LMFDB - Embedded newform 38.4.e.a.35.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,4,Mod(5,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("38.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	38.e (of order $9$, degree $6$, 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:	$2.24207258022$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} - 135 x^{10} + 730 x^{9} + 7953 x^{8} - 36258 x^{7} - 262940 x^{6} + 918855 x^{5} + \cdots + 272110107 $ x^12 - 6x^11 - 135x^10 + 730x^9 + 7953x^8 - 36258x^7 - 262940x^6 + 918855x^5 + 5157591x^4 - 11890401x^3 - 56759508x^2 + 62864118*x + 272110107
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			35.2
Root			$6.28151 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	38.35
Dual form			38.4.e.a.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.53209 + 1.28558i) q^{2} +(4.68284 - 1.70441i) q^{3} +(0.694593 + 3.93923i) q^{4} +(0.408053 - 2.31419i) q^{5} +(9.36568 + 3.40883i) q^{6} +(-1.42158 - 2.46225i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(-1.65925 + 1.39227i) q^{9} +O(q^{10})$	\(q+(1.53209 + 1.28558i) q^{2} +(4.68284 - 1.70441i) q^{3} +(0.694593 + 3.93923i) q^{4} +(0.408053 - 2.31419i) q^{5} +(9.36568 + 3.40883i) q^{6} +(-1.42158 - 2.46225i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(-1.65925 + 1.39227i) q^{9} +(3.60023 - 3.02095i) q^{10} +(-1.90096 + 3.29257i) q^{11} +(9.96675 + 17.2629i) q^{12} +(-15.4040 - 5.60661i) q^{13} +(0.987418 - 5.59993i) q^{14} +(-2.03348 - 11.5325i) q^{15} +(-15.0351 + 5.47232i) q^{16} +(-57.2974 - 48.0782i) q^{17} -4.33198 q^{18} +(-41.0556 - 71.9266i) q^{19} +9.39954 q^{20} +(-10.8537 - 9.10735i) q^{21} +(-7.14529 + 2.60067i) q^{22} +(6.08655 + 34.5185i) q^{23} +(-6.92283 + 39.2613i) q^{24} +(112.273 + 40.8639i) q^{25} +(-16.3926 - 28.3928i) q^{26} +(-72.6725 + 125.872i) q^{27} +(8.71194 - 7.31019i) q^{28} +(59.8802 - 50.2455i) q^{29} +(11.7104 - 20.2829i) q^{30} +(114.867 + 198.955i) q^{31} +(-30.0702 - 10.9446i) q^{32} +(-3.29001 + 18.6586i) q^{33} +(-25.9765 - 147.320i) q^{34} +(-6.27818 + 2.28507i) q^{35} +(-6.63699 - 5.56909i) q^{36} +401.456 q^{37} +(29.5662 - 162.978i) q^{38} -81.6905 q^{39} +(14.4009 + 12.0838i) q^{40} +(60.9251 - 22.1749i) q^{41} +(-4.92067 - 27.9065i) q^{42} +(-13.5220 + 76.6872i) q^{43} +(-14.2906 - 5.20135i) q^{44} +(2.54492 + 4.40793i) q^{45} +(-35.0510 + 60.7102i) q^{46} +(-356.545 + 299.176i) q^{47} +(-61.0798 + 51.2520i) q^{48} +(167.458 - 290.046i) q^{49} +(119.478 + 206.942i) q^{50} +(-350.260 - 127.484i) q^{51} +(11.3862 - 64.5743i) q^{52} +(-12.3203 - 69.8721i) q^{53} +(-273.159 + 99.4219i) q^{54} +(6.84392 + 5.74273i) q^{55} +22.7453 q^{56} +(-314.850 - 266.845i) q^{57} +156.336 q^{58} +(-508.257 - 426.478i) q^{59} +(44.0165 - 16.0207i) q^{60} +(-27.4270 - 155.546i) q^{61} +(-79.7855 + 452.486i) q^{62} +(5.78687 + 2.10625i) q^{63} +(-32.0000 - 55.4256i) q^{64} +(-19.2604 + 33.3600i) q^{65} +(-29.0276 + 24.3571i) q^{66} +(68.6778 - 57.6275i) q^{67} +(149.593 - 259.103i) q^{68} +(87.3362 + 151.271i) q^{69} +(-12.5564 - 4.57014i) q^{70} +(-109.611 + 621.638i) q^{71} +(-3.00897 - 17.0647i) q^{72} +(713.200 - 259.583i) q^{73} +(615.066 + 516.102i) q^{74} +595.404 q^{75} +(254.819 - 211.687i) q^{76} +10.8095 q^{77} +(-125.157 - 105.019i) q^{78} +(774.641 - 281.946i) q^{79} +(6.52885 + 37.0270i) q^{80} +(-115.620 + 655.711i) q^{81} +(121.850 + 44.3498i) q^{82} +(66.3727 + 114.961i) q^{83} +(28.3370 - 49.0812i) q^{84} +(-134.642 + 112.978i) q^{85} +(-119.304 + 100.108i) q^{86} +(194.770 - 337.352i) q^{87} +(-15.2077 - 26.3405i) q^{88} +(-1326.11 - 482.664i) q^{89} +(-1.76768 + 10.0250i) q^{90} +(8.09319 + 45.8987i) q^{91} +(-131.749 + 47.9527i) q^{92} +(877.003 + 735.892i) q^{93} -930.872 q^{94} +(-183.204 + 65.6605i) q^{95} -159.468 q^{96} +(-1011.58 - 848.815i) q^{97} +(629.437 - 229.096i) q^{98} +(-1.42998 - 8.10984i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 9 q^{3} - 18 q^{6} + 21 q^{7} - 48 q^{8} - 27 q^{9}+O(q^{10}) $ 12 * q - 9 * q^3 - 18 * q^6 + 21 * q^7 - 48 * q^8 - 27 * q^9	\( 12 q - 9 q^{3} - 18 q^{6} + 21 q^{7} - 48 q^{8} - 27 q^{9} - 9 q^{11} + 36 q^{12} + 39 q^{13} - 138 q^{14} + 423 q^{15} + 69 q^{17} + 132 q^{18} - 462 q^{19} - 216 q^{20} - 279 q^{21} + 204 q^{22} - 66 q^{23} - 72 q^{24} + 342 q^{25} + 48 q^{26} + 189 q^{27} + 192 q^{28} + 159 q^{29} + 72 q^{31} - 1560 q^{33} + 408 q^{34} - 135 q^{35} - 108 q^{36} + 1116 q^{37} - 294 q^{38} - 1248 q^{39} + 147 q^{41} + 414 q^{42} - 117 q^{43} + 408 q^{44} + 1296 q^{45} + 528 q^{46} + 783 q^{47} + 288 q^{48} + 1413 q^{49} - 354 q^{50} - 2301 q^{51} - 348 q^{52} - 249 q^{53} - 540 q^{54} + 2187 q^{55} - 336 q^{56} - 2670 q^{57} - 1932 q^{58} - 4248 q^{59} + 324 q^{60} + 3114 q^{61} - 438 q^{62} + 363 q^{63} - 384 q^{64} + 495 q^{65} + 822 q^{66} + 3060 q^{67} + 408 q^{68} - 237 q^{69} - 270 q^{70} + 1686 q^{71} + 432 q^{72} + 1626 q^{73} + 90 q^{74} - 1854 q^{75} - 1416 q^{77} - 108 q^{78} - 327 q^{79} + 3483 q^{81} + 294 q^{82} + 927 q^{83} + 204 q^{84} - 3294 q^{85} + 1188 q^{86} + 2892 q^{87} - 72 q^{88} - 6366 q^{89} - 5076 q^{90} + 840 q^{91} - 156 q^{92} + 870 q^{93} + 3432 q^{94} + 513 q^{95} - 576 q^{96} - 8052 q^{97} + 378 q^{98} + 4494 q^{99}+O(q^{100}) \) 12 * q - 9 * q^3 - 18 * q^6 + 21 * q^7 - 48 * q^8 - 27 * q^9 - 9 * q^11 + 36 * q^12 + 39 * q^13 - 138 * q^14 + 423 * q^15 + 69 * q^17 + 132 * q^18 - 462 * q^19 - 216 * q^20 - 279 * q^21 + 204 * q^22 - 66 * q^23 - 72 * q^24 + 342 * q^25 + 48 * q^26 + 189 * q^27 + 192 * q^28 + 159 * q^29 + 72 * q^31 - 1560 * q^33 + 408 * q^34 - 135 * q^35 - 108 * q^36 + 1116 * q^37 - 294 * q^38 - 1248 * q^39 + 147 * q^41 + 414 * q^42 - 117 * q^43 + 408 * q^44 + 1296 * q^45 + 528 * q^46 + 783 * q^47 + 288 * q^48 + 1413 * q^49 - 354 * q^50 - 2301 * q^51 - 348 * q^52 - 249 * q^53 - 540 * q^54 + 2187 * q^55 - 336 * q^56 - 2670 * q^57 - 1932 * q^58 - 4248 * q^59 + 324 * q^60 + 3114 * q^61 - 438 * q^62 + 363 * q^63 - 384 * q^64 + 495 * q^65 + 822 * q^66 + 3060 * q^67 + 408 * q^68 - 237 * q^69 - 270 * q^70 + 1686 * q^71 + 432 * q^72 + 1626 * q^73 + 90 * q^74 - 1854 * q^75 - 1416 * q^77 - 108 * q^78 - 327 * q^79 + 3483 * q^81 + 294 * q^82 + 927 * q^83 + 204 * q^84 - 3294 * q^85 + 1188 * q^86 + 2892 * q^87 - 72 * q^88 - 6366 * q^89 - 5076 * q^90 + 840 * q^91 - 156 * q^92 + 870 * q^93 + 3432 * q^94 + 513 * q^95 - 576 * q^96 - 8052 * q^97 + 378 * q^98 + 4494 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

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 $

$2$	1.53209	+	1.28558i	0.541675	+	0.454519i
$2$	1.53209	+	1.28558i	0.541675	+	0.454519i
$3$	4.68284	−	1.70441i	0.901213	−	0.328015i	0.150474	−	0.988614i	$-0.451920\pi$
$3$	4.68284	−	1.70441i	0.901213	−	0.328015i	0.750739	+	0.660599i	$0.229698\pi$
$4$	0.694593	+	3.93923i	0.0868241	+	0.492404i
$5$	0.408053	−	2.31419i	0.0364974	−	0.206987i	−0.961106	−	0.276180i	$-0.910931\pi$
$5$	0.408053	−	2.31419i	0.0364974	−	0.206987i	0.997603	+	0.0691931i	$0.0220425\pi$
$6$	9.36568	+	3.40883i	0.637254	+	0.231941i
$7$	−1.42158	−	2.46225i	−0.0767581	−	0.132949i	0.825091	−	0.564999i	$-0.191124\pi$
$7$	−1.42158	−	2.46225i	−0.0767581	−	0.132949i	−0.901849	+	0.432050i	$0.857790\pi$
$8$	−4.00000	+	6.92820i	−0.176777	+	0.306186i
$9$	−1.65925	+	1.39227i	−0.0614536	+	0.0515657i
$10$	3.60023	−	3.02095i	0.113849	−	0.0955310i
$11$	−1.90096	+	3.29257i	−0.0521057	+	0.0902497i	−0.890902	−	0.454196i	$-0.849927\pi$
$11$	−1.90096	+	3.29257i	−0.0521057	+	0.0902497i	0.838796	+	0.544446i	$0.183260\pi$
$12$	9.96675	+	17.2629i	0.239763	+	0.415281i
$13$	−15.4040	−	5.60661i	−0.328639	−	0.119615i	0.172431	−	0.985022i	$-0.444838\pi$
$13$	−15.4040	−	5.60661i	−0.328639	−	0.119615i	−0.501070	+	0.865407i	$0.667060\pi$
$14$	0.987418	−	5.59993i	0.0188499	−	0.106903i
$15$	−2.03348	−	11.5325i	−0.0350029	−	0.198511i
$16$	−15.0351	+	5.47232i	−0.234923	+	0.0855050i
$17$	−57.2974	−	48.0782i	−0.817451	−	0.685923i	0.134923	−	0.990856i	$-0.456921\pi$
$17$	−57.2974	−	48.0782i	−0.817451	−	0.685923i	−0.952374	+	0.304933i	$0.901366\pi$
$18$	−4.33198			−0.0567255
$19$	−41.0556	−	71.9266i	−0.495727	−	0.868479i
$19$	−41.0556	−	71.9266i	−0.495727	−	0.868479i
$20$	9.39954			0.105090
$21$	−10.8537	−	9.10735i	−0.112785	−	0.0946374i
$22$	−7.14529	+	2.60067i	−0.0692446	+	0.0252030i
$23$	6.08655	+	34.5185i	0.0551797	+	0.312940i	0.999888	−	0.0149725i	$-0.00476607\pi$
$23$	6.08655	+	34.5185i	0.0551797	+	0.312940i	−0.944708	+	0.327912i	$0.893655\pi$
$24$	−6.92283	+	39.2613i	−0.0588799	+	0.333924i
$25$	112.273	+	40.8639i	0.898181	+	0.326911i
$26$	−16.3926	−	28.3928i	−0.123648	−	0.214165i
$27$	−72.6725	+	125.872i	−0.517994	+	0.897191i
$28$	8.71194	−	7.31019i	0.0588001	−	0.0493391i
$29$	59.8802	−	50.2455i	0.383430	−	0.321736i	−0.430617	−	0.902535i	$-0.641704\pi$
$29$	59.8802	−	50.2455i	0.383430	−	0.321736i	0.814047	+	0.580799i	$0.197260\pi$
$30$	11.7104	−	20.2829i	0.0712670	−	0.123438i
$31$	114.867	+	198.955i	0.665504	+	1.15269i	0.979148	+	0.203147i	$0.0651169\pi$
$31$	114.867	+	198.955i	0.665504	+	1.15269i	−0.313644	+	0.949541i	$0.601550\pi$
$32$	−30.0702	−	10.9446i	−0.166116	−	0.0604612i
$33$	−3.29001	+	18.6586i	−0.0173551	+	0.0984256i
$34$	−25.9765	−	147.320i	−0.131028	−	0.743095i
$35$	−6.27818	+	2.28507i	−0.0303202	+	0.0110356i
$36$	−6.63699	−	5.56909i	−0.0307268	−	0.0257828i
$37$	401.456			1.78376			0.891878	−	0.452276i	$-0.149388\pi$
$37$	401.456			1.78376			0.891878	+	0.452276i	$0.149388\pi$
$38$	29.5662	−	162.978i	0.126217	−	0.695751i
$39$	−81.6905			−0.335409
$40$	14.4009	+	12.0838i	0.0569247	+	0.0477655i
$41$	60.9251	−	22.1749i	0.232071	−	0.0844668i	−0.223367	−	0.974734i	$-0.571705\pi$
$41$	60.9251	−	22.1749i	0.232071	−	0.0844668i	0.455438	+	0.890268i	$0.349483\pi$
$42$	−4.92067	−	27.9065i	−0.0180780	−	0.102526i
$43$	−13.5220	+	76.6872i	−0.0479555	+	0.271969i	−0.999352	−	0.0360001i	$-0.988538\pi$
$43$	−13.5220	+	76.6872i	−0.0479555	+	0.271969i	0.951396	+	0.307969i	$0.0996495\pi$
$44$	−14.2906	−	5.20135i	−0.0489633	−	0.0178212i
$45$	2.54492	+	4.40793i	0.00843053	+	0.0146021i
$46$	−35.0510	+	60.7102i	−0.112348	+	0.194592i
$47$	−356.545	+	299.176i	−1.10654	+	0.928497i	−0.997847	−	0.0655782i	$-0.979111\pi$
$47$	−356.545	+	299.176i	−1.10654	+	0.928497i	−0.108693	+	0.994075i	$0.534666\pi$
$48$	−61.0798	+	51.2520i	−0.183669	+	0.154116i
$49$	167.458	−	290.046i	0.488216	−	0.845616i
$50$	119.478	+	206.942i	0.337935	+	0.585320i
$51$	−350.260	−	127.484i	−0.961690	−	0.350026i
$52$	11.3862	−	64.5743i	0.0303650	−	0.172209i
$53$	−12.3203	−	69.8721i	−0.0319307	−	0.181088i	0.964671	−	0.263457i	$-0.0848626\pi$
$53$	−12.3203	−	69.8721i	−0.0319307	−	0.181088i	−0.996602	+	0.0823686i	$0.973752\pi$
$54$	−273.159	+	99.4219i	−0.688375	+	0.250548i
$55$	6.84392	+	5.74273i	0.0167788	+	0.0140791i
$56$	22.7453			0.0542761
$57$	−314.850	−	266.845i	−0.731629	−	0.620078i
$58$	156.336			0.353930
$59$	−508.257	−	426.478i	−1.12152	−	0.941064i	−0.122836	−	0.992427i	$-0.539199\pi$
$59$	−508.257	−	426.478i	−1.12152	−	0.941064i	−0.998680	+	0.0513634i	$0.983643\pi$
$60$	44.0165	−	16.0207i	0.0947085	−	0.0344711i
$61$	−27.4270	−	155.546i	−0.0575683	−	0.326486i	0.942400	−	0.334489i	$-0.108564\pi$
$61$	−27.4270	−	155.546i	−0.0575683	−	0.326486i	−0.999968	+	0.00800277i	$0.997453\pi$
$62$	−79.7855	+	452.486i	−0.163432	+	0.926867i
$63$	5.78687	+	2.10625i	0.0115727	+	0.00421210i
$64$	−32.0000	−	55.4256i	−0.0625000	−	0.108253i
$65$	−19.2604	+	33.3600i	−0.0367532	+	0.0636584i
$66$	−29.0276	+	24.3571i	−0.0541372	+	0.0454265i
$67$	68.6778	−	57.6275i	0.125229	−	0.105079i	−0.578022	−	0.816021i	$-0.696175\pi$
$67$	68.6778	−	57.6275i	0.125229	−	0.105079i	0.703251	+	0.710942i	$0.251731\pi$
$68$	149.593	−	259.103i	0.266777	−	0.462071i
$69$	87.3362	+	151.271i	0.152377	+	0.263926i
$70$	−12.5564	−	4.57014i	−0.0214396	−	0.00780337i
$71$	−109.611	+	621.638i	−0.183218	+	1.03908i	0.745005	+	0.667059i	$0.232447\pi$
$71$	−109.611	+	621.638i	−0.183218	+	1.03908i	−0.928223	+	0.372023i	$0.878664\pi$
$72$	−3.00897	−	17.0647i	−0.00492514	−	0.0279318i
$73$	713.200	−	259.583i	1.14348	−	0.416191i	0.300308	−	0.953842i	$-0.402911\pi$
$73$	713.200	−	259.583i	1.14348	−	0.416191i	0.843167	+	0.537651i	$0.180688\pi$
$74$	615.066	+	516.102i	0.966217	+	0.810752i
$75$	595.404			0.916684
$76$	254.819	−	211.687i	0.384601	−	0.319503i
$77$	10.8095			0.0159981
$78$	−125.157	−	105.019i	−0.181683	−	0.152450i
$79$	774.641	−	281.946i	1.10321	−	0.401537i	0.274714	−	0.961526i	$-0.411417\pi$
$79$	774.641	−	281.946i	1.10321	−	0.401537i	0.828500	+	0.559989i	$0.189194\pi$
$80$	6.52885	+	37.0270i	0.00912435	+	0.0517468i
$81$	−115.620	+	655.711i	−0.158600	+	0.899467i
$82$	121.850	+	44.3498i	0.164099	+	0.0597270i
$83$	66.3727	+	114.961i	0.0877753	+	0.152031i	0.906570	−	0.422055i	$-0.138691\pi$
$83$	66.3727	+	114.961i	0.0877753	+	0.152031i	−0.818795	+	0.574086i	$0.805358\pi$
$84$	28.3370	−	49.0812i	0.0368074	−	0.0637523i
$85$	−134.642	+	112.978i	−0.171812	+	0.144167i
$86$	−119.304	+	100.108i	−0.149592	+	0.125522i
$87$	194.770	−	337.352i	0.240018	−	0.415723i
$88$	−15.2077	−	26.3405i	−0.0184221	−	0.0319081i
$89$	−1326.11	−	482.664i	−1.57941	−	0.574857i	−0.604332	−	0.796733i	$-0.706560\pi$
$89$	−1326.11	−	482.664i	−1.57941	−	0.574857i	−0.975075	+	0.221876i	$0.928782\pi$
$90$	−1.76768	+	10.0250i	−0.00207033	+	0.0117414i
$91$	8.09319	+	45.8987i	0.00932304	+	0.0528736i
$92$	−131.749	+	47.9527i	−0.149302	+	0.0543414i
$93$	877.003	+	735.892i	0.977859	+	0.820521i
$94$	−930.872			−1.02141
$95$	−183.204	+	65.6605i	−0.197857	+	0.0709118i
$96$	−159.468			−0.169538
$97$	−1011.58	−	848.815i	−1.05887	−	0.888496i	−0.0648699	−	0.997894i	$-0.520663\pi$
$97$	−1011.58	−	848.815i	−1.05887	−	0.888496i	−0.993998	+	0.109398i	$0.965108\pi$
$98$	629.437	−	229.096i	0.648803	−	0.236145i
$99$	−1.42998	−	8.10984i	−0.00145171	−	0.00823303i
$100$	−82.9886	+	470.652i	−0.0829886	+	0.470652i
$101$	272.864	+	99.3143i	0.268821	+	0.0978430i	0.472914	−	0.881109i	$-0.343202\pi$
$101$	272.864	+	99.3143i	0.268821	+	0.0978430i	−0.204093	+	0.978952i	$0.565424\pi$
$102$	−372.739	−	645.602i	−0.361830	−	0.626707i
$103$	−303.088	+	524.964i	−0.289943	+	0.502197i	−0.973796	−	0.227424i	$-0.926970\pi$
$103$	−303.088	+	524.964i	−0.289943	+	0.502197i	0.683853	+	0.729620i	$0.260303\pi$
$104$	100.460	−	84.2958i	0.0947201	−	0.0794796i
$105$	−25.5050	+	21.4012i	−0.0237051	+	0.0198909i
$106$	70.9500	−	122.889i	0.0650120	−	0.112604i
$107$	−364.367	−	631.101i	−0.329202	−	0.570195i	0.653151	−	0.757227i	$-0.273446\pi$
$107$	−364.367	−	631.101i	−0.329202	−	0.570195i	−0.982354	+	0.187032i	$0.940113\pi$
$108$	−546.319	−	198.844i	−0.486755	−	0.177164i
$109$	−260.479	+	1477.25i	−0.228893	+	1.29812i	0.626207	+	0.779657i	$0.284607\pi$
$109$	−260.479	+	1477.25i	−0.228893	+	1.29812i	−0.855100	+	0.518463i	$0.826505\pi$
$110$	3.10278	+	17.5967i	0.00268944	+	0.0152526i
$111$	1879.95	−	684.247i	1.60754	−	0.585098i
$112$	34.8478	+	29.2407i	0.0294000	+	0.0246696i
$113$	−1048.77			−0.873094			−0.436547	−	0.899681i	$-0.643799\pi$
$113$	−1048.77			−0.873094			−0.436547	+	0.899681i	$0.643799\pi$
$114$	−139.328	−	813.593i	−0.114468	−	0.668421i
$115$	82.3660			0.0667884
$116$	239.521	+	200.982i	0.191715	+	0.160868i
$117$	33.3650	−	12.1439i	0.0263641	−	0.00959573i
$118$	−230.425	−	1306.81i	−0.179766	−	1.01950i
$119$	−36.9277	+	209.427i	−0.0284467	+	0.161329i
$120$	88.0331	+	32.0414i	0.0669690	+	0.0243747i
$121$	658.273	+	1140.16i	0.494570	+	0.856620i
$122$	157.946	−	273.570i	0.117211	−	0.203015i
$123$	247.507	−	207.683i	0.181439	−	0.152245i
$124$	−703.943	+	590.678i	−0.509806	+	0.427778i
$125$	287.248	−	497.528i	0.205538	−	0.356002i
$126$	6.15826	+	10.6664i	0.00435414	+	0.00754159i
$127$	−2220.44	−	808.176i	−1.55144	−	0.564677i	−0.582683	−	0.812699i	$-0.697997\pi$
$127$	−2220.44	−	808.176i	−1.55144	−	0.564677i	−0.968754	+	0.248022i	$0.920219\pi$
$128$	22.2270	−	126.055i	0.0153485	−	0.0870455i
$129$	67.3853	+	382.161i	0.0459918	+	0.260832i
$130$	−72.3954	+	26.3498i	−0.0488423	+	0.0177771i
$131$	1360.37	+	1141.48i	0.907297	+	0.761312i	0.971603	−	0.236618i	$-0.0760390\pi$
$131$	1360.37	+	1141.48i	0.907297	+	0.761312i	−0.0643062	+	0.997930i	$0.520483\pi$
$132$	−75.7857			−0.0499720
$133$	−118.737	+	203.338i	−0.0774122	+	0.132569i
$134$	179.305			0.115594
$135$	261.638	+	219.540i	0.166802	+	0.139963i
$136$	562.285	−	204.655i	0.354526	−	0.129037i
$137$	−329.182	−	1866.88i	−0.205284	−	1.16422i	−0.896993	−	0.442046i	$-0.854253\pi$
$137$	−329.182	−	1866.88i	−0.205284	−	1.16422i	0.691709	−	0.722177i	$-0.256858\pi$
$138$	−60.6631	+	344.038i	−0.0374202	+	0.212220i
$139$	177.152	+	64.4779i	0.108099	+	0.0393449i	0.395504	−	0.918464i	$-0.370570\pi$
$139$	177.152	+	64.4779i	0.108099	+	0.0393449i	−0.287404	+	0.957809i	$0.592792\pi$
$140$	−13.3622	−	23.1440i	−0.00806651	−	0.0139716i
$141$	−1159.72	+	2008.69i	−0.692667	+	1.19973i
$142$	−967.097	+	811.490i	−0.571528	+	0.479569i
$143$	47.7426	−	40.0608i	0.0279192	−	0.0234270i
$144$	17.3279	−	30.0129i	0.0100277	−	0.0173686i
$145$	−91.8430	−	159.077i	−0.0526010	−	0.0911076i
$146$	1426.40	+	519.167i	0.808559	+	0.294291i
$147$	289.821	−	1643.66i	0.162613	−	0.922222i
$148$	278.849	+	1581.43i	0.154873	+	0.878328i
$149$	2329.07	−	847.713i	1.28057	−	0.466090i	0.389950	−	0.920836i	$-0.372492\pi$
$149$	2329.07	−	847.713i	1.28057	−	0.466090i	0.890621	+	0.454746i	$0.150270\pi$
$150$	912.211	+	765.436i	0.496545	+	0.416651i
$151$	885.978			0.477483			0.238741	−	0.971083i	$-0.423265\pi$
$151$	885.978			0.477483			0.238741	+	0.971083i	$0.423265\pi$
$152$	662.545	+	3.26457i	0.353549	+	0.00174205i
$153$	162.009			0.0856053
$154$	16.5611	+	13.8964i	0.00866579	+	0.00727146i
$155$	507.290	−	184.638i	0.262881	−	0.0956807i
$156$	−56.7416	−	321.798i	−0.0291216	−	0.165157i
$157$	−213.486	+	1210.74i	−0.108523	+	0.615462i	0.881232	+	0.472684i	$0.156715\pi$
$157$	−213.486	+	1210.74i	−0.108523	+	0.615462i	−0.989755	+	0.142778i	$0.954396\pi$
$158$	1549.28	+	563.893i	0.780091	+	0.283930i
$159$	−176.785	−	306.201i	−0.0881760	−	0.152725i
$160$	−37.5982	+	65.1219i	−0.0185775	+	0.0321771i
$161$	76.3407	−	64.0574i	0.0373695	−	0.0313567i
$162$	−1020.11	+	855.970i	−0.494735	+	0.415132i
$163$	−233.423	+	404.300i	−0.112166	+	0.194277i	−0.916643	−	0.399706i	$-0.869112\pi$
$163$	−233.423	+	404.300i	−0.112166	+	0.194277i	0.804477	+	0.593983i	$0.202446\pi$
$164$	129.670	+	224.595i	0.0617411	+	0.106939i
$165$	41.8369	+	15.2274i	0.0197394	+	0.00718456i
$166$	−46.1020	+	261.457i	−0.0215555	+	0.122247i
$167$	−623.548	−	3536.32i	−0.288932	−	1.63861i	−0.690894	−	0.722957i	$-0.742783\pi$
$167$	−623.548	−	3536.32i	−0.288932	−	1.63861i	0.401962	−	0.915656i	$-0.368328\pi$
$168$	106.512	−	38.7673i	0.0489143	−	0.0178034i
$169$	−1477.15	−	1239.48i	−0.672349	−	0.564167i
$170$	−351.526			−0.158593
$171$	168.263	+	62.1833i	0.0752479	+	0.0278086i
$172$	−311.481			−0.138082
$173$	221.077	+	185.505i	0.0971569	+	0.0815244i	0.690072	−	0.723740i	$-0.257579\pi$
$173$	221.077	+	185.505i	0.0971569	+	0.0815244i	−0.592915	+	0.805265i	$0.702023\pi$
$174$	732.097	−	266.461i	0.318966	−	0.116094i
$175$	−58.9874	−	334.534i	−0.0254802	−	0.144505i
$176$	10.5632	−	59.9067i	0.00452403	−	0.0256570i
$177$	−3106.98	−	1130.85i	−1.31941	−	0.480225i
$178$	−1411.22	−	2444.30i	−0.594242	−	1.02926i
$179$	−1987.87	+	3443.10i	−0.830060	+	1.43771i	0.0679306	+	0.997690i	$0.478360\pi$
$179$	−1987.87	+	3443.10i	−0.830060	+	1.43771i	−0.897990	+	0.440015i	$0.854973\pi$
$180$	−15.5962	+	13.0867i	−0.00645816	+	0.00541904i
$181$	529.525	−	444.324i	0.217455	−	0.182466i	−0.527553	−	0.849522i	$-0.676890\pi$
$181$	529.525	−	444.324i	0.217455	−	0.182466i	0.745007	+	0.667056i	$0.232446\pi$
$182$	−46.6068	+	80.7253i	−0.0189820	+	0.0328778i
$183$	−393.552	−	681.651i	−0.158974	−	0.275350i
$184$	−263.498	−	95.9053i	−0.105572	−	0.0384252i
$185$	163.816	−	929.044i	0.0651025	−	0.369214i
$186$	397.601	+	2254.91i	0.156739	+	0.888912i
$187$	267.221	−	97.2606i	0.104498	−	0.0380342i
$188$	−1426.18	−	1196.71i	−0.553270	−	0.464249i
$189$	413.239			0.159041
$190$	−365.097	−	134.925i	−0.139405	−	0.0515185i
$191$	2235.13			0.846746			0.423373	−	0.905955i	$-0.360846\pi$
$191$	2235.13			0.846746			0.423373	+	0.905955i	$0.360846\pi$
$192$	−244.319	−	205.008i	−0.0918344	−	0.0770582i
$193$	−3759.67	+	1368.41i	−1.40221	+	0.510363i	−0.928834	−	0.370497i	$-0.879187\pi$
$193$	−3759.67	+	1368.41i	−1.40221	+	0.510363i	−0.473377	+	0.880860i	$0.656965\pi$
$194$	−458.612	−	2600.92i	−0.169724	−	0.962552i
$195$	−33.3341	+	189.047i	−0.0122416	+	0.0694253i
$196$	1258.87	+	458.193i	0.458773	+	0.166980i
$197$	1048.97	+	1816.87i	0.379371	+	0.657089i	0.990971	−	0.134078i	$-0.0428072\pi$
$197$	1048.97	+	1816.87i	0.379371	+	0.657089i	−0.611600	+	0.791167i	$0.709474\pi$
$198$	8.23495	−	14.2634i	0.00295572	−	0.00511946i
$199$	−1449.02	+	1215.87i	−0.516171	+	0.433119i	−0.863294	−	0.504701i	$-0.831603\pi$
$199$	−1449.02	+	1215.87i	−0.516171	+	0.433119i	0.347123	+	0.937819i	$0.387158\pi$
$200$	−732.204	+	614.392i	−0.258873	+	0.217220i
$201$	223.386	−	386.916i	0.0783902	−	0.135776i
$202$	290.376	+	502.945i	0.101142	+	0.175184i
$203$	−208.841	−	76.0120i	−0.0722058	−	0.0262808i
$204$	258.902	−	1468.30i	0.0888565	−	0.503930i
$205$	−26.4562	−	150.040i	−0.00901356	−	0.0511184i
$206$	−1139.24	+	414.649i	−0.385313	+	0.140243i
$207$	−58.1583	−	48.8006i	−0.0195279	−	0.0163859i
$208$	262.282			0.0874326
$209$	314.868	+	1.55146i	0.104210	+	0.000513477i
$210$	−66.5888			−0.0218813
$211$	1583.33	+	1328.57i	0.516591	+	0.433471i	0.863441	−	0.504449i	$-0.168304\pi$
$211$	1583.33	+	1328.57i	0.516591	+	0.433471i	−0.346850	+	0.937920i	$0.612749\pi$
$212$	266.685	−	97.0653i	0.0863962	−	0.0314456i
$213$	546.235	+	3097.85i	0.175716	+	0.996532i
$214$	253.086	−	1435.32i	0.0808441	−	0.458489i
$215$	171.951	+	62.5849i	0.0545439	+	0.0198524i
$216$	−581.380	−	1006.98i	−0.183138	−	0.317205i
$217$	326.584	−	565.660i	0.102166	−	0.176956i
$218$	−2298.20	+	1928.41i	−0.714007	+	0.599123i
$219$	2897.36	−	2431.17i	0.893998	−	0.750153i
$220$	−17.8682	+	30.9486i	−0.00547579	+	0.00948435i
$221$	613.055	+	1061.84i	0.186600	+	0.323200i
$222$	3759.91	+	1368.49i	1.13671	+	0.413727i
$223$	200.455	−	1136.83i	0.0601948	−	0.341381i	−0.939805	−	0.341711i	$-0.888994\pi$
$223$	200.455	−	1136.83i	0.0601948	−	0.341381i	1.00000		0.000329250i	$0.000104803\pi$
$224$	15.7987	+	89.5988i	0.00471248	+	0.0267258i
$225$	−243.182	+	88.5109i	−0.0720538	+	0.0262254i
$226$	−1606.80	−	1348.27i	−0.472933	−	0.396838i
$227$	829.315			0.242483			0.121241	−	0.992623i	$-0.461312\pi$
$227$	829.315			0.242483			0.121241	+	0.992623i	$0.461312\pi$
$228$	832.471	−	1425.61i	0.241806	−	0.414095i
$229$	5032.36			1.45217			0.726087	−	0.687603i	$-0.241337\pi$
$229$	5032.36			1.45217			0.726087	+	0.687603i	$0.241337\pi$
$230$	126.192	+	105.888i	0.0361776	+	0.0303566i
$231$	50.6191	−	18.4238i	0.0144177	−	0.00524762i
$232$	108.590	+	615.844i	0.0307296	+	0.174276i
$233$	216.866	−	1229.91i	0.0609758	−	0.345811i	−0.939022	−	0.343856i	$-0.888267\pi$
$233$	216.866	−	1229.91i	0.0609758	−	0.345811i	0.999998	−	0.00195479i	$-0.000622230\pi$
$234$	66.7300	+	24.2877i	0.0186422	+	0.00678521i
$235$	546.861	+	947.190i	0.151801	+	0.262927i
$236$	1326.97	−	2298.37i	0.366009	−	0.633946i
$237$	3146.97	−	2640.62i	0.862521	−	0.723741i
$238$	−325.811	+	273.388i	−0.0887361	+	0.0744585i
$239$	−2364.18	+	4094.89i	−0.639859	+	1.10827i	0.345604	+	0.938380i	$0.387674\pi$
$239$	−2364.18	+	4094.89i	−0.639859	+	1.10827i	−0.985463	+	0.169888i	$0.945659\pi$
$240$	93.6829	+	162.263i	0.0251967	+	0.0436419i
$241$	−379.823	−	138.244i	−0.101521	−	0.0369506i	0.290760	−	0.956796i	$-0.406092\pi$
$241$	−379.823	−	138.244i	−0.101521	−	0.0369506i	−0.392281	+	0.919845i	$0.628314\pi$
$242$	−457.231	+	2593.09i	−0.121454	+	0.688802i
$243$	−105.275	−	597.042i	−0.0277917	−	0.157614i
$244$	593.682	−	216.083i	0.155765	−	0.0566937i
$245$	−602.889	−	505.884i	−0.157213	−	0.131917i
$246$	646.195			0.167479
$247$	229.158	+	1338.14i	0.0590323	+	0.344712i
$248$	−1837.86			−0.470583
$249$	506.754	+	425.217i	0.128973	+	0.108221i
$250$	1079.70	−	392.978i	0.273144	−	0.0994164i
$251$	1103.55	+	6258.53i	0.277511	+	1.57384i	0.730870	+	0.682517i	$0.239115\pi$
$251$	1103.55	+	6258.53i	0.277511	+	1.57384i	−0.453359	+	0.891328i	$0.649774\pi$
$252$	−4.27748	+	24.2588i	−0.00106927	+	0.00606413i
$253$	−125.225	−	45.5782i	−0.0311179	−	0.0113260i
$254$	−2362.95	−	4092.74i	−0.583718	−	1.01103i
$255$	−437.947	+	758.546i	−0.107550	+	0.186282i
$256$	196.107	−	164.554i	0.0478778	−	0.0401742i
$257$	3325.92	−	2790.78i	0.807257	−	0.677369i	−0.142695	−	0.989767i	$-0.545577\pi$
$257$	3325.92	−	2790.78i	0.807257	−	0.677369i	0.949951	+	0.312398i	$0.101132\pi$
$258$	−388.056	+	672.133i	−0.0936408	+	0.162191i
$259$	−570.702	−	988.484i	−0.136918	−	0.237148i
$260$	−144.791	−	52.6995i	−0.0345367	−	0.0125703i
$261$	−29.4006	+	166.739i	−0.00697262	+	0.0395437i
$262$	616.740	+	3497.71i	0.145429	+	0.824768i
$263$	−5755.73	+	2094.92i	−1.34948	+	0.491171i	−0.912786	−	0.408438i	$-0.866074\pi$
$263$	−5755.73	+	2094.92i	−1.34948	+	0.491171i	−0.436696	+	0.899609i	$0.643851\pi$
$264$	−116.110	−	97.4283i	−0.0270686	−	0.0227132i
$265$	−166.724			−0.0386483
$266$	−443.323	+	158.887i	−0.102187	+	0.0366240i
$267$	−7032.61			−1.61194
$268$	274.711	+	230.510i	0.0626144	+	0.0525397i
$269$	−5575.72	+	2029.40i	−1.26378	+	0.459980i	−0.885037	−	0.465521i	$-0.845867\pi$
$269$	−5575.72	+	2029.40i	−1.26378	+	0.459980i	−0.378747	+	0.925500i	$0.623645\pi$
$270$	118.617	+	672.711i	0.0267363	+	0.151629i
$271$	1127.05	−	6391.80i	0.252632	−	1.43275i	−0.549448	−	0.835528i	$-0.685162\pi$
$271$	1127.05	−	6391.80i	0.252632	−	1.43275i	0.802079	−	0.597218i	$-0.203727\pi$
$272$	1124.57	+	409.310i	0.250688	+	0.0912429i
$273$	116.130	+	201.142i	0.0257453	+	0.0445922i
$274$	1895.68	−	3283.42i	0.417965	−	0.723936i
$275$	−347.973	+	291.984i	−0.0763040	+	0.0640266i
$276$	−535.227	+	449.109i	−0.116728	+	0.0979464i
$277$	1187.20	−	2056.30i	0.257517	−	0.446032i	−0.708059	−	0.706153i	$-0.750429\pi$
$277$	1187.20	−	2056.30i	0.257517	−	0.446032i	0.965576	+	0.260121i	$0.0837625\pi$
$278$	188.521	+	326.528i	0.0406717	+	0.0704454i
$279$	−467.591	−	170.189i	−0.100337	−	0.0365196i
$280$	9.28128	−	52.6368i	0.00198094	−	0.0112345i
$281$	−808.693	−	4586.33i	−0.171682	−	0.973656i	−0.941905	−	0.335881i	$-0.890966\pi$
$281$	−808.693	−	4586.33i	−0.171682	−	0.973656i	0.770223	−	0.637775i	$-0.220145\pi$
$282$	−4359.12	+	1586.59i	−0.920504	+	0.335036i
$283$	−2339.64	−	1963.19i	−0.491439	−	0.412366i	0.363103	−	0.931749i	$-0.381717\pi$
$283$	−2339.64	−	1963.19i	−0.491439	−	0.412366i	−0.854542	+	0.519383i	$0.826162\pi$
$284$	−2524.91			−0.527556
$285$	−746.004	+	619.734i	−0.155051	+	0.128806i
$286$	124.647			0.0257711
$287$	−141.210	−	118.489i	−0.0290430	−	0.0243700i
$288$	65.1317	−	23.7060i	0.0133261	−	0.00485031i
$289$	118.343	+	671.156i	0.0240877	+	0.136608i
$290$	63.7935	−	361.791i	0.0129175	−	0.0732589i
$291$	−6183.79	−	2250.71i	−1.24570	−	0.453399i
$292$	1517.94	+	2629.15i	0.304215	+	0.526916i
$293$	4828.41	−	8363.06i	0.962727	−	1.66749i	0.247125	−	0.968984i	$-0.420514\pi$
$293$	4828.41	−	8363.06i	0.962727	−	1.66749i	0.715602	−	0.698508i	$-0.246153\pi$
$294$	2557.08	−	2145.64i	0.507251	−	0.425634i
$295$	−1194.35	+	1002.18i	−0.235720	+	0.197793i
$296$	−1605.82	+	2781.37i	−0.315327	+	0.546162i
$297$	−276.296	−	478.558i	−0.0539808	−	0.0934975i
$298$	4658.15	+	1695.43i	0.905501	+	0.329575i
$299$	99.7745	−	565.849i	0.0192980	−	0.109445i
$300$	413.563	+	2345.43i	0.0795902	+	0.451379i
$301$	208.045	−	75.7223i	0.0398390	−	0.0145002i
$302$	1357.40	+	1138.99i	0.258640	+	0.217025i
$303$	1447.05			0.274359
$304$	1010.88	+	856.753i	0.190717	+	0.161639i
$305$	−371.155			−0.0696795
$306$	248.211	+	208.274i	0.0463703	+	0.0389093i
$307$	1194.03	−	434.591i	0.221977	−	0.0807929i	−0.228638	−	0.973512i	$-0.573427\pi$
$307$	1194.03	−	434.591i	0.221977	−	0.0807929i	0.450614	+	0.892719i	$0.351205\pi$
$308$	7.50819	+	42.5811i	0.00138902	+	0.00787754i
$309$	−524.557	+	2974.91i	−0.0965728	+	0.547692i
$310$	1014.58	+	369.277i	0.185885	+	0.0676565i
$311$	2593.69	+	4492.40i	0.472908	+	0.819101i	0.999519	−	0.0310052i	$-0.00987085\pi$
$311$	2593.69	+	4492.40i	0.472908	+	0.819101i	−0.526611	+	0.850106i	$0.676538\pi$
$312$	326.762	−	565.969i	0.0592925	−	0.102698i
$313$	5953.19	−	4995.32i	1.07506	−	0.902084i	0.0795603	−	0.996830i	$-0.474648\pi$
$313$	5953.19	−	4995.32i	1.07506	−	0.902084i	0.995501	+	0.0947462i	$0.0302039\pi$
$314$	−1883.58	+	1580.51i	−0.338523	+	0.284055i
$315$	7.23560	−	12.5324i	0.00129422	−	0.00224166i
$316$	1648.71	+	2855.65i	0.293504	+	0.508364i
$317$	6133.80	+	2232.52i	1.08678	+	0.395555i	0.822426	−	0.568872i	$-0.192620\pi$
$317$	6133.80	+	2232.52i	1.08678	+	0.395555i	0.264351	+	0.964426i	$0.414842\pi$
$318$	122.794	−	696.398i	0.0216539	−	0.122805i
$319$	51.6064	+	292.674i	0.00905769	+	0.0513687i
$320$	−141.323	+	51.4373i	−0.0246881	+	0.00898573i
$321$	−2781.93	−	2334.31i	−0.483714	−	0.405884i
$322$	199.311			0.0344944
$323$	−1105.72	+	6095.09i	−0.190477	+	1.04997i
$324$	−2663.31			−0.456671
$325$	−1500.34	−	1258.94i	−0.256074	−	0.214871i
$326$	−877.382	+	319.341i	−0.149060	+	0.0542536i
$327$	1298.07	+	7361.70i	0.219520	+	1.24496i
$328$	−90.0680	+	510.801i	−0.0151621	+	0.0859886i
$329$	1243.50	+	452.598i	0.208378	+	0.0758436i
$330$	44.5219	+	77.1143i	0.00742683	+	0.0128636i
$331$	4241.73	−	7346.90i	0.704371	−	1.22001i	−0.262547	−	0.964919i	$-0.584563\pi$
$331$	4241.73	−	7346.90i	0.704371	−	1.22001i	0.966918	−	0.255087i	$-0.0821041\pi$
$332$	−406.756	+	341.308i	−0.0672398	+	0.0564209i
$333$	−666.115	+	558.937i	−0.109618	+	0.0919806i
$334$	3590.87	−	6219.57i	0.588274	−	1.01892i
$335$	−105.337	−	182.448i	−0.0171795	−	0.0297558i
$336$	213.025	+	77.5347i	0.0345877	+	0.0125889i
$337$	−960.420	+	5446.81i	−0.155245	+	0.880435i	0.803317	+	0.595551i	$0.203066\pi$
$337$	−960.420	+	5446.81i	−0.155245	+	0.880435i	−0.958562	+	0.284884i	$0.908045\pi$
$338$	−669.685	−	3797.97i	−0.107769	−	0.611191i
$339$	−4911.20	+	1787.53i	−0.786843	+	0.286388i
$340$	−538.569	−	451.913i	−0.0859060	−	0.0720837i
$341$	−873.429			−0.138706
$342$	177.852	+	311.585i	0.0281203	+	0.0492649i
$343$	−1927.42			−0.303414
$344$	−477.216	−	400.432i	−0.0747959	−	0.0627612i
$345$	385.707	−	140.386i	0.0601906	−	0.0219076i
$346$	100.228	+	568.421i	0.0155731	+	0.0883194i
$347$	1616.52	−	9167.75i	0.250085	−	1.41830i	−0.558296	−	0.829642i	$-0.688545\pi$
$347$	1616.52	−	9167.75i	0.250085	−	1.41830i	0.808381	−	0.588660i	$-0.200344\pi$
$348$	1464.19	+	532.923i	0.225543	+	0.0820910i
$349$	4328.92	+	7497.92i	0.663960	+	1.15001i	0.979566	+	0.201122i	$0.0644588\pi$
$349$	4328.92	+	7497.92i	0.663960	+	1.15001i	−0.315606	+	0.948890i	$0.602208\pi$
$350$	339.695	−	588.369i	0.0518785	−	0.0898561i
$351$	1825.17	−	1531.50i	0.277550	−	0.232892i
$352$	93.1983	−	78.2027i	0.0141122	−	0.0118415i
$353$	−1571.37	+	2721.69i	−0.236928	+	0.410371i	−0.959831	−	0.280578i	$-0.909474\pi$
$353$	−1571.37	+	2721.69i	−0.236928	+	0.410371i	0.722904	+	0.690949i	$0.242807\pi$
$354$	−3306.38	−	5726.82i	−0.496419	−	0.859822i
$355$	1393.86	+	507.323i	0.208390	+	0.0758476i
$356$	980.220	−	5559.10i	0.145931	−	0.827617i
$357$	184.024	+	1043.65i	0.0272818	+	0.154723i
$358$	−7471.96	+	2719.57i	−1.10309	+	0.401491i
$359$	4268.27	+	3581.50i	0.627494	+	0.526530i	0.900149	−	0.435582i	$-0.143457\pi$
$359$	4268.27	+	3581.50i	0.627494	+	0.526530i	−0.272655	+	0.962112i	$0.587902\pi$
$360$	−40.7187			−0.00596129
$361$	−3487.87	+	5905.98i	−0.508510	+	0.861056i
$362$	1382.49			0.200724
$363$	5025.89	+	4217.22i	0.726697	+	0.609771i
$364$	−175.184	+	63.7619i	−0.0252257	+	0.00918140i
$365$	−309.701	−	1756.40i	−0.0444123	−	0.251875i
$366$	273.358	−	1550.29i	0.0390400	−	0.221407i
$367$	710.105	+	258.457i	0.101000	+	0.0367612i	0.392026	−	0.919954i	$-0.371774\pi$
$367$	710.105	+	258.457i	0.101000	+	0.0367612i	−0.291026	+	0.956715i	$0.593996\pi$
$368$	−280.408	−	485.682i	−0.0397209	−	0.0687986i
$369$	−70.2162	+	121.618i	−0.00990598	+	0.0171577i
$370$	1445.34	−	1212.78i	0.203080	−	0.170404i
$371$	−154.528	+	129.664i	−0.0216245	+	0.0181451i
$372$	−2289.69	+	3965.86i	−0.319126	+	0.552743i
$373$	−251.203	−	435.096i	−0.0348708	−	0.0603980i	0.848063	−	0.529895i	$-0.177769\pi$
$373$	−251.203	−	435.096i	−0.0348708	−	0.0603980i	−0.882934	+	0.469497i	$0.844435\pi$
$374$	534.442	+	194.521i	0.0738913	+	0.0268942i
$375$	497.142	−	2819.43i	0.0684594	−	0.388253i
$376$	−646.577	−	3666.92i	−0.0886826	−	0.502944i
$377$	−1204.10	+	438.257i	−0.164495	+	0.0598711i
$378$	633.119	+	531.250i	0.0861484	+	0.0722871i
$379$	2045.80			0.277270			0.138635	−	0.990344i	$-0.455728\pi$
$379$	2045.80			0.277270			0.138635	+	0.990344i	$0.455728\pi$
$380$	−385.904	−	676.077i	−0.0520960	−	0.0912685i
$381$	−11775.4			−1.58340
$382$	3424.42	+	2873.43i	0.458662	+	0.384863i
$383$	5015.47	−	1825.48i	0.669134	−	0.243545i	0.0149590	−	0.999888i	$-0.495238\pi$
$383$	5015.47	−	1825.48i	0.669134	−	0.243545i	0.654175	+	0.756343i	$0.273016\pi$
$384$	−110.765	−	628.181i	−0.0147200	−	0.0834811i
$385$	4.41085	−	25.0152i	0.000583890	−	0.00331140i
$386$	−7519.33	−	2736.81i	−0.991513	−	0.360881i
$387$	−84.3331	−	146.069i	−0.0110772	−	0.0191864i
$388$	2641.04	−	4574.42i	0.345563	−	0.598533i
$389$	−75.8876	+	63.6773i	−0.00989114	+	0.00829965i	−0.647720	−	0.761879i	$-0.724277\pi$
$389$	−75.8876	+	63.6773i	−0.00989114	+	0.00829965i	0.637829	+	0.770178i	$0.279833\pi$
$390$	−294.105	+	246.783i	−0.0381861	+	0.0320420i
$391$	1310.85	−	2270.45i	0.169546	−	0.293662i
$392$	1339.67	+	2320.37i	0.172611	+	0.298970i
$393$	8315.94	+	3026.76i	1.06739	+	0.388498i
$394$	−728.607	+	4132.14i	−0.0931642	+	0.528360i
$395$	−336.381	−	1907.71i	−0.0428486	−	0.243006i
$396$	30.9533	−	11.2661i	0.00392793	−	0.00142965i
$397$	−8907.18	−	7474.01i	−1.12604	−	0.944861i	−0.127148	−	0.991884i	$-0.540582\pi$
$397$	−8907.18	−	7474.01i	−1.12604	−	0.944861i	−0.998894	+	0.0470226i	$0.985027\pi$
$398$	−3783.11			−0.476458
$399$	−209.454	+	1154.58i	−0.0262803	+	0.144865i
$400$	−1911.65			−0.238956
$401$	−4387.55	−	3681.59i	−0.546393	−	0.458478i	0.327324	−	0.944912i	$-0.393853\pi$
$401$	−4387.55	−	3681.59i	−0.546393	−	0.458478i	−0.873717	+	0.486434i	$0.838297\pi$
$402$	839.656	−	305.610i	0.104175	−	0.0379165i
$403$	−653.946	−	3708.71i	−0.0808322	−	0.458422i
$404$	−201.693	+	1143.86i	−0.0248381	+	0.140864i
$405$	1470.26	+	535.130i	0.180389	+	0.0656564i
$406$	−222.244	−	384.938i	−0.0271670	−	0.0470546i
$407$	−763.154	+	1321.82i	−0.0929438	+	0.160983i
$408$	2284.27	−	1916.73i	0.277178	−	0.232580i
$409$	−4936.31	+	4142.06i	−0.596785	+	0.500762i	−0.890410	−	0.455159i	$-0.849583\pi$
$409$	−4936.31	+	4142.06i	−0.596785	+	0.500762i	0.293626	+	0.955920i	$0.405138\pi$
$410$	152.355	−	263.887i	0.0183519	−	0.0317864i
$411$	−4723.44	−	8181.24i	−0.566886	−	0.981876i
$412$	−2278.48	−	829.298i	−0.272458	−	0.0991665i
$413$	−327.567	+	1857.73i	−0.0390279	+	0.221338i
$414$	−26.3668	−	149.534i	−0.00313010	−	0.0177517i
$415$	293.124	−	106.689i	0.0346721	−	0.0126196i
$416$	401.839	+	337.183i	0.0473601	+	0.0397398i
$417$	939.470			0.110326
$418$	480.412	+	407.164i	0.0562146	+	0.0476436i
$419$	2695.30			0.314258			0.157129	−	0.987578i	$-0.449776\pi$
$419$	2695.30			0.314258			0.157129	+	0.987578i	$0.449776\pi$
$420$	−102.020	−	85.6049i	−0.0118525	−	0.00994546i
$421$	−15398.6	+	5604.63i	−1.78262	+	0.648819i	−0.782974	+	0.622054i	$0.786298\pi$
$421$	−15398.6	+	5604.63i	−1.78262	+	0.648819i	−0.999642	+	0.0267649i	$0.991479\pi$
$422$	717.822	+	4070.97i	0.0828034	+	0.469601i
$423$	175.060	−	992.815i	0.0201222	−	0.114119i
$424$	533.370	+	194.131i	0.0610913	+	0.0222354i
$425$	−4468.27	−	7739.26i	−0.509983	−	0.883316i
$426$	−3145.64	+	5448.41i	−0.357763	+	0.619663i
$427$	−344.004	+	288.653i	−0.0389871	+	0.0327141i
$428$	2232.97	−	1873.68i	0.252184	−	0.211607i
$429$	155.291	−	268.972i	0.0174767	−	0.0302706i
$430$	182.986	+	316.941i	0.0205218	+	0.0355448i
$431$	164.535	+	59.8858i	0.0183883	+	0.00669281i	0.351198	−	0.936301i	$-0.385774\pi$
$431$	164.535	+	59.8858i	0.0183883	+	0.00669281i	−0.332810	+	0.942994i	$0.607997\pi$
$432$	403.822	−	2290.19i	0.0449743	−	0.255062i
$433$	2122.35	+	12036.4i	0.235551	+	1.33588i	0.841451	+	0.540334i	$0.181702\pi$
$433$	2122.35	+	12036.4i	0.235551	+	1.33588i	−0.605900	+	0.795541i	$0.707187\pi$
$434$	1227.55	−	446.793i	0.135771	−	0.0494165i
$435$	−701.219	−	588.392i	−0.0772893	−	0.0648535i
$436$	−6000.16			−0.659073
$437$	2232.91	−	1854.97i	0.244427	−	0.203055i
$438$	7564.47			0.825216
$439$	2482.96	+	2083.45i	0.269943	+	0.226509i	0.767703	−	0.640805i	$-0.221399\pi$
$439$	2482.96	+	2083.45i	0.269943	+	0.226509i	−0.497760	+	0.867315i	$0.665844\pi$
$440$	−67.1625	+	24.4451i	−0.00727692	+	0.00264858i
$441$	125.969	+	714.406i	0.0136021	+	0.0771413i
$442$	−425.823	+	2414.96i	−0.0458243	+	0.259883i
$443$	7846.02	+	2855.72i	0.841481	+	0.306274i	0.726562	−	0.687101i	$-0.241117\pi$
$443$	7846.02	+	2855.72i	0.841481	+	0.306274i	0.114919	+	0.993375i	$0.463339\pi$
$444$	4001.21	+	6930.30i	0.427678	+	0.740760i
$445$	−1658.10	+	2871.91i	−0.176632	+	0.305936i
$446$	1768.60	−	1484.03i	0.187771	−	0.157558i
$447$	9461.82	−	7939.41i	1.00118	−	0.840092i
$448$	−90.9811	+	157.584i	−0.00959476	+	0.0166186i
$449$	5682.25	+	9841.94i	0.597242	+	1.03445i	0.993226	+	0.116197i	$0.0370703\pi$
$449$	5682.25	+	9841.94i	0.597242	+	1.03445i	−0.395984	+	0.918257i	$0.629596\pi$
$450$	−486.363	−	177.022i	−0.0509497	−	0.0185442i
$451$	−42.8040	+	242.754i	−0.00446909	+	0.0253455i
$452$	−728.465	−	4131.33i	−0.0758056	−	0.429915i
$453$	4148.89	−	1510.07i	0.430313	−	0.156621i
$454$	1270.58	+	1066.15i	0.131347	+	0.110213i
$455$	109.521			0.0112844
$456$	3108.15	−	1113.96i	0.319194	−	0.114399i
$457$	12215.7			1.25038			0.625192	−	0.780471i	$-0.285021\pi$
$457$	12215.7			1.25038			0.625192	+	0.780471i	$0.285021\pi$
$458$	7710.03	+	6469.48i	0.786607	+	0.660041i
$459$	10215.7	−	3718.20i	1.03884	−	0.378106i
$460$	57.2108	+	324.459i	0.00579884	+	0.0328869i
$461$	1454.74	−	8250.23i	0.146972	−	0.833517i	−0.818791	−	0.574091i	$-0.805356\pi$
$461$	1454.74	−	8250.23i	0.146972	−	0.833517i	0.965763	−	0.259426i	$-0.0835334\pi$
$462$	101.238	+	36.8477i	0.0101949	+	0.00371063i
$463$	−3115.90	−	5396.90i	−0.312761	−	0.541718i	0.666198	−	0.745775i	$-0.267920\pi$
$463$	−3115.90	−	5396.90i	−0.312761	−	0.541718i	−0.978959	+	0.204057i	$0.934587\pi$
$464$	−625.344	+	1083.13i	−0.0625666	+	0.108368i
$465$	2060.86	−	1729.26i	0.205527	−	0.172457i
$466$	1913.40	−	1605.53i	0.190207	−	0.159603i
$467$	−6218.51	+	10770.8i	−0.616185	+	1.06726i	0.373990	+	0.927433i	$0.377989\pi$
$467$	−6218.51	+	10770.8i	−0.616185	+	1.06726i	−0.990175	+	0.139831i	$0.955344\pi$
$468$	71.0126	+	122.997i	0.00701401	+	0.0121486i
$469$	−239.524	−	87.1796i	−0.0235825	−	0.00858333i
$470$	−379.845	+	2154.21i	−0.0372786	+	0.211418i
$471$	1063.88	+	6033.57i	0.104079	+	0.590259i
$472$	4987.76	−	1815.40i	0.486399	−	0.177035i
$473$	−226.793	−	190.302i	−0.0220464	−	0.0184991i
$474$	8216.15			0.796161
$475$	−1670.22	−	9753.08i	−0.161337	−	0.942110i
$476$	−850.633			−0.0819090
$477$	117.724	+	98.7818i	0.0113002	+	0.00948199i
$478$	−8886.42	+	3234.39i	−0.850326	+	0.309493i
$479$	−1098.88	−	6232.07i	−0.104821	−	0.594469i	−0.991292	−	0.131684i	$-0.957961\pi$
$479$	−1098.88	−	6232.07i	−0.104821	−	0.594469i	0.886471	−	0.462785i	$-0.153150\pi$
$480$	−65.0714	+	369.038i	−0.00618769	+	0.0350921i
$481$	−6184.04	−	2250.81i	−0.586212	−	0.213364i
$482$	−404.199	−	700.094i	−0.0381966	−	0.0661585i
$483$	248.311	−	430.087i	0.0233924	−	0.0405168i
$484$	−4034.13	+	3385.04i	−0.378863	+	0.317903i
$485$	−2377.09	+	1994.62i	−0.222553	+	0.186744i
$486$	606.253	−	1050.06i	0.0565847	−	0.0980077i
$487$	−1799.28	−	3116.44i	−0.167419	−	0.289979i	0.770093	−	0.637932i	$-0.220210\pi$
$487$	−1799.28	−	3116.44i	−0.167419	−	0.289979i	−0.937512	+	0.347954i	$0.886877\pi$
$488$	1187.36	+	432.165i	0.110142	+	0.0400885i
$489$	−403.986	+	2291.12i	−0.0373597	+	0.211877i
$490$	−273.328	−	1550.12i	−0.0251993	−	0.142913i
$491$	4014.46	−	1461.15i	0.368982	−	0.134298i	−0.150873	−	0.988553i	$-0.548208\pi$
$491$	4014.46	−	1461.15i	0.368982	−	0.134298i	0.519855	+	0.854255i	$0.325986\pi$
$492$	990.028	+	830.732i	0.0907193	+	0.0761225i
$493$	−5846.69			−0.534121
$494$	−1369.19	+	2344.75i	−0.124702	+	0.213553i
$495$	−19.3512			−0.00175711
$496$	−2815.77	−	2362.71i	−0.254903	−	0.213889i
$497$	1686.45	−	613.816i	0.152208	−	0.0553993i
$498$	229.743	+	1302.94i	0.0206728	+	0.117241i
$499$	−403.857	+	2290.39i	−0.0362307	+	0.205474i	−0.997550	−	0.0699634i	$-0.977712\pi$
$499$	−403.857	+	2290.39i	−0.0362307	+	0.205474i	0.961319	+	0.275438i	$0.0888228\pi$
$500$	2159.40	+	785.956i	0.193142	+	0.0702980i
$501$	−8947.32	−	15497.2i	−0.797878	−	1.38197i
$502$	−6355.08	+	11007.3i	−0.565022	+	0.978647i
$503$	−17155.6	+	14395.2i	−1.52073	+	1.27605i	−0.682252	+	0.731117i	$0.738999\pi$
$503$	−17155.6	+	14395.2i	−1.52073	+	1.27605i	−0.838482	+	0.544930i	$0.816556\pi$
$504$	−37.7400	+	31.6676i	−0.00333546	+	0.00279879i
$505$	341.175	−	590.932i	0.0300635	−	0.0520715i
$506$	−133.262	−	230.816i	−0.0117079	−	0.0202787i
$507$	−9029.83	−	3286.59i	−0.790984	−	0.287895i
$508$	1641.29	−	9308.19i	0.143347	−	0.812961i
$509$	−1412.91	−	8013.02i	−0.123038	−	0.697782i	−0.982454	−	0.186505i	$-0.940284\pi$
$509$	−1412.91	−	8013.02i	−0.123038	−	0.697782i	0.859416	−	0.511277i	$-0.170827\pi$
$510$	−1646.14	+	599.146i	−0.142926	+	0.0520209i
$511$	−1653.03	−	1387.06i	−0.143103	−	0.120078i
$512$	512.000			0.0441942
$513$	12037.2	+	59.3112i	1.03597	+	0.00510458i
$514$	8683.35			0.745148
$515$	1091.19	+	915.616i	0.0933660	+	0.0783434i
$516$	−1458.61	+	530.892i	−0.124442	+	0.0452931i
$517$	−307.280	−	1742.67i	−0.0261396	−	0.148245i
$518$	396.405	−	2248.13i	0.0336236	−	0.190689i
$519$	1351.44	+	491.886i	0.114300	+	0.0416019i
$520$	−154.083	−	266.880i	−0.0129942	−	0.0225066i
$521$	−6690.70	+	11588.6i	−0.562620	+	0.974486i	0.434647	+	0.900601i	$0.356873\pi$
$521$	−6690.70	+	11588.6i	−0.562620	+	0.974486i	−0.997267	+	0.0738851i	$0.976460\pi$
$522$	−259.400	+	217.663i	−0.0217503	+	0.0182506i
$523$	−9579.15	+	8037.86i	−0.800893	+	0.672029i	−0.948416	−	0.317030i	$-0.897314\pi$
$523$	−9579.15	+	8037.86i	−0.800893	+	0.672029i	0.147523	+	0.989059i	$0.452870\pi$
$524$	−3551.67	+	6151.67i	−0.296098	+	0.512857i
$525$	−846.413	−	1466.03i	−0.0703629	−	0.121872i
$526$	−11511.5	−	4189.83i	−0.954228	−	0.347310i
$527$	2983.83	−	16922.2i	0.246637	−	1.39875i
$528$	−52.6402	−	298.537i	−0.00433877	−	0.0246064i
$529$	10278.8	−	3741.16i	0.844806	−	0.307484i
$530$	−255.437	−	214.337i	−0.0209348	−	0.0175664i
$531$	1437.10			0.117448
$532$	−883.471	−	326.496i	−0.0719987	−	0.0266079i
$533$	−1062.82			−0.0863709
$534$	−10774.6	−	9040.95i	−0.873150	−	0.732660i
$535$	−1609.17	+	585.689i	−0.130038	+	0.0473300i
$536$	124.544	+	706.323i	0.0100363	+	0.0569189i
$537$	−3440.43	+	19511.6i	−0.276472	+	1.56795i
$538$	−11151.4	−	4058.79i	−0.893630	−	0.325255i
$539$	636.664	+	1102.73i	0.0508777	+	0.0881227i
$540$	−683.088	+	1183.14i	−0.0544360	+	0.0942859i
$541$	−3292.32	+	2762.58i	−0.261641	+	0.219543i	−0.764166	−	0.645020i	$-0.776849\pi$
$541$	−3292.32	+	2762.58i	−0.261641	+	0.219543i	0.502525	+	0.864563i	$0.332405\pi$
$542$	9943.87	−	8343.90i	0.788055	−	0.661257i
$543$	1722.37	−	2983.23i	0.136121	−	0.235769i
$544$	1196.74	+	2072.82i	0.0943197	+	0.163367i
$545$	3312.34	+	1205.59i	0.260340	+	0.0947560i
$546$	−80.6627	+	457.461i	−0.00632243	+	0.0358563i
$547$	2938.44	+	16664.7i	0.229686	+	1.30262i	0.853520	+	0.521059i	$0.174463\pi$
$547$	2938.44	+	16664.7i	0.229686	+	1.30262i	−0.623834	+	0.781557i	$0.714426\pi$
$548$	7125.43	−	2593.44i	0.555444	−	0.202165i
$549$	262.071	+	219.904i	0.0203733	+	0.0170952i
$550$	−908.494			−0.0704333
$551$	−6072.40	−	2244.12i	−0.469498	−	0.173508i
$552$	−1397.38			−0.107747
$553$	−1795.44	−	1506.55i	−0.138065	−	0.115850i
$554$	4462.42	−	1624.19i	0.342221	−	0.124558i
$555$	−816.354	−	4629.77i	−0.0624366	−	0.354095i
$556$	−130.945	+	742.627i	−0.00998798	+	0.0566446i
$557$	6235.19	+	2269.42i	0.474315	+	0.172637i	0.568106	−	0.822955i	$-0.307676\pi$
$557$	6235.19	+	2269.42i	0.474315	+	0.172637i	−0.0937910	+	0.995592i	$0.529899\pi$
$558$	−497.600	−	861.869i	−0.0377511	−	0.0653867i
$559$	638.248	−	1105.48i	0.0482916	−	0.0836436i
$560$	81.8883	−	68.7124i	0.00617931	−	0.00518505i
$561$	1085.58	−	910.911i	0.0816993	−	0.0685538i
$562$	4657.08	−	8066.29i	0.349550	−	0.605438i
$563$	1810.93	+	3136.62i	0.135562	+	0.234800i	0.925812	−	0.377984i	$-0.123383\pi$
$563$	1810.93	+	3136.62i	0.135562	+	0.234800i	−0.790250	+	0.612785i	$0.790049\pi$
$564$	−8718.25	−	3173.18i	−0.650894	−	0.236906i
$565$	−427.953	+	2427.04i	−0.0318657	+	0.180719i
$566$	−1060.71	−	6015.57i	−0.0787718	−	0.446737i
$567$	1778.89	−	647.461i	0.131757	−	0.0479556i
$568$	−3868.39	−	3245.96i	−0.285764	−	0.239784i
$569$	4576.86			0.337209			0.168604	−	0.985684i	$-0.446074\pi$
$569$	4576.86			0.337209			0.168604	+	0.985684i	$0.446074\pi$
$570$	−1939.66	−	9.55732i	−0.142532	−	0.000702302i
$571$	18109.2			1.32723			0.663614	−	0.748075i	$-0.269022\pi$
$571$	18109.2			1.32723			0.663614	+	0.748075i	$0.269022\pi$
$572$	190.970	+	160.243i	0.0139596	+	0.0117135i
$573$	10466.8	−	3809.59i	0.763099	−	0.277745i
$574$	−64.0194	−	363.072i	−0.00465525	−	0.0264013i
$575$	−727.209	+	4124.21i	−0.0527421	+	0.299115i
$576$	130.263	+	47.4120i	0.00942300	+	0.00342969i
$577$	748.863	+	1297.07i	0.0540304	+	0.0935835i	0.891776	−	0.452478i	$-0.149460\pi$
$577$	748.863	+	1297.07i	0.0540304	+	0.0935835i	−0.837745	+	0.546061i	$0.816127\pi$
$578$	−681.509	+	1180.41i	−0.0490433	+	0.0849456i
$579$	−15273.6	+	12816.1i	−1.09628	+	0.919891i
$580$	562.847	−	472.284i	0.0402947	−	0.0338113i
$581$	188.708	−	326.852i	0.0134749	−	0.0233393i
$582$	−6580.65	−	11398.0i	−0.468689	−	0.811792i
$583$	253.479	+	92.2589i	0.0180069	+	0.00655398i
$584$	−1054.35	+	5979.53i	−0.0747079	+	0.423689i
$585$	−14.4885	−	82.1681i	−0.00102397	−	0.00580724i
$586$	18148.9	−	6605.66i	1.27939	−	0.465661i
$587$	16119.6	+	13526.0i	1.13344	+	0.951068i	0.999204	−	0.0398814i	$-0.0126980\pi$
$587$	16119.6	+	13526.0i	1.13344	+	0.951068i	0.134235	+	0.990950i	$0.457142\pi$
$588$	6676.05			0.468224
$589$	9594.21	−	16430.2i	0.671176	−	1.14939i
$590$	−3118.22			−0.217585
$591$	8008.86	+	6720.23i	0.557429	+	0.467738i
$592$	−6035.93	+	2196.90i	−0.419046	+	0.152520i
$593$	−3697.11	−	20967.4i	−0.256024	−	1.45198i	−0.793431	−	0.608660i	$-0.791707\pi$
$593$	−3697.11	−	20967.4i	−0.256024	−	1.45198i	0.537407	−	0.843323i	$-0.319404\pi$
$594$	191.913	−	1088.39i	0.0132564	−	0.0751806i
$595$	469.585	+	170.915i	0.0323548	+	0.0117762i
$596$	4957.10	+	8585.94i	0.340689	+	0.590090i
$597$	−4713.17	+	8163.44i	−0.323111	+	0.559644i
$598$	880.305	−	738.664i	0.0601979	−	0.0505121i
$599$	−6005.51	+	5039.22i	−0.409647	+	0.343735i	−0.824208	−	0.566287i	$-0.808379\pi$
$599$	−6005.51	+	5039.22i	−0.409647	+	0.343735i	0.414561	+	0.910021i	$0.363935\pi$
$600$	−2381.61	+	4125.08i	−0.162048	+	0.280676i
$601$	8038.35	+	13922.8i	0.545576	+	0.944965i	0.998570	+	0.0534517i	$0.0170223\pi$
$601$	8038.35	+	13922.8i	0.545576	+	0.944965i	−0.452995	+	0.891513i	$0.649644\pi$
$602$	416.091	+	151.445i	0.0281704	+	0.0102532i
$603$	−33.7201	+	191.236i	−0.00227726	+	0.0129150i
$604$	615.394	+	3490.07i	0.0414570	+	0.235114i
$605$	2907.16	−	1058.12i	0.195360	−	0.0711052i
$606$	2217.01	+	1860.29i	0.148614	+	0.124702i
$607$	−11810.5			−0.789741			−0.394870	−	0.918737i	$-0.629210\pi$
$607$	−11810.5			−0.789741			−0.394870	+	0.918737i	$0.629210\pi$
$608$	447.339	+	2612.18i	0.0298388	+	0.174240i
$609$	−1107.53			−0.0736933
$610$	−568.642	−	477.147i	−0.0377437	−	0.0316707i
$611$	7169.58	−	2609.52i	0.474714	−	0.172782i
$612$	112.530	+	638.189i	0.00743260	+	0.0421524i
$613$	−3885.03	+	22033.1i	−0.255979	+	1.45173i	0.537569	+	0.843220i	$0.319343\pi$
$613$	−3885.03	+	22033.1i	−0.255979	+	1.45173i	−0.793548	+	0.608508i	$0.791768\pi$
$614$	2388.06	+	869.182i	0.156961	+	0.0571292i
$615$	−379.621	−	657.523i	−0.0248907	−	0.0431120i
$616$	−43.2379	+	74.8903i	−0.00282809	+	0.00489840i
$617$	10051.0	−	8433.83i	0.655818	−	0.550297i	−0.253012	−	0.967463i	$-0.581421\pi$
$617$	10051.0	−	8433.83i	0.655818	−	0.550297i	0.908830	+	0.417166i	$0.136977\pi$
$618$	−4628.14	+	3883.47i	−0.301248	+	0.252777i
$619$	13291.3	−	23021.2i	0.863041	−	1.49483i	−0.00593889	−	0.999982i	$-0.501890\pi$
$619$	13291.3	−	23021.2i	0.863041	−	1.49483i	0.868980	−	0.494848i	$-0.164776\pi$
$620$	1079.69	+	1870.08i	0.0699379	+	0.121136i
$621$	−4787.26	−	1742.42i	−0.309350	−	0.112594i
$622$	−1801.56	+	10217.1i	−0.116135	+	0.658633i
$623$	696.730	+	3951.35i	0.0448056	+	0.254105i
$624$	1228.22	−	447.037i	0.0787954	−	0.0286792i
$625$	10406.5	+	8732.11i	0.666018	+	0.558855i
$626$	15542.7			0.992349
$627$	1477.12	−	529.401i	0.0940839	−	0.0337197i
$628$	−4917.67			−0.312478
$629$	−23002.4	−	19301.3i	−1.45813	−	1.22352i
$630$	27.1970	−	9.89889i	0.00171993	−	0.000626002i
$631$	−1680.72	−	9531.82i	−0.106035	−	0.601356i	−0.990802	−	0.135321i	$-0.956793\pi$
$631$	−1680.72	−	9531.82i	−0.106035	−	0.601356i	0.884766	−	0.466035i	$-0.154318\pi$
$632$	−1145.18	+	6494.66i	−0.0720775	+	0.408772i
$633$	9678.90	+	3522.83i	0.607743	+	0.221201i
$634$	6527.45	+	11305.9i	0.408893	+	0.708224i
$635$	−2776.33	+	4808.74i	−0.173504	+	0.300518i
$636$	1083.40	−	909.083i	0.0675467	−	0.0566784i
$637$	−4205.70	+	3529.00i	−0.261595	+	0.219504i
$638$	−297.189	+	514.747i	−0.0184418	+	0.0319421i
$639$	−683.617	−	1184.06i	−0.0423215	−	0.0733031i
$640$	−282.646	−	102.875i	−0.0174571	−	0.00635387i
$641$	−668.805	+	3792.98i	−0.0412110	+	0.233719i	−0.998455	−	0.0555618i	$-0.982305\pi$
$641$	−668.805	+	3792.98i	−0.0412110	+	0.233719i	0.957244	+	0.289281i	$0.0934161\pi$
$642$	−1261.22	−	7152.76i	−0.0775335	−	0.439715i
$643$	−18519.6	+	6740.58i	−1.13583	+	0.413410i	−0.840407	−	0.541955i	$-0.817684\pi$
$643$	−18519.6	+	6740.58i	−1.13583	+	0.413410i	−0.295427	+	0.955365i	$0.595462\pi$
$644$	305.363	+	256.230i	0.0186847	+	0.0156784i
$645$	911.888			0.0556675
$646$	−9529.76	+	7916.73i	−0.580408	+	0.482167i
$647$	−15500.5			−0.941867			−0.470933	−	0.882169i	$-0.656083\pi$
$647$	−15500.5			−0.941867			−0.470933	+	0.882169i	$0.656083\pi$
$648$	−4080.42	−	3423.88i	−0.247368	−	0.207566i
$649$	2370.39	−	862.750i	0.143368	−	0.0521817i
$650$	−680.200	−	3857.61i	−0.0410456	−	0.232781i
$651$	565.221	−	3205.53i	0.0340288	−	0.192987i
$652$	−1754.76	−	638.682i	−0.105402	−	0.0383631i
$653$	−14876.8	−	25767.4i	−0.891538	−	1.54419i	−0.838031	−	0.545622i	$-0.816293\pi$
$653$	−14876.8	−	25767.4i	−0.891538	−	1.54419i	−0.0535073	−	0.998567i	$-0.517040\pi$
$654$	−7475.26	+	12947.5i	−0.446951	+	0.774142i
$655$	3196.71	−	2682.36i	0.190696	−	0.160013i
$656$	−794.665	+	666.803i	−0.0472964	+	0.0396864i
$657$	−821.963	+	1423.68i	−0.0488095	+	0.0845405i
$658$	1323.31	+	2292.04i	0.0784011	+	0.135795i
$659$	−20984.8	−	7637.83i	−1.24044	−	0.451483i	−0.363280	−	0.931680i	$-0.618343\pi$
$659$	−20984.8	−	7637.83i	−1.24044	−	0.451483i	−0.877161	+	0.480197i	$0.840565\pi$
$660$	−30.9246	+	175.382i	−0.00182385	+	0.0103436i
$661$	−3187.21	−	18075.5i	−0.187546	−	1.06363i	−0.922640	−	0.385662i	$-0.873973\pi$
$661$	−3187.21	−	18075.5i	−0.187546	−	1.06363i	0.735094	−	0.677965i	$-0.237138\pi$
$662$	15943.7	−	5803.03i	0.936057	−	0.340697i
$663$	4680.66	+	3927.54i	0.274180	+	0.230065i
$664$	−1061.96			−0.0620665
$665$	422.112	+	357.753i	0.0246147	+	0.0208617i
$666$	−1739.10			−0.101184
$667$	2098.86	+	1761.16i	0.121842	+	0.102237i
$668$	13497.3	−	4912.60i	0.781773	−	0.284542i
$669$	−998.940	−	5665.27i	−0.0577298	−	0.327402i
$670$	73.1660	−	414.945i	0.00421888	−	0.0239264i
$671$	564.284	+	205.383i	0.0324649	+	0.0118163i
$672$	226.696	+	392.649i	0.0130134	+	0.0225399i
$673$	9160.13	−	15865.8i	0.524661	−	0.908740i	−0.474926	−	0.880026i	$-0.657525\pi$
$673$	9160.13	−	15865.8i	0.524661	−	0.908740i	0.999588	−	0.0287147i	$-0.00914143\pi$
$674$	−8473.73	+	7110.31i	−0.484267	+	0.406348i
$675$	−13302.8	+	11162.4i	−0.758554	+	0.636502i
$676$	3856.56	−	6679.77i	0.219422	−	0.380050i
$677$	−7740.26	−	13406.5i	−0.439413	−	0.761086i	0.558231	−	0.829685i	$-0.311480\pi$
$677$	−7740.26	−	13406.5i	−0.439413	−	0.761086i	−0.997644	+	0.0685998i	$0.978147\pi$
$678$	−9822.41	−	3575.06i	−0.556382	−	0.202507i
$679$	−651.954	+	3697.41i	−0.0368478	+	0.208974i
$680$	−244.168	−	1384.74i	−0.0137697	−	0.0780919i
$681$	3883.55	−	1413.50i	0.218529	−	0.0795379i
$682$	−1338.17	−	1122.86i	−0.0751337	−	0.0630447i
$683$	−27505.7			−1.54096			−0.770481	−	0.637463i	$-0.779984\pi$
$683$	−27505.7			−1.54096			−0.770481	+	0.637463i	$0.779984\pi$
$684$	−128.080	+	706.018i	−0.00715975	+	0.0394668i
$685$	−4454.63			−0.248471
$686$	−2952.98	−	2477.85i	−0.164352	−	0.137908i
$687$	23565.7	−	8577.23i	1.30872	−	0.476334i
$688$	−216.352	−	1226.99i	−0.0119889	−	0.0679924i
$689$	−201.963	+	1145.39i	−0.0111671	+	0.0633320i
$690$	771.413	+	280.771i	0.0425611	+	0.0154910i
$691$	17033.7	+	29503.2i	0.937761	+	1.62425i	0.769635	+	0.638484i	$0.220438\pi$
$691$	17033.7	+	29503.2i	0.937761	+	1.62425i	0.168125	+	0.985766i	$0.446229\pi$
$692$	−577.190	+	999.723i	−0.0317073	+	0.0549187i
$693$	−17.9356	+	15.0498i	−0.000983142	+	0.000824954i
$694$	14262.5	−	11967.6i	0.780110	−	0.654590i
$695$	221.501	−	383.651i	0.0120892	−	0.0209392i
$696$	1558.16	+	2698.82i	0.0848592	+	0.146980i
$697$	−4556.98	−	1658.60i	−0.247644	−	0.0901350i
$698$	−3006.84	+	17052.6i	−0.163052	+	0.924716i
$699$	−1080.72	−	6129.09i	−0.0584789	−	0.331650i
$700$	1276.84	−	464.730i	0.0689426	−	0.0250931i
$701$	24756.7	+	20773.3i	1.33387	+	1.11925i	0.983155	+	0.182773i	$0.0585072\pi$
$701$	24756.7	+	20773.3i	1.33387	+	1.11925i	0.350719	+	0.936481i	$0.385937\pi$
$702$	4765.17			0.256196
$703$	−16482.0	−	28875.4i	−0.884256	−	1.54915i
$704$	243.323			0.0130264
$705$	4175.26	+	3503.46i	0.223049	+	0.187160i
$706$	−5906.41	+	2149.76i	−0.314859	+	0.114599i
$707$	−143.361	−	813.041i	−0.00762609	−	0.0432497i
$708$	2296.59	−	13024.6i	0.121908	−	0.691376i
$709$	11701.6	+	4259.03i	0.619834	+	0.225601i	0.632801	−	0.774315i	$-0.281905\pi$
$709$	11701.6	+	4259.03i	0.619834	+	0.225601i	−0.0129667	+	0.999916i	$0.504128\pi$
$710$	1483.31	+	2569.17i	0.0784052	+	0.135802i
$711$	−892.775	+	1546.33i	−0.0470909	+	0.0815639i
$712$	8648.43	−	7256.89i	0.455216	−	0.381971i
$713$	−6168.48	+	5175.97i	−0.323999	+	0.271868i
$714$	−1059.75	+	1835.55i	−0.0555467	+	0.0962097i
$715$	−73.2266	−	126.832i	−0.00383010	−	0.00663393i
$716$	−14943.9	−	5439.14i	−0.780001	−	0.283897i
$717$	−4091.71	+	23205.2i	−0.213121	+	1.20867i
$718$	1935.07	+	10974.4i	0.100580	+	0.570417i
$719$	−17348.1	+	6314.18i	−0.899825	+	0.327509i	−0.750183	−	0.661231i	$-0.770034\pi$
$719$	−17348.1	+	6314.18i	−0.899825	+	0.327509i	−0.149642	+	0.988740i	$0.547812\pi$
$720$	−62.3846	−	52.3469i	−0.00322908	−	0.00270952i
$721$	1723.46			0.0890220
$722$	−12936.3	+	4564.57i	−0.666814	+	0.235285i
$723$	−2014.28			−0.103612
$724$	2118.10	+	1777.30i	0.108727	+	0.0912330i
$725$	8776.13	−	3194.25i	0.449569	−	0.163630i
$726$	2278.55	+	12922.3i	0.116481	+	0.660596i
$727$	−4237.82	+	24033.8i	−0.216192	+	1.22609i	0.662633	+	0.748944i	$0.269439\pi$
$727$	−4237.82	+	24033.8i	−0.216192	+	1.22609i	−0.878825	+	0.477144i	$0.841672\pi$
$728$	−350.369	−	127.524i	−0.0178373	−	0.00649223i
$729$	−10499.3	−	18185.2i	−0.533417	−	0.923906i
$730$	1783.50	−	3089.11i	0.0904248	−	0.156620i
$731$	4461.76	−	3743.86i	0.225751	−	0.189428i
$732$	2411.82	−	2023.76i	0.121781	−	0.102186i
$733$	8876.56	−	15374.7i	0.447290	−	0.774728i	−0.550919	−	0.834559i	$-0.685723\pi$
$733$	8876.56	−	15374.7i	0.447290	−	0.774728i	0.998209	+	0.0598303i	$0.0190560\pi$
$734$	755.678	+	1308.87i	0.0380008	+	0.0658193i
$735$	−3685.47	−	1341.40i	−0.184953	−	0.0673174i
$736$	194.770	−	1104.59i	0.00975449	−	0.0553205i
$737$	59.1884	+	335.674i	0.00295825	+	0.0167771i
$738$	−263.926	+	96.0614i	−0.0131643	+	0.00479142i
$739$	624.792	+	524.263i	0.0311006	+	0.0260965i	0.658205	−	0.752838i	$-0.271316\pi$
$739$	624.792	+	524.263i	0.0311006	+	0.0260965i	−0.627105	+	0.778935i	$0.715760\pi$
$740$	3773.50			0.187455
$741$	3353.86	+	5875.72i	0.166271	+	0.291296i
$742$	−403.444			−0.0199608
$743$	2007.61	+	1684.58i	0.0991278	+	0.0831781i	0.691005	−	0.722850i	$-0.257168\pi$
$743$	2007.61	+	1684.58i	0.0991278	+	0.0831781i	−0.591877	+	0.806028i	$0.701613\pi$
$744$	−8606.42	+	3132.48i	−0.424095	+	0.154358i
$745$	−1011.38	−	5735.82i	−0.0497370	−	0.282073i
$746$	174.484	−	989.547i	0.00856341	−	0.0485655i
$747$	−270.186	−	98.3395i	−0.0132337	−	0.00481667i
$748$	568.742	+	985.089i	0.0278011	+	0.0481530i
$749$	−1035.95	+	1794.32i	−0.0505379	+	0.0875341i
$750$	4386.26	−	3680.51i	0.213551	−	0.179191i
$751$	9806.84	−	8228.91i	0.476507	−	0.399837i	−0.372655	−	0.927970i	$-0.621552\pi$
$751$	9806.84	−	8228.91i	0.476507	−	0.399837i	0.849161	+	0.528133i	$0.177108\pi$
$752$	3723.49	−	6449.27i	0.180561	−	0.312740i
$753$	15834.9	+	27426.8i	0.766341	+	1.32734i
$754$	−2408.20	−	876.515i	−0.116315	−	0.0423353i
$755$	361.526	−	2050.32i	0.0174269	−	0.0988327i
$756$	287.033	+	1627.84i	0.0138086	+	0.0783123i
$757$	3759.02	−	1368.17i	0.180481	−	0.0656896i	−0.250199	−	0.968194i	$-0.580496\pi$
$757$	3759.02	−	1368.17i	0.180481	−	0.0656896i	0.430680	+	0.902505i	$0.358274\pi$
$758$	3134.34	+	2630.02i	0.150191	+	0.126025i
$759$	−664.092			−0.0317589
$760$	277.908	−	1531.92i	0.0132642	−	0.0731165i
$761$	−12934.0			−0.616104			−0.308052	−	0.951369i	$-0.599677\pi$
$761$	−12934.0			−0.616104			−0.308052	+	0.951369i	$0.599677\pi$
$762$	−18041.0	−	15138.2i	−0.857687	−	0.719685i
$763$	4007.65	−	1458.67i	0.190153	−	0.0692100i
$764$	1552.51	+	8804.71i	0.0735180	+	0.416941i
$765$	66.1081	−	374.918i	0.00312437	−	0.0177192i
$766$	10030.9	+	3650.96i	0.473149	+	0.172212i
$767$	5438.11	+	9419.08i	0.256009	+	0.443420i
$768$	637.872	−	1104.83i	0.0299703	−	0.0519101i
$769$	22976.5	−	19279.5i	1.07744	−	0.904081i	0.0817359	−	0.996654i	$-0.473954\pi$
$769$	22976.5	−	19279.5i	1.07744	−	0.904081i	0.995706	+	0.0925730i	$0.0295092\pi$
$770$	38.9167	−	32.6550i	0.00182138	−	0.00152832i
$771$	10818.1	−	18737.5i	0.505323	−	0.875246i
$772$	−8001.91	−	13859.7i	−0.373050	−	0.646142i
$773$	24211.1	+	8812.13i	1.12654	+	0.410026i	0.837034	−	0.547151i	$-0.184288\pi$
$773$	24211.1	+	8812.13i	1.12654	+	0.410026i	0.289504	+	0.957177i	$0.406510\pi$
$774$	58.5772	−	332.208i	0.00272030	−	0.0154276i
$775$	4766.30	+	27031.1i	0.220917	+	1.25288i
$776$	9927.07	−	3613.16i	0.459228	−	0.167145i
$777$	−4357.29	−	3656.20i	−0.201180	−	0.168810i
$778$	−198.128			−0.00913014
$779$	−4096.28	−	3471.73i	−0.188401	−	0.159676i
$780$	−767.854			−0.0352482
$781$	−1838.42	−	1542.61i	−0.0842301	−	0.0706774i
$782$	4927.17	−	1793.34i	0.225314	−	0.0820075i
$783$	1972.88	+	11188.7i	0.0900445	+	0.510668i
$784$	−930.522	+	5277.25i	−0.0423889	+	0.240400i
$785$	2714.76	+	988.093i	0.123432	+	0.0449255i
$786$	8849.64	+	15328.0i	0.401598	+	0.695589i
$787$	8066.62	−	13971.8i	0.365367	−	0.632834i	−0.623468	−	0.781849i	$-0.714277\pi$
$787$	8066.62	−	13971.8i	0.365367	−	0.632834i	0.988835	+	0.149015i	$0.0476102\pi$
$788$	−6428.46	+	5394.12i	−0.290615	+	0.243855i
$789$	−23382.6	+	19620.3i	−1.05506	+	0.885299i
$790$	1937.14	−	3355.23i	0.0872411	−	0.151106i
$791$	1490.90	+	2582.32i	0.0670170	+	0.116077i
$792$	61.9066	+	22.5322i	0.00277747	+	0.00101092i
$793$	−449.600	+	2549.81i	−0.0201334	+	0.114182i
$794$	−4038.19	−	22901.7i	−0.180491	−	1.02362i
$795$	−780.744	+	284.167i	−0.0348303	+	0.0126772i
$796$	−5796.06	−	4863.48i	−0.258086	−	0.216559i
$797$	19210.4			0.853786			0.426893	−	0.904302i	$-0.359608\pi$
$797$	19210.4			0.853786			0.426893	+	0.904302i	$0.359608\pi$
$798$	−1805.20	+	1499.65i	−0.0800794	+	0.0665250i
$799$	34813.0			1.54142
$800$	−2928.82	−	2457.57i	−0.129437	−	0.108610i
$801$	2872.34	−	1045.45i	0.126703	−	0.0461161i
$802$	−1989.15	−	11281.0i	−0.0875803	−	0.496692i
$803$	−501.071	+	2841.72i	−0.0220205	+	0.124884i
$804$	1679.31	+	611.220i	0.0736626	+	0.0268110i
$805$	−117.090	−	202.805i	−0.00512655	−	0.00887944i
$806$	3765.93	−	6522.77i	0.164577	−	0.285056i
$807$	−22651.3	+	19006.7i	−0.988058	+	0.829079i
$808$	−1779.52	+	1493.20i	−0.0774795	+	0.0650130i
$809$	−17173.0	+	29744.5i	−0.746316	+	1.29266i	0.203262	+	0.979124i	$0.434846\pi$
$809$	−17173.0	+	29744.5i	−0.746316	+	1.29266i	−0.949577	+	0.313532i	$0.898488\pi$
$810$	1564.62	+	2710.00i	0.0678704	+	0.117555i
$811$	2435.30	+	886.378i	0.105444	+	0.0383785i	0.394203	−	0.919023i	$-0.371021\pi$
$811$	2435.30	+	886.378i	0.105444	+	0.0383785i	−0.288759	+	0.957402i	$0.593243\pi$
$812$	154.369	−	875.471i	0.00667155	−	0.0378362i
$813$	−5616.49	−	31852.7i	−0.242287	−	1.37408i
$814$	−2868.52	+	1044.06i	−0.123515	+	0.0449560i
$815$	840.376	+	705.159i	0.0361191	+	0.0303076i
$816$	5963.82			0.255852
$817$	6071.00	−	2175.85i	0.259972	−	0.0931742i
$818$	−12887.8			−0.550870
$819$	−77.3322	−	64.8894i	−0.00329940	−	0.00276852i
$820$	572.668	−	208.434i	0.0243883	−	0.00887662i
$821$	6455.89	+	36613.2i	0.274436	+	1.55640i	0.740747	+	0.671784i	$0.234472\pi$
$821$	6455.89	+	36613.2i	0.274436	+	1.55640i	−0.466311	+	0.884621i	$0.654417\pi$
$822$	3280.87	−	18606.7i	0.139213	−	0.789519i
$823$	−4882.89	−	1777.23i	−0.206813	−	0.0752736i	0.236537	−	0.971623i	$-0.423988\pi$
$823$	−4882.89	−	1777.23i	−0.206813	−	0.0752736i	−0.443349	+	0.896349i	$0.646210\pi$
$824$	−2424.71	−	4199.71i	−0.102510	−	0.177553i
$825$	−1131.84	+	1960.41i	−0.0477644	+	0.0827304i
$826$	−2890.11	+	2425.09i	−0.121743	+	0.102155i
$827$	23528.0	−	19742.3i	0.989297	−	0.830119i	0.00383107	−	0.999993i	$-0.498781\pi$
$827$	23528.0	−	19742.3i	0.989297	−	0.830119i	0.985466	+	0.169874i	$0.0543361\pi$
$828$	151.841	−	262.996i	0.00637298	−	0.0110383i
$829$	−848.908	−	1470.35i	−0.0355655	−	0.0616012i	0.847695	−	0.530484i	$-0.177990\pi$
$829$	−848.908	−	1470.35i	−0.0355655	−	0.0616012i	−0.883260	+	0.468883i	$0.844657\pi$
$830$	586.249	+	213.377i	0.0245169	+	0.00892341i
$831$	2054.70	−	11652.8i	0.0857723	−	0.486439i
$832$	182.179	+	1033.19i	0.00759125	+	0.0430521i
$833$	−23539.8	+	8567.80i	−0.979120	+	0.356370i
$834$	1439.35	+	1207.76i	0.0597610	+	0.0501454i
$835$	−8438.13			−0.349717
$836$	212.594	+	1241.42i	0.00879511	+	0.0513580i
$837$	−33390.6			−1.37891
$838$	4129.44	+	3465.02i	0.170226	+	0.142836i
$839$	−2880.07	+	1048.26i	−0.118511	+	0.0431346i	−0.400595	−	0.916255i	$-0.631197\pi$
$839$	−2880.07	+	1048.26i	−0.118511	+	0.0431346i	0.282084	+	0.959390i	$0.408974\pi$
$840$	−46.2521	−	262.309i	−0.00189982	−	0.0107744i
$841$	−3174.07	+	18001.1i	−0.130144	+	0.738081i
$842$	−30797.2	−	11209.3i	−1.26050	−	0.458784i
$843$	−11604.0	−	20098.7i	−0.474095	−	0.821157i
$844$	−4133.77	+	7159.90i	−0.168590	+	0.292007i
$845$	−3471.13	+	2912.63i	−0.141314	+	0.118577i
$846$	1544.55	−	1296.03i	0.0627690	−	0.0526695i
$847$	1871.57	−	3241.66i	0.0759245	−	0.131505i
$848$	567.600	+	983.112i	0.0229852	+	0.0398116i
$849$	−14302.2	−	5205.59i	−0.578153	−	0.210430i
$850$	3103.63	−	17601.5i	0.125239	−	0.710268i
$851$	2443.48	+	13857.7i	0.0984272	+	0.558208i
$852$	−11823.7	+	4303.49i	−0.475440	+	0.173046i
$853$	−21666.7	−	18180.6i	−0.869701	−	0.729766i	0.0943339	−	0.995541i	$-0.469928\pi$
$853$	−21666.7	−	18180.6i	−0.869701	−	0.729766i	−0.964035	+	0.265775i	$0.914372\pi$
$854$	−898.130			−0.0359876
$855$	212.564	−	364.017i	0.00850238	−	0.0145604i
$856$	5829.87			0.232781
$857$	−22313.8	−	18723.5i	−0.889412	−	0.746305i	0.0786805	−	0.996900i	$-0.474929\pi$
$857$	−22313.8	−	18723.5i	−0.889412	−	0.746305i	−0.968092	+	0.250595i	$0.919374\pi$
$858$	583.702	−	212.450i	0.0232253	−	0.00845330i
$859$	−3170.89	−	17983.0i	−0.125948	−	0.714286i	−0.980740	−	0.195316i	$-0.937427\pi$
$859$	−3170.89	−	17983.0i	−0.125948	−	0.714286i	0.854793	−	0.518970i	$-0.173684\pi$
$860$	−127.101	+	720.824i	−0.00503965	+	0.0285813i
$861$	−863.218	−	314.186i	−0.0341677	−	0.0124360i
$862$	175.095	+	303.273i	0.00691849	+	0.0119832i
$863$	9315.94	−	16135.7i	0.367460	−	0.636460i	−0.621708	−	0.783250i	$-0.713561\pi$
$863$	9315.94	−	16135.7i	0.367460	−	0.636460i	0.989168	+	0.146790i	$0.0468941\pi$
$864$	3562.90	−	2989.63i	0.140292	−	0.117719i
$865$	519.505	−	435.916i	0.0204205	−	0.0171348i
$866$	−12222.1	+	21169.3i	−0.479589	+	0.830673i
$867$	1698.11	+	2941.21i	0.0665176	+	0.115212i
$868$	2455.11	+	893.586i	0.0960043	+	0.0349427i
$869$	−544.238	+	3086.53i	−0.0212451	+	0.120487i
$870$	−317.907	−	1802.94i	−0.0123886	−	0.0702590i
$871$	−1381.01	+	502.646i	−0.0537241	+	0.0195540i
$872$	−9192.78	−	7713.66i	−0.357003	−	0.299561i
$873$	2860.24			0.110887
$874$	5805.72	+	28.6067i	0.224693	+	0.00110713i
$875$	−1633.38			−0.0631067
$876$	11589.4	+	9724.70i	0.446999	+	0.375077i
$877$	−46901.7	+	17070.8i	−1.80588	+	0.657288i	−0.808226	+	0.588872i	$0.799572\pi$
$877$	−46901.7	+	17070.8i	−1.80588	+	0.657288i	−0.997657	+	0.0684157i	$0.978206\pi$
$878$	1125.68	+	6384.06i	0.0432687	+	0.245389i
$879$	8356.57	−	47392.5i	0.320660	−	1.81855i
$880$	−134.325	−	48.8903i	−0.00514556	−	0.00187283i
$881$	−14388.9	−	24922.3i	−0.550254	−	0.953068i	−0.998256	−	0.0590356i	$-0.981197\pi$
$881$	−14388.9	−	24922.3i	−0.550254	−	0.953068i	0.448002	−	0.894033i	$-0.352136\pi$
$882$	−725.426	+	1256.48i	−0.0276943	+	0.0479679i
$883$	−16240.2	+	13627.1i	−0.618942	+	0.519354i	−0.897471	−	0.441074i	$-0.854598\pi$
$883$	−16240.2	+	13627.1i	−0.618942	+	0.519354i	0.278529	+	0.960428i	$0.410153\pi$
$884$	−3757.02	+	3152.51i	−0.142944	+	0.119944i
$885$	−3884.81	+	6728.69i	−0.147555	+	0.255573i
$886$	8349.56	+	14461.9i	0.316602	+	0.548370i
$887$	15106.1	+	5498.19i	0.571832	+	0.208130i	0.611720	−	0.791074i	$-0.290478\pi$
$887$	15106.1	+	5498.19i	0.571832	+	0.208130i	−0.0398881	+	0.999204i	$0.512700\pi$
$888$	−2779.21	+	15761.7i	−0.105027	+	0.595640i
$889$	1166.61	+	6616.17i	0.0440122	+	0.249605i
$890$	−6232.41	+	2268.41i	−0.234731	+	0.0854351i
$891$	−1939.18	−	1627.17i	−0.0729126	−	0.0611809i
$892$	4617.49			0.173324
$893$	36156.9	+	13362.2i	1.35492	+	0.500725i
$894$	24703.1			0.924154
$895$	7156.81	+	6005.28i	0.267291	+	0.224284i
$896$	−341.977	+	124.469i	−0.0127507	+	0.00464088i
$897$	−497.214	−	2819.84i	−0.0185078	−	0.104963i
$898$	−3946.85	+	22383.7i	−0.146668	+	0.831796i
$899$	16874.8	+	6141.92i	0.626036	+	0.227858i
$900$	−517.577	−	896.470i	−0.0191695	−	0.0332026i
$901$	−2653.40	+	4595.83i	−0.0981107	+	0.169933i
$902$	−377.657	+	316.892i	−0.0139408	+	0.0116977i
$903$	845.181	−	709.191i	0.0311471	−	0.0261355i
$904$	4195.06	−	7266.07i	0.154343	−	0.267329i
$905$	−812.174	−	1406.73i	−0.0298316	−	0.0516698i
$906$	8297.78	+	3020.15i	0.304277	+	0.110748i
$907$	6278.41	−	35606.7i	0.229847	−	1.30353i	−0.623352	−	0.781942i	$-0.714229\pi$
$907$	6278.41	−	35606.7i	0.229847	−	1.30353i	0.853199	−	0.521586i	$-0.174659\pi$
$908$	576.036	+	3266.86i	0.0210533	+	0.119399i
$909$	−591.021	+	215.114i	−0.0215654	+	0.00784915i
$910$	167.795	+	140.797i	0.00611249	+	0.00512898i
$911$	38879.0			1.41396			0.706981	−	0.707232i	$-0.250057\pi$
$911$	38879.0			1.41396			0.706981	+	0.707232i	$0.250057\pi$
$912$	6194.05	+	2289.08i	0.224896	+	0.0831128i
$913$	−504.689			−0.0182944
$914$	18715.5	+	15704.2i	0.677302	+	0.568323i
$915$	−1738.06	+	632.601i	−0.0627961	+	0.0228559i
$916$	3495.44	+	19823.6i	0.126084	+	0.715056i
$917$	876.745	−	4972.27i	0.0315733	−	0.179061i
$918$	20431.3	+	7436.40i	0.734570	+	0.267361i
$919$	20660.1	+	35784.4i	0.741584	+	1.28446i	0.951774	+	0.306800i	$0.0992582\pi$
$919$	20660.1	+	35784.4i	0.741584	+	1.28446i	−0.210191	+	0.977660i	$0.567408\pi$
$920$	−329.464	+	570.648i	−0.0118066	+	0.0204497i
$921$	4850.72	−	4070.24i	0.173547	−	0.145623i
$922$	12835.1	−	10769.9i	0.458461	−	0.384694i
$923$	5173.73	−	8961.17i	0.184502	−	0.319567i
$924$	107.735	+	186.603i	0.00383575	+	0.00664372i
$925$	45072.5	+	16405.1i	1.60214	+	0.583130i
$926$	2164.28	−	12274.3i	0.0768064	−	0.435591i
$927$	−227.995	−	1293.03i	−0.00807805	−	0.0458129i
$928$	−2350.53	+	855.522i	−0.0831463	+	0.0302628i
$929$	−19335.8	−	16224.6i	−0.682870	−	0.572996i	0.233973	−	0.972243i	$-0.424827\pi$
$929$	−19335.8	−	16224.6i	−0.682870	−	0.572996i	−0.916843	+	0.399247i	$0.869272\pi$
$930$	5380.51			0.189714
$931$	−27737.1	−	136.670i	−0.976421	−	0.00481114i
$932$	4995.53			0.175573
$933$	19802.7	+	16616.5i	0.694868	+	0.583064i
$934$	−23374.0	+	8507.43i	−0.818864	+	0.298042i
$935$	−116.038	−	658.087i	−0.00405868	−	0.0230179i
$936$	−49.3248	+	279.735i	−0.00172247	+	0.00976861i
$937$	−42341.8	−	15411.2i	−1.47625	−	0.537312i	−0.526461	−	0.850199i	$-0.676481\pi$
$937$	−42341.8	−	15411.2i	−1.47625	−	0.537312i	−0.949790	+	0.312888i	$0.898704\pi$
$938$	−254.896	−	441.493i	−0.00887276	−	0.0153681i
$939$	19363.7	−	33539.0i	0.672963	−	1.16561i
$940$	−3351.36	+	2812.12i	−0.116286	+	0.0975759i
$941$	14030.0	−	11772.5i	0.486040	−	0.407836i	−0.366565	−	0.930393i	$-0.619466\pi$
$941$	14030.0	−	11772.5i	0.486040	−	0.407836i	0.852605	+	0.522557i	$0.175022\pi$
$942$	−6126.65	+	10611.7i	−0.211908	+	0.367035i
$943$	1136.27	+	1968.08i	0.0392386	+	0.0679633i
$944$	9975.51	+	3630.79i	0.343936	+	0.125182i
$945$	168.624	−	956.311i	0.00580457	−	0.0329194i
$946$	−102.820	−	583.118i	−0.00353377	−	0.0200410i
$947$	−1092.33	+	397.577i	−0.0374827	+	0.0136426i	−0.360693	−	0.932684i	$-0.617460\pi$
$947$	−1092.33	+	397.577i	−0.0374827	+	0.0136426i	0.323211	+	0.946327i	$0.395238\pi$
$948$	12587.9	+	10562.5i	0.431261	+	0.361871i
$949$	−12441.5			−0.425573
$950$	9979.39	−	17089.8i	0.340815	−	0.583648i
$951$	32528.7			1.10917
$952$	−1303.24	−	1093.55i	−0.0443681	−	0.0372292i
$953$	18370.6	−	6686.37i	0.624432	−	0.227275i	−0.0103742	−	0.999946i	$-0.503302\pi$
$953$	18370.6	−	6686.37i	0.624432	−	0.227275i	0.634806	+	0.772672i	$0.281080\pi$
$954$	53.3715	+	302.685i	0.00181129	+	0.0102723i
$955$	912.054	−	5172.51i	0.0309040	−	0.175266i
$956$	−17772.8	−	6468.79i	−0.601271	−	0.218845i
$957$	740.503	+	1282.59i	0.0250126	+	0.0433231i
$958$	6328.21	−	10960.8i	0.213419	−	0.369652i
$959$	−4128.77	+	3464.45i	−0.139025	+	0.116656i
$960$	−574.122	+	481.745i	−0.0193018	+	0.0161961i
$961$	−11493.1	+	19906.7i	−0.385792	+	0.668212i
$962$	−6580.92	−	11398.5i	−0.220558	−	0.382018i
$963$	1483.24	+	539.855i	0.0496331	+	0.0180650i
$964$	280.754	−	1592.23i	0.00938016	−	0.0531975i
$965$	1632.60	+	9258.95i	0.0544615	+	0.308866i
$966$	933.343	−	339.709i	0.0310868	−	0.0113147i
$967$	−42020.7	−	35259.5i	−1.39741	−	1.17256i	−0.962236	−	0.272216i	$-0.912243\pi$
$967$	−42020.7	−	35259.5i	−1.39741	−	1.17256i	−0.435171	−	0.900348i	$-0.643312\pi$
$968$	−10532.4			−0.349714
$969$	5210.64	+	30426.9i	0.172745	+	1.00872i
$970$	−6206.15			−0.205430
$971$	26692.9	+	22398.0i	0.882199	+	0.740253i	0.966630	−	0.256176i	$-0.0824628\pi$
$971$	26692.9	+	22398.0i	0.882199	+	0.740253i	−0.0844309	+	0.996429i	$0.526907\pi$
$972$	2278.77	−	829.403i	0.0751969	−	0.0273694i
$973$	−93.0745	−	527.852i	−0.00306663	−	0.0173917i
$974$	1249.77	−	7087.78i	0.0411141	−	0.233170i
$975$	−9171.61	−	3338.19i	−0.301258	−	0.109649i
$976$	1263.57	+	2188.56i	0.0414404	+	0.0717768i
$977$	−24853.2	+	43047.0i	−0.813842	+	1.40962i	0.0963149	+	0.995351i	$0.469294\pi$
$977$	−24853.2	+	43047.0i	−0.813842	+	1.40962i	−0.910157	+	0.414264i	$0.864039\pi$
$978$	−3564.35	+	2990.85i	−0.116539	+	0.0977880i
$979$	4110.09	−	3448.77i	0.134177	−	0.112588i
$980$	1574.03	−	2726.30i	0.0513067	−	0.0888658i
$981$	−1624.54	−	2813.78i	−0.0528721	−	0.0915771i
$982$	8028.93	+	2922.29i	0.260910	+	0.0949634i
$983$	4783.53	−	27128.7i	0.155209	−	0.880237i	−0.803385	−	0.595460i	$-0.796970\pi$
$983$	4783.53	−	27128.7i	0.155209	−	0.880237i	0.958594	−	0.284776i	$-0.0919193\pi$
$984$	448.842	+	2545.51i	0.0145412	+	0.0824674i
$985$	4632.61	−	1686.13i	0.149855	−	0.0545428i
$986$	−8957.65	−	7516.36i	−0.289320	−	0.242769i
$987$	6594.54			0.212671
$988$	−5112.08	+	1832.17i	−0.164612	+	0.0589970i
$989$	−2729.43			−0.0877562
$990$	−29.6477	−	24.8774i	−0.000951785	−	0.000798642i
$991$	−45788.0	+	16665.5i	−1.46771	+	0.534204i	−0.947478	−	0.319820i	$-0.896377\pi$
$991$	−45788.0	+	16665.5i	−1.46771	+	0.534204i	−0.520234	+	0.854024i	$0.674155\pi$
$992$	−1276.57	−	7239.77i	−0.0408579	−	0.231717i
$993$	7341.20	−	41634.0i	0.234608	−	1.33053i
$994$	3372.89	+	1227.63i	0.107627	+	0.0391732i
$995$	2222.47	+	3849.43i	0.0708111	+	0.122648i
$996$	−1323.04	+	2291.57i	−0.0420905	+	0.0729029i
$997$	15567.5	−	13062.7i	0.494510	−	0.414943i	−0.361129	−	0.932516i	$-0.617609\pi$
$997$	15567.5	−	13062.7i	0.494510	−	0.414943i	0.855639	+	0.517572i	$0.173164\pi$
$998$	−3563.21	+	2989.89i	−0.113017	+	0.0948329i
$999$	−29174.8	+	50532.3i	−0.923975	+	1.60037i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.4.e.a.35.2	yes	12
19.5	even	9		722.4.a.p.1.3		6
19.6	even	9	inner	38.4.e.a.25.2	✓	12
19.14	odd	18		722.4.a.o.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.4.e.a.25.2	✓	12	19.6	even	9	inner
38.4.e.a.35.2	yes	12	1.1	even	1	trivial
722.4.a.o.1.4		6	19.14	odd	18
722.4.a.p.1.3		6	19.5	even	9

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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	38.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.53209 + 1.28558i) q^{2} +(4.68284 - 1.70441i) q^{3} +(0.694593 + 3.93923i) q^{4} +(0.408053 - 2.31419i) q^{5} +(9.36568 + 3.40883i) q^{6} +(-1.42158 - 2.46225i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(-1.65925 + 1.39227i) q^{9} +O(q^{10})\)	\(q+(1.53209 + 1.28558i) q^{2} +(4.68284 - 1.70441i) q^{3} +(0.694593 + 3.93923i) q^{4} +(0.408053 - 2.31419i) q^{5} +(9.36568 + 3.40883i) q^{6} +(-1.42158 - 2.46225i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(-1.65925 + 1.39227i) q^{9} +(3.60023 - 3.02095i) q^{10} +(-1.90096 + 3.29257i) q^{11} +(9.96675 + 17.2629i) q^{12} +(-15.4040 - 5.60661i) q^{13} +(0.987418 - 5.59993i) q^{14} +(-2.03348 - 11.5325i) q^{15} +(-15.0351 + 5.47232i) q^{16} +(-57.2974 - 48.0782i) q^{17} -4.33198 q^{18} +(-41.0556 - 71.9266i) q^{19} +9.39954 q^{20} +(-10.8537 - 9.10735i) q^{21} +(-7.14529 + 2.60067i) q^{22} +(6.08655 + 34.5185i) q^{23} +(-6.92283 + 39.2613i) q^{24} +(112.273 + 40.8639i) q^{25} +(-16.3926 - 28.3928i) q^{26} +(-72.6725 + 125.872i) q^{27} +(8.71194 - 7.31019i) q^{28} +(59.8802 - 50.2455i) q^{29} +(11.7104 - 20.2829i) q^{30} +(114.867 + 198.955i) q^{31} +(-30.0702 - 10.9446i) q^{32} +(-3.29001 + 18.6586i) q^{33} +(-25.9765 - 147.320i) q^{34} +(-6.27818 + 2.28507i) q^{35} +(-6.63699 - 5.56909i) q^{36} +401.456 q^{37} +(29.5662 - 162.978i) q^{38} -81.6905 q^{39} +(14.4009 + 12.0838i) q^{40} +(60.9251 - 22.1749i) q^{41} +(-4.92067 - 27.9065i) q^{42} +(-13.5220 + 76.6872i) q^{43} +(-14.2906 - 5.20135i) q^{44} +(2.54492 + 4.40793i) q^{45} +(-35.0510 + 60.7102i) q^{46} +(-356.545 + 299.176i) q^{47} +(-61.0798 + 51.2520i) q^{48} +(167.458 - 290.046i) q^{49} +(119.478 + 206.942i) q^{50} +(-350.260 - 127.484i) q^{51} +(11.3862 - 64.5743i) q^{52} +(-12.3203 - 69.8721i) q^{53} +(-273.159 + 99.4219i) q^{54} +(6.84392 + 5.74273i) q^{55} +22.7453 q^{56} +(-314.850 - 266.845i) q^{57} +156.336 q^{58} +(-508.257 - 426.478i) q^{59} +(44.0165 - 16.0207i) q^{60} +(-27.4270 - 155.546i) q^{61} +(-79.7855 + 452.486i) q^{62} +(5.78687 + 2.10625i) q^{63} +(-32.0000 - 55.4256i) q^{64} +(-19.2604 + 33.3600i) q^{65} +(-29.0276 + 24.3571i) q^{66} +(68.6778 - 57.6275i) q^{67} +(149.593 - 259.103i) q^{68} +(87.3362 + 151.271i) q^{69} +(-12.5564 - 4.57014i) q^{70} +(-109.611 + 621.638i) q^{71} +(-3.00897 - 17.0647i) q^{72} +(713.200 - 259.583i) q^{73} +(615.066 + 516.102i) q^{74} +595.404 q^{75} +(254.819 - 211.687i) q^{76} +10.8095 q^{77} +(-125.157 - 105.019i) q^{78} +(774.641 - 281.946i) q^{79} +(6.52885 + 37.0270i) q^{80} +(-115.620 + 655.711i) q^{81} +(121.850 + 44.3498i) q^{82} +(66.3727 + 114.961i) q^{83} +(28.3370 - 49.0812i) q^{84} +(-134.642 + 112.978i) q^{85} +(-119.304 + 100.108i) q^{86} +(194.770 - 337.352i) q^{87} +(-15.2077 - 26.3405i) q^{88} +(-1326.11 - 482.664i) q^{89} +(-1.76768 + 10.0250i) q^{90} +(8.09319 + 45.8987i) q^{91} +(-131.749 + 47.9527i) q^{92} +(877.003 + 735.892i) q^{93} -930.872 q^{94} +(-183.204 + 65.6605i) q^{95} -159.468 q^{96} +(-1011.58 - 848.815i) q^{97} +(629.437 - 229.096i) q^{98} +(-1.42998 - 8.10984i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 9 q^{3} - 18 q^{6} + 21 q^{7} - 48 q^{8} - 27 q^{9}+O(q^{10}) \) 12 * q - 9 * q^3 - 18 * q^6 + 21 * q^7 - 48 * q^8 - 27 * q^9	\( 12 q - 9 q^{3} - 18 q^{6} + 21 q^{7} - 48 q^{8} - 27 q^{9} - 9 q^{11} + 36 q^{12} + 39 q^{13} - 138 q^{14} + 423 q^{15} + 69 q^{17} + 132 q^{18} - 462 q^{19} - 216 q^{20} - 279 q^{21} + 204 q^{22} - 66 q^{23} - 72 q^{24} + 342 q^{25} + 48 q^{26} + 189 q^{27} + 192 q^{28} + 159 q^{29} + 72 q^{31} - 1560 q^{33} + 408 q^{34} - 135 q^{35} - 108 q^{36} + 1116 q^{37} - 294 q^{38} - 1248 q^{39} + 147 q^{41} + 414 q^{42} - 117 q^{43} + 408 q^{44} + 1296 q^{45} + 528 q^{46} + 783 q^{47} + 288 q^{48} + 1413 q^{49} - 354 q^{50} - 2301 q^{51} - 348 q^{52} - 249 q^{53} - 540 q^{54} + 2187 q^{55} - 336 q^{56} - 2670 q^{57} - 1932 q^{58} - 4248 q^{59} + 324 q^{60} + 3114 q^{61} - 438 q^{62} + 363 q^{63} - 384 q^{64} + 495 q^{65} + 822 q^{66} + 3060 q^{67} + 408 q^{68} - 237 q^{69} - 270 q^{70} + 1686 q^{71} + 432 q^{72} + 1626 q^{73} + 90 q^{74} - 1854 q^{75} - 1416 q^{77} - 108 q^{78} - 327 q^{79} + 3483 q^{81} + 294 q^{82} + 927 q^{83} + 204 q^{84} - 3294 q^{85} + 1188 q^{86} + 2892 q^{87} - 72 q^{88} - 6366 q^{89} - 5076 q^{90} + 840 q^{91} - 156 q^{92} + 870 q^{93} + 3432 q^{94} + 513 q^{95} - 576 q^{96} - 8052 q^{97} + 378 q^{98} + 4494 q^{99}+O(q^{100}) \) 12 * q - 9 * q^3 - 18 * q^6 + 21 * q^7 - 48 * q^8 - 27 * q^9 - 9 * q^11 + 36 * q^12 + 39 * q^13 - 138 * q^14 + 423 * q^15 + 69 * q^17 + 132 * q^18 - 462 * q^19 - 216 * q^20 - 279 * q^21 + 204 * q^22 - 66 * q^23 - 72 * q^24 + 342 * q^25 + 48 * q^26 + 189 * q^27 + 192 * q^28 + 159 * q^29 + 72 * q^31 - 1560 * q^33 + 408 * q^34 - 135 * q^35 - 108 * q^36 + 1116 * q^37 - 294 * q^38 - 1248 * q^39 + 147 * q^41 + 414 * q^42 - 117 * q^43 + 408 * q^44 + 1296 * q^45 + 528 * q^46 + 783 * q^47 + 288 * q^48 + 1413 * q^49 - 354 * q^50 - 2301 * q^51 - 348 * q^52 - 249 * q^53 - 540 * q^54 + 2187 * q^55 - 336 * q^56 - 2670 * q^57 - 1932 * q^58 - 4248 * q^59 + 324 * q^60 + 3114 * q^61 - 438 * q^62 + 363 * q^63 - 384 * q^64 + 495 * q^65 + 822 * q^66 + 3060 * q^67 + 408 * q^68 - 237 * q^69 - 270 * q^70 + 1686 * q^71 + 432 * q^72 + 1626 * q^73 + 90 * q^74 - 1854 * q^75 - 1416 * q^77 - 108 * q^78 - 327 * q^79 + 3483 * q^81 + 294 * q^82 + 927 * q^83 + 204 * q^84 - 3294 * q^85 + 1188 * q^86 + 2892 * q^87 - 72 * q^88 - 6366 * q^89 - 5076 * q^90 + 840 * q^91 - 156 * q^92 + 870 * q^93 + 3432 * q^94 + 513 * q^95 - 576 * q^96 - 8052 * q^97 + 378 * q^98 + 4494 * q^99

Introduction

L-functions

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