1.34713e6i	0.801632	−	1.38847i
$986$	−439787.	+	761733.i	−0.452364	+	0.783518i
$987$		−	89627.6i		−	0.0920041i
$988$	−4973.09	+	126935.i	−0.00509463	+	0.130037i
$989$	−1.29201e6			−1.32091
$990$	1.38452e6	+	799354.i	1.41263	+	0.815584i
$991$	−759839.	−	438693.i	−0.773703	−	0.446697i	0.0604913	−	0.998169i	$-0.480733\pi$
$991$	−759839.	−	438693.i	−0.773703	−	0.446697i	−0.834194	+	0.551471i	$0.814067\pi$
$992$	−34695.5	−	60094.4i	−0.0352574	−	0.0610675i
$993$	−1.27824e6	+	2.21397e6i	−1.29632	+	2.24530i
$994$	360857.	+	625023.i	0.365227	+	0.632591i
$995$	−598094.			−0.604120
$996$			1.58630e6i			1.59906i
$997$	−28262.4	−	48952.0i	−0.0284328	−	0.0492470i	0.851459	−	0.524421i	$-0.175718\pi$
$997$	−28262.4	−	48952.0i	−0.0284328	−	0.0492470i	−0.879892	+	0.475174i	$0.842385\pi$
$998$	−811890.	+	468745.i	−0.815147	+	0.470625i
$999$	−2.31678e6			−2.32142

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.5.d.a.27.4	✓	16
3.2	odd	2		342.5.m.c.217.8		16
4.3	odd	2		304.5.r.c.65.1		16
19.12	odd	6	inner	38.5.d.a.31.4	yes	16
57.50	even	6		342.5.m.c.145.8		16
76.31	even	6		304.5.r.c.145.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.5.d.a.27.4	✓	16	1.1	even	1	trivial
38.5.d.a.31.4	yes	16	19.12	odd	6	inner
304.5.r.c.65.1		16	4.3	odd	2
304.5.r.c.145.1		16	76.31	even	6
342.5.m.c.145.8		16	57.50	even	6
342.5.m.c.217.8		16	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	38.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.44949 - 1.41421i) q^{2} +(14.2931 + 8.25212i) q^{3} +(4.00000 + 6.92820i) q^{4} +(-13.5555 + 23.4789i) q^{5} +(-23.3405 - 40.4270i) q^{6} -45.5687 q^{7} -22.6274i q^{8} +(95.6949 + 165.748i) q^{9} +O(q^{10})\)	\(q+(-2.44949 - 1.41421i) q^{2} +(14.2931 + 8.25212i) q^{3} +(4.00000 + 6.92820i) q^{4} +(-13.5555 + 23.4789i) q^{5} +(-23.3405 - 40.4270i) q^{6} -45.5687 q^{7} -22.6274i q^{8} +(95.6949 + 165.748i) q^{9} +(66.4083 - 38.3408i) q^{10} +108.933 q^{11} +132.034i q^{12} +(38.0933 - 21.9932i) q^{13} +(111.620 + 64.4439i) q^{14} +(-387.501 + 223.724i) q^{15} +(-32.0000 + 55.4256i) q^{16} +(248.218 - 429.926i) q^{17} -541.332i q^{18} +(168.123 + 319.462i) q^{19} -216.888 q^{20} +(-651.317 - 376.038i) q^{21} +(-266.830 - 154.054i) q^{22} +(-360.199 - 623.882i) q^{23} +(186.724 - 323.416i) q^{24} +(-55.0047 - 95.2709i) q^{25} -124.412 q^{26} +1821.90i q^{27} +(-182.275 - 315.709i) q^{28} +(542.493 - 313.209i) q^{29} +1265.57 q^{30} -383.335i q^{31} +(156.767 - 90.5097i) q^{32} +(1556.99 + 898.926i) q^{33} +(-1216.01 + 702.067i) q^{34} +(617.708 - 1069.90i) q^{35} +(-765.559 + 1325.99i) q^{36} +1271.63i q^{37} +(39.9727 - 1020.28i) q^{38} +725.962 q^{39} +(531.266 + 306.727i) q^{40} +(-2510.24 - 1449.29i) q^{41} +(1063.60 + 1842.20i) q^{42} +(896.735 - 1553.19i) q^{43} +(435.731 + 754.708i) q^{44} -5188.78 q^{45} +2037.59i q^{46} +(59.5867 + 103.207i) q^{47} +(-914.758 + 528.136i) q^{48} -324.494 q^{49} +311.153i q^{50} +(7095.60 - 4096.65i) q^{51} +(304.747 + 175.945i) q^{52} +(760.310 - 438.965i) q^{53} +(2576.56 - 4462.73i) q^{54} +(-1476.64 + 2557.62i) q^{55} +1031.10i q^{56} +(-233.246 + 5953.46i) q^{57} -1771.78 q^{58} +(733.885 + 423.708i) q^{59} +(-3100.01 - 1789.79i) q^{60} +(1523.85 + 2639.38i) q^{61} +(-542.117 + 938.974i) q^{62} +(-4360.69 - 7552.94i) q^{63} -512.000 q^{64} +1192.52i q^{65} +(-2542.55 - 4403.82i) q^{66} +(-740.319 + 427.423i) q^{67} +3971.49 q^{68} -11889.6i q^{69} +(-3026.14 + 1747.14i) q^{70} +(4849.36 + 2799.78i) q^{71} +(3750.46 - 2165.33i) q^{72} +(-2747.54 + 4758.89i) q^{73} +(1798.35 - 3114.84i) q^{74} -1815.62i q^{75} +(-1540.81 + 2442.63i) q^{76} -4963.93 q^{77} +(-1778.24 - 1026.66i) q^{78} +(-8841.44 - 5104.61i) q^{79} +(-867.554 - 1502.65i) q^{80} +(-7283.25 + 12615.0i) q^{81} +(4099.21 + 7100.04i) q^{82} +12014.3 q^{83} -6016.61i q^{84} +(6729.45 + 11655.8i) q^{85} +(-4393.09 + 2536.35i) q^{86} +10338.5 q^{87} -2464.87i q^{88} +(-2610.25 + 1507.03i) q^{89} +(12709.9 + 7338.04i) q^{90} +(-1735.86 + 1002.20i) q^{91} +(2881.59 - 4991.06i) q^{92} +(3163.32 - 5479.04i) q^{93} -337.073i q^{94} +(-9779.59 - 383.146i) q^{95} +2987.59 q^{96} +(-7644.86 - 4413.76i) q^{97} +(794.844 + 458.904i) q^{98} +(10424.3 + 18055.4i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{3} + 64 q^{4} - 18 q^{5} - 16 q^{6} + 72 q^{7} + 352 q^{9}+O(q^{10}) \) 16 * q - 12 * q^3 + 64 * q^4 - 18 * q^5 - 16 * q^6 + 72 * q^7 + 352 * q^9	\( 16 q - 12 q^{3} + 64 q^{4} - 18 q^{5} - 16 q^{6} + 72 q^{7} + 352 q^{9} - 84 q^{11} + 450 q^{13} + 288 q^{14} - 390 q^{15} - 512 q^{16} + 606 q^{17} - 306 q^{19} - 288 q^{20} - 2160 q^{21} - 1680 q^{22} - 54 q^{23} + 128 q^{24} - 434 q^{25} + 1344 q^{26} + 288 q^{28} - 4914 q^{29} + 2752 q^{30} + 7890 q^{33} - 1536 q^{34} + 2328 q^{35} - 2816 q^{36} + 1344 q^{38} + 7620 q^{39} - 1692 q^{41} + 2080 q^{42} - 7402 q^{43} - 336 q^{44} - 16720 q^{45} + 3198 q^{47} + 768 q^{48} + 24816 q^{49} + 10710 q^{51} + 3600 q^{52} + 3870 q^{53} - 16 q^{54} - 13588 q^{55} + 3702 q^{57} - 1728 q^{58} - 18288 q^{59} - 3120 q^{60} - 6522 q^{61} - 6144 q^{62} - 15676 q^{63} - 8192 q^{64} + 4960 q^{66} - 30168 q^{67} + 9696 q^{68} + 15360 q^{70} + 35874 q^{71} + 5376 q^{72} - 8080 q^{73} - 9120 q^{74} + 480 q^{76} + 34560 q^{77} - 46560 q^{78} - 30738 q^{79} - 1152 q^{80} - 30920 q^{81} + 6720 q^{82} - 1476 q^{83} + 33626 q^{85} + 288 q^{86} + 113100 q^{87} + 19782 q^{89} + 44256 q^{90} - 34260 q^{91} + 432 q^{92} - 4272 q^{93} - 23706 q^{95} + 2048 q^{96} - 9936 q^{97} + 12672 q^{98} + 3848 q^{99}+O(q^{100}) \) 16 * q - 12 * q^3 + 64 * q^4 - 18 * q^5 - 16 * q^6 + 72 * q^7 + 352 * q^9 - 84 * q^11 + 450 * q^13 + 288 * q^14 - 390 * q^15 - 512 * q^16 + 606 * q^17 - 306 * q^19 - 288 * q^20 - 2160 * q^21 - 1680 * q^22 - 54 * q^23 + 128 * q^24 - 434 * q^25 + 1344 * q^26 + 288 * q^28 - 4914 * q^29 + 2752 * q^30 + 7890 * q^33 - 1536 * q^34 + 2328 * q^35 - 2816 * q^36 + 1344 * q^38 + 7620 * q^39 - 1692 * q^41 + 2080 * q^42 - 7402 * q^43 - 336 * q^44 - 16720 * q^45 + 3198 * q^47 + 768 * q^48 + 24816 * q^49 + 10710 * q^51 + 3600 * q^52 + 3870 * q^53 - 16 * q^54 - 13588 * q^55 + 3702 * q^57 - 1728 * q^58 - 18288 * q^59 - 3120 * q^60 - 6522 * q^61 - 6144 * q^62 - 15676 * q^63 - 8192 * q^64 + 4960 * q^66 - 30168 * q^67 + 9696 * q^68 + 15360 * q^70 + 35874 * q^71 + 5376 * q^72 - 8080 * q^73 - 9120 * q^74 + 480 * q^76 + 34560 * q^77 - 46560 * q^78 - 30738 * q^79 - 1152 * q^80 - 30920 * q^81 + 6720 * q^82 - 1476 * q^83 + 33626 * q^85 + 288 * q^86 + 113100 * q^87 + 19782 * q^89 + 44256 * q^90 - 34260 * q^91 + 432 * q^92 - 4272 * q^93 - 23706 * q^95 + 2048 * q^96 - 9936 * q^97 + 12672 * q^98 + 3848 * q^99

Introduction

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