LMFDB - Embedded newform 38.5.d.a.31.4

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			31.4
Root			$0.500000 + 15.9560i$ of defining polynomial
Character	$\chi$	$=$	38.31
Dual form			38.5.d.a.27.4

$q$-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 $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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	0.594504	−	0.804092i	$-0.297348\pi$
$3$	14.2931	−	8.25212i	1.58812	−	0.916902i	0.993617	−	0.112810i	$-0.0359851\pi$
$4$	4.00000	−	6.92820i	0.250000	−	0.433013i
$5$	−13.5555	−	23.4789i	−0.542221	−	0.939155i	−0.998776	−	0.0494593i	$-0.984250\pi$
$5$	−13.5555	−	23.4789i	−0.542221	−	0.939155i	0.456555	−	0.889695i	$-0.349083\pi$
$6$	−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	0.608450	−	0.793592i	$-0.291792\pi$
$13$	38.0933	+	21.9932i	0.225404	+	0.130137i	−0.383046	+	0.923729i	$0.625125\pi$
$14$	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	0.872993	+	0.487733i	$0.162176\pi$
$17$	248.218	+	429.926i	0.858886	+	1.48763i	−0.0141067	+	0.999900i	$0.504490\pi$
$18$			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	0.293800	+	0.955867i	$0.405080\pi$
$23$	−360.199	+	623.882i	−0.680905	+	1.17936i	−0.974705	+	0.223495i	$0.928253\pi$
$24$	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	0.786560	−	0.617514i	$-0.211860\pi$
$29$	542.493	+	313.209i	0.645058	+	0.372424i	−0.141503	+	0.989938i	$0.545193\pi$
$30$	1265.57			1.40619
$31$			383.335i			0.398891i	0.979909	+	0.199446i	$0.0639142\pi$
$31$			383.335i			0.398891i	−0.979909	+	0.199446i	$0.936086\pi$
$32$	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	$-0.846257\pi$
$37$		−	1271.63i		−	0.928873i	0.885607	−	0.464436i	$-0.153743\pi$
$38$	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	−0.999970	−	0.00768156i	$-0.997555\pi$
$41$	−2510.24	+	1449.29i	−1.49330	+	0.862159i	−0.493333	+	0.869841i	$0.664222\pi$
$42$	1063.60	−	1842.20i	0.602946	−	1.04433i
$43$	896.735	+	1553.19i	0.484984	+	0.840017i	0.999851	−	0.0172532i	$-0.00549212\pi$
$43$	896.735	+	1553.19i	0.484984	+	0.840017i	−0.514867	+	0.857270i	$0.672159\pi$
$44$	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	−0.852223	−	0.523179i	$-0.824746\pi$
$47$	59.5867	−	103.207i	0.0269745	−	0.0467213i	0.879198	+	0.476457i	$0.158079\pi$
$48$	−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	0.629192	−	0.777250i	$-0.283386\pi$
$53$	760.310	+	438.965i	0.270669	+	0.156271i	−0.358523	+	0.933521i	$0.616719\pi$
$54$	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	−0.390869	−	0.920446i	$-0.627826\pi$
$59$	733.885	−	423.708i	0.210826	−	0.121720i	0.601695	+	0.798726i	$0.294492\pi$
$60$	−3100.01	+	1789.79i	−0.861113	+	0.497164i
$61$	1523.85	−	2639.38i	0.409527	−	0.709321i	−0.585310	−	0.810809i	$-0.699027\pi$
$61$	1523.85	−	2639.38i	0.409527	−	0.709321i	0.994837	+	0.101489i	$0.0323606\pi$
$62$	−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	0.415269	−	0.909699i	$-0.363687\pi$
$67$	−740.319	−	427.423i	−0.164918	−	0.0952157i	−0.580188	+	0.814483i	$0.697021\pi$
$68$	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	0.0652006	−	0.997872i	$-0.479231\pi$
$71$	4849.36	−	2799.78i	0.961984	−	0.555401i	0.896783	+	0.442471i	$0.145898\pi$
$72$	3750.46	+	2165.33i	0.723468	+	0.417695i
$73$	−2747.54	−	4758.89i	−0.515584	−	0.893017i	−0.999836	−	0.0180887i	$-0.994242\pi$
$73$	−2747.54	−	4758.89i	−0.515584	−	0.893017i	0.484253	−	0.874928i	$-0.339091\pi$
$74$	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	−0.996005	−	0.0893006i	$-0.971537\pi$
$79$	−8841.44	+	5104.61i	−1.41667	+	0.817915i	−0.420666	+	0.907216i	$0.638203\pi$
$80$	−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	0.326100	−	0.945335i	$-0.394265\pi$
$89$	−2610.25	−	1507.03i	−0.329535	−	0.190257i	−0.655635	+	0.755078i	$0.727599\pi$
$90$	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	−0.847825	−	0.530276i	$-0.822088\pi$
$97$	−7644.86	+	4413.76i	−0.812505	+	0.469100i	0.0353202	+	0.999376i	$0.488755\pi$
$98$	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	−0.950203	−	0.311632i	$-0.899124\pi$
$101$	−2093.45	+	3625.97i	−0.205220	+	0.355452i	0.744983	+	0.667084i	$0.232458\pi$
$102$	−23174.1			−2.22743
$103$			1131.66i			0.106669i	0.998577	+	0.0533347i	$0.0169850\pi$
$103$			1131.66i			0.106669i	−0.998577	+	0.0533347i	$0.983015\pi$
$104$	−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	$-0.887941\pi$
$107$		−	7895.65i		−	0.689636i	0.938669	−	0.344818i	$-0.112059\pi$
$108$	−12622.5	−	7287.60i	−1.08218	−	0.624794i
$109$	−6676.28	+	3854.55i	−0.561929	+	0.324430i	−0.753919	−	0.656967i	$-0.771839\pi$
$109$	−6676.28	+	3854.55i	−0.561929	+	0.324430i	0.191990	+	0.981397i	$0.438506\pi$
$110$	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	$0.227397\pi$
$113$			16731.4i			1.31031i	−0.755494	+	0.655156i	$0.772603\pi$
$114$	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	0.963260	−	0.268569i	$-0.0865507\pi$
$127$	19553.2	+	11289.1i	1.21230	+	0.699924i	0.249043	+	0.968493i	$0.419884\pi$
$128$	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	0.825017	−	0.565108i	$-0.191166\pi$
$131$	−1319.50	−	2285.44i	−0.0768895	−	0.133176i	−0.901906	+	0.431932i	$0.857832\pi$
$132$		−	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	0.417577	+	0.908642i	$0.362879\pi$
$137$	−10850.7	+	18794.0i	−0.578118	+	1.00133i	−0.995695	+	0.0926888i	$0.970454\pi$
$138$	−16814.4	−	29123.5i	−0.882926	−	1.52927i
$139$	1417.08	−	2454.45i	0.0733440	−	0.127036i	−0.827021	−	0.562171i	$-0.809966\pi$
$139$	1417.08	−	2454.45i	0.0733440	−	0.127036i	0.900365	+	0.435136i	$0.143300\pi$
$140$	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	−0.859595	−	0.510976i	$-0.829284\pi$
$149$	−19366.3	−	33543.4i	−0.872315	−	1.51089i	−0.0127203	−	0.999919i	$-0.504049\pi$
$150$	−2567.67	−	4447.34i	−0.114119	−	0.197660i
$151$		−	3211.72i		−	0.140859i	−0.997517	−	0.0704293i	$-0.977563\pi$
$151$		−	3211.72i		−	0.140859i	0.997517	−	0.0704293i	$-0.0224369\pi$
$152$	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	0.824480	−	0.565891i	$-0.191468\pi$
$157$	−1918.57	−	3323.07i	−0.0778357	−	0.134815i	−0.902316	+	0.431075i	$0.858134\pi$
$158$	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	0.772122	−	0.635474i	$-0.219195\pi$
$167$	16952.2	+	9787.38i	0.607847	+	0.350940i	−0.164276	+	0.986414i	$0.552529\pi$
$168$	−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	−0.390785	−	0.920482i	$-0.627796\pi$
$173$	6314.53	−	3645.69i	0.210984	−	0.121811i	0.601768	+	0.798671i	$0.294463\pi$
$174$	−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	$0.0837496\pi$
$179$			16666.6i			0.520164i	−0.965587	+	0.260082i	$0.916250\pi$
$180$	−20755.1	+	35948.9i	−0.640590	+	1.10953i
$181$	27509.3	+	15882.5i	0.839696	+	0.484799i	0.857161	−	0.515049i	$-0.172226\pi$
$181$	27509.3	+	15882.5i	0.839696	+	0.484799i	−0.0174648	+	0.999847i	$0.505559\pi$
$182$	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	−0.835178	−	0.549980i	$-0.814635\pi$
$193$	−28922.8	+	16698.6i	−0.776471	+	0.448295i	0.0587074	+	0.998275i	$0.481302\pi$
$194$	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	−0.692483	−	0.721435i	$-0.743483\pi$
$199$	11030.4	−	19105.3i	0.278539	−	0.482444i	0.971022	+	0.238990i	$0.0768164\pi$
$200$	−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	−0.560511	−	0.828147i	$-0.689395\pi$
$211$	−5501.42	+	3176.25i	−0.123569	+	0.0713427i	0.436941	+	0.899490i	$0.356062\pi$
$212$	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	−0.456687	−	0.889627i	$-0.650964\pi$
$223$	4247.34	−	2452.20i	0.0854096	−	0.0493113i	0.542097	+	0.840316i	$0.317631\pi$
$224$	−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	$0.0403515\pi$
$227$			13029.5i			0.252858i	−0.991976	+	0.126429i	$0.959648\pi$
$228$	−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	0.779590	−	0.626290i	$-0.215427\pi$
$233$	−8283.86	−	14348.1i	−0.152588	−	0.264290i	−0.932178	+	0.362000i	$0.882094\pi$
$234$	−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	0.725817	−	0.687888i	$-0.241462\pi$
$241$	28633.8	+	16531.7i	0.492997	+	0.284632i	−0.232820	+	0.972520i	$0.574795\pi$
$242$	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	−0.812433	−	0.583055i	$-0.801857\pi$
$251$	6219.69	−	10772.8i	0.0987237	−	0.170994i	0.911157	+	0.412060i	$0.135191\pi$
$252$	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	0.770251	−	0.637741i	$-0.220131\pi$
$257$	39832.7	+	22997.4i	0.603077	+	0.348187i	−0.167174	+	0.985927i	$0.553464\pi$
$258$	−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	0.990982	−	0.133994i	$-0.0427803\pi$
$263$	26246.1	+	45459.6i	0.379449	+	0.657225i	−0.611533	+	0.791219i	$0.709447\pi$
$264$	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	−0.678208	−	0.734870i	$-0.737243\pi$
$269$	−27562.0	+	15913.0i	−0.380896	+	0.219911i	0.297312	+	0.954780i	$0.403910\pi$
$270$	69853.2	−	120989.i	0.958205	−	1.65966i
$271$	23483.6	+	40674.8i	0.319761	+	0.553843i	0.980438	−	0.196828i	$-0.0630640\pi$
$271$	23483.6	+	40674.8i	0.319761	+	0.553843i	−0.660677	+	0.750670i	$0.729731\pi$
$272$	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	0.438974	−	0.898500i	$-0.355342\pi$
$281$	−9448.74	−	5455.23i	−0.119663	−	0.0690877i	−0.558637	+	0.829412i	$0.688675\pi$
$282$	2781.57	+	4817.82i	0.0349777	+	0.0605832i
$283$	6280.81	+	10878.7i	0.0784229	+	0.135832i	0.902570	−	0.430544i	$-0.141678\pi$
$283$	6280.81	+	10878.7i	0.0784229	+	0.135832i	−0.824147	+	0.566376i	$0.808345\pi$
$284$		−	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	$0.146970\pi$
$293$			76489.5i			0.890977i	−0.895288	+	0.445488i	$0.853030\pi$
$294$	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	−0.894077	−	0.447914i	$-0.852167\pi$
$307$	−89839.1	+	51868.7i	−0.953211	+	0.550336i	−0.0591338	+	0.998250i	$0.518834\pi$
$308$	−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	−0.269679	−	0.962950i	$-0.586917\pi$
$313$	68490.1	−	118628.i	0.699100	−	1.21088i	0.968779	−	0.247927i	$-0.0797492\pi$
$314$	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	−0.131658	−	0.991295i	$-0.542030\pi$
$317$	−106114.	−	61264.8i	−1.05597	−	0.609667i	−0.924316	+	0.381629i	$0.875363\pi$
$318$	−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	$-0.750091\pi$
$331$		−	154898.i		−	1.41381i	0.707310	−	0.706904i	$-0.249909\pi$
$332$	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	−0.227657	−	0.973741i	$-0.573106\pi$
$337$	56988.9	−	32902.6i	0.501800	−	0.289714i	0.729457	+	0.684027i	$0.239773\pi$
$338$	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	−0.856758	−	0.515718i	$-0.827525\pi$
$347$	−105358.	−	182486.i	−0.875004	−	1.51555i	−0.0182458	−	0.999834i	$-0.505808\pi$
$348$	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	0.988055	+	0.154102i	$0.0492484\pi$
$359$	80870.7	+	140072.i	0.627484	+	1.08683i	−0.360571	+	0.932732i	$0.617418\pi$
$360$		−	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	0.229060	−	0.973412i	$-0.426435\pi$
$367$	128969.	−	223380.i	0.957530	−	1.65849i	0.728470	−	0.685078i	$-0.240232\pi$
$368$	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	$-0.919026\pi$
$373$		−	70024.0i		−	0.503303i	0.967818	−	0.251651i	$-0.0809736\pi$
$374$	−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	$-0.753122\pi$
$379$		−	201137.i		−	1.40027i	0.714008	−	0.700137i	$-0.246878\pi$
$380$	−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	−0.853308	−	0.521407i	$-0.825408\pi$
$383$	−121519.	+	70158.9i	−0.828411	+	0.478284i	0.0248971	+	0.999690i	$0.492074\pi$
$384$	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	0.116069	−	0.993241i	$-0.462971\pi$
$389$	138944.	−	240658.i	0.918207	−	1.59038i	0.802137	−	0.597140i	$-0.203696\pi$
$390$	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	0.783171	−	0.621806i	$-0.213601\pi$
$397$	−23155.0	−	40105.6i	−0.146914	−	0.254463i	−0.930085	+	0.367343i	$0.880267\pi$
$398$			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	−0.723383	−	0.690447i	$-0.757414\pi$
$401$	−78330.8	+	45224.3i	−0.487129	+	0.281244i	0.236254	+	0.971691i	$0.424080\pi$
$402$	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	−0.303365	−	0.952874i	$-0.598110\pi$
$409$	−214163.	−	123647.i	−1.28026	−	0.739159i	−0.976896	+	0.213715i	$0.931444\pi$
$410$	−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	0.292240	−	0.956345i	$-0.405600\pi$
$421$	224490.	−	129609.i	1.26658	−	0.731259i	0.974339	+	0.225086i	$0.0722662\pi$
$422$	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	0.990901	−	0.134589i	$-0.0429715\pi$
$431$	254454.	+	146909.i	1.36979	+	0.790851i	0.378893	+	0.925441i	$0.376305\pi$
$432$	−100980.	+	58300.8i	−0.541088	+	0.312397i
$433$	168884.	+	97505.3i	0.900768	+	0.520059i	0.877449	−	0.479669i	$-0.159243\pi$
$433$	168884.	+	97505.3i	0.900768	+	0.520059i	0.0233190	+	0.999728i	$0.492577\pi$
$434$	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	−0.770324	−	0.637653i	$-0.779906\pi$
$439$	−116261.	+	67123.5i	−0.603263	+	0.348294i	0.167061	+	0.985946i	$0.446572\pi$
$440$	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	−0.986832	−	0.161747i	$-0.948287\pi$
$443$	−69342.5	+	120105.i	−0.353339	+	0.612002i	0.633493	+	0.773748i	$0.281621\pi$
$444$	−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	$-0.972359\pi$
$449$		−	34968.8i		−	0.173455i	0.996232	−	0.0867276i	$-0.0276410\pi$
$450$	−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	0.995150	−	0.0983700i	$-0.0313629\pi$
$461$	87640.3	+	151797.i	0.412384	+	0.714270i	−0.582766	+	0.812640i	$0.698030\pi$
$462$	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	−0.602601	−	0.798042i	$-0.705869\pi$
$479$	89441.7	−	154918.i	0.389824	−	0.675196i	0.992426	+	0.122847i	$0.0392024\pi$
$480$	−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	$0.163881\pi$
$487$			233565.i			0.984806i	−0.870367	+	0.492403i	$0.836119\pi$
$488$	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	−0.977888	−	0.209129i	$-0.932937\pi$
$491$	−161537.	−	279791.i	−0.670055	−	1.16057i	0.307833	−	0.951440i	$-0.400396\pi$
$492$	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	0.979132	+	0.203226i	$0.0651427\pi$
$499$	165726.	+	287046.i	0.665565	+	1.15279i	−0.313567	+	0.949566i	$0.601524\pi$
$500$	−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	−0.244283	−	0.969704i	$-0.578552\pi$
$503$	181571.	−	314490.i	0.717647	−	1.24300i	0.961930	−	0.273297i	$-0.0881142\pi$
$504$	−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	−0.337016	−	0.941499i	$-0.609418\pi$
$509$	−342217.	−	197579.i	−1.32089	−	0.762614i	−0.983870	+	0.178885i	$0.942751\pi$
$510$	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	$-0.955149\pi$
$521$		−	76241.3i		−	0.280876i	0.990089	−	0.140438i	$-0.0448511\pi$
$522$	−169550.	+	293669.i	−0.622238	+	1.07775i
$523$	427334.	+	246722.i	1.56230	+	0.901994i	0.997024	+	0.0770925i	$0.0245637\pi$
$523$	427334.	+	246722.i	1.56230	+	0.901994i	0.565276	+	0.824902i	$0.308770\pi$
$524$	−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	−0.0435535	−	0.999051i	$-0.513868\pi$
$541$	246855.	−	427565.i	0.843427	−	1.46086i	0.886980	−	0.461807i	$-0.152799\pi$
$542$	−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	0.652601	−	0.757702i	$-0.273678\pi$
$547$	96558.3	+	55748.0i	0.322712	+	0.186318i	−0.329889	+	0.944020i	$0.607011\pi$
$548$	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	−0.950359	−	0.311156i	$-0.899284\pi$
$557$	−63821.5	+	110542.i	−0.205711	+	0.356301i	0.744648	+	0.667457i	$0.232617\pi$
$558$	−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	$0.0159303\pi$
$563$			31713.1i			0.100051i	−0.998748	+	0.0500256i	$0.984070\pi$
$564$	−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	$0.0982337\pi$
$569$			196675.i			0.607470i	−0.952757	+	0.303735i	$0.901766\pi$
$570$	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	0.720825	−	0.693117i	$-0.243763\pi$
$587$	−82643.2	−	143142.i	−0.239845	−	0.415424i	−0.960670	+	0.277694i	$0.910430\pi$
$588$			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	−0.419377	−	0.907812i	$-0.637751\pi$
$593$	202726.	−	351131.i	0.576500	−	0.998527i	0.995877	−	0.0907151i	$-0.0289153\pi$
$594$	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	−0.398049	−	0.917364i	$-0.630313\pi$
$599$	−499284.	−	288262.i	−1.39153	−	0.803403i	−0.993485	+	0.113962i	$0.963646\pi$
$600$	−41082.8			−0.114119
$601$			274026.i			0.758651i	0.925263	+	0.379326i	$0.123844\pi$
$601$			274026.i			0.758651i	−0.925263	+	0.379326i	$0.876156\pi$
$602$	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	$-0.861805\pi$
$607$		−	309970.i		−	0.841283i	0.907227	−	0.420642i	$-0.138195\pi$
$608$	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	0.984237	+	0.176853i	$0.0565917\pi$
$613$	242475.	+	419980.i	0.645278	+	1.11765i	−0.338959	+	0.940801i	$0.610075\pi$
$614$	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	−0.919762	−	0.392477i	$-0.871618\pi$
$617$	−45677.1	+	79115.1i	−0.119985	+	0.207821i	0.799776	+	0.600298i	$0.204951\pi$
$618$	−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	−0.0220686	−	0.999756i	$-0.507025\pi$
$631$	340340.	−	589486.i	0.854780	−	1.48052i	0.876849	−	0.480766i	$-0.159641\pi$
$632$	−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	−0.776198	−	0.630490i	$-0.782854\pi$
$641$	−254038.	+	146669.i	−0.618276	+	0.356962i	0.157921	+	0.987452i	$0.449521\pi$
$642$	319197.	+	184288.i	0.774442	+	0.447124i
$643$	202790.	+	351243.i	0.490484	+	0.849543i	0.999940	−	0.0109537i	$-0.00348673\pi$
$643$	202790.	+	351243.i	0.490484	+	0.849543i	−0.509456	+	0.860497i	$0.670153\pi$
$644$	−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	0.285041	−	0.958515i	$-0.407993\pi$
$659$	−174814.	−	100929.i	−0.402537	−	0.232405i	−0.687578	+	0.726110i	$0.741326\pi$
$660$	−337692.	+	194967.i	−0.775235	+	0.447582i
$661$	385678.	+	222671.i	0.882718	+	0.509638i	0.871554	−	0.490300i	$-0.163113\pi$
$661$	385678.	+	222671.i	0.882718	+	0.509638i	0.0111647	+	0.999938i	$0.496446\pi$
$662$	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	$-0.965123\pi$
$673$		−	99055.7i		−	0.218700i	0.994003	−	0.109350i	$-0.0348770\pi$
$674$	−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	$0.124280\pi$
$677$			348874.i			0.761187i	−0.924743	+	0.380593i	$0.875720\pi$
$678$	−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	$0.182373\pi$
$683$			505774.i			1.08421i	−0.840309	+	0.542107i	$0.817627\pi$
$684$	−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	0.803398	−	0.595442i	$-0.203023\pi$
$701$	−56004.4	−	97002.5i	−0.113969	−	0.197400i	−0.917367	+	0.398042i	$0.869690\pi$
$702$			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	−0.926119	−	0.377231i	$-0.876876\pi$
$709$	−68549.6	+	118731.i	−0.136368	+	0.236196i	0.789751	+	0.613427i	$0.210210\pi$
$710$	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	0.718394	−	0.695637i	$-0.244878\pi$
$719$	−125747.	−	217800.i	−0.243242	−	0.421308i	−0.961636	+	0.274329i	$0.911544\pi$
$720$	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	0.716072	−	0.698027i	$-0.245938\pi$
$727$	−130268.	−	225631.i	−0.246473	−	0.426903i	−0.962545	+	0.271123i	$0.912605\pi$
$728$	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	0.812413	−	0.583082i	$-0.198153\pi$
$739$	−53933.3	−	93415.2i	−0.0987571	−	0.171052i	−0.911170	+	0.412030i	$0.864820\pi$
$740$			275801.i			0.503654i
$741$	122051.	−	231917.i	0.222281	−	0.422373i
$742$	113154.			0.205525
$743$	−187525.	+	108268.i	−0.339690	+	0.196120i	−0.660135	−	0.751147i	$-0.729501\pi$
$743$	−187525.	+	108268.i	−0.339690	+	0.196120i	0.320445	+	0.947267i	$0.396168\pi$
$744$	−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	0.996265	−	0.0863516i	$-0.0275208\pi$
$751$	800664.	+	462264.i	1.41961	+	0.819615i	0.423350	+	0.905966i	$0.360854\pi$
$752$	−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	−0.904383	−	0.426722i	$-0.859668\pi$
$757$	−470899.	−	815622.i	−0.821744	−	1.42330i	0.0826389	−	0.996580i	$-0.473665\pi$
$758$	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	−0.421269	−	0.906936i	$-0.638415\pi$
$769$	339911.	−	588744.i	0.574795	−	0.995575i	0.996064	−	0.0886386i	$-0.0282516\pi$
$770$	−329646.	−	190321.i	−0.555989	−	0.321000i
$771$	759109.			1.27701
$772$			267177.i			0.448295i
$773$	382639.	+	220917.i	0.640369	+	0.369717i	0.784756	−	0.619804i	$-0.212788\pi$
$773$	382639.	+	220917.i	0.640369	+	0.369717i	−0.144388	+	0.989521i	$0.546121\pi$
$774$	−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	$0.346400\pi$
$787$			1.09729e6i			1.77163i	−0.464040	+	0.885814i	$0.653600\pi$
$788$	−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	$-0.715921\pi$
$797$		−	989170.i		−	1.55724i	0.627499	−	0.778618i	$-0.284079\pi$
$798$	−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	−0.374829	−	0.927094i	$-0.622299\pi$
$811$	−897875.	−	518388.i	−1.36513	−	0.788159i	−0.990301	+	0.138935i	$0.955632\pi$
$812$	−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	−0.719375	−	0.694622i	$-0.755572\pi$
$821$	163032.	−	282380.i	0.241873	−	0.418937i	0.961248	+	0.275686i	$0.0889049\pi$
$822$	−506522.	−	877322.i	−0.749643	−	1.29842i
$823$	160326.	−	277693.i	0.236703	−	0.409982i	−0.723063	−	0.690782i	$-0.757266\pi$
$823$	160326.	−	277693.i	0.236703	−	0.409982i	0.959766	+	0.280800i	$0.0905997\pi$
$824$	−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	0.963553	−	0.267517i	$-0.0862031\pi$
$827$	830053.	+	479231.i	1.21365	+	0.700703i	0.250100	+	0.968220i	$0.419536\pi$
$828$	1.10301e6			1.60887
$829$			311615.i			0.453429i	0.973961	+	0.226715i	$0.0727985\pi$
$829$			311615.i			0.453429i	−0.973961	+	0.226715i	$0.927202\pi$
$830$	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	−0.466487	−	0.884528i	$-0.654480\pi$
$839$	46665.7	−	26942.4i	0.0662939	−	0.0382748i	0.532781	+	0.846253i	$0.321147\pi$
$840$	−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	−0.992589	−	0.121518i	$-0.961224\pi$
$853$	−437680.	−	758084.i	−0.601532	−	1.04188i	0.391057	−	0.920366i	$-0.372109\pi$
$854$		−	392811.i		−	0.538601i
$855$	−872351.	+	1.65762e6i	−1.19333	+	2.26752i
$856$	178658.			0.243823
$857$	−925783.	+	534501.i	−1.26051	+	0.727758i	−0.973174	−	0.230071i	$-0.926104\pi$
$857$	−925783.	+	534501.i	−1.26051	+	0.727758i	−0.287340	+	0.957829i	$0.592771\pi$
$858$	−193708.	+	111837.i	−0.263132	+	0.151919i
$859$	−94002.2	+	162817.i	−0.127395	+	0.220654i	−0.922666	−	0.385599i	$-0.873995\pi$
$859$	−94002.2	+	162817.i	−0.127395	+	0.220654i	0.795272	+	0.606253i	$0.207328\pi$
$860$	−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	$-0.925090\pi$
$863$		−	347316.i		−	0.466341i	0.972436	−	0.233170i	$-0.0749100\pi$
$864$	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	−0.958444	−	0.285280i	$-0.907913\pi$
$877$	−915730.	+	528697.i	−1.19061	+	0.687397i	−0.232162	+	0.972677i	$0.574580\pi$
$878$	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	−0.922124	−	0.386893i	$-0.873548\pi$
$883$	−98242.9	+	170162.i	−0.126003	+	0.218243i	0.796122	+	0.605136i	$0.206881\pi$
$884$	151287.	+	87345.7i	0.193597	+	0.111773i
$885$	−379174.			−0.484119
$886$		−	392260.i		−	0.499697i
$887$	571698.	+	330070.i	0.726640	+	0.419526i	0.817192	−	0.576366i	$-0.195530\pi$
$887$	571698.	+	330070.i	0.726640	+	0.419526i	−0.0905515	+	0.995892i	$0.528863\pi$
$888$	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	0.562999	−	0.826458i	$-0.309648\pi$
$907$	1.28352e6	−	741042.i	1.56023	−	0.900800i	0.997233	−	0.0743424i	$-0.0236858\pi$
$908$	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	$-0.697393\pi$
$911$		−	1.35079e6i		−	1.62761i	0.581139	−	0.813804i	$-0.302607\pi$
$912$	−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	0.975352	−	0.220654i	$-0.0708190\pi$
$929$	255965.	+	443344.i	0.296584	+	0.513699i	−0.678768	+	0.734353i	$0.737486\pi$
$930$			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	−0.996210	−	0.0869812i	$-0.972278\pi$
$937$	−371185.	+	642912.i	−0.422777	+	0.732271i	0.573433	+	0.819253i	$0.305611\pi$
$938$	−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	0.126754	−	0.991934i	$-0.459544\pi$
$941$	−592306.	−	341968.i	−0.668909	−	0.386195i	−0.795663	+	0.605739i	$0.792877\pi$
$942$	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	0.916584	−	0.399843i	$-0.130935\pi$
$947$	100459.	+	173999.i	0.112018	+	0.194021i	−0.804566	+	0.593863i	$0.797602\pi$
$948$	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	−0.555854	−	0.831280i	$-0.687609\pi$
$953$	−103420.	+	59709.6i	−0.113872	+	0.0657443i	0.441982	+	0.897024i	$0.354276\pi$
$954$	−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	−0.996842	−	0.0794163i	$-0.974694\pi$
$967$	−530380.	−	918645.i	−0.567197	−	0.982415i	0.429644	−	0.902998i	$-0.358639\pi$
$968$		−	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	−0.503087	−	0.864236i	$-0.667803\pi$
$971$	−5827.53	+	3364.53i	−0.00618082	+	0.00356850i	0.496906	+	0.867804i	$0.334469\pi$
$972$	−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	$-0.945239\pi$
$977$		−	326810.i		−	0.342379i	0.985238	−	0.171189i	$-0.0547610\pi$
$978$	−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	−0.873663	−	0.486532i	$-0.838262\pi$
$983$	−859172.	+	496043.i	−0.889146	+	0.513349i	−0.0154828	+	0.999880i	$0.504929\pi$
$984$	−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	−0.834194	−	0.551471i	$-0.814067\pi$
$991$	−759839.	+	438693.i	−0.773703	+	0.446697i	0.0604913	+	0.998169i	$0.480733\pi$
$992$	−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	−0.879892	−	0.475174i	$-0.842385\pi$
$997$	−28262.4	+	48952.0i	−0.0284328	+	0.0492470i	0.851459	+	0.524421i	$0.175718\pi$
$998$	−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.31.4	yes	16
3.2	odd	2		342.5.m.c.145.8		16
4.3	odd	2		304.5.r.c.145.1		16
19.8	odd	6	inner	38.5.d.a.27.4	✓	16
57.8	even	6		342.5.m.c.217.8		16
76.27	even	6		304.5.r.c.65.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.5.d.a.27.4	✓	16	19.8	odd	6	inner
38.5.d.a.31.4	yes	16	1.1	even	1	trivial
304.5.r.c.65.1		16	76.27	even	6
304.5.r.c.145.1		16	4.3	odd	2
342.5.m.c.145.8		16	3.2	odd	2
342.5.m.c.217.8		16	57.8	even	6

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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