LMFDB - Embedded newform 22.5.d.a.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,5,Mod(7,22)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([7]))

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

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

chi := DirichletCharacter("22.7");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	22.d (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.27413918784$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
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} - 4 x^{15} + 138 x^{14} - 428 x^{13} + 7783 x^{12} - 18620 x^{11} + 235604 x^{10} + \cdots + 1499670491 $ x^16 - 4x^15 + 138x^14 - 428x^13 + 7783x^12 - 18620x^11 + 235604x^10 - 425164x^9 + 4199998x^8 - 5446172x^7 + 45313276x^6 - 38408204x^5 + 290282498x^4 - 132888724x^3 + 1016893202x^2 - 153602264*x + 1499670491
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8}\cdot 11^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			19.3
Root			$-0.309017 - 4.73267i$ of defining polynomial
Character	$\chi$	$=$	22.19
Dual form			22.5.d.a.7.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.66251 + 2.28825i) q^{2} +(0.309288 + 0.951890i) q^{3} +(-2.47214 + 7.60845i) q^{4} +(35.4031 + 25.7219i) q^{5} +(-1.66396 + 2.29025i) q^{6} +(-65.6073 - 21.3171i) q^{7} +(-21.5200 + 6.99226i) q^{8} +(64.7199 - 47.0218i) q^{9} +O(q^{10})$	\(q+(1.66251 + 2.28825i) q^{2} +(0.309288 + 0.951890i) q^{3} +(-2.47214 + 7.60845i) q^{4} +(35.4031 + 25.7219i) q^{5} +(-1.66396 + 2.29025i) q^{6} +(-65.6073 - 21.3171i) q^{7} +(-21.5200 + 6.99226i) q^{8} +(64.7199 - 47.0218i) q^{9} +123.774i q^{10} +(65.6374 - 101.650i) q^{11} -8.00701 q^{12} +(-100.269 - 138.009i) q^{13} +(-60.2938 - 185.565i) q^{14} +(-13.5346 + 41.6553i) q^{15} +(-51.7771 - 37.6183i) q^{16} +(-130.596 + 179.749i) q^{17} +(215.195 + 69.9210i) q^{18} +(141.801 - 46.0739i) q^{19} +(-283.225 + 205.775i) q^{20} -69.0440i q^{21} +(341.723 - 18.7995i) q^{22} -272.896 q^{23} +(-13.3117 - 18.3220i) q^{24} +(398.631 + 1226.86i) q^{25} +(149.100 - 458.882i) q^{26} +(130.364 + 94.7153i) q^{27} +(324.380 - 446.471i) q^{28} +(571.633 + 185.735i) q^{29} +(-117.819 + 38.2817i) q^{30} +(-714.607 + 519.192i) q^{31} -181.019i q^{32} +(117.060 + 31.0405i) q^{33} -628.427 q^{34} +(-1774.39 - 2442.23i) q^{35} +(197.767 + 608.663i) q^{36} +(440.083 - 1354.44i) q^{37} +(341.174 + 247.877i) q^{38} +(100.357 - 138.130i) q^{39} +(-941.728 - 305.986i) q^{40} +(-1050.88 + 341.452i) q^{41} +(157.990 - 114.786i) q^{42} +1489.14i q^{43} +(611.135 + 750.692i) q^{44} +3500.78 q^{45} +(-453.692 - 624.454i) q^{46} +(-772.201 - 2376.59i) q^{47} +(19.7944 - 60.9209i) q^{48} +(1907.45 + 1385.84i) q^{49} +(-2144.63 + 2951.83i) q^{50} +(-211.493 - 68.7183i) q^{51} +(1297.91 - 421.718i) q^{52} +(-3070.02 + 2230.50i) q^{53} +455.771i q^{54} +(4938.40 - 1910.41i) q^{55} +1560.92 q^{56} +(87.7146 + 120.729i) q^{57} +(525.337 + 1616.82i) q^{58} +(-338.601 + 1042.11i) q^{59} +(-283.473 - 205.955i) q^{60} +(-1856.32 + 2555.01i) q^{61} +(-2376.08 - 772.035i) q^{62} +(-5248.47 + 1705.33i) q^{63} +(414.217 - 300.946i) q^{64} -7465.07i q^{65} +(123.586 + 319.468i) q^{66} +251.628 q^{67} +(-1044.76 - 1437.99i) q^{68} +(-84.4035 - 259.767i) q^{69} +(2638.50 - 8120.47i) q^{70} +(3590.99 + 2609.01i) q^{71} +(-1063.98 + 1464.45i) q^{72} +(3983.96 + 1294.47i) q^{73} +(3830.93 - 1244.74i) q^{74} +(-1044.54 + 758.906i) q^{75} +1192.79i q^{76} +(-6473.17 + 5269.78i) q^{77} +482.920 q^{78} +(-3109.83 - 4280.32i) q^{79} +(-865.459 - 2663.61i) q^{80} +(1952.55 - 6009.32i) q^{81} +(-2528.43 - 1837.01i) q^{82} +(261.533 - 359.969i) q^{83} +(525.318 + 170.686i) q^{84} +(-9246.98 + 3004.53i) q^{85} +(-3407.51 + 2475.70i) q^{86} +601.577i q^{87} +(-701.751 + 2646.46i) q^{88} +8935.75 q^{89} +(5820.07 + 8010.64i) q^{90} +(3636.45 + 11191.8i) q^{91} +(674.637 - 2076.32i) q^{92} +(-715.233 - 519.647i) q^{93} +(4154.43 - 5718.09i) q^{94} +(6205.31 + 2016.23i) q^{95} +(172.310 - 55.9871i) q^{96} +(1684.12 - 1223.58i) q^{97} +6668.67i q^{98} +(-531.718 - 9665.17i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{3} + 32 q^{4} + 30 q^{5} - 80 q^{6} + 150 q^{7} + 110 q^{9}+O(q^{10}) $ 16 * q - 2 * q^3 + 32 * q^4 + 30 * q^5 - 80 * q^6 + 150 * q^7 + 110 * q^9	\( 16 q - 2 q^{3} + 32 q^{4} + 30 q^{5} - 80 q^{6} + 150 q^{7} + 110 q^{9} - 30 q^{11} - 384 q^{12} - 510 q^{13} - 96 q^{14} - 1398 q^{15} - 256 q^{16} + 1770 q^{17} + 1120 q^{18} + 1020 q^{19} - 240 q^{20} + 240 q^{22} - 2424 q^{23} - 640 q^{24} - 858 q^{25} + 480 q^{26} + 2224 q^{27} + 1600 q^{28} + 4890 q^{29} + 3360 q^{30} + 602 q^{31} - 2648 q^{33} - 3904 q^{34} - 8670 q^{35} + 720 q^{36} - 4518 q^{37} - 4800 q^{38} - 1130 q^{39} - 1280 q^{40} + 1290 q^{41} - 3808 q^{42} + 720 q^{44} + 12152 q^{45} + 4480 q^{46} + 642 q^{47} - 128 q^{48} + 9534 q^{49} + 6720 q^{50} - 1500 q^{51} + 4000 q^{52} + 2598 q^{53} + 2582 q^{55} - 3072 q^{56} + 9140 q^{57} - 6496 q^{58} + 6660 q^{59} - 5776 q^{60} - 27410 q^{61} - 19680 q^{62} - 27260 q^{63} + 2048 q^{64} + 2528 q^{66} + 21524 q^{67} + 14160 q^{68} + 11416 q^{69} + 34400 q^{70} - 5562 q^{71} + 10240 q^{72} - 7790 q^{73} + 5760 q^{74} + 3576 q^{75} - 1110 q^{77} - 39424 q^{78} - 2770 q^{79} - 3840 q^{80} - 25464 q^{81} - 17472 q^{82} - 36900 q^{83} - 24480 q^{84} - 24750 q^{85} + 624 q^{86} - 5760 q^{88} + 46596 q^{89} + 55360 q^{90} + 32370 q^{91} + 14112 q^{92} + 20722 q^{93} + 58880 q^{94} + 74250 q^{95} - 3732 q^{97} + 45802 q^{99}+O(q^{100}) \) 16 * q - 2 * q^3 + 32 * q^4 + 30 * q^5 - 80 * q^6 + 150 * q^7 + 110 * q^9 - 30 * q^11 - 384 * q^12 - 510 * q^13 - 96 * q^14 - 1398 * q^15 - 256 * q^16 + 1770 * q^17 + 1120 * q^18 + 1020 * q^19 - 240 * q^20 + 240 * q^22 - 2424 * q^23 - 640 * q^24 - 858 * q^25 + 480 * q^26 + 2224 * q^27 + 1600 * q^28 + 4890 * q^29 + 3360 * q^30 + 602 * q^31 - 2648 * q^33 - 3904 * q^34 - 8670 * q^35 + 720 * q^36 - 4518 * q^37 - 4800 * q^38 - 1130 * q^39 - 1280 * q^40 + 1290 * q^41 - 3808 * q^42 + 720 * q^44 + 12152 * q^45 + 4480 * q^46 + 642 * q^47 - 128 * q^48 + 9534 * q^49 + 6720 * q^50 - 1500 * q^51 + 4000 * q^52 + 2598 * q^53 + 2582 * q^55 - 3072 * q^56 + 9140 * q^57 - 6496 * q^58 + 6660 * q^59 - 5776 * q^60 - 27410 * q^61 - 19680 * q^62 - 27260 * q^63 + 2048 * q^64 + 2528 * q^66 + 21524 * q^67 + 14160 * q^68 + 11416 * q^69 + 34400 * q^70 - 5562 * q^71 + 10240 * q^72 - 7790 * q^73 + 5760 * q^74 + 3576 * q^75 - 1110 * q^77 - 39424 * q^78 - 2770 * q^79 - 3840 * q^80 - 25464 * q^81 - 17472 * q^82 - 36900 * q^83 - 24480 * q^84 - 24750 * q^85 + 624 * q^86 - 5760 * q^88 + 46596 * q^89 + 55360 * q^90 + 32370 * q^91 + 14112 * q^92 + 20722 * q^93 + 58880 * q^94 + 74250 * q^95 - 3732 * q^97 + 45802 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$13$
$\chi(n)$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	1.66251	+	2.28825i	0.415627	+	0.572061i
$2$	1.66251	+	2.28825i	0.415627	+	0.572061i
$3$	0.309288	+	0.951890i	0.0343653	+	0.105766i	0.966768	−	0.255656i	$-0.0822915\pi$
$3$	0.309288	+	0.951890i	0.0343653	+	0.105766i	−0.932402	+	0.361422i	$0.882291\pi$
$4$	−2.47214	+	7.60845i	−0.154508	+	0.475528i
$5$	35.4031	+	25.7219i	1.41613	+	1.02888i	0.992396	+	0.123087i	$0.0392793\pi$
$5$	35.4031	+	25.7219i	1.41613	+	1.02888i	0.423730	+	0.905789i	$0.360721\pi$
$6$	−1.66396	+	2.29025i	−0.0462212	+	0.0636181i
$7$	−65.6073	−	21.3171i	−1.33892	−	0.435043i	−0.449972	−	0.893043i	$-0.648566\pi$
$7$	−65.6073	−	21.3171i	−1.33892	−	0.435043i	−0.888952	+	0.458000i	$0.848566\pi$
$8$	−21.5200	+	6.99226i	−0.336249	+	0.109254i
$9$	64.7199	−	47.0218i	0.799012	−	0.580516i
$10$			123.774i			1.23774i
$11$	65.6374	−	101.650i	0.542458	−	0.840083i
$11$	65.6374	−	101.650i	0.542458	−	0.840083i
$12$	−8.00701			−0.0556042
$13$	−100.269	−	138.009i	−0.593310	−	0.816621i	0.401766	−	0.915743i	$-0.368397\pi$
$13$	−100.269	−	138.009i	−0.593310	−	0.816621i	−0.995075	+	0.0991217i	$0.968397\pi$
$14$	−60.2938	−	185.565i	−0.307622	−	0.946762i
$15$	−13.5346	+	41.6553i	−0.0601540	+	0.185135i
$16$	−51.7771	−	37.6183i	−0.202254	−	0.146946i
$17$	−130.596	+	179.749i	−0.451888	+	0.621970i	−0.972802	−	0.231639i	$-0.925591\pi$
$17$	−130.596	+	179.749i	−0.451888	+	0.621970i	0.520914	+	0.853609i	$0.325591\pi$
$18$	215.195	+	69.9210i	0.664182	+	0.215806i
$19$	141.801	−	46.0739i	0.392800	−	0.127629i	−0.105956	−	0.994371i	$-0.533790\pi$
$19$	141.801	−	46.0739i	0.392800	−	0.127629i	0.498756	+	0.866742i	$0.333790\pi$
$20$	−283.225	+	205.775i	−0.708063	+	0.514438i
$21$		−	69.0440i		−	0.156562i
$22$	341.723	−	18.7995i	0.706039	−	0.0388419i
$23$	−272.896			−0.515872			−0.257936	−	0.966162i	$-0.583042\pi$
$23$	−272.896			−0.515872			−0.257936	+	0.966162i	$0.583042\pi$
$24$	−13.3117	−	18.3220i	−0.0231106	−	0.0318090i
$25$	398.631	+	1226.86i	0.637810	+	1.96298i
$26$	149.100	−	458.882i	0.220562	−	0.678819i
$27$	130.364	+	94.7153i	0.178826	+	0.129925i
$28$	324.380	−	446.471i	0.413750	−	0.569478i
$29$	571.633	+	185.735i	0.679706	+	0.220850i	0.628467	−	0.777837i	$-0.283683\pi$
$29$	571.633	+	185.735i	0.679706	+	0.220850i	0.0512393	+	0.998686i	$0.483683\pi$
$30$	−117.819	+	38.2817i	−0.130910	+	0.0425353i
$31$	−714.607	+	519.192i	−0.743607	+	0.540262i	−0.893839	−	0.448388i	$-0.851998\pi$
$31$	−714.607	+	519.192i	−0.743607	+	0.540262i	0.150231	+	0.988651i	$0.451998\pi$
$32$		−	181.019i		−	0.176777i
$33$	117.060	+	31.0405i	0.107494	+	0.0285036i
$34$	−628.427			−0.543622
$35$	−1774.39	−	2442.23i	−1.44848	−	1.99366i
$36$	197.767	+	608.663i	0.152598	+	0.469647i
$37$	440.083	−	1354.44i	0.321463	−	0.989363i	−0.651548	−	0.758607i	$-0.725880\pi$
$37$	440.083	−	1354.44i	0.321463	−	0.989363i	0.973012	−	0.230756i	$-0.0741198\pi$
$38$	341.174	+	247.877i	0.236270	+	0.171660i
$39$	100.357	−	138.130i	0.0659811	−	0.0908151i
$40$	−941.728	−	305.986i	−0.588580	−	0.191241i
$41$	−1050.88	+	341.452i	−0.625153	+	0.203124i	−0.604427	−	0.796661i	$-0.706598\pi$
$41$	−1050.88	+	341.452i	−0.625153	+	0.203124i	−0.0207260	+	0.999785i	$0.506598\pi$
$42$	157.990	−	114.786i	0.0895633	−	0.0650715i
$43$			1489.14i			0.805374i	0.915338	+	0.402687i	$0.131924\pi$
$43$			1489.14i			0.805374i	−0.915338	+	0.402687i	$0.868076\pi$
$44$	611.135	+	750.692i	0.315669	+	0.387754i
$45$	3500.78			1.72878
$46$	−453.692	−	624.454i	−0.214410	−	0.295111i
$47$	−772.201	−	2376.59i	−0.349570	−	1.07587i	−0.959091	−	0.283097i	$-0.908638\pi$
$47$	−772.201	−	2376.59i	−0.349570	−	1.07587i	0.609521	−	0.792770i	$-0.291362\pi$
$48$	19.7944	−	60.9209i	0.00859132	−	0.0264414i
$49$	1907.45	+	1385.84i	0.794438	+	0.577193i
$50$	−2144.63	+	2951.83i	−0.857853	+	1.18073i
$51$	−211.493	−	68.7183i	−0.0813122	−	0.0264199i
$52$	1297.91	−	421.718i	0.479998	−	0.155961i
$53$	−3070.02	+	2230.50i	−1.09292	+	0.794055i	−0.979891	−	0.199536i	$-0.936057\pi$
$53$	−3070.02	+	2230.50i	−1.09292	+	0.794055i	−0.113033	+	0.993591i	$0.536057\pi$
$54$			455.771i			0.156300i
$55$	4938.40	−	1910.41i	1.63253	−	0.631541i
$56$	1560.92			0.497742
$57$	87.7146	+	120.729i	0.0269974	+	0.0371587i
$58$	525.337	+	1616.82i	0.156164	+	0.480625i
$59$	−338.601	+	1042.11i	−0.0972711	+	0.299370i	−0.987839	−	0.155481i	$-0.950307\pi$
$59$	−338.601	+	1042.11i	−0.0972711	+	0.299370i	0.890568	+	0.454851i	$0.150307\pi$
$60$	−283.473	−	205.955i	−0.0787426	−	0.0572098i
$61$	−1856.32	+	2555.01i	−0.498878	+	0.686646i	−0.981994	−	0.188910i	$-0.939505\pi$
$61$	−1856.32	+	2555.01i	−0.498878	+	0.686646i	0.483117	+	0.875556i	$0.339505\pi$
$62$	−2376.08	−	772.035i	−0.618127	−	0.200842i
$63$	−5248.47	+	1705.33i	−1.32236	+	0.429662i
$64$	414.217	−	300.946i	0.101127	−	0.0734732i
$65$		−	7465.07i		−	1.76688i
$66$	123.586	+	319.468i	0.0283714	+	0.0733398i
$67$	251.628			0.0560544			0.0280272	−	0.999607i	$-0.491078\pi$
$67$	251.628			0.0560544			0.0280272	+	0.999607i	$0.491078\pi$
$68$	−1044.76	−	1437.99i	−0.225944	−	0.310985i
$69$	−84.4035	−	259.767i	−0.0177281	−	0.0545615i
$70$	2638.50	−	8120.47i	0.538469	−	1.65724i
$71$	3590.99	+	2609.01i	0.712356	+	0.517557i	0.883933	−	0.467614i	$-0.154886\pi$
$71$	3590.99	+	2609.01i	0.712356	+	0.517557i	−0.171577	+	0.985171i	$0.554886\pi$
$72$	−1063.98	+	1464.45i	−0.205243	+	0.282493i
$73$	3983.96	+	1294.47i	0.747599	+	0.242910i	0.657948	−	0.753064i	$-0.271425\pi$
$73$	3983.96	+	1294.47i	0.747599	+	0.242910i	0.0896513	+	0.995973i	$0.471425\pi$
$74$	3830.93	−	1244.74i	0.699585	−	0.227309i
$75$	−1044.54	+	758.906i	−0.185697	+	0.134917i
$76$			1192.79i			0.206507i
$77$	−6473.17	+	5269.78i	−1.09178	+	0.888815i
$78$	482.920			0.0793753
$79$	−3109.83	−	4280.32i	−0.498291	−	0.685838i	0.483600	−	0.875289i	$-0.339329\pi$
$79$	−3109.83	−	4280.32i	−0.498291	−	0.685838i	−0.981890	+	0.189451i	$0.939329\pi$
$80$	−865.459	−	2663.61i	−0.135228	−	0.416189i
$81$	1952.55	−	6009.32i	0.297599	−	0.915916i
$82$	−2528.43	−	1837.01i	−0.376030	−	0.273202i
$83$	261.533	−	359.969i	0.0379638	−	0.0522527i	−0.789613	−	0.613605i	$-0.789719\pi$
$83$	261.533	−	359.969i	0.0379638	−	0.0522527i	0.827577	+	0.561352i	$0.189719\pi$
$84$	525.318	+	170.686i	0.0744498	+	0.0241902i
$85$	−9246.98	+	3004.53i	−1.27986	+	0.415852i
$86$	−3407.51	+	2475.70i	−0.460723	+	0.334735i
$87$			601.577i			0.0794790i
$88$	−701.751	+	2646.46i	−0.0906186	+	0.341743i
$89$	8935.75			1.12811			0.564054	−	0.825738i	$-0.309241\pi$
$89$	8935.75			1.12811			0.564054	+	0.825738i	$0.309241\pi$
$90$	5820.07	+	8010.64i	0.718527	+	0.988968i
$91$	3636.45	+	11191.8i	0.439132	+	1.35151i
$92$	674.637	−	2076.32i	0.0797066	−	0.245312i
$93$	−715.233	−	519.647i	−0.0826954	−	0.0600817i
$94$	4154.43	−	5718.09i	0.470171	−	0.647135i
$95$	6205.31	+	2016.23i	0.687568	+	0.223405i
$96$	172.310	−	55.9871i	0.0186969	−	0.00607498i
$97$	1684.12	−	1223.58i	0.178990	−	0.130044i	−0.494683	−	0.869074i	$-0.664716\pi$
$97$	1684.12	−	1223.58i	0.178990	−	0.130044i	0.673673	+	0.739030i	$0.264716\pi$
$98$			6668.67i			0.694364i
$99$	−531.718	−	9665.17i	−0.0542514	−	0.986142i
$100$	−10320.0			−1.03200
$101$	−1308.06	−	1800.39i	−0.128229	−	0.176492i	0.740075	−	0.672524i	$-0.234790\pi$
$101$	−1308.06	−	1800.39i	−0.128229	−	0.176492i	−0.868304	+	0.496032i	$0.834790\pi$
$102$	−194.365	−	598.193i	−0.0186817	−	0.0574964i
$103$	−6206.12	+	19100.5i	−0.584986	+	1.80040i	0.0143398	+	0.999897i	$0.495435\pi$
$103$	−6206.12	+	19100.5i	−0.584986	+	1.80040i	−0.599326	+	0.800505i	$0.704565\pi$
$104$	3122.79	+	2268.84i	0.288719	+	0.209767i
$105$	1775.94	−	2444.37i	0.161083	−	0.221712i
$106$	−10207.9	−	3316.74i	−0.908497	−	0.295189i
$107$	16829.4	−	5468.19i	1.46994	−	0.477613i	0.538851	−	0.842401i	$-0.318859\pi$
$107$	16829.4	−	5468.19i	1.46994	−	0.477613i	0.931090	+	0.364789i	$0.118859\pi$
$108$	−1042.92	+	757.722i	−0.0894132	+	0.0649625i
$109$		−	7937.04i		−	0.668045i	−0.942565	−	0.334023i	$-0.891594\pi$
$109$		−	7937.04i		−	0.668045i	0.942565	−	0.334023i	$-0.108406\pi$
$110$	12581.6	+	8124.20i	1.03980	+	0.671421i
$111$	1425.39			0.115688
$112$	2595.04	+	3571.77i	0.206875	+	0.284739i
$113$	−5237.55	−	16119.5i	−0.410177	−	1.26240i	−0.916494	−	0.400048i	$-0.868993\pi$
$113$	−5237.55	−	16119.5i	−0.410177	−	1.26240i	0.506317	−	0.862348i	$-0.331007\pi$
$114$	−130.431	+	401.425i	−0.0100362	+	0.0308883i
$115$	−9661.39	−	7019.41i	−0.730540	−	0.530768i
$116$	−2826.31	+	3890.08i	−0.210041	+	0.289096i
$117$	−12978.9	−	4217.09i	−0.948123	−	0.308064i
$118$	−2947.52	+	957.708i	−0.211686	+	0.0687811i
$119$	12399.8	−	9008.95i	0.875627	−	0.636180i
$120$		−	991.059i		−	0.0688235i
$121$	−6024.46	−	13344.1i	−0.411479	−	0.911419i
$122$	−8932.64			−0.600151
$123$	−650.050	−	894.716i	−0.0429671	−	0.0591392i
$124$	−2183.64	−	6720.57i	−0.142016	−	0.437082i
$125$	−8992.63	+	27676.5i	−0.575528	+	1.77129i
$126$	−12627.8	−	9174.66i	−0.795404	−	0.577895i
$127$	3322.47	−	4572.99i	0.205994	−	0.283526i	−0.693503	−	0.720454i	$-0.743933\pi$
$127$	3322.47	−	4572.99i	0.205994	−	0.283526i	0.899497	+	0.436928i	$0.143933\pi$
$128$	1377.28	+	447.504i	0.0840623	+	0.0273135i
$129$	−1417.49	+	460.572i	−0.0851808	+	0.0276769i
$130$	17081.9	−	12410.7i	1.01076	−	0.734363i
$131$			16641.0i			0.969699i	0.874598	+	0.484849i	$0.161126\pi$
$131$			16641.0i			0.969699i	−0.874598	+	0.484849i	$0.838874\pi$
$132$	−525.559	+	813.913i	−0.0301629	+	0.0467122i
$133$	−10285.3			−0.581454
$134$	418.334	+	575.787i	0.0232977	+	0.0320665i
$135$	2179.05	+	6706.44i	0.119564	+	0.367980i
$136$	1553.56	−	4781.35i	0.0839942	−	0.258508i
$137$	9008.52	+	6545.07i	0.479968	+	0.348717i	0.801313	−	0.598245i	$-0.204135\pi$
$137$	9008.52	+	6545.07i	0.479968	+	0.348717i	−0.321345	+	0.946962i	$0.604135\pi$
$138$	454.090	−	625.001i	0.0238442	−	0.0328188i
$139$	24814.4	+	8062.67i	1.28432	+	0.417301i	0.870100	−	0.492876i	$-0.164054\pi$
$139$	24814.4	+	8062.67i	1.28432	+	0.417301i	0.414221	+	0.910177i	$0.364054\pi$
$140$	22968.2	−	7462.81i	1.17184	−	0.380755i
$141$	2023.42	−	1470.10i	0.101777	−	0.0739450i
$142$			12554.6i			0.622622i
$143$	−20610.0	+	1133.84i	−1.00787	+	0.0554471i
$144$	−5119.89			−0.246908
$145$	15460.1	+	21279.1i	0.735322	+	1.01208i
$146$	3661.30	+	11268.3i	0.171763	+	0.528632i
$147$	−729.218	+	2244.30i	−0.0337460	+	0.103860i
$148$	9217.23	+	6696.71i	0.420801	+	0.305730i
$149$	19071.0	−	26249.0i	0.859016	−	1.18233i	−0.122788	−	0.992433i	$-0.539183\pi$
$149$	19071.0	−	26249.0i	0.859016	−	1.18233i	0.981803	−	0.189901i	$-0.0608166\pi$
$150$	−3473.13	−	1128.49i	−0.154361	−	0.0501550i
$151$	−8988.06	+	2920.40i	−0.394196	+	0.128082i	−0.499406	−	0.866368i	$-0.666448\pi$
$151$	−8988.06	+	2920.40i	−0.394196	+	0.128082i	0.105210	+	0.994450i	$0.466448\pi$
$152$	−2729.39	+	1983.02i	−0.118135	+	0.0858300i
$153$			17774.2i			0.759289i
$154$	−22820.3	−	6051.16i	−0.962231	−	0.255151i
$155$	−38653.9			−1.60890
$156$	802.858	+	1105.04i	0.0329905	+	0.0454076i
$157$	1192.27	+	3669.42i	0.0483698	+	0.148867i	0.972324	−	0.233636i	$-0.0750623\pi$
$157$	1192.27	+	3669.42i	0.0483698	+	0.148867i	−0.923954	+	0.382503i	$0.875062\pi$
$158$	4624.29	−	14232.1i	0.185239	−	0.570106i
$159$	−3072.71	−	2232.46i	−0.121542	−	0.0883057i
$160$	4656.16	−	6408.65i	0.181881	−	0.250338i
$161$	17904.0	+	5817.36i	0.690714	+	0.224426i
$162$	16996.9	−	5522.64i	0.647650	−	0.210434i
$163$	−13650.3	+	9917.54i	−0.513769	+	0.373275i	−0.814251	−	0.580513i	$-0.802852\pi$
$163$	−13650.3	+	9917.54i	−0.513769	+	0.373275i	0.300483	+	0.953787i	$0.402852\pi$
$164$		−	8839.70i		−	0.328662i
$165$	3345.89	+	4109.95i	0.122898	+	0.150962i
$166$	1258.50			0.0456706
$167$	8510.67	+	11713.9i	0.305162	+	0.420020i	0.933865	−	0.357626i	$-0.116414\pi$
$167$	8510.67	+	11713.9i	0.305162	+	0.420020i	−0.628703	+	0.777646i	$0.716414\pi$
$168$	482.773	+	1485.82i	0.0171051	+	0.0526440i
$169$	−166.687	+	513.009i	−0.00583617	+	0.0179619i
$170$	−22248.3	−	16164.3i	−0.769837	−	0.559319i
$171$	7010.87	−	9649.63i	0.239762	−	0.330004i
$172$	−11330.0	−	3681.35i	−0.382978	−	0.124437i
$173$	−22622.7	+	7350.55i	−0.755878	+	0.245600i	−0.661509	−	0.749938i	$-0.730084\pi$
$173$	−22622.7	+	7350.55i	−0.755878	+	0.245600i	−0.0943695	+	0.995537i	$0.530084\pi$
$174$	−1376.56	+	1000.13i	−0.0454669	+	0.0330336i
$175$		−	88988.6i		−	2.90575i
$176$	−7222.41	+	2793.98i	−0.233162	+	0.0901982i
$177$	−1096.70			−0.0350057
$178$	14855.7	+	20447.2i	0.468872	+	0.645347i
$179$	−11256.1	−	34642.7i	−0.351303	−	1.08120i	−0.958122	−	0.286359i	$-0.907555\pi$
$179$	−11256.1	−	34642.7i	−0.351303	−	1.08120i	0.606820	−	0.794839i	$-0.292445\pi$
$180$	−8654.40	+	26635.5i	−0.267111	+	0.822083i
$181$	−9246.62	−	6718.06i	−0.282245	−	0.205063i	0.437651	−	0.899145i	$-0.355810\pi$
$181$	−9246.62	−	6718.06i	−0.282245	−	0.205063i	−0.719896	+	0.694082i	$0.755810\pi$
$182$	−19564.1	+	26927.6i	−0.590631	+	0.812934i
$183$	−3006.23	−	976.782i	−0.0897676	−	0.0291672i
$184$	5872.72	−	1908.16i	0.173462	−	0.0563611i
$185$	50419.0	−	36631.6i	1.47316	−	1.07032i
$186$		−	2500.55i		−	0.0722785i
$187$	9699.58	+	25073.3i	0.277376	+	0.717016i
$188$	19991.2			0.565617
$189$	−6533.80	−	8993.00i	−0.182912	−	0.251757i
$190$	5702.75	+	17551.3i	0.157971	+	0.486184i
$191$	−2741.84	+	8438.52i	−0.0751581	+	0.231313i	−0.981577	−	0.191067i	$-0.938805\pi$
$191$	−2741.84	+	8438.52i	−0.0751581	+	0.231313i	0.906419	+	0.422380i	$0.138805\pi$
$192$	414.580	+	301.210i	0.0112462	+	0.00817084i
$193$	−6099.99	+	8395.91i	−0.163762	+	0.225400i	−0.883010	−	0.469354i	$-0.844487\pi$
$193$	−6099.99	+	8395.91i	−0.163762	+	0.225400i	0.719248	+	0.694754i	$0.244487\pi$
$194$	5599.71	+	1819.46i	0.148786	+	0.0483435i
$195$	7105.92	−	2308.85i	0.186875	−	0.0607193i
$196$	−15259.6	+	11086.7i	−0.397219	+	0.288596i
$197$			75824.1i			1.95378i	0.213753	+	0.976888i	$0.431431\pi$
$197$			75824.1i			1.95378i	−0.213753	+	0.976888i	$0.568569\pi$
$198$	21232.3	−	17285.1i	0.541585	−	0.440902i
$199$	65301.9			1.64900			0.824498	−	0.565865i	$-0.191458\pi$
$199$	65301.9			1.64900			0.824498	+	0.565865i	$0.191458\pi$
$200$	−17157.1	−	23614.7i	−0.428926	−	0.590366i
$201$	77.8254	+	239.522i	0.00192632	+	0.00592862i
$202$	1945.08	−	5986.34i	0.0476688	−	0.146710i
$203$	−33543.9	−	24371.1i	−0.813995	−	0.591402i
$204$	1045.68	−	1439.25i	0.0251269	−	0.0345842i
$205$	−45987.3	−	14942.2i	−1.09428	−	0.355555i
$206$	−54024.3	+	17553.6i	−1.27308	+	0.413648i
$207$	−17661.8	+	12832.1i	−0.412188	+	0.299472i
$208$			10917.7i			0.252350i
$209$	4624.03	−	17438.2i	0.105859	−	0.399218i
$210$	8545.85			0.193783
$211$	23859.2	+	32839.4i	0.535909	+	0.737615i	0.988016	−	0.154348i	$-0.0493278\pi$
$211$	23859.2	+	32839.4i	0.535909	+	0.737615i	−0.452108	+	0.891963i	$0.649328\pi$
$212$	−9381.15	−	28872.2i	−0.208730	−	0.642404i
$213$	−1372.84	+	4225.16i	−0.0302594	+	0.0931287i
$214$	40491.5	+	29418.8i	0.884171	+	0.642388i
$215$	−38303.4	+	52720.1i	−0.828630	+	1.14051i
$216$	−3467.71	−	1126.73i	−0.0743251	−	0.0241497i
$217$	57951.1	−	18829.4i	1.23067	−	0.399869i
$218$	18161.9	−	13195.4i	0.382163	−	0.277658i
$219$			4192.65i			0.0874179i
$220$	2326.89	+	42296.4i	0.0480762	+	0.873892i
$221$	37901.7			0.776023
$222$	2369.72	+	3261.64i	0.0480829	+	0.0661804i
$223$	−2160.07	−	6648.00i	−0.0434367	−	0.133685i	0.926986	−	0.375095i	$-0.122390\pi$
$223$	−2160.07	−	6648.00i	−0.0434367	−	0.133685i	−0.970423	+	0.241411i	$0.922390\pi$
$224$	−3858.81	+	11876.2i	−0.0769054	+	0.236691i
$225$	83488.6	+	60658.0i	1.64916	+	1.19818i
$226$	28178.0	−	38783.7i	0.551687	−	0.759332i
$227$	−55512.3	−	18037.0i	−1.07730	−	0.350036i	−0.283974	−	0.958832i	$-0.591653\pi$
$227$	−55512.3	−	18037.0i	−1.07730	−	0.350036i	−0.793327	+	0.608795i	$0.791653\pi$
$228$	−1135.40	+	368.914i	−0.0218414	+	0.00709669i
$229$	−64594.9	+	46931.0i	−1.23176	+	0.894929i	−0.997021	−	0.0771287i	$-0.975425\pi$
$229$	−64594.9	+	46931.0i	−1.23176	+	0.894929i	−0.234743	+	0.972058i	$0.575425\pi$
$230$		−	33777.5i		−	0.638515i
$231$	−7018.33	−	4531.87i	−0.131525	−	0.0849285i
$232$	−13600.2			−0.252679
$233$	−46025.5	−	63348.7i	−0.847787	−	1.16688i	−0.984346	−	0.176247i	$-0.943604\pi$
$233$	−46025.5	−	63348.7i	−0.847787	−	1.16688i	0.136559	−	0.990632i	$-0.456396\pi$
$234$	−11927.7	−	36709.7i	−0.217834	−	0.670424i
$235$	33792.1	−	104001.i	0.611898	−	1.88323i
$236$	−7091.75	−	5152.46i	−0.127330	−	0.0925103i
$237$	3112.56	−	4284.06i	0.0554141	−	0.0762710i
$238$	41229.4	+	13396.2i	0.727868	+	0.236499i
$239$	−70428.8	+	22883.7i	−1.23298	+	0.400618i	−0.851792	−	0.523881i	$-0.824484\pi$
$239$	−70428.8	+	22883.7i	−1.23298	+	0.400618i	−0.381184	+	0.924499i	$0.624484\pi$
$240$	2267.79	−	1647.64i	0.0393713	−	0.0286049i
$241$		−	12085.3i		−	0.208076i	−0.994573	−	0.104038i	$-0.966824\pi$
$241$		−	12085.3i		−	0.208076i	0.994573	−	0.104038i	$-0.0331764\pi$
$242$	20518.8	−	35970.1i	0.350366	−	0.614202i
$243$	19376.4			0.328141
$244$	−14850.6	−	20440.1i	−0.249439	−	0.343323i
$245$	31883.1	+	98126.2i	0.531164	+	1.63476i
$246$	966.619	−	2974.95i	0.0159729	−	0.0491597i
$247$	−20576.9	−	14950.0i	−0.337276	−	0.245046i
$248$	11748.0	−	16169.7i	0.191012	−	0.262905i
$249$	423.540	+	137.616i	0.00683118	+	0.00221958i
$250$	−78280.9	+	25435.0i	−1.25249	+	0.406960i
$251$	−5768.29	+	4190.91i	−0.0915587	+	0.0665213i	−0.632623	−	0.774460i	$-0.718022\pi$
$251$	−5768.29	+	4190.91i	−0.0915587	+	0.0665213i	0.541064	+	0.840981i	$0.318022\pi$
$252$		−	44148.5i		−	0.695208i
$253$	−17912.2	+	27739.9i	−0.279839	+	0.433375i
$254$	15987.8			0.247811
$255$	−5719.96	−	7872.85i	−0.0879655	−	0.121074i
$256$	1265.73	+	3895.53i	0.0193136	+	0.0594410i
$257$	39182.2	−	120591.i	0.593230	−	1.82577i	0.0298821	−	0.999553i	$-0.490487\pi$
$257$	39182.2	−	120591.i	0.593230	−	1.82577i	0.563348	−	0.826220i	$-0.309513\pi$
$258$	−3410.50	−	2477.87i	−0.0512363	−	0.0372254i
$259$	−57745.4	+	79479.7i	−0.860830	+	1.18483i
$260$	56797.6	+	18454.7i	0.840201	+	0.272998i
$261$	45729.6	−	14858.5i	0.671300	−	0.218119i
$262$	−38078.7	+	27665.8i	−0.554727	+	0.403033i
$263$		−	16826.9i		−	0.243272i	−0.992575	−	0.121636i	$-0.961186\pi$
$263$		−	16826.9i		−	0.243272i	0.992575	−	0.121636i	$-0.0388140\pi$
$264$	−2736.18	+	150.528i	−0.0392588	+	0.00215978i
$265$	−166061.			−2.36470
$266$	−17099.4	−	23535.4i	−0.241668	−	0.332627i
$267$	2763.72	+	8505.84i	0.0387678	+	0.119315i
$268$	−622.059	+	1914.50i	−0.00866087	+	0.0266554i
$269$	−19506.7	−	14172.4i	−0.269574	−	0.195857i	0.444783	−	0.895638i	$-0.353281\pi$
$269$	−19506.7	−	14172.4i	−0.269574	−	0.195857i	−0.714357	+	0.699781i	$0.753281\pi$
$270$	−11723.3	+	16135.7i	−0.160813	+	0.221340i
$271$	130875.	+	42523.8i	1.78204	+	0.579020i	0.999073	−	0.0430434i	$-0.0137054\pi$
$271$	130875.	+	42523.8i	1.78204	+	0.579020i	0.782967	+	0.622063i	$0.213705\pi$
$272$	13523.7	−	4394.12i	0.182792	−	0.0593929i
$273$	−9528.69	+	6923.00i	−0.127852	+	0.0928900i
$274$			31494.9i			0.419507i
$275$	150876.	+	40007.1i	1.99505	+	0.529019i
$276$	2185.08			0.0286847
$277$	−65996.2	−	90835.9i	−0.860120	−	1.18385i	−0.981541	−	0.191253i	$-0.938745\pi$
$277$	−65996.2	−	90835.9i	−0.860120	−	1.18385i	0.121421	−	0.992601i	$-0.461255\pi$
$278$	22804.7	+	70185.6i	0.295076	+	0.908152i
$279$	−21836.0	+	67204.2i	−0.280520	+	0.863352i
$280$	55261.5	+	40149.8i	0.704866	+	0.512115i
$281$	641.902	−	883.502i	0.00812936	−	0.0111891i	−0.804933	−	0.593366i	$-0.797799\pi$
$281$	641.902	−	883.502i	0.00812936	−	0.0111891i	0.813062	+	0.582177i	$0.197799\pi$
$282$	6727.90	+	2186.03i	0.0846022	+	0.0274889i
$283$	131828.	−	42833.7i	1.64602	−	0.534826i	0.668152	−	0.744025i	$-0.267086\pi$
$283$	131828.	−	42833.7i	1.64602	−	0.534826i	0.977873	+	0.209199i	$0.0670858\pi$
$284$	−28727.9	+	20872.0i	−0.356178	+	0.258779i
$285$			6530.36i			0.0803984i
$286$	−36858.8	−	45275.8i	−0.450619	−	0.553521i
$287$	76224.2			0.925400
$288$	−8511.85	−	11715.6i	−0.102622	−	0.141247i
$289$	10554.8	+	32484.3i	0.126373	+	0.388935i
$290$	−22989.1	+	70753.2i	−0.273354	+	0.841299i
$291$	1685.59	+	1224.65i	0.0199052	+	0.0144620i
$292$	−19697.8	+	27111.6i	−0.231021	+	0.317973i
$293$	−29274.9	−	9512.00i	−0.341005	−	0.110799i	0.133508	−	0.991048i	$-0.457376\pi$
$293$	−29274.9	−	9512.00i	−0.341005	−	0.110799i	−0.474513	+	0.880249i	$0.657376\pi$
$294$	−6347.84	+	2062.54i	−0.0734398	+	0.0238620i
$295$	−38792.5	+	28184.4i	−0.445762	+	0.323865i
$296$			32224.6i			0.367794i
$297$	18184.6	−	7034.68i	0.206154	−	0.0797502i
$298$	91769.8			1.03340
$299$	27363.1	+	37662.1i	0.306072	+	0.421272i
$300$	−3191.84	−	9823.48i	−0.0354649	−	0.109150i
$301$	31744.1	−	97698.2i	0.350372	−	1.07833i
$302$	−21625.3	−	15711.7i	−0.237109	−	0.172270i
$303$	1309.21	−	1801.97i	0.0142601	−	0.0196274i
$304$	−9075.26	−	2948.73i	−0.0982001	−	0.0319071i
$305$	−131439.	+	42707.2i	−1.41295	+	0.459094i
$306$	−40671.7	+	29549.8i	−0.434360	+	0.315581i
$307$			47816.2i			0.507340i	0.967291	+	0.253670i	$0.0816376\pi$
$307$			47816.2i			0.507340i	−0.967291	+	0.253670i	$0.918362\pi$
$308$	−24092.3	−	62278.5i	−0.253967	−	0.656503i
$309$	−20101.0			−0.210524
$310$	−64262.5	−	88449.7i	−0.668704	−	0.920392i
$311$	−33332.0	−	102585.i	−0.344620	−	1.06063i	−0.961787	−	0.273799i	$-0.911720\pi$
$311$	−33332.0	−	102585.i	−0.344620	−	1.06063i	0.617167	−	0.786832i	$-0.288280\pi$
$312$	−1193.84	+	3674.27i	−0.0122642	+	0.0377452i
$313$	16908.4	+	12284.7i	0.172589	+	0.125393i	0.670727	−	0.741705i	$-0.265982\pi$
$313$	16908.4	+	12284.7i	0.172589	+	0.125393i	−0.498137	+	0.867098i	$0.665982\pi$
$314$	−6414.38	+	8828.64i	−0.0650572	+	0.0895436i
$315$	−229677.	−	74626.4i	−2.31470	−	0.752093i
$316$	40254.5	−	13079.5i	0.403125	−	0.130983i
$317$	72173.0	−	52436.8i	0.718218	−	0.521816i	−0.167596	−	0.985856i	$-0.553601\pi$
$317$	72173.0	−	52436.8i	0.718218	−	0.521816i	0.885814	+	0.464040i	$0.153601\pi$
$318$		−	10742.6i		−	0.106232i
$319$	56400.4	−	45915.3i	0.554244	−	0.451208i
$320$	22405.5			0.218803
$321$	10410.2	+	14328.4i	0.101030	+	0.139056i
$322$	16454.0	+	50640.1i	0.158693	+	0.488408i
$323$	−10236.8	+	31505.7i	−0.0981205	+	0.301984i
$324$	40894.7	+	29711.7i	0.389562	+	0.283034i
$325$	129347.	−	178031.i	1.22459	−	1.68550i
$326$	−45387.5	−	14747.3i	−0.427072	−	0.138764i
$327$	7555.19	−	2454.83i	0.0706561	−	0.0229576i
$328$	20227.4	−	14696.1i	0.188015	−	0.136601i
$329$			172383.i			1.59258i
$330$	−3842.00	+	14489.0i	−0.0352801	+	0.133049i
$331$	−108817.			−0.993211			−0.496605	−	0.867976i	$-0.665420\pi$
$331$	−108817.			−0.993211			−0.496605	+	0.867976i	$0.665420\pi$
$332$	2092.26	+	2879.75i	0.0189819	+	0.0261264i
$333$	−35205.9	−	108353.i	−0.317488	−	0.977127i
$334$	−12655.3	+	38949.0i	−0.113444	+	0.349143i
$335$	8908.42	+	6472.35i	0.0793800	+	0.0576730i
$336$	−2597.31	+	3574.90i	−0.0230063	+	0.0316654i
$337$	−4809.85	−	1562.81i	−0.0423517	−	0.0137609i	0.287765	−	0.957701i	$-0.407088\pi$
$337$	−4809.85	−	1562.81i	−0.0423517	−	0.0137609i	−0.330116	+	0.943940i	$0.607088\pi$
$338$	−1451.01	+	471.461i	−0.0127010	+	0.00412679i
$339$	13724.1	−	9971.15i	0.119422	−	0.0867652i
$340$		−	77782.8i		−	0.672862i
$341$	5870.98	+	106718.i	0.0504896	+	0.917762i
$342$	33736.4			0.288434
$343$	1754.39	+	2414.72i	0.0149121	+	0.0205247i
$344$	−10412.4	−	32046.2i	−0.0879903	−	0.270806i
$345$	3693.55	−	11367.6i	0.0310318	−	0.0955059i
$346$	−54430.3	−	39545.9i	−0.454661	−	0.330331i
$347$	−68742.8	+	94616.4i	−0.570911	+	0.785791i	−0.992662	−	0.120920i	$-0.961416\pi$
$347$	−68742.8	+	94616.4i	−0.570911	+	0.785791i	0.421751	+	0.906712i	$0.361416\pi$
$348$	−4577.07	−	1487.18i	−0.0377945	−	0.0122802i
$349$	−65879.6	+	21405.6i	−0.540879	+	0.175742i	−0.566700	−	0.823924i	$-0.691780\pi$
$349$	−65879.6	+	21405.6i	−0.540879	+	0.175742i	0.0258206	+	0.999667i	$0.491780\pi$
$350$	203628.	−	147944.i	1.66227	−	1.20771i
$351$		−	27488.5i		−	0.223119i
$352$	−18400.6	−	11881.6i	−0.148507	−	0.0958939i
$353$	56886.4			0.456519			0.228259	−	0.973600i	$-0.426697\pi$
$353$	56886.4			0.456519			0.228259	+	0.973600i	$0.426697\pi$
$354$	−1823.26	−	2509.51i	−0.0145493	−	0.0200254i
$355$	60023.7	+	184734.i	0.476284	+	1.46585i
$356$	−22090.4	+	67987.2i	−0.174302	+	0.536447i
$357$	12410.6	+	9016.84i	0.0973771	+	0.0707486i
$358$	60557.6	−	83350.4i	0.472501	−	0.650342i
$359$	141042.	+	45827.4i	1.09436	+	0.355579i	0.799930	−	0.600093i	$-0.204870\pi$
$359$	141042.	+	45827.4i	1.09436	+	0.355579i	0.294431	+	0.955673i	$0.404870\pi$
$360$	−75336.6	+	24478.3i	−0.581301	+	0.188876i
$361$	−87447.2	+	63534.1i	−0.671014	+	0.487520i
$362$		−	32327.4i		−	0.246691i
$363$	10838.8	−	9861.79i	0.0822561	−	0.0748415i
$364$	−94142.4			−0.710530
$365$	107748.	+	148303.i	0.808770	+	1.11318i
$366$	−2762.76	−	8502.89i	−0.0206244	−	0.0634752i
$367$	−39191.0	+	120617.i	−0.290974	+	0.895525i	0.693571	+	0.720389i	$0.256037\pi$
$367$	−39191.0	+	120617.i	−0.290974	+	0.895525i	−0.984544	+	0.175136i	$0.943963\pi$
$368$	14129.8	+	10265.9i	0.104337	+	0.0758055i
$369$	−51957.3	+	71513.1i	−0.381587	+	0.525210i
$370$	167644.	+	54470.9i	1.22457	+	0.397888i
$371$	248964.	−	80893.2i	1.80879	−	0.587711i
$372$	5721.86	−	4157.18i	0.0413477	−	0.0300409i
$373$		−	47200.3i		−	0.339256i	−0.985508	−	0.169628i	$-0.945743\pi$
$373$		−	47200.3i		−	0.339256i	0.985508	−	0.169628i	$-0.0542566\pi$
$374$	−41248.3	+	63879.6i	−0.294892	+	0.456687i
$375$	−29126.3			−0.207120
$376$	33235.5	+	45744.7i	0.235086	+	0.323568i
$377$	−31684.2	−	97513.9i	−0.222926	−	0.686094i
$378$	9715.71	−	29901.9i	0.0679972	−	0.209274i
$379$	−222539.	−	161684.i	−1.54927	−	1.12561i	−0.944168	−	0.329465i	$-0.893132\pi$
$379$	−222539.	−	161684.i	−1.54927	−	1.12561i	−0.605103	−	0.796147i	$-0.706868\pi$
$380$	−30680.7	+	42228.4i	−0.212470	+	0.292440i
$381$	5380.59	+	1748.26i	0.0370663	+	0.0120436i
$382$	−23867.7	+	7755.10i	−0.163563	+	0.0531448i
$383$	−45891.7	+	33342.3i	−0.312850	+	0.227299i	−0.733119	−	0.680101i	$-0.761936\pi$
$383$	−45891.7	+	33342.3i	−0.312850	+	0.227299i	0.420268	+	0.907400i	$0.361936\pi$
$384$			1449.42i			0.00982953i
$385$	−364719.	+	20064.6i	−2.46058	+	0.135366i
$386$	−29353.2			−0.197006
$387$	70021.9	+	96376.8i	0.467533	+	0.643503i
$388$	5146.20	+	15838.4i	0.0341840	+	0.105208i
$389$	29662.0	−	91290.2i	0.196020	−	0.603288i	−0.803943	−	0.594706i	$-0.797268\pi$
$389$	29662.0	−	91290.2i	0.196020	−	0.603288i	0.999963	−	0.00858182i	$-0.00273171\pi$
$390$	17096.9	+	12421.6i	0.112405	+	0.0816673i
$391$	35639.1	−	49052.9i	0.233116	−	0.320857i
$392$	−50738.3	−	16485.9i	−0.330190	−	0.107285i
$393$	−15840.4	+	5146.86i	−0.102561	+	0.0333240i
$394$	−173504.	+	126058.i	−1.11768	+	0.812042i
$395$		−	231527.i		−	1.48391i
$396$	74851.5	+	19848.1i	0.477320	+	0.126569i
$397$	146750.			0.931102			0.465551	−	0.885021i	$-0.345856\pi$
$397$	146750.			0.931102			0.465551	+	0.885021i	$0.345856\pi$
$398$	108565.	+	149427.i	0.685367	+	0.943327i
$399$	−3181.13	−	9790.50i	−0.0199818	−	0.0614977i
$400$	25512.4	−	78519.1i	0.159452	−	0.490744i
$401$	67876.7	+	49315.3i	0.422116	+	0.306685i	0.778489	−	0.627659i	$-0.215987\pi$
$401$	67876.7	+	49315.3i	0.422116	+	0.306685i	−0.356372	+	0.934344i	$0.615987\pi$
$402$	−418.700	+	576.291i	−0.00259090	+	0.00356607i
$403$	143306.	+	46563.0i	0.882379	+	0.286702i
$404$	16931.9	−	5501.51i	0.103739	−	0.0337070i
$405$	223697.	−	162526.i	1.36380	−	0.990860i
$406$		−	117274.i		−	0.711458i
$407$	−108793.	−	133636.i	−0.656767	−	0.806744i
$408$	5031.82			0.0302277
$409$	162402.	+	223528.i	0.970836	+	1.33624i	0.941623	+	0.336668i	$0.109300\pi$
$409$	162402.	+	223528.i	0.970836	+	1.33624i	0.0292126	+	0.999573i	$0.490700\pi$
$410$	−42262.9	−	130072.i	−0.251415	−	0.773776i
$411$	−3443.96	+	10599.4i	−0.0203880	+	0.0627478i
$412$	−129983.	−	94437.9i	−0.765757	−	0.556355i
$413$	44429.3	−	61151.8i	0.260477	−	0.358516i
$414$	−58725.9	−	19081.2i	−0.342633	−	0.111328i
$415$	18518.2	−	6016.92i	0.107523	−	0.0349364i
$416$	−24982.3	+	18150.7i	−0.144360	+	0.104883i
$417$			26114.2i			0.150177i
$418$	47590.5	−	18410.3i	0.272375	−	0.105368i
$419$	−245758.			−1.39984			−0.699922	−	0.714220i	$-0.746782\pi$
$419$	−245758.			−1.39984			−0.699922	+	0.714220i	$0.746782\pi$
$420$	14207.5	+	19555.0i	0.0805416	+	0.110856i
$421$	18943.8	+	58303.1i	0.106882	+	0.328948i	0.990168	−	0.139887i	$-0.0446739\pi$
$421$	18943.8	+	58303.1i	0.106882	+	0.328948i	−0.883286	+	0.468835i	$0.844674\pi$
$422$	−35478.4	+	109191.i	−0.199223	+	0.613145i
$423$	−161728.	−	117503.i	−0.903869	−	0.656699i
$424$	50470.5	−	69466.7i	0.280741	−	0.386407i
$425$	−272587.	−	88568.8i	−1.50913	−	0.490347i
$426$	−11950.5	+	3882.97i	−0.0658520	+	0.0213966i
$427$	176254.	−	128056.i	0.966680	−	0.702334i
$428$			141563.i			0.772794i
$429$	−7453.72	−	19267.8i	−0.0405003	−	0.104693i
$430$	−184316.			−0.996843
$431$	−170697.	−	234945.i	−0.918908	−	1.26477i	−0.964032	−	0.265786i	$-0.914368\pi$
$431$	−170697.	−	234945.i	−0.918908	−	1.26477i	0.0451244	−	0.998981i	$-0.485632\pi$
$432$	−3186.87	−	9808.16i	−0.0170764	−	0.0525557i
$433$	−14346.5	+	44154.1i	−0.0765193	+	0.235502i	−0.981999	−	0.188888i	$-0.939512\pi$
$433$	−14346.5	+	44154.1i	−0.0765193	+	0.235502i	0.905479	+	0.424390i	$0.139512\pi$
$434$	139430.	+	101302.i	0.740250	+	0.537823i
$435$	−15473.7	+	21297.7i	−0.0817740	+	0.112552i
$436$	60388.6	+	19621.5i	0.317674	+	0.103219i
$437$	−38697.0	+	12573.4i	−0.202635	+	0.0658400i
$438$	−9593.81	+	6970.31i	−0.0500084	+	0.0363332i
$439$		−	9971.85i		−	0.0517424i	−0.999665	−	0.0258712i	$-0.991764\pi$
$439$		−	9971.85i		−	0.0517424i	0.999665	−	0.0258712i	$-0.00823598\pi$
$440$	−92916.1	+	75642.6i	−0.479938	+	0.390716i
$441$	188614.			0.969835
$442$	63011.9	+	86728.5i	0.322536	+	0.443933i
$443$	−70757.7	−	217770.i	−0.360551	−	1.10966i	−0.952721	−	0.303848i	$-0.901729\pi$
$443$	−70757.7	−	217770.i	−0.360551	−	1.10966i	0.592170	−	0.805813i	$-0.298271\pi$
$444$	−3523.75	+	10845.0i	−0.0178747	+	0.0550127i
$445$	316353.	+	229844.i	1.59754	+	1.16068i
$446$	11621.1	−	15995.1i	0.0584223	−	0.0804114i
$447$	30884.6	+	10035.0i	0.154570	+	0.0502230i
$448$	−33590.9	+	10914.4i	−0.167365	+	0.0543803i
$449$	177611.	−	129042.i	0.881002	−	0.640085i	−0.0525145	−	0.998620i	$-0.516724\pi$
$449$	177611.	−	129042.i	0.881002	−	0.640085i	0.933516	+	0.358535i	$0.116724\pi$
$450$			291887.i			1.44142i
$451$	−34268.5	+	129234.i	−0.168478	+	0.635367i
$452$	135593.			0.663681
$453$	−5559.79	−	7652.40i	−0.0270933	−	0.0372908i
$454$	−51016.4	−	157012.i	−0.247513	−	0.761767i
$455$	−159134.	+	489763.i	−0.768668	+	2.36572i
$456$	−2731.78	−	1984.75i	−0.0131376	−	0.00954502i
$457$	20840.6	−	28684.6i	0.0997877	−	0.137346i	−0.756203	−	0.654337i	$-0.772948\pi$
$457$	20840.6	−	28684.6i	0.0997877	−	0.137346i	0.855991	+	0.516991i	$0.172948\pi$
$458$	−214779.	−	69786.0i	−1.02391	−	0.332688i
$459$	−34050.0	+	11063.5i	−0.161619	+	0.0525132i
$460$	77291.1	−	56155.3i	0.365270	−	0.265384i
$461$			112097.i			0.527462i	0.964596	+	0.263731i	$0.0849531\pi$
$461$			112097.i			0.527462i	−0.964596	+	0.263731i	$0.915047\pi$
$462$	−1297.99	−	23593.9i	−0.00608118	−	0.110539i
$463$	−75195.8			−0.350777			−0.175389	−	0.984499i	$-0.556118\pi$
$463$	−75195.8			−0.350777			−0.175389	+	0.984499i	$0.556118\pi$
$464$	−22610.5	−	31120.6i	−0.105020	−	0.144548i
$465$	−11955.2	−	36794.3i	−0.0552905	−	0.170167i
$466$	68439.6	−	210635.i	0.315163	−	0.969972i
$467$	−8465.10	−	6150.25i	−0.0388149	−	0.0282007i	0.568209	−	0.822885i	$-0.307637\pi$
$467$	−8465.10	−	6150.25i	−0.0388149	−	0.0282007i	−0.607024	+	0.794684i	$0.707637\pi$
$468$	64171.0	−	88323.8i	0.292986	−	0.403261i
$469$	−16508.6	−	5363.98i	−0.0750525	−	0.0243860i
$470$	294160.	−	95578.4i	1.33164	−	0.432677i
$471$	−3124.13	+	2269.81i	−0.0140827	+	0.0102317i
$472$		−	24793.7i		−	0.111290i
$473$	151371.	+	97743.1i	0.676581	+	0.436882i
$474$	14977.6			0.0666633
$475$	113053.	+	155603.i	0.501064	+	0.689655i
$476$	37890.3	+	116614.i	0.167230	+	0.514681i
$477$	−93809.5	+	288716.i	−0.412297	+	1.26892i
$478$	−169452.	−	123114.i	−0.741636	−	0.538830i
$479$	58592.5	−	80645.7i	0.255371	−	0.351488i	−0.662012	−	0.749493i	$-0.730297\pi$
$479$	58592.5	−	80645.7i	0.255371	−	0.351488i	0.917383	+	0.398005i	$0.130297\pi$
$480$	7540.42	+	2450.03i	0.0327275	+	0.0106338i
$481$	−231051.	+	75073.1i	−0.998662	+	0.324485i
$482$	27654.1	−	20091.9i	0.119032	−	0.0864822i
$483$			18841.9i			0.0807662i
$484$	116421.	−	12848.4i	0.496983	−	0.0548479i
$485$	91095.8			0.387271
$486$	32213.4	+	44337.9i	0.136384	+	0.187717i
$487$	129497.	+	398552.i	0.546013	+	1.68045i	0.718570	+	0.695455i	$0.244797\pi$
$487$	129497.	+	398552.i	0.546013	+	1.68045i	−0.172557	+	0.985000i	$0.555203\pi$
$488$	22082.7	−	67963.6i	0.0927284	−	0.285389i
$489$	−13662.3	−	9926.22i	−0.0571354	−	0.0415113i
$490$	−171531.	+	236092.i	−0.714414	+	0.983307i
$491$	74522.5	+	24213.8i	0.309118	+	0.100439i	0.459468	−	0.888194i	$-0.348040\pi$
$491$	74522.5	+	24213.8i	0.309118	+	0.100439i	−0.150350	+	0.988633i	$0.548040\pi$
$492$	8414.42	−	2734.01i	0.0347611	−	0.0112946i
$493$	−108038.	+	78494.5i	−0.444513	+	0.322957i
$494$		−	71939.5i		−	0.294790i
$495$	229782.	−	355854.i	0.937790	−	1.45232i
$496$	56531.4			0.229787
$497$	−179978.	−	247719.i	−0.728631	−	1.00287i
$498$	389.238	+	1197.95i	0.00156948	+	0.00483037i
$499$	119981.	−	369265.i	0.481851	−	1.48299i	−0.354639	−	0.935003i	$-0.615396\pi$
$499$	119981.	−	369265.i	0.481851	−	1.48299i	0.836490	−	0.547982i	$-0.184604\pi$
$500$	−188344.	−	136840.i	−0.753376	−	0.547360i
$501$	−8518.13	+	11724.2i	−0.0339366	+	0.0467098i
$502$	−19179.7	−	6231.85i	−0.0761085	−	0.0247292i
$503$	15968.4	−	5188.46i	0.0631141	−	0.0205070i	−0.277290	−	0.960786i	$-0.589436\pi$
$503$	15968.4	−	5188.46i	0.0631141	−	0.0205070i	0.340404	+	0.940279i	$0.389436\pi$
$504$	101023.	−	73397.2i	0.397702	−	0.288947i
$505$		−	97385.4i		−	0.381866i
$506$	−93255.0	+	5130.31i	−0.364226	+	0.0200375i
$507$	−539.882			−0.00210031
$508$	26579.8	+	36584.0i	0.102997	+	0.141763i
$509$	−101400.	−	312078.i	−0.391384	−	1.20456i	−0.931742	−	0.363121i	$-0.881711\pi$
$509$	−101400.	−	312078.i	−0.391384	−	1.20456i	0.540358	−	0.841435i	$-0.318289\pi$
$510$	8505.53	−	26177.3i	0.0327010	−	0.100643i
$511$	−233782.	−	169853.i	−0.895302	−	0.650475i
$512$	−6809.63	+	9372.65i	−0.0259767	+	0.0357538i
$513$	22849.7	+	7424.32i	0.0868252	+	0.0282112i
$514$	341081.	−	110824.i	1.29102	−	0.419477i
$515$	−711016.	+	516583.i	−2.68080	+	1.94772i
$516$		−	11923.5i		−	0.0447822i
$517$	−292266.	−	77499.0i	−1.09345	−	0.289944i
$518$	−277871.			−1.03558
$519$	−13993.8	−	19260.9i	−0.0519520	−	0.0715057i
$520$	52197.7	+	160648.i	0.193039	+	0.594112i
$521$	−57854.4	+	178058.i	−0.213138	+	0.655971i	0.786143	+	0.618045i	$0.212075\pi$
$521$	−57854.4	+	178058.i	−0.213138	+	0.655971i	−0.999281	+	0.0379262i	$0.987925\pi$
$522$	110026.	+	79938.3i	0.403787	+	0.293369i
$523$	118132.	−	162595.i	0.431881	−	0.594434i	−0.536502	−	0.843899i	$-0.680255\pi$
$523$	118132.	−	162595.i	0.431881	−	0.594434i	0.968384	+	0.249465i	$0.0802548\pi$
$524$	−126612.	−	41138.8i	−0.461119	−	0.149827i
$525$	84707.4	−	27523.1i	0.307328	−	0.0998570i
$526$	38504.0	−	27974.8i	0.139166	−	0.101110i
$527$		−	196254.i		−	0.706640i
$528$	−4893.36	−	6010.79i	−0.0175525	−	0.0215608i
$529$	−205369.			−0.733876
$530$	−276078.	−	379989.i	−0.982833	−	1.35275i
$531$	27087.5	+	83366.7i	0.0960681	+	0.295667i
$532$	25426.7	−	78255.5i	0.0898395	−	0.276498i
$533$	152495.	+	110794.i	0.536785	+	0.389997i
$534$	−14868.8	+	20465.1i	−0.0521426	+	0.0717681i
$535$	736464.	+	239292.i	2.57303	+	0.836027i
$536$	−5415.02	+	1759.45i	−0.0188482	+	0.00612416i
$537$	29494.6	−	21429.1i	0.102281	−	0.0743114i
$538$		−	68197.8i		−	0.235617i
$539$	266071.	−	102929.i	0.915839	−	0.354291i
$540$	−56412.5			−0.193459
$541$	−227843.	−	313599.i	−0.778469	−	1.07147i	−0.995449	−	0.0952945i	$-0.969621\pi$
$541$	−227843.	−	313599.i	−0.778469	−	1.07147i	0.216980	−	0.976176i	$-0.430379\pi$
$542$	120275.	+	370170.i	0.409429	+	1.26009i
$543$	3534.99	−	10879.6i	0.0119891	−	0.0368988i
$544$	32538.1	+	23640.3i	0.109950	+	0.0798832i
$545$	204156.	−	280996.i	0.687335	−	0.946036i
$546$	−31683.0	−	10294.4i	−0.106278	−	0.0345317i
$547$	−251350.	+	81668.6i	−0.840048	+	0.272948i	−0.697272	−	0.716807i	$-0.745603\pi$
$547$	−251350.	+	81668.6i	−0.840048	+	0.272948i	−0.142776	+	0.989755i	$0.545603\pi$
$548$	−72068.1	+	52360.6i	−0.239984	+	0.174359i
$549$			252648.i			0.838245i
$550$	159286.	+	411752.i	0.526565	+	1.36117i
$551$	89615.6			0.295175
$552$	3632.72	+	5000.01i	0.0119221	+	0.0164094i
$553$	112784.	+	347112.i	0.368804	+	1.13506i
$554$	98135.8	−	302031.i	0.319748	−	0.984083i
$555$	50463.2	+	36663.7i	0.163828	+	0.119028i
$556$	−122689.	+	168867.i	−0.396877	+	0.546254i
$557$	138711.	+	45069.9i	0.447095	+	0.145270i	0.523907	−	0.851776i	$-0.324474\pi$
$557$	138711.	+	45069.9i	0.447095	+	0.145270i	−0.0768117	+	0.997046i	$0.524474\pi$
$558$	−190082.	+	61761.4i	−0.610482	+	0.198358i
$559$	205514.	−	149315.i	0.657685	−	0.477836i
$560$			193201.i			0.616075i
$561$	−20867.1	+	16987.8i	−0.0663034	+	0.0539773i
$562$	3088.84			0.00977963
$563$	153456.	+	211214.i	0.484136	+	0.666356i	0.979293	−	0.202447i	$-0.0648895\pi$
$563$	153456.	+	211214.i	0.484136	+	0.666356i	−0.495157	+	0.868803i	$0.664890\pi$
$564$	6183.02	+	19029.4i	0.0194376	+	0.0598228i
$565$	229199.	−	705402.i	0.717986	−	2.20973i
$566$	317180.	+	230445.i	0.990085	+	0.719339i
$567$	−256203.	+	352633.i	−0.796925	+	1.09687i
$568$	−95520.7	−	31036.6i	−0.296074	−	0.0962004i
$569$	−231581.	+	75245.2i	−0.715284	+	0.232410i	−0.643977	−	0.765045i	$-0.722717\pi$
$569$	−231581.	+	75245.2i	−0.715284	+	0.232410i	−0.0713065	+	0.997454i	$0.522717\pi$
$570$	−14943.1	+	10856.8i	−0.0459928	+	0.0334157i
$571$		−	166213.i		−	0.509792i	−0.966968	−	0.254896i	$-0.917959\pi$
$571$		−	166213.i		−	0.509792i	0.966968	−	0.254896i	$-0.0820412\pi$
$572$	42324.1	−	159613.i	0.129359	−	0.487840i
$573$	−8880.56			−0.0270477
$574$	126723.	+	174420.i	0.384621	+	0.529385i
$575$	−108785.	−	334806.i	−0.329028	−	1.01265i
$576$	12657.1	−	38954.4i	0.0381494	−	0.117412i
$577$	200993.	+	146030.i	0.603710	+	0.438621i	0.847194	−	0.531284i	$-0.178290\pi$
$577$	200993.	+	146030.i	0.603710	+	0.438621i	−0.243484	+	0.969905i	$0.578290\pi$
$578$	−56784.6	+	78157.3i	−0.169971	+	0.233945i
$579$	−9878.63	−	3209.76i	−0.0294672	−	0.00957449i
$580$	−200120.	+	65023.0i	−0.594888	+	0.193291i
$581$	−24831.9	+	18041.5i	−0.0735629	+	0.0534465i
$582$			5893.04i			0.0173978i
$583$	25222.3	+	458472.i	0.0742075	+	1.34889i
$584$	−94785.8			−0.277919
$585$	−351021.	−	483139.i	−1.02570	−	1.41176i
$586$	−26904.0	−	82802.0i	−0.0783468	−	0.241127i
$587$	−79755.8	+	245463.i	−0.231465	+	0.712377i	0.766105	+	0.642715i	$0.222192\pi$
$587$	−79755.8	+	245463.i	−0.231465	+	0.712377i	−0.997571	+	0.0696620i	$0.977808\pi$
$588$	−15272.9	−	11096.4i	−0.0441741	−	0.0320944i
$589$	−77410.7	+	106547.i	−0.223136	+	0.307121i
$590$	−128986.	−	41909.9i	−0.370542	−	0.120396i
$591$	−72176.2	+	23451.5i	−0.206642	+	0.0671421i
$592$	−73737.8	+	53573.7i	−0.210401	+	0.152865i
$593$			277923.i			0.790342i	0.918608	+	0.395171i	$0.129315\pi$
$593$			277923.i			0.790342i	−0.918608	+	0.395171i	$0.870685\pi$
$594$	46329.1	+	29915.6i	0.131305	+	0.0847861i
$595$	670717.			1.89455
$596$	152568.	+	209992.i	0.429508	+	0.591167i
$597$	20197.1	+	62160.2i	0.0566682	+	0.174407i
$598$	−40688.8	+	125227.i	−0.113782	+	0.350184i
$599$	392348.	+	285058.i	1.09350	+	0.794472i	0.979986	−	0.199064i	$-0.0637902\pi$
$599$	392348.	+	285058.i	1.09350	+	0.794472i	0.113511	+	0.993537i	$0.463790\pi$
$600$	17172.1	−	23635.3i	0.0477002	−	0.0656537i
$601$	−281101.	−	91335.1i	−0.778239	−	0.252865i	−0.107151	−	0.994243i	$-0.534173\pi$
$601$	−281101.	−	91335.1i	−0.778239	−	0.252865i	−0.671088	+	0.741378i	$0.734173\pi$
$602$	276332.	−	89785.8i	0.762498	−	0.247751i
$603$	16285.3	−	11832.0i	0.0447881	−	0.0325404i
$604$		−	75604.9i		−	0.207241i
$605$	129950.	−	627383.i	0.355031	−	1.71404i
$606$	6299.92			0.0171550
$607$	−387086.	−	532778.i	−1.05058	−	1.44600i	−0.888303	−	0.459258i	$-0.848115\pi$
$607$	−387086.	−	532778.i	−1.05058	−	1.44600i	−0.162279	−	0.986745i	$-0.551885\pi$
$608$	−8340.27	−	25668.7i	−0.0225618	−	0.0694379i
$609$	12823.9	−	39467.8i	0.0345768	−	0.106416i
$610$	−316244.	−	229764.i	−0.849889	−	0.617480i
$611$	−250563.	+	344870.i	−0.671172	+	0.923789i
$612$	−135234.	−	43940.2i	−0.361064	−	0.117317i
$613$	−195640.	+	63567.3i	−0.520639	+	0.169166i	−0.557535	−	0.830153i	$-0.688253\pi$
$613$	−195640.	+	63567.3i	−0.520639	+	0.169166i	0.0368963	+	0.999319i	$0.488253\pi$
$614$	−109415.	+	79494.9i	−0.290229	+	0.210864i
$615$		−	48396.3i		−	0.127956i
$616$	102455.	−	158668.i	0.270004	−	0.418145i
$617$	298927.			0.785226			0.392613	−	0.919704i	$-0.371571\pi$
$617$	298927.			0.785226			0.392613	+	0.919704i	$0.371571\pi$
$618$	−33418.1	−	45996.1i	−0.0874993	−	0.120432i
$619$	−89798.4	−	276371.i	−0.234362	−	0.721293i	−0.997205	−	0.0747091i	$-0.976197\pi$
$619$	−89798.4	−	276371.i	−0.234362	−	0.721293i	0.762843	−	0.646584i	$-0.223803\pi$
$620$	95557.8	−	294097.i	0.248589	−	0.765079i
$621$	−35576.0	−	25847.5i	−0.0922515	−	0.0670247i
$622$	179326.	−	246821.i	0.463513	−	0.637971i
$623$	−586250.	−	190484.i	−1.51045	−	0.490775i
$624$	−10392.4	+	3376.70i	−0.0266899	+	0.00867207i
$625$	−377989.	+	274625.i	−0.967653	+	0.703041i
$626$			59113.9i			0.150849i
$627$	18029.4	−	991.869i	0.0458614	−	0.00252301i
$628$	−30866.1			−0.0782640
$629$	185986.	+	255988.i	0.470089	+	0.647022i
$630$	−211075.	−	649623.i	−0.531810	−	1.63674i
$631$	−37040.0	+	113997.i	−0.0930276	+	0.286310i	−0.986735	−	0.162341i	$-0.948095\pi$
$631$	−37040.0	+	113997.i	−0.0930276	+	0.286310i	0.893707	+	0.448651i	$0.148095\pi$
$632$	96852.5	+	70367.4i	0.242480	+	0.176172i
$633$	−23880.1	+	32868.1i	−0.0595976	+	0.0820290i
$634$	239976.	+	77973.0i	0.597021	+	0.193984i
$635$	235252.	−	76438.0i	0.583426	−	0.189567i
$636$	24581.7	−	17859.6i	0.0607712	−	0.0441528i
$637$		−	402202.i		−	0.991209i
$638$	198832.	+	52723.4i	0.488477	+	0.129528i
$639$	355089.			0.869631
$640$	37249.3	+	51269.2i	0.0909406	+	0.125169i
$641$	139619.	+	429704.i	0.339805	+	1.04581i	0.964307	+	0.264788i	$0.0853020\pi$
$641$	139619.	+	429704.i	0.339805	+	1.04581i	−0.624502	+	0.781023i	$0.714698\pi$
$642$	−15479.9	+	47642.3i	−0.0375577	+	0.115591i
$643$	23468.8	+	17051.1i	0.0567636	+	0.0412412i	0.615805	−	0.787898i	$-0.288831\pi$
$643$	23468.8	+	17051.1i	0.0567636	+	0.0412412i	−0.559042	+	0.829140i	$0.688831\pi$
$644$	−88522.2	+	121840.i	−0.213442	+	0.293778i
$645$	−62030.5	−	20154.9i	−0.149103	−	0.0484464i
$646$	−89111.5	+	28954.1i	−0.213535	+	0.0693817i
$647$	197122.	−	143218.i	0.470898	−	0.342127i	−0.326893	−	0.945061i	$-0.606002\pi$
$647$	197122.	−	143218.i	0.470898	−	0.342127i	0.797791	+	0.602934i	$0.206002\pi$
$648$			142973.i			0.340490i
$649$	83705.3	+	102820.i	0.198730	+	0.244111i
$650$	622420.			1.47318
$651$	35847.1	+	49339.3i	0.0845848	+	0.116421i
$652$	−41711.7	−	128375.i	−0.0981211	−	0.301986i
$653$	−29840.9	+	91840.8i	−0.0699819	+	0.215382i	−0.979931	−	0.199339i	$-0.936121\pi$
$653$	−29840.9	+	91840.8i	−0.0699819	+	0.215382i	0.909949	+	0.414721i	$0.136121\pi$
$654$	18177.8	+	13207.0i	0.0424997	+	0.0308779i
$655$	−428038.	+	589144.i	−0.997699	+	1.37322i
$656$	67256.4	+	21852.9i	0.156288	+	0.0507811i
$657$	318709.	−	103555.i	0.738353	−	0.239906i
$658$	−394454.	+	286588.i	−0.911055	+	0.661920i
$659$		−	442730.i		−	1.01946i	−0.860336	−	0.509728i	$-0.829746\pi$
$659$		−	442730.i		−	1.01946i	0.860336	−	0.509728i	$-0.170254\pi$
$660$	−39541.8	+	15296.7i	−0.0907755	+	0.0351164i
$661$	−666291.			−1.52497			−0.762485	−	0.647006i	$-0.776021\pi$
$661$	−666291.			−1.52497			−0.762485	+	0.647006i	$0.776021\pi$
$662$	−180909.	−	249000.i	−0.412805	−	0.568178i
$663$	11722.5	+	36078.3i	0.0266683	+	0.0820765i
$664$	−3111.18	+	9575.22i	−0.00705649	+	0.0217176i
$665$	−364133.	−	264558.i	−0.823411	−	0.598243i
$666$	189407.	−	260697.i	0.427020	−	0.587743i
$667$	−155996.	−	50686.3i	−0.350641	−	0.113930i
$668$	−110164.	+	35794.6i	−0.246882	+	0.0802167i
$669$	5660.08	−	4112.29i	0.0126465	−	0.00918822i
$670$			31145.0i			0.0693807i
$671$	137873.	+	356400.i	0.306220	+	0.791575i
$672$	−12498.3			−0.0276766
$673$	−111806.	−	153887.i	−0.246850	−	0.339760i	0.667555	−	0.744561i	$-0.267341\pi$
$673$	−111806.	−	153887.i	−0.246850	−	0.339760i	−0.914405	+	0.404801i	$0.867341\pi$
$674$	−4420.30	−	13604.3i	−0.00973044	−	0.0299472i
$675$	−64235.1	+	197695.i	−0.140982	+	0.433900i
$676$	−3491.13	−	2536.46i	−0.00763964	−	0.00555052i
$677$	42042.5	−	57866.5i	0.0917300	−	0.126255i	−0.760685	−	0.649121i	$-0.775137\pi$
$677$	42042.5	−	57866.5i	0.0917300	−	0.126255i	0.852415	+	0.522865i	$0.175137\pi$
$678$	45632.9	+	14827.0i	0.0992701	+	0.0322548i
$679$	−136573.	+	44375.4i	−0.296228	+	0.0962504i
$680$	177986.	−	129315.i	0.384918	−	0.279660i
$681$		−	58420.2i		−	0.125970i
$682$	−234437.	+	190854.i	−0.504031	+	0.410330i
$683$	503504.			1.07935			0.539674	−	0.841874i	$-0.318547\pi$
$683$	503504.			1.07935			0.539674	+	0.841874i	$0.318547\pi$
$684$	56087.0	+	77197.1i	0.119881	+	0.165002i
$685$	150578.	+	463432.i	0.320908	+	0.987654i
$686$	−2608.77	+	8028.97i	−0.00554354	+	0.0170613i
$687$	−64651.5	−	46972.1i	−0.136983	−	0.0995236i
$688$	56018.7	−	77103.2i	0.118347	−	0.162890i
$689$	615658.	+	200040.i	1.29688	+	0.421383i
$690$	32152.4	−	10447.0i	0.0675329	−	0.0219428i
$691$	124167.	−	90212.5i	0.260046	−	0.188934i	−0.450122	−	0.892967i	$-0.648619\pi$
$691$	124167.	−	90212.5i	0.260046	−	0.188934i	0.710167	+	0.704033i	$0.248619\pi$
$692$		−	190295.i		−	0.397389i
$693$	−171149.	+	645440.i	−0.356375	+	1.34397i
$694$	−330791.			−0.686807
$695$	671119.	+	923716.i	1.38941	+	1.91236i
$696$	−4206.38	−	12945.9i	−0.00868340	−	0.0267248i
$697$	75864.7	−	233487.i	0.156161	−	0.480616i
$698$	−158507.	−	115162.i	−0.325339	−	0.236373i
$699$	46065.8	−	63404.2i	0.0942811	−	0.129767i
$700$	677066.	+	219992.i	1.38177	+	0.448963i
$701$	−624194.	+	202813.i	−1.27023	+	0.412724i	−0.865130	−	0.501548i	$-0.832764\pi$
$701$	−624194.	+	202813.i	−1.27023	+	0.412724i	−0.405103	+	0.914271i	$0.632764\pi$
$702$	62900.4	−	45699.8i	0.127638	−	0.0927343i
$703$		−	212337.i		−	0.429650i
$704$	−3403.07	−	61858.5i	−0.00686635	−	0.124811i
$705$	109449.			0.220209
$706$	94574.0	+	130170.i	0.189742	+	0.261157i
$707$	47439.3	+	146003.i	0.0949072	+	0.292094i
$708$	2711.18	−	8344.15i	0.00540869	−	0.0166462i
$709$	447847.	+	325380.i	0.890917	+	0.647289i	0.936117	−	0.351689i	$-0.114393\pi$
$709$	447847.	+	325380.i	0.890917	+	0.647289i	−0.0452003	+	0.998978i	$0.514393\pi$
$710$	−322927.	+	444471.i	−0.640601	+	0.881711i
$711$	−402536.	−	130792.i	−0.796280	−	0.258727i
$712$	−192297.	+	62481.0i	−0.379326	+	0.123250i
$713$	195014.	−	141686.i	0.383606	−	0.278706i
$714$			43389.1i			0.0851107i
$715$	−758824.	−	489988.i	−1.48433	−	0.958458i
$716$	291404.			0.568420
$717$	−43565.5	−	59962.8i	−0.0847432	−	0.116639i
$718$	129620.	+	398928.i	0.251433	+	0.773830i
$719$	298506.	−	918707.i	0.577425	−	1.77713i	−0.0503452	−	0.998732i	$-0.516032\pi$
$719$	298506.	−	918707.i	0.577425	−	1.77713i	0.627770	−	0.778399i	$-0.283968\pi$
$720$	−181260.	−	131693.i	−0.349653	−	0.254038i
$721$	814333.	−	1.12083e6i	1.56650	−	2.15611i
$722$	−290763.	−	94474.7i	−0.557783	−	0.181235i
$723$	11503.9	−	3737.83i	0.0220073	−	0.00715061i
$724$	73973.0	−	53744.5i	0.141122	−	0.102531i
$725$			775353.i			1.47511i
$726$	40585.8	+	8406.56i	0.0770018	+	0.0159494i
$727$	−744756.			−1.40911			−0.704555	−	0.709649i	$-0.748853\pi$
$727$	−744756.			−1.40911			−0.704555	+	0.709649i	$0.748853\pi$
$728$	−156512.	−	215421.i	−0.295315	−	0.406467i
$729$	−152163.	−	468311.i	−0.286322	−	0.881210i
$730$	−160221.	+	493110.i	−0.300659	+	0.925333i
$731$	−267671.	−	194475.i	−0.500919	−	0.363939i
$732$	14863.6	−	20458.0i	0.0277397	−	0.0381804i
$733$	417784.	+	135746.i	0.777577	+	0.252650i	0.670805	−	0.741634i	$-0.265949\pi$
$733$	417784.	+	135746.i	0.777577	+	0.252650i	0.106772	+	0.994284i	$0.465949\pi$
$734$	−341157.	+	110849.i	−0.633232	+	0.205749i
$735$	−83544.2	+	60698.5i	−0.154647	+	0.112358i
$736$			49399.5i			0.0911942i
$737$	16516.2	−	25578.0i	0.0304071	−	0.0470903i
$738$	−250019.			−0.459050
$739$	−237582.	−	327003.i	−0.435035	−	0.598774i	0.534065	−	0.845443i	$-0.320664\pi$
$739$	−237582.	−	327003.i	−0.435035	−	0.598774i	−0.969100	+	0.246670i	$0.920664\pi$
$740$	154067.	+	474169.i	0.281349	+	0.865904i
$741$	7866.56	−	24210.8i	0.0143268	−	0.0440933i
$742$	599007.	+	435204.i	1.08799	+	0.790470i
$743$	539969.	−	743203.i	0.978117	−	1.34626i	0.0402795	−	0.999188i	$-0.487175\pi$
$743$	539969.	−	743203.i	0.978117	−	1.34626i	0.937838	−	0.347074i	$-0.112825\pi$
$744$	19025.3	+	6181.69i	0.0343704	+	0.0111676i
$745$	1.35035e6	−	438754.i	2.43295	−	0.790513i
$746$	108006.	−	78470.9i	0.194075	−	0.141004i
$747$		−	35594.9i		−	0.0637891i
$748$	−214748.	+	11814.1i	−0.383818	+	0.0211153i
$749$	−1.22069e6			−2.17592
$750$	−48422.6	−	66648.0i	−0.0860847	−	0.118485i
$751$	−182885.	−	562862.i	−0.324264	−	0.997981i	−0.971772	−	0.235922i	$-0.924189\pi$
$751$	−182885.	−	562862.i	−0.324264	−	0.997981i	0.647508	−	0.762058i	$-0.275811\pi$
$752$	−49420.9	+	152102.i	−0.0873926	+	0.268967i
$753$	−5773.34	−	4194.58i	−0.0101821	−	0.00739773i
$754$	170461.	−	234619.i	0.299834	−	0.412686i
$755$	−393324.	−	127799.i	−0.690012	−	0.224198i
$756$	84575.3	−	27480.2i	0.147979	−	0.0480813i
$757$	−104124.	+	75650.7i	−0.181702	+	0.132014i	−0.674918	−	0.737892i	$-0.735821\pi$
$757$	−104124.	+	75650.7i	−0.181702	+	0.132014i	0.493216	+	0.869907i	$0.335821\pi$
$758$		−	778024.i		−	1.35411i
$759$	−31945.4	−	8470.83i	−0.0554529	−	0.0147042i
$760$	−147636.			−0.255602
$761$	506042.	+	696507.i	0.873811	+	1.20270i	0.978097	+	0.208150i	$0.0667443\pi$
$761$	506042.	+	696507.i	0.873811	+	1.20270i	−0.104286	+	0.994547i	$0.533256\pi$
$762$	4944.82	+	15218.6i	0.00851610	+	0.0262099i
$763$	−169195.	+	520728.i	−0.290628	+	0.894462i
$764$	−57425.9	−	41722.3i	−0.0983832	−	0.0714796i
$765$	−457186.	+	629263.i	−0.781214	+	1.07525i
$766$	−152591.	−	49579.7i	−0.260058	−	0.0844980i
$767$	177771.	−	57761.4i	0.302184	−	0.0981854i
$768$	−3316.64	+	2409.68i	−0.00562310	+	0.00408542i
$769$			344406.i			0.582395i	0.956663	+	0.291197i	$0.0940537\pi$
$769$			344406.i			0.582395i	−0.956663	+	0.291197i	$0.905946\pi$
$770$	−652262.	−	801210.i	−1.10012	−	1.35134i
$771$	126907.			0.213490
$772$	−48799.9	−	67167.3i	−0.0818812	−	0.112700i
$773$	−164043.	−	504873.i	−0.274536	−	0.844935i	−0.989342	−	0.145612i	$-0.953485\pi$
$773$	−164043.	−	504873.i	−0.274536	−	0.844935i	0.714806	−	0.699323i	$-0.246515\pi$
$774$	−104122.	+	320454.i	−0.173804	+	0.534915i
$775$	−921841.	−	669757.i	−1.53480	−	1.11510i
$776$	−27686.5	+	38107.2i	−0.0459774	+	0.0632825i
$777$	−93515.8	−	30385.1i	−0.154897	−	0.0503291i
$778$	258208.	−	83896.7i	0.426589	−	0.138607i
$779$	−133284.	+	96836.5i	−0.219636	+	0.159575i
$780$			59772.8i			0.0982460i
$781$	500909.	−	193776.i	0.821214	−	0.317685i
$782$	171495.			0.280439
$783$	56928.6	+	78355.6i	0.0928554	+	0.127805i
$784$	−46629.1	−	143510.i	−0.0758621	−	0.233479i
$785$	−52174.4	+	160576.i	−0.0846678	+	0.260581i
$786$	−38112.0	−	27690.0i	−0.0616903	−	0.0448207i
$787$	−290841.	+	400308.i	−0.469576	+	0.646316i	−0.976460	−	0.215698i	$-0.930797\pi$
$787$	−290841.	+	400308.i	−0.469576	+	0.646316i	0.506884	+	0.862014i	$0.330797\pi$
$788$	−576904.	−	187447.i	−0.929075	−	0.301875i
$789$	16017.3	−	5204.34i	0.0257297	−	0.00836010i
$790$	529791.	−	384916.i	0.848889	−	0.616754i
$791$			1.16921e6i			1.86870i
$792$	79023.9	+	204276.i	0.125982	+	0.325662i
$793$	538747.			0.856719
$794$	243973.	+	335800.i	0.386991	+	0.532648i
$795$	−51360.7	−	158072.i	−0.0812637	−	0.250104i
$796$	−161435.	+	496846.i	−0.254784	+	0.784144i
$797$	−524007.	−	380713.i	−0.824937	−	0.599351i	0.0931857	−	0.995649i	$-0.470295\pi$
$797$	−524007.	−	380713.i	−0.824937	−	0.599351i	−0.918122	+	0.396297i	$0.870295\pi$
$798$	17114.4	−	23556.0i	0.0268755	−	0.0369909i
$799$	528037.	+	171570.i	0.827124	+	0.268749i
$800$	222086.	−	72160.0i	0.347009	−	0.112750i
$801$	578321.	−	420175.i	0.901372	−	0.654885i
$802$			237306.i			0.368943i
$803$	393079.	−	320004.i	0.609605	−	0.496277i
$804$	−2014.79			−0.00311686
$805$	484224.	+	666477.i	0.747230	+	1.02847i
$806$	131700.	+	405332.i	0.202729	+	0.623936i
$807$	7457.41	−	22951.6i	0.0114509	−	0.0352424i
$808$	40738.3	+	29598.1i	0.0623993	+	0.0453357i
$809$	−152306.	+	209632.i	−0.232713	+	0.320302i	−0.909364	−	0.416002i	$-0.863431\pi$
$809$	−152306.	+	209632.i	−0.232713	+	0.320302i	0.676650	+	0.736305i	$0.263431\pi$
$810$	743798.	+	241674.i	1.13366	+	0.368350i
$811$	156597.	−	50881.3i	0.238090	−	0.0773601i	−0.187542	−	0.982257i	$-0.560052\pi$
$811$	156597.	−	50881.3i	0.238090	−	0.0773601i	0.425632	+	0.904897i	$0.360052\pi$
$812$	268351.	−	194969.i	0.406998	−	0.295701i
$813$			137730.i			0.208377i
$814$	124924.	−	471116.i	0.188537	−	0.711015i
$815$	−738362.			−1.11161
$816$	8365.44	+	11514.0i	0.0125634	+	0.0172921i
$817$	68610.4	+	211161.i	0.102789	+	0.316351i
$818$	−241491.	+	743233.i	−0.360906	+	1.11076i
$819$	761611.	+	553343.i	1.13544	+	0.824948i
$820$	227374.	−	312953.i	0.338152	−	0.465427i
$821$	−500058.	−	162479.i	−0.741880	−	0.241051i	−0.0863964	−	0.996261i	$-0.527535\pi$
$821$	−500058.	−	162479.i	−0.741880	−	0.241051i	−0.655484	+	0.755209i	$0.727535\pi$
$822$	−29979.7	+	9740.99i	−0.0443694	+	0.0144165i
$823$	854678.	−	620960.i	1.26184	−	0.916778i	0.262990	−	0.964799i	$-0.415291\pi$
$823$	854678.	−	620960.i	1.26184	−	0.916778i	0.998846	+	0.0480208i	$0.0152914\pi$
$824$		−	454436.i		−	0.669296i
$825$	8581.64	+	155991.i	0.0126085	+	0.229187i
$826$	213794.			0.313355
$827$	149221.	+	205385.i	0.218182	+	0.300302i	0.904052	−	0.427422i	$-0.140578\pi$
$827$	149221.	+	205385.i	0.218182	+	0.300302i	−0.685870	+	0.727724i	$0.740578\pi$
$828$	−53969.8	−	166102.i	−0.0787209	−	0.242278i
$829$	−376939.	+	1.16010e6i	−0.548482	+	1.68805i	0.164082	+	0.986447i	$0.447534\pi$
$829$	−376939.	+	1.16010e6i	−0.548482	+	1.68805i	−0.712564	+	0.701607i	$0.752466\pi$
$830$	44554.8	+	32370.9i	0.0646753	+	0.0469893i
$831$	66054.0	−	90915.5i	0.0956526	−	0.131655i
$832$	−83066.5	−	26989.9i	−0.119999	−	0.0389902i
$833$	−498208.	+	161878.i	−0.717993	+	0.233290i
$834$	−59755.7	+	43415.1i	−0.0859107	+	0.0624178i
$835$			633621.i			0.908775i
$836$	121247.	+	78291.4i	0.173483	+	0.112022i
$837$	−142335.			−0.203170
$838$	−408574.	−	562354.i	−0.581813	−	0.800796i
$839$	−90994.6	−	280053.i	−0.129268	−	0.397847i	0.865386	−	0.501105i	$-0.167073\pi$
$839$	−90994.6	−	280053.i	−0.129268	−	0.397847i	−0.994655	+	0.103259i	$0.967073\pi$
$840$	−21126.5	+	65020.7i	−0.0299412	+	0.0921495i
$841$	−279936.	−	203385.i	−0.395792	−	0.287559i
$842$	−101918.	+	140278.i	−0.143756	+	0.197863i
$843$	1039.53	+	337.763i	0.00146279	+	0.000475289i
$844$	−308840.	+	100348.i	−0.433559	+	0.140872i
$845$	−19096.8	+	13874.6i	−0.0267453	+	0.0194316i
$846$		−	565423.i		−	0.790010i
$847$	110791.	+	1.00389e6i	0.154433	+	1.39933i
$848$	242864.			0.337732
$849$	81545.8	+	112238.i	0.113132	+	0.155713i
$850$	−250511.	−	770992.i	−0.346727	−	1.06712i
$851$	−120097.	+	369621.i	−0.165834	+	0.510385i
$852$	−28753.1	−	20890.3i	−0.0396100	−	0.0287784i
$853$	−40665.6	+	55971.4i	−0.0558894	+	0.0769251i	−0.836047	−	0.548658i	$-0.815139\pi$
$853$	−40665.6	+	55971.4i	−0.0558894	+	0.0769251i	0.780157	+	0.625583i	$0.215139\pi$
$854$	586046.	+	190418.i	0.803556	+	0.261091i
$855$	496414.	−	161295.i	0.679065	−	0.220642i
$856$	−323932.	+	235350.i	−0.442085	+	0.321194i
$857$		−	888080.i		−	1.20918i	−0.796537	−	0.604589i	$-0.793337\pi$
$857$		−	888080.i		−	1.20918i	0.796537	−	0.604589i	$-0.206663\pi$
$858$	31697.6	−	49088.8i	0.0430578	−	0.0666819i
$859$	−1.42192e6			−1.92703			−0.963517	−	0.267648i	$-0.913753\pi$
$859$	−1.42192e6			−1.92703			−0.963517	+	0.267648i	$0.913753\pi$
$860$	−306427.	−	421761.i	−0.414315	−	0.570255i
$861$	23575.2	+	72557.1i	0.0318016	+	0.0978754i
$862$	253825.	−	781194.i	0.341602	−	1.05134i
$863$	−345303.	−	250878.i	−0.463638	−	0.336853i	0.331319	−	0.943519i	$-0.392506\pi$
$863$	−345303.	−	250878.i	−0.463638	−	0.336853i	−0.794957	+	0.606666i	$0.792506\pi$
$864$	17145.3	−	23598.5i	0.0229677	−	0.0316123i
$865$	−989984.	−	321665.i	−1.32311	−	0.429904i
$866$	−124887.	+	40578.1i	−0.166525	+	0.0541073i
$867$	−27657.0	+	20094.0i	−0.0367931	+	0.0267318i
$868$			487467.i			0.647002i
$869$	−639215.	+	35165.7i	−0.846463	+	0.0465672i
$870$	−74459.5			−0.0983743
$871$	−25230.6	−	34726.9i	−0.0332576	−	0.0457752i
$872$	55497.8	+	170805.i	0.0729866	+	0.224630i
$873$	51460.9	−	158380.i	0.0675225	−	0.207813i
$874$	−93105.0	−	67644.8i	−0.121885	−	0.0885546i
$875$	1.17996e6	−	1.62408e6i	1.54118	−	2.12125i
$876$	−31899.6	−	10364.8i	−0.0415697	−	0.0135068i
$877$	1.38361e6	−	449562.i	1.79893	−	0.584509i	0.799072	−	0.601235i	$-0.205324\pi$
$877$	1.38361e6	−	449562.i	1.79893	−	0.584509i	0.999860	+	0.0167265i	$0.00532445\pi$
$878$	22818.0	−	16578.3i	0.0295998	−	0.0215055i
$879$		−	30808.4i		−	0.0398742i
$880$	−327562.	−	86858.4i	−0.422989	−	0.112162i
$881$	−50384.3			−0.0649147			−0.0324574	−	0.999473i	$-0.510333\pi$
$881$	−50384.3			−0.0649147			−0.0324574	+	0.999473i	$0.510333\pi$
$882$	313573.	+	431596.i	0.403090	+	0.554805i
$883$	436301.	+	1.34280e6i	0.559583	+	1.72222i	0.683522	+	0.729930i	$0.260448\pi$
$883$	436301.	+	1.34280e6i	0.559583	+	1.72222i	−0.123938	+	0.992290i	$0.539552\pi$
$884$	−93698.3	+	288374.i	−0.119902	+	0.369021i
$885$	−38826.4	−	28209.1i	−0.0495725	−	0.0360166i
$886$	380676.	−	523955.i	0.484939	−	0.667462i
$887$	−109485.	−	35573.8i	−0.139158	−	0.0452151i	0.238610	−	0.971115i	$-0.423308\pi$
$887$	−109485.	−	35573.8i	−0.139158	−	0.0452151i	−0.377768	+	0.925900i	$0.623308\pi$
$888$	−30674.3	+	9966.68i	−0.0388999	+	0.0126393i
$889$	−315461.	+	229196.i	−0.399156	+	0.290004i
$890$			1.10601e6i			1.39630i
$891$	−482688.	−	592913.i	−0.608010	−	0.746854i
$892$	55920.9			0.0702821
$893$	−218998.	−	301424.i	−0.274623	−	0.377986i
$894$	28383.3	+	87354.7i	0.0355130	+	0.109298i
$895$	492574.	−	1.51599e6i	0.614930	−	1.89256i
$896$	−80819.9	−	58719.1i	−0.100670	−	0.0731414i
$897$	−27387.1	+	37695.1i	−0.0340378	+	0.0468490i
$898$	590559.	+	191884.i	0.732336	+	0.237950i
$899$	−504925.	+	164060.i	−0.624751	+	0.202994i
$900$	−667909.	+	485264.i	−0.824579	+	0.599091i
$901$		−	843128.i		−	1.03859i
$902$	−352691.	+	136438.i	−0.433493	+	0.167696i
$903$	102816.			0.126091
$904$	225424.	+	310269.i	0.275844	+	0.379666i
$905$	−154558.	−	475681.i	−0.188710	−	0.580789i
$906$	8267.37	−	25444.4i	0.0100719	−	0.0309981i
$907$	195228.	+	141842.i	0.237316	+	0.172421i	0.700087	−	0.714058i	$-0.253145\pi$
$907$	195228.	+	141842.i	0.237316	+	0.172421i	−0.462770	+	0.886478i	$0.653145\pi$
$908$	274468.	−	377772.i	0.332904	−	0.458204i
$909$	−169315.	−	55013.9i	−0.204913	−	0.0665802i
$910$	−1.38526e6	+	450098.i	−1.67281	+	0.543530i
$911$	−160010.	+	116254.i	−0.192801	+	0.140078i	−0.679998	−	0.733214i	$-0.738019\pi$
$911$	−160010.	+	116254.i	−0.192801	+	0.140078i	0.487197	+	0.873292i	$0.338019\pi$
$912$		−	9550.65i		−	0.0114827i
$913$	−19424.5	−	50212.3i	−0.0233029	−	0.0602377i
$914$	100285.			0.120045
$915$	−81305.2	−	111907.i	−0.0971127	−	0.133664i
$916$	−197385.	−	607487.i	−0.235246	−	0.724013i
$917$	354738.	−	1.09177e6i	0.421860	−	1.29835i
$918$	−81924.5	−	59521.6i	−0.0972139	−	0.0706300i
$919$	−754825.	+	1.03893e6i	−0.893748	+	1.23014i	0.0786719	+	0.996901i	$0.474932\pi$
$919$	−754825.	+	1.03893e6i	−0.893748	+	1.23014i	−0.972420	+	0.233238i	$0.925068\pi$
$920$	256994.	+	83502.5i	0.303632	+	0.0986560i
$921$	−45515.8	+	14789.0i	−0.0536590	+	0.0174349i
$922$	−256505.	+	186362.i	−0.301741	+	0.219227i
$923$		−	757192.i		−	0.888797i
$924$	51830.8	−	42195.2i	0.0607077	−	0.0494219i
$925$	1.83714e6			2.14713
$926$	−125014.	−	172066.i	−0.145793	−	0.200666i
$927$	496479.	+	1.52800e6i	0.577751	+	1.77814i
$928$	33621.6	−	103477.i	0.0390411	−	0.120156i
$929$	503249.	+	365632.i	0.583111	+	0.423655i	0.839844	−	0.542827i	$-0.182646\pi$
$929$	503249.	+	365632.i	0.583111	+	0.423655i	−0.256733	+	0.966482i	$0.582646\pi$
$930$	64318.7	−	88527.2i	0.0743655	−	0.102355i
$931$	334329.	+	108630.i	0.385722	+	0.125329i
$932$	595767.	−	193576.i	0.685874	−	0.222854i
$933$	87340.7	−	63456.8i	0.100335	−	0.0728978i
$934$		−	29595.1i		−	0.0339254i
$935$	−301538.	+	1.13717e6i	−0.344920	+	1.30077i
$936$	308791.			0.352463
$937$	505212.	+	695365.i	0.575433	+	0.792015i	0.993185	−	0.116545i	$-0.0371821\pi$
$937$	505212.	+	695365.i	0.575433	+	0.792015i	−0.417752	+	0.908561i	$0.637182\pi$
$938$	−15171.6	−	46693.4i	−0.0172435	−	0.0530701i
$939$	−6464.09	+	19894.4i	−0.00733122	+	0.0225632i
$940$	707750.	+	514210.i	0.800985	+	0.581949i
$941$	−619437.	+	852581.i	−0.699548	+	0.962845i	0.300411	+	0.953810i	$0.402876\pi$
$941$	−619437.	+	852581.i	−0.699548	+	0.962845i	−0.999959	+	0.00903557i	$0.997124\pi$
$942$	−10387.8	−	3375.19i	−0.0117063	−	0.00380362i
$943$	286782.	−	93181.1i	0.322499	−	0.104786i
$944$	56734.0	−	41219.6i	0.0636648	−	0.0462552i
$945$		−	486442.i		−	0.544713i
$946$	27995.0	+	508872.i	0.0312823	+	0.568626i
$947$	−57720.0			−0.0643616			−0.0321808	−	0.999482i	$-0.510245\pi$
$947$	−57720.0			−0.0643616			−0.0321808	+	0.999482i	$0.510245\pi$
$948$	24900.4	+	34272.5i	0.0277071	+	0.0381355i
$949$	−220821.	−	679617.i	−0.245193	−	0.754626i
$950$	−168108.	+	517384.i	−0.186270	+	0.573279i
$951$	72236.2	+	52482.7i	0.0798719	+	0.0580303i
$952$	−203849.	+	280574.i	−0.224924	+	0.309581i
$953$	311593.	+	101243.i	0.343085	+	0.111475i	0.475491	−	0.879721i	$-0.342270\pi$
$953$	311593.	+	101243.i	0.343085	+	0.111475i	−0.132406	+	0.991196i	$0.542270\pi$
$954$	−816612.	+	265333.i	−0.897261	+	0.291538i
$955$	−314125.	+	228225.i	−0.344425	+	0.250240i
$956$		−	592426.i		−	0.648214i
$957$	61150.3	+	39485.9i	0.0667690	+	0.0431140i
$958$	281948.			0.307211
$959$	−451502.	−	621440.i	−0.490934	−	0.675712i
$960$	6929.74	+	21327.5i	0.00751925	+	0.0231419i
$961$	−44281.4	+	136284.i	−0.0479484	+	0.147570i
$962$	−555911.	−	403893.i	−0.600696	−	0.436431i
$963$	832071.	−	1.14525e6i	0.897238	−	1.23494i
$964$	91950.3	+	29876.5i	0.0989462	+	0.0321496i
$965$	−431917.	+	140338.i	−0.463816	+	0.150703i
$966$	−43114.8	+	31324.7i	−0.0462032	+	0.0335686i
$967$			1.36682e6i			1.46170i	0.682540	+	0.730848i	$0.260875\pi$
$967$			1.36682e6i			1.46170i	−0.682540	+	0.730848i	$0.739125\pi$
$968$	222951.	+	245040.i	0.237936	+	0.261508i
$969$	−33156.0			−0.0353114
$970$	151447.	+	208450.i	0.160960	+	0.221543i
$971$	14536.2	+	44737.9i	0.0154175	+	0.0474501i	0.958469	−	0.285196i	$-0.0920586\pi$
$971$	14536.2	+	44737.9i	0.0154175	+	0.0474501i	−0.943052	+	0.332646i	$0.892059\pi$
$972$	−47901.1	+	147424.i	−0.0507006	+	0.156040i
$973$	−1.45613e6	−	1.05794e6i	−1.53806	−	1.11747i
$974$	−696694.	+	958917.i	−0.734385	+	1.01079i
$975$	209472.	+	68061.4i	0.220351	+	0.0715965i
$976$	192230.	−	62459.3i	0.201800	−	0.0655689i
$977$	111116.	−	80730.2i	0.116409	−	0.0845760i	−0.528058	−	0.849209i	$-0.677080\pi$
$977$	111116.	−	80730.2i	0.116409	−	0.0845760i	0.644467	+	0.764633i	$0.277080\pi$
$978$		−	47765.1i		−	0.0499382i
$979$	586519.	−	908319.i	0.611951	−	0.947705i
$980$	−825408.			−0.859442
$981$	−373214.	−	513685.i	−0.387811	−	0.533776i
$982$	68487.1	+	210782.i	0.0710208	+	0.218580i
$983$	136330.	−	419580.i	0.141086	−	0.434218i	−0.855401	−	0.517967i	$-0.826689\pi$
$983$	136330.	−	419580.i	0.141086	−	0.434218i	0.996487	+	0.0837482i	$0.0266891\pi$
$984$	20245.1	+	14708.9i	0.0209089	+	0.0151912i
$985$	−1.95034e6	+	2.68441e6i	−2.01019	+	2.76679i
$986$	−359229.	−	116721.i	−0.369503	−	0.120059i
$987$	−164089.	+	53315.9i	−0.168440	+	0.0547296i
$988$	164615.	−	119600.i	0.168638	−	0.122523i
$989$		−	406380.i		−	0.415470i
$990$	1.19630e6	−	65812.9i	1.22059	−	0.0671491i
$991$	1.11050e6			1.13076			0.565379	−	0.824831i	$-0.308730\pi$
$991$	1.11050e6			1.13076			0.565379	+	0.824831i	$0.308730\pi$
$992$	93983.8	+	129358.i	0.0955058	+	0.131452i
$993$	−33655.8	−	103582.i	−0.0341320	−	0.105047i
$994$	267627.	−	823670.i	0.270867	−	0.833644i
$995$	2.31189e6	+	1.67969e6i	2.33518	+	1.69661i
$996$	−2094.10	+	2882.28i	−0.00211095	+	0.00290547i
$997$	−966994.	−	314196.i	−0.972823	−	0.316089i	−0.220868	−	0.975304i	$-0.570889\pi$
$997$	−966994.	−	314196.i	−0.972823	−	0.316089i	−0.751955	+	0.659215i	$0.770889\pi$
$998$	1.04444e6	−	339359.i	1.04863	−	0.340720i
$999$	185657.	−	134888.i	0.186029	−	0.135158i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.5.d.a.19.3	yes	16
3.2	odd	2		198.5.j.a.19.1		16
4.3	odd	2		176.5.n.c.129.3		16
11.2	odd	10		242.5.b.e.241.12		16
11.7	odd	10	inner	22.5.d.a.7.3	✓	16
11.9	even	5		242.5.b.e.241.4		16
33.29	even	10		198.5.j.a.73.1		16
44.7	even	10		176.5.n.c.161.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.5.d.a.7.3	✓	16	11.7	odd	10	inner
22.5.d.a.19.3	yes	16	1.1	even	1	trivial
176.5.n.c.129.3		16	4.3	odd	2
176.5.n.c.161.3		16	44.7	even	10
198.5.j.a.19.1		16	3.2	odd	2
198.5.j.a.73.1		16	33.29	even	10
242.5.b.e.241.4		16	11.9	even	5
242.5.b.e.241.12		16	11.2	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	22.d (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.66251 + 2.28825i) q^{2} +(0.309288 + 0.951890i) q^{3} +(-2.47214 + 7.60845i) q^{4} +(35.4031 + 25.7219i) q^{5} +(-1.66396 + 2.29025i) q^{6} +(-65.6073 - 21.3171i) q^{7} +(-21.5200 + 6.99226i) q^{8} +(64.7199 - 47.0218i) q^{9} +O(q^{10})\)	\(q+(1.66251 + 2.28825i) q^{2} +(0.309288 + 0.951890i) q^{3} +(-2.47214 + 7.60845i) q^{4} +(35.4031 + 25.7219i) q^{5} +(-1.66396 + 2.29025i) q^{6} +(-65.6073 - 21.3171i) q^{7} +(-21.5200 + 6.99226i) q^{8} +(64.7199 - 47.0218i) q^{9} +123.774i q^{10} +(65.6374 - 101.650i) q^{11} -8.00701 q^{12} +(-100.269 - 138.009i) q^{13} +(-60.2938 - 185.565i) q^{14} +(-13.5346 + 41.6553i) q^{15} +(-51.7771 - 37.6183i) q^{16} +(-130.596 + 179.749i) q^{17} +(215.195 + 69.9210i) q^{18} +(141.801 - 46.0739i) q^{19} +(-283.225 + 205.775i) q^{20} -69.0440i q^{21} +(341.723 - 18.7995i) q^{22} -272.896 q^{23} +(-13.3117 - 18.3220i) q^{24} +(398.631 + 1226.86i) q^{25} +(149.100 - 458.882i) q^{26} +(130.364 + 94.7153i) q^{27} +(324.380 - 446.471i) q^{28} +(571.633 + 185.735i) q^{29} +(-117.819 + 38.2817i) q^{30} +(-714.607 + 519.192i) q^{31} -181.019i q^{32} +(117.060 + 31.0405i) q^{33} -628.427 q^{34} +(-1774.39 - 2442.23i) q^{35} +(197.767 + 608.663i) q^{36} +(440.083 - 1354.44i) q^{37} +(341.174 + 247.877i) q^{38} +(100.357 - 138.130i) q^{39} +(-941.728 - 305.986i) q^{40} +(-1050.88 + 341.452i) q^{41} +(157.990 - 114.786i) q^{42} +1489.14i q^{43} +(611.135 + 750.692i) q^{44} +3500.78 q^{45} +(-453.692 - 624.454i) q^{46} +(-772.201 - 2376.59i) q^{47} +(19.7944 - 60.9209i) q^{48} +(1907.45 + 1385.84i) q^{49} +(-2144.63 + 2951.83i) q^{50} +(-211.493 - 68.7183i) q^{51} +(1297.91 - 421.718i) q^{52} +(-3070.02 + 2230.50i) q^{53} +455.771i q^{54} +(4938.40 - 1910.41i) q^{55} +1560.92 q^{56} +(87.7146 + 120.729i) q^{57} +(525.337 + 1616.82i) q^{58} +(-338.601 + 1042.11i) q^{59} +(-283.473 - 205.955i) q^{60} +(-1856.32 + 2555.01i) q^{61} +(-2376.08 - 772.035i) q^{62} +(-5248.47 + 1705.33i) q^{63} +(414.217 - 300.946i) q^{64} -7465.07i q^{65} +(123.586 + 319.468i) q^{66} +251.628 q^{67} +(-1044.76 - 1437.99i) q^{68} +(-84.4035 - 259.767i) q^{69} +(2638.50 - 8120.47i) q^{70} +(3590.99 + 2609.01i) q^{71} +(-1063.98 + 1464.45i) q^{72} +(3983.96 + 1294.47i) q^{73} +(3830.93 - 1244.74i) q^{74} +(-1044.54 + 758.906i) q^{75} +1192.79i q^{76} +(-6473.17 + 5269.78i) q^{77} +482.920 q^{78} +(-3109.83 - 4280.32i) q^{79} +(-865.459 - 2663.61i) q^{80} +(1952.55 - 6009.32i) q^{81} +(-2528.43 - 1837.01i) q^{82} +(261.533 - 359.969i) q^{83} +(525.318 + 170.686i) q^{84} +(-9246.98 + 3004.53i) q^{85} +(-3407.51 + 2475.70i) q^{86} +601.577i q^{87} +(-701.751 + 2646.46i) q^{88} +8935.75 q^{89} +(5820.07 + 8010.64i) q^{90} +(3636.45 + 11191.8i) q^{91} +(674.637 - 2076.32i) q^{92} +(-715.233 - 519.647i) q^{93} +(4154.43 - 5718.09i) q^{94} +(6205.31 + 2016.23i) q^{95} +(172.310 - 55.9871i) q^{96} +(1684.12 - 1223.58i) q^{97} +6668.67i q^{98} +(-531.718 - 9665.17i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} + 32 q^{4} + 30 q^{5} - 80 q^{6} + 150 q^{7} + 110 q^{9}+O(q^{10}) \) 16 * q - 2 * q^3 + 32 * q^4 + 30 * q^5 - 80 * q^6 + 150 * q^7 + 110 * q^9	\( 16 q - 2 q^{3} + 32 q^{4} + 30 q^{5} - 80 q^{6} + 150 q^{7} + 110 q^{9} - 30 q^{11} - 384 q^{12} - 510 q^{13} - 96 q^{14} - 1398 q^{15} - 256 q^{16} + 1770 q^{17} + 1120 q^{18} + 1020 q^{19} - 240 q^{20} + 240 q^{22} - 2424 q^{23} - 640 q^{24} - 858 q^{25} + 480 q^{26} + 2224 q^{27} + 1600 q^{28} + 4890 q^{29} + 3360 q^{30} + 602 q^{31} - 2648 q^{33} - 3904 q^{34} - 8670 q^{35} + 720 q^{36} - 4518 q^{37} - 4800 q^{38} - 1130 q^{39} - 1280 q^{40} + 1290 q^{41} - 3808 q^{42} + 720 q^{44} + 12152 q^{45} + 4480 q^{46} + 642 q^{47} - 128 q^{48} + 9534 q^{49} + 6720 q^{50} - 1500 q^{51} + 4000 q^{52} + 2598 q^{53} + 2582 q^{55} - 3072 q^{56} + 9140 q^{57} - 6496 q^{58} + 6660 q^{59} - 5776 q^{60} - 27410 q^{61} - 19680 q^{62} - 27260 q^{63} + 2048 q^{64} + 2528 q^{66} + 21524 q^{67} + 14160 q^{68} + 11416 q^{69} + 34400 q^{70} - 5562 q^{71} + 10240 q^{72} - 7790 q^{73} + 5760 q^{74} + 3576 q^{75} - 1110 q^{77} - 39424 q^{78} - 2770 q^{79} - 3840 q^{80} - 25464 q^{81} - 17472 q^{82} - 36900 q^{83} - 24480 q^{84} - 24750 q^{85} + 624 q^{86} - 5760 q^{88} + 46596 q^{89} + 55360 q^{90} + 32370 q^{91} + 14112 q^{92} + 20722 q^{93} + 58880 q^{94} + 74250 q^{95} - 3732 q^{97} + 45802 q^{99}+O(q^{100}) \) 16 * q - 2 * q^3 + 32 * q^4 + 30 * q^5 - 80 * q^6 + 150 * q^7 + 110 * q^9 - 30 * q^11 - 384 * q^12 - 510 * q^13 - 96 * q^14 - 1398 * q^15 - 256 * q^16 + 1770 * q^17 + 1120 * q^18 + 1020 * q^19 - 240 * q^20 + 240 * q^22 - 2424 * q^23 - 640 * q^24 - 858 * q^25 + 480 * q^26 + 2224 * q^27 + 1600 * q^28 + 4890 * q^29 + 3360 * q^30 + 602 * q^31 - 2648 * q^33 - 3904 * q^34 - 8670 * q^35 + 720 * q^36 - 4518 * q^37 - 4800 * q^38 - 1130 * q^39 - 1280 * q^40 + 1290 * q^41 - 3808 * q^42 + 720 * q^44 + 12152 * q^45 + 4480 * q^46 + 642 * q^47 - 128 * q^48 + 9534 * q^49 + 6720 * q^50 - 1500 * q^51 + 4000 * q^52 + 2598 * q^53 + 2582 * q^55 - 3072 * q^56 + 9140 * q^57 - 6496 * q^58 + 6660 * q^59 - 5776 * q^60 - 27410 * q^61 - 19680 * q^62 - 27260 * q^63 + 2048 * q^64 + 2528 * q^66 + 21524 * q^67 + 14160 * q^68 + 11416 * q^69 + 34400 * q^70 - 5562 * q^71 + 10240 * q^72 - 7790 * q^73 + 5760 * q^74 + 3576 * q^75 - 1110 * q^77 - 39424 * q^78 - 2770 * q^79 - 3840 * q^80 - 25464 * q^81 - 17472 * q^82 - 36900 * q^83 - 24480 * q^84 - 24750 * q^85 + 624 * q^86 - 5760 * q^88 + 46596 * q^89 + 55360 * q^90 + 32370 * q^91 + 14112 * q^92 + 20722 * q^93 + 58880 * q^94 + 74250 * q^95 - 3732 * q^97 + 45802 * q^99

Introduction

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