LMFDB - Embedded newform 75.3.k.a.67.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,3,Mod(13,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 19]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("75.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	75.k (of order $20$, degree $8$, 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:	$2.04360198270$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			67.8
Character	$\chi$	$=$	75.67
Dual form			75.3.k.a.28.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.03753 - 2.03626i) q^{2} +(0.270952 - 1.71073i) q^{3} +(-0.718759 - 0.989286i) q^{4} +(-3.06942 - 3.94698i) q^{5} +(-3.20237 - 2.32666i) q^{6} +(0.410561 + 0.410561i) q^{7} +(6.26868 - 0.992861i) q^{8} +(-2.85317 - 0.927051i) q^{9} +O(q^{10})$	\(q+(1.03753 - 2.03626i) q^{2} +(0.270952 - 1.71073i) q^{3} +(-0.718759 - 0.989286i) q^{4} +(-3.06942 - 3.94698i) q^{5} +(-3.20237 - 2.32666i) q^{6} +(0.410561 + 0.410561i) q^{7} +(6.26868 - 0.992861i) q^{8} +(-2.85317 - 0.927051i) q^{9} +(-11.2217 + 2.15504i) q^{10} +(0.00192198 + 0.00591526i) q^{11} +(-1.88715 + 0.961550i) q^{12} +(9.19450 + 18.0452i) q^{13} +(1.26198 - 0.410042i) q^{14} +(-7.58387 + 4.18149i) q^{15} +(5.99369 - 18.4467i) q^{16} +(-1.16847 - 7.37741i) q^{17} +(-4.84796 + 4.84796i) q^{18} +(-3.79052 + 5.21721i) q^{19} +(-1.69852 + 5.87346i) q^{20} +(0.813601 - 0.591115i) q^{21} +(0.0140391 + 0.00222358i) q^{22} +(35.1301 + 17.8997i) q^{23} -10.9930i q^{24} +(-6.15733 + 24.2299i) q^{25} +46.2843 q^{26} +(-2.35900 + 4.62981i) q^{27} +(0.111068 - 0.701257i) q^{28} +(-5.20713 - 7.16700i) q^{29} +(0.646138 + 19.7812i) q^{30} +(-22.1165 - 16.0686i) q^{31} +(-13.3922 - 13.3922i) q^{32} +(0.0106402 - 0.00168524i) q^{33} +(-16.2346 - 5.27496i) q^{34} +(0.360293 - 2.88066i) q^{35} +(1.13362 + 3.48893i) q^{36} +(2.08045 - 1.06004i) q^{37} +(6.69083 + 13.1315i) q^{38} +(33.3617 - 10.8399i) q^{39} +(-23.1600 - 21.6948i) q^{40} +(-14.5675 + 44.8341i) q^{41} +(-0.359533 - 2.27000i) q^{42} +(-39.9674 + 39.9674i) q^{43} +(0.00447044 - 0.00615304i) q^{44} +(5.09852 + 14.1069i) q^{45} +(72.8969 - 52.9627i) q^{46} +(-91.4202 - 14.4795i) q^{47} +(-29.9332 - 15.2517i) q^{48} -48.6629i q^{49} +(42.9500 + 37.6771i) q^{50} -12.9373 q^{51} +(11.2433 - 22.0661i) q^{52} +(12.8641 - 81.2210i) q^{53} +(6.97997 + 9.60710i) q^{54} +(0.0174481 - 0.0257425i) q^{55} +(2.98131 + 2.16605i) q^{56} +(7.89816 + 7.89816i) q^{57} +(-19.9964 + 3.16712i) q^{58} +(-48.4185 - 15.7321i) q^{59} +(9.58767 + 4.49714i) q^{60} +(8.83561 + 27.1932i) q^{61} +(-55.6663 + 28.3634i) q^{62} +(-0.790790 - 1.55201i) q^{63} +(32.6221 - 10.5996i) q^{64} +(43.0024 - 91.6789i) q^{65} +(0.00760787 - 0.0234146i) q^{66} +(4.58023 + 28.9184i) q^{67} +(-6.45852 + 6.45852i) q^{68} +(40.1401 - 55.2481i) q^{69} +(-5.49197 - 3.72242i) q^{70} +(-38.0412 + 27.6386i) q^{71} +(-18.8060 - 2.97858i) q^{72} +(94.5348 + 48.1679i) q^{73} -5.33616i q^{74} +(39.7824 + 17.0987i) q^{75} +7.88578 q^{76} +(-0.00163948 + 0.00321767i) q^{77} +(12.5409 - 79.1798i) q^{78} +(2.24525 + 3.09032i) q^{79} +(-91.2059 + 32.9636i) q^{80} +(7.28115 + 5.29007i) q^{81} +(76.1798 + 76.1798i) q^{82} +(-26.0100 + 4.11959i) q^{83} +(-1.16956 - 0.380015i) q^{84} +(-25.5320 + 27.2563i) q^{85} +(39.9169 + 122.851i) q^{86} +(-13.6717 + 6.96606i) q^{87} +(0.0179213 + 0.0351726i) q^{88} +(26.2598 - 8.53234i) q^{89} +(34.0152 + 4.25439i) q^{90} +(-3.63376 + 11.1836i) q^{91} +(-7.54216 - 47.6193i) q^{92} +(-33.4815 + 33.4815i) q^{93} +(-124.335 + 171.133i) q^{94} +(32.2269 - 1.05267i) q^{95} +(-26.5390 + 19.2817i) q^{96} +(185.544 + 29.3872i) q^{97} +(-99.0904 - 50.4891i) q^{98} -0.0186590i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8}+O(q^{10}) $ 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8	$ 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8} - 4 q^{10} - 24 q^{12} + 32 q^{13} - 24 q^{15} + 80 q^{16} - 100 q^{17} - 48 q^{18} - 100 q^{19} - 244 q^{20} - 100 q^{22} - 96 q^{23} - 16 q^{25} - 40 q^{26} + 196 q^{28} + 200 q^{29} + 264 q^{30} + 636 q^{32} + 216 q^{33} + 100 q^{34} + 260 q^{35} - 120 q^{36} - 184 q^{37} - 564 q^{38} - 948 q^{40} + 160 q^{41} - 12 q^{42} - 472 q^{43} - 700 q^{44} - 36 q^{45} - 288 q^{47} - 48 q^{48} + 16 q^{50} + 620 q^{52} + 304 q^{53} + 604 q^{55} + 72 q^{57} + 1272 q^{58} + 800 q^{59} + 84 q^{60} - 240 q^{61} + 1212 q^{62} - 12 q^{63} + 100 q^{64} + 272 q^{65} - 80 q^{67} + 104 q^{68} - 260 q^{70} + 36 q^{72} - 116 q^{73} - 24 q^{75} - 88 q^{77} - 120 q^{78} + 200 q^{79} - 164 q^{80} + 180 q^{81} - 168 q^{82} - 1264 q^{83} - 1200 q^{84} - 212 q^{85} - 876 q^{87} - 212 q^{88} - 1500 q^{89} - 444 q^{90} - 1504 q^{92} - 648 q^{93} - 200 q^{94} - 784 q^{95} + 60 q^{96} - 260 q^{97} - 92 q^{98}+O(q^{100}) $ 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8 - 4 * q^10 - 24 * q^12 + 32 * q^13 - 24 * q^15 + 80 * q^16 - 100 * q^17 - 48 * q^18 - 100 * q^19 - 244 * q^20 - 100 * q^22 - 96 * q^23 - 16 * q^25 - 40 * q^26 + 196 * q^28 + 200 * q^29 + 264 * q^30 + 636 * q^32 + 216 * q^33 + 100 * q^34 + 260 * q^35 - 120 * q^36 - 184 * q^37 - 564 * q^38 - 948 * q^40 + 160 * q^41 - 12 * q^42 - 472 * q^43 - 700 * q^44 - 36 * q^45 - 288 * q^47 - 48 * q^48 + 16 * q^50 + 620 * q^52 + 304 * q^53 + 604 * q^55 + 72 * q^57 + 1272 * q^58 + 800 * q^59 + 84 * q^60 - 240 * q^61 + 1212 * q^62 - 12 * q^63 + 100 * q^64 + 272 * q^65 - 80 * q^67 + 104 * q^68 - 260 * q^70 + 36 * q^72 - 116 * q^73 - 24 * q^75 - 88 * q^77 - 120 * q^78 + 200 * q^79 - 164 * q^80 + 180 * q^81 - 168 * q^82 - 1264 * q^83 - 1200 * q^84 - 212 * q^85 - 876 * q^87 - 212 * q^88 - 1500 * q^89 - 444 * q^90 - 1504 * q^92 - 648 * q^93 - 200 * q^94 - 784 * q^95 + 60 * q^96 - 260 * q^97 - 92 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{13}{20}\right)$

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 $

$2$	1.03753	−	2.03626i	0.518764	−	1.01813i	−0.471881	−	0.881662i	$-0.656425\pi$
$2$	1.03753	−	2.03626i	0.518764	−	1.01813i	0.990644	−	0.136469i	$-0.0435753\pi$
$3$	0.270952	−	1.71073i	0.0903175	−	0.570242i
$3$	0.270952	−	1.71073i	0.0903175	−	0.570242i
$4$	−0.718759	−	0.989286i	−0.179690	−	0.247322i
$5$	−3.06942	−	3.94698i	−0.613884	−	0.789396i
$5$	−3.06942	−	3.94698i	−0.613884	−	0.789396i
$6$	−3.20237	−	2.32666i	−0.533728	−	0.387776i
$7$	0.410561	+	0.410561i	0.0586516	+	0.0586516i	0.735824	−	0.677173i	$-0.236795\pi$
$7$	0.410561	+	0.410561i	0.0586516	+	0.0586516i	−0.677173	+	0.735824i	$0.736795\pi$
$8$	6.26868	−	0.992861i	0.783585	−	0.124108i
$9$	−2.85317	−	0.927051i	−0.317019	−	0.103006i
$10$	−11.2217	+	2.15504i	−1.12217	+	0.215504i
$11$	0.00192198	+	0.00591526i	0.000174726	+	0.000537751i	0.951144	−	0.308748i	$-0.0999100\pi$
$11$	0.00192198	+	0.00591526i	0.000174726	+	0.000537751i	−0.950969	+	0.309286i	$0.899910\pi$
$12$	−1.88715	+	0.961550i	−0.157262	+	0.0801291i
$13$	9.19450	+	18.0452i	0.707269	+	1.38809i	0.912376	+	0.409354i	$0.134246\pi$
$13$	9.19450	+	18.0452i	0.707269	+	1.38809i	−0.205106	+	0.978740i	$0.565754\pi$
$14$	1.26198	−	0.410042i	0.0901413	−	0.0292887i
$15$	−7.58387	+	4.18149i	−0.505592	+	0.278766i
$16$	5.99369	−	18.4467i	0.374606	−	1.15292i
$17$	−1.16847	−	7.37741i	−0.0687333	−	0.433965i	−0.997926	−	0.0643697i	$-0.979496\pi$
$17$	−1.16847	−	7.37741i	−0.0687333	−	0.433965i	0.929193	−	0.369595i	$-0.120504\pi$
$18$	−4.84796	+	4.84796i	−0.269331	+	0.269331i
$19$	−3.79052	+	5.21721i	−0.199501	+	0.274590i	−0.897033	−	0.441964i	$-0.854282\pi$
$19$	−3.79052	+	5.21721i	−0.199501	+	0.274590i	0.697531	+	0.716554i	$0.254282\pi$
$20$	−1.69852	+	5.87346i	−0.0849262	+	0.293673i
$21$	0.813601	−	0.591115i	0.0387429	−	0.0281484i
$22$	0.0140391	+	0.00222358i	0.000638142	+	0.000101072i
$23$	35.1301	+	17.8997i	1.52740	+	0.778248i	0.997557	−	0.0698502i	$-0.0222521\pi$
$23$	35.1301	+	17.8997i	1.52740	+	0.778248i	0.529840	+	0.848098i	$0.322252\pi$
$24$		−	10.9930i		−	0.458042i
$25$	−6.15733	+	24.2299i	−0.246293	+	0.969195i
$26$	46.2843			1.78017
$27$	−2.35900	+	4.62981i	−0.0873705	+	0.171474i
$28$	0.111068	−	0.701257i	0.00396672	−	0.0250449i
$29$	−5.20713	−	7.16700i	−0.179556	−	0.247138i	0.709746	−	0.704457i	$-0.248810\pi$
$29$	−5.20713	−	7.16700i	−0.179556	−	0.247138i	−0.889302	+	0.457320i	$0.848810\pi$
$30$	0.646138	+	19.7812i	0.0215379	+	0.659372i
$31$	−22.1165	−	16.0686i	−0.713436	−	0.518341i	0.170844	−	0.985298i	$-0.445350\pi$
$31$	−22.1165	−	16.0686i	−0.713436	−	0.518341i	−0.884280	+	0.466957i	$0.845350\pi$
$32$	−13.3922	−	13.3922i	−0.418505	−	0.418505i
$33$	0.0106402	−	0.00168524i	0.000322429	−	5.10677e-5i
$34$	−16.2346	−	5.27496i	−0.477490	−	0.155146i
$35$	0.360293	−	2.88066i	0.0102941	−	0.0823046i
$36$	1.13362	+	3.48893i	0.0314895	+	0.0969146i
$37$	2.08045	−	1.06004i	0.0562284	−	0.0286498i	−0.425650	−	0.904888i	$-0.639955\pi$
$37$	2.08045	−	1.06004i	0.0562284	−	0.0286498i	0.481879	+	0.876238i	$0.339955\pi$
$38$	6.69083	+	13.1315i	0.176074	+	0.345565i
$39$	33.3617	−	10.8399i	0.855428	−	0.277946i
$40$	−23.1600	−	21.6948i	−0.579000	−	0.542371i
$41$	−14.5675	+	44.8341i	−0.355304	+	1.09351i	0.600529	+	0.799603i	$0.294957\pi$
$41$	−14.5675	+	44.8341i	−0.355304	+	1.09351i	−0.955833	+	0.293911i	$0.905043\pi$
$42$	−0.359533	−	2.27000i	−0.00856031	−	0.0540477i
$43$	−39.9674	+	39.9674i	−0.929475	+	0.929475i	−0.997672	−	0.0681965i	$-0.978276\pi$
$43$	−39.9674	+	39.9674i	−0.929475	+	0.929475i	0.0681965	+	0.997672i	$0.478276\pi$
$44$	0.00447044	−	0.00615304i	0.000101601	−	0.000139842i
$45$	5.09852	+	14.1069i	0.113300	+	0.313487i
$46$	72.8969	−	52.9627i	1.58472	−	1.15136i
$47$	−91.4202	−	14.4795i	−1.94511	−	0.308075i	−0.945276	−	0.326272i	$-0.894208\pi$
$47$	−91.4202	−	14.4795i	−1.94511	−	0.308075i	−0.999834	+	0.0181965i	$0.994208\pi$
$48$	−29.9332	−	15.2517i	−0.623609	−	0.317745i
$49$		−	48.6629i		−	0.993120i
$50$	42.9500	+	37.6771i	0.859000	+	0.753542i
$51$	−12.9373			−0.253673
$52$	11.2433	−	22.0661i	0.216217	−	0.424349i
$53$	12.8641	−	81.2210i	0.242720	−	1.53247i	−0.501867	−	0.864945i	$-0.667353\pi$
$53$	12.8641	−	81.2210i	0.242720	−	1.53247i	0.744586	−	0.667526i	$-0.232647\pi$
$54$	6.97997	+	9.60710i	0.129259	+	0.177909i
$55$	0.0174481	−	0.0257425i	0.000317237	−	0.000468045i
$56$	2.98131	+	2.16605i	0.0532376	+	0.0386794i
$57$	7.89816	+	7.89816i	0.138564	+	0.138564i
$58$	−19.9964	+	3.16712i	−0.344766	+	0.0546056i
$59$	−48.4185	−	15.7321i	−0.820652	−	0.266646i	−0.131549	−	0.991310i	$-0.541995\pi$
$59$	−48.4185	−	15.7321i	−0.820652	−	0.266646i	−0.689103	+	0.724664i	$0.741995\pi$
$60$	9.58767	+	4.49714i	0.159794	+	0.0749523i
$61$	8.83561	+	27.1932i	0.144846	+	0.445790i	0.996991	−	0.0775153i	$-0.0246987\pi$
$61$	8.83561	+	27.1932i	0.144846	+	0.445790i	−0.852145	+	0.523305i	$0.824699\pi$
$62$	−55.6663	+	28.3634i	−0.897844	+	0.457474i
$63$	−0.790790	−	1.55201i	−0.0125522	−	0.0246351i
$64$	32.6221	−	10.5996i	0.509720	−	0.165618i
$65$	43.0024	−	91.6789i	0.661575	−	1.41044i
$66$	0.00760787	−	0.0234146i	0.000115271	−	0.000354767i
$67$	4.58023	+	28.9184i	0.0683617	+	0.431619i	0.998004	+	0.0631547i	$0.0201162\pi$
$67$	4.58023	+	28.9184i	0.0683617	+	0.431619i	−0.929642	+	0.368464i	$0.879884\pi$
$68$	−6.45852	+	6.45852i	−0.0949783	+	0.0949783i
$69$	40.1401	−	55.2481i	0.581740	−	0.800697i
$70$	−5.49197	−	3.72242i	−0.0784567	−	0.0531774i
$71$	−38.0412	+	27.6386i	−0.535792	+	0.389276i	−0.822520	−	0.568737i	$-0.807432\pi$
$71$	−38.0412	+	27.6386i	−0.535792	+	0.389276i	0.286728	+	0.958012i	$0.407432\pi$
$72$	−18.8060	−	2.97858i	−0.261195	−	0.0413692i
$73$	94.5348	+	48.1679i	1.29500	+	0.659834i	0.959367	−	0.282160i	$-0.0910509\pi$
$73$	94.5348	+	48.1679i	1.29500	+	0.659834i	0.335630	+	0.941994i	$0.391051\pi$
$74$		−	5.33616i		−	0.0721103i
$75$	39.7824	+	17.0987i	0.530431	+	0.227982i
$76$	7.88578			0.103760
$77$	−0.00163948	+	0.00321767i	−2.12920e−5	+	4.17879e-5i
$78$	12.5409	−	79.1798i	0.160780	−	1.01513i
$79$	2.24525	+	3.09032i	0.0284209	+	0.0391180i	0.822991	−	0.568054i	$-0.192304\pi$
$79$	2.24525	+	3.09032i	0.0284209	+	0.0391180i	−0.794570	+	0.607172i	$0.792304\pi$
$80$	−91.2059	+	32.9636i	−1.14007	+	0.412045i
$81$	7.28115	+	5.29007i	0.0898908	+	0.0653095i
$82$	76.1798	+	76.1798i	0.929022	+	0.929022i
$83$	−26.0100	+	4.11959i	−0.313374	+	0.0496336i	−0.311140	−	0.950364i	$-0.600711\pi$
$83$	−26.0100	+	4.11959i	−0.313374	+	0.0496336i	−0.00223356	+	0.999998i	$0.500711\pi$
$84$	−1.16956	−	0.380015i	−0.0139234	−	0.00452398i
$85$	−25.5320	+	27.2563i	−0.300376	+	0.320662i
$86$	39.9169	+	122.851i	0.464150	+	1.42851i
$87$	−13.6717	+	6.96606i	−0.157146	+	0.0800696i
$88$	0.0179213	+	0.0351726i	0.000203652	+	0.000399689i
$89$	26.2598	−	8.53234i	0.295054	−	0.0958690i	−0.157749	−	0.987479i	$-0.550424\pi$
$89$	26.2598	−	8.53234i	0.295054	−	0.0958690i	0.452804	+	0.891610i	$0.350424\pi$
$90$	34.0152	+	4.25439i	0.377947	+	0.0472710i
$91$	−3.63376	+	11.1836i	−0.0399315	+	0.122896i
$92$	−7.54216	−	47.6193i	−0.0819800	−	0.517601i
$93$	−33.4815	+	33.4815i	−0.360016	+	0.360016i
$94$	−124.335	+	171.133i	−1.32271	+	1.82056i
$95$	32.2269	−	1.05267i	0.339231	−	0.0110807i
$96$	−26.5390	+	19.2817i	−0.276448	+	0.200851i
$97$	185.544	+	29.3872i	1.91282	+	0.302961i	0.995467	−	0.0951079i	$-0.0303196\pi$
$97$	185.544	+	29.3872i	1.91282	+	0.302961i	0.917355	+	0.398069i	$0.130320\pi$
$98$	−99.0904	−	50.4891i	−1.01113	−	0.515195i
$99$		−	0.0186590i		−	0.000188475i
$100$	28.3959	−	11.3241i	0.283959	−	0.113241i
$101$	−110.527			−1.09433			−0.547164	−	0.837025i	$-0.684293\pi$
$101$	−110.527			−1.09433			−0.547164	+	0.837025i	$0.684293\pi$
$102$	−13.4228	+	26.3438i	−0.131596	+	0.258272i
$103$	9.51649	−	60.0847i	0.0923931	−	0.583347i	−0.897443	−	0.441131i	$-0.854577\pi$
$103$	9.51649	−	60.0847i	0.0923931	−	0.583347i	0.989836	−	0.142216i	$-0.0454227\pi$
$104$	75.5537	+	103.991i	0.726478	+	0.999911i
$105$	−4.83040	−	1.39689i	−0.0460038	−	0.0133037i
$106$	−152.040	−	110.464i	−1.43434	−	1.04211i
$107$	34.1192	+	34.1192i	0.318871	+	0.318871i	0.848333	−	0.529462i	$-0.177606\pi$
$107$	34.1192	+	34.1192i	0.318871	+	0.318871i	−0.529462	+	0.848333i	$0.677606\pi$
$108$	6.27576	−	0.993982i	0.0581089	−	0.00920354i
$109$	−11.7936	−	3.83198i	−0.108198	−	0.0351558i	0.254417	−	0.967094i	$-0.418116\pi$
$109$	−11.7936	−	3.83198i	−0.108198	−	0.0351558i	−0.362616	+	0.931939i	$0.618116\pi$
$110$	−0.0343155	−	0.0622373i	−0.000311960	−	0.000565794i
$111$	−1.24974	−	3.84630i	−0.0112589	−	0.0346514i
$112$	10.0343	−	5.11272i	0.0895917	−	0.0456493i
$113$	40.2919	+	79.0773i	0.356565	+	0.699799i	0.997711	−	0.0676201i	$-0.0215406\pi$
$113$	40.2919	+	79.0773i	0.356565	+	0.699799i	−0.641146	+	0.767419i	$0.721541\pi$
$114$	24.2773	−	7.88817i	0.212959	−	0.0691944i
$115$	−37.1793	−	193.600i	−0.323298	−	1.68348i
$116$	−3.34754	+	10.3027i	−0.0288581	+	0.0888162i
$117$	−9.50462	−	60.0098i	−0.0812361	−	0.512905i
$118$	−82.2702	+	82.2702i	−0.697205	+	0.697205i
$119$	2.54915	−	3.50860i	0.0214214	−	0.0294841i
$120$	−43.3892	+	33.7422i	−0.361577	+	0.281185i
$121$	97.8910	−	71.1220i	0.809017	−	0.587785i
$122$	64.5397	+	10.2221i	0.529014	+	0.0837875i
$123$	72.7517	+	37.0689i	0.591478	+	0.301373i
$124$			33.4290i			0.269589i
$125$	114.534	−	50.0688i	0.916275	−	0.400550i
$126$	−3.98077			−0.0315934
$127$	76.8876	−	150.900i	0.605414	−	1.18819i	−0.361328	−	0.932439i	$-0.617677\pi$
$127$	76.8876	−	150.900i	0.605414	−	1.18819i	0.966742	−	0.255753i	$-0.0823234\pi$
$128$	24.1139	−	152.249i	0.188390	−	1.18945i
$129$	57.5441	+	79.2026i	0.446078	+	0.613974i
$130$	−142.066	−	182.683i	−1.09282	−	1.40526i
$131$	−189.453	−	137.646i	−1.44621	−	1.05073i	−0.986699	−	0.162560i	$-0.948025\pi$
$131$	−189.453	−	137.646i	−1.44621	−	1.05073i	−0.459511	−	0.888172i	$-0.651975\pi$
$132$	−0.00931489	−	0.00931489i	−7.05673e−5	−	7.05673e-5i
$133$	−3.69822	+	0.585741i	−0.0278062	+	0.00440407i
$134$	63.6376	+	20.6771i	0.474908	+	0.154307i
$135$	25.5145	−	4.89987i	0.188997	−	0.0362953i
$136$	−14.6495	−	45.0865i	−0.107717	−	0.331518i
$137$	207.074	−	105.510i	1.51149	−	0.770144i	0.515273	−	0.857026i	$-0.327690\pi$
$137$	207.074	−	105.510i	1.51149	−	0.770144i	0.996219	+	0.0868822i	$0.0276904\pi$
$138$	−70.8531	−	139.057i	−0.513428	−	1.00766i
$139$	−172.545	+	56.0633i	−1.24133	+	0.403333i	−0.854807	−	0.518945i	$-0.826325\pi$
$139$	−172.545	+	56.0633i	−1.24133	+	0.403333i	−0.386525	+	0.922279i	$0.626325\pi$
$140$	−3.10876	+	1.71407i	−0.0222055	+	0.0122433i
$141$	−49.5410	+	152.472i	−0.351355	+	1.08136i
$142$	16.8106	+	106.138i	0.118384	+	0.747448i
$143$	−0.0890705	+	0.0890705i	−0.000622871	+	0.000622871i
$144$	−34.2020	+	47.0751i	−0.237514	+	0.326910i
$145$	−12.3052	+	42.5510i	−0.0848631	+	0.293455i
$146$	196.165	−	142.522i	1.34359	−	0.976179i
$147$	−83.2489	−	13.1853i	−0.566319	−	0.0896961i
$148$	−2.54403	−	1.29625i	−0.0171894	−	0.00875842i
$149$			53.1373i			0.356626i	0.983974	+	0.178313i	$0.0570640\pi$
$149$			53.1373i			0.356626i	−0.983974	+	0.178313i	$0.942936\pi$
$150$	76.0926	−	63.2670i	0.507284	−	0.421780i
$151$	−30.5495			−0.202315			−0.101157	−	0.994870i	$-0.532255\pi$
$151$	−30.5495			−0.202315			−0.101157	+	0.994870i	$0.532255\pi$
$152$	−18.5816	+	36.4684i	−0.122247	+	0.239924i
$153$	−3.50540	+	22.1322i	−0.0229111	+	0.144655i
$154$	0.00485101	+	0.00667684i	3.15000e−5	+	4.33561e-5i
$155$	4.46243	+	136.615i	0.0287898	+	0.881385i
$156$	−34.7028	−	25.2130i	−0.222454	−	0.161622i
$157$	−188.083	−	188.083i	−1.19798	−	1.19798i	−0.974771	−	0.223209i	$-0.928347\pi$
$157$	−188.083	−	188.083i	−1.19798	−	1.19798i	−0.223209	−	0.974771i	$-0.571653\pi$
$158$	8.62222	−	1.36563i	0.0545710	−	0.00864320i
$159$	−135.461	−	44.0140i	−0.851958	−	0.276818i
$160$	−11.7525	+	93.9648i	−0.0734529	+	0.587280i
$161$	7.07415	+	21.7720i	0.0439388	+	0.135230i
$162$	18.3264	−	9.33775i	0.113126	−	0.0576404i
$163$	75.0262	+	147.247i	0.460283	+	0.903357i	0.998178	+	0.0603448i	$0.0192200\pi$
$163$	75.0262	+	147.247i	0.460283	+	0.903357i	−0.537894	+	0.843012i	$0.680780\pi$
$164$	54.8242	−	17.8135i	0.334294	−	0.108619i
$165$	−0.0393107	−	0.0368238i	−0.000238247	−	0.000223175i
$166$	−18.5976	+	57.2374i	−0.112034	+	0.344804i
$167$	32.6674	+	206.254i	0.195613	+	1.23505i	0.868644	+	0.495437i	$0.164992\pi$
$167$	32.6674	+	206.254i	0.195613	+	1.23505i	−0.673031	+	0.739614i	$0.735008\pi$
$168$	4.51330	−	4.51330i	0.0268649	−	0.0268649i
$169$	−141.755	+	195.110i	−0.838789	+	1.15449i
$170$	29.0108	+	80.2689i	0.170652	+	0.472170i
$171$	15.6516	−	11.3716i	0.0915299	−	0.0665004i
$172$	68.2662	+	10.8123i	0.396896	+	0.0628622i
$173$	−198.618	−	101.201i	−1.14808	−	0.584976i	−0.226825	−	0.973935i	$-0.572835\pi$
$173$	−198.618	−	101.201i	−1.14808	−	0.584976i	−0.921255	+	0.388959i	$0.872835\pi$
$174$			35.0666i			0.201532i
$175$	−12.4758	+	7.41989i	−0.0712904	+	0.0423994i
$176$	0.120637			0.000685436
$177$	−40.0325	+	78.5681i	−0.226172	+	0.443888i
$178$	9.87122	−	62.3244i	0.0554563	−	0.350137i
$179$	−36.6378	−	50.4276i	−0.204680	−	0.281718i	0.694320	−	0.719667i	$-0.255705\pi$
$179$	−36.6378	−	50.4276i	−0.204680	−	0.281718i	−0.899000	+	0.437948i	$0.855705\pi$
$180$	10.2912	−	15.1834i	0.0571732	−	0.0843520i
$181$	128.685	+	93.4950i	0.710966	+	0.516547i	0.883485	−	0.468459i	$-0.155191\pi$
$181$	128.685	+	93.4950i	0.710966	+	0.516547i	−0.172519	+	0.985006i	$0.555191\pi$
$182$	19.0026	+	19.0026i	0.104410	+	0.104410i
$183$	48.9142	−	7.74724i	0.267290	−	0.0423346i
$184$	237.991	+	77.3281i	1.29343	+	0.420261i
$185$	−10.5697	−	4.95778i	−0.0571337	−	0.0267988i
$186$	33.4391	+	102.915i	0.179780	+	0.553306i
$187$	0.0413935	−	0.0210910i	0.000221356	−	0.000112786i
$188$	51.3846	+	100.848i	0.273323	+	0.536426i
$189$	−2.86933	+	0.932303i	−0.0151817	+	0.00493282i
$190$	31.2928	−	66.7146i	0.164699	−	0.351130i
$191$	−35.8562	+	110.354i	−0.187729	+	0.577771i	−0.999985	−	0.00553100i	$-0.998239\pi$
$191$	−35.8562	+	110.354i	−0.187729	+	0.577771i	0.812256	+	0.583302i	$0.198239\pi$
$192$	−9.29391	−	58.6794i	−0.0484058	−	0.305622i
$193$	−108.290	+	108.290i	−0.561090	+	0.561090i	−0.929617	−	0.368527i	$-0.879862\pi$
$193$	−108.290	+	108.290i	−0.561090	+	0.561090i	0.368527	+	0.929617i	$0.379862\pi$
$194$	252.347	−	347.326i	1.30076	−	1.79034i
$195$	−145.186	−	98.4059i	−0.744543	−	0.504646i
$196$	−48.1415	+	34.9769i	−0.245620	+	0.178453i
$197$	−22.0852	−	3.49795i	−0.112108	−	0.0177561i	0.100129	−	0.994975i	$-0.468075\pi$
$197$	−22.0852	−	3.49795i	−0.112108	−	0.0177561i	−0.212236	+	0.977218i	$0.568075\pi$
$198$	−0.0379947	−	0.0193592i	−0.000191892	−	9.77739e-5i
$199$		−	172.519i		−	0.866929i	−0.901171	−	0.433464i	$-0.857291\pi$
$199$		−	172.519i		−	0.866929i	0.901171	−	0.433464i	$-0.142709\pi$
$200$	−14.5414	+	158.003i	−0.0727071	+	0.790013i
$201$	50.7126			0.252301
$202$	−114.675	+	225.062i	−0.567698	+	1.11417i
$203$	0.804646	−	5.08034i	0.00396378	−	0.0250263i
$204$	9.29881	+	12.7987i	0.0455824	+	0.0627388i
$205$	221.673	−	80.1170i	1.08133	−	0.390815i
$206$	−112.475	−	81.7176i	−0.545993	−	0.396687i
$207$	−83.6383	−	83.6383i	−0.404050	−	0.404050i
$208$	387.984	−	61.4506i	1.86531	−	0.295435i
$209$	−0.0381465	−	0.0123945i	−0.000182519	−	5.93040e-5i
$210$	−7.85610	+	8.38666i	−0.0374100	+	0.0399365i
$211$	26.8526	+	82.6437i	0.127263	+	0.391677i	0.994307	−	0.106556i	$-0.0339825\pi$
$211$	26.8526	+	82.6437i	0.127263	+	0.391677i	−0.867043	+	0.498233i	$0.833982\pi$
$212$	−89.5970	+	45.6519i	−0.422627	+	0.215339i
$213$	36.9747	+	72.5669i	0.173590	+	0.340689i
$214$	104.875	−	34.0760i	0.490071	−	0.159234i
$215$	280.428	+	35.0739i	1.30431	+	0.163135i
$216$	−10.1911	+	31.3649i	−0.0471809	+	0.145208i
$217$	−2.48304	−	15.6773i	−0.0114426	−	0.0722457i
$218$	−20.0391	+	20.0391i	−0.0919226	+	0.0919226i
$219$	108.017	−	148.672i	0.493226	−	0.678867i
$220$	−0.0380076	+	0.00124149i	−0.000172762	+	5.64315e-6i
$221$	122.383	−	88.9168i	0.553771	−	0.402338i
$222$	−9.12871	−	1.44585i	−0.0411203	−	0.00651282i
$223$	−255.426	−	130.146i	−1.14541	−	0.583615i	−0.224917	−	0.974378i	$-0.572211\pi$
$223$	−255.426	−	130.146i	−1.14541	−	0.583615i	−0.920491	+	0.390763i	$0.872211\pi$
$224$		−	10.9966i		−	0.0490920i
$225$	40.0302	−	63.4238i	0.177912	−	0.281884i
$226$	202.826			0.897460
$227$	−55.7533	+	109.422i	−0.245609	+	0.482035i	−0.980594	−	0.196048i	$-0.937189\pi$
$227$	−55.7533	+	109.422i	−0.245609	+	0.482035i	0.734985	+	0.678083i	$0.237189\pi$
$228$	2.13667	−	13.4904i	0.00937137	−	0.0591685i
$229$	−151.706	−	208.805i	−0.662470	−	0.911812i	0.337090	−	0.941472i	$-0.390557\pi$
$229$	−151.706	−	208.805i	−0.662470	−	0.911812i	−0.999560	+	0.0296606i	$0.990557\pi$
$230$	−432.794	−	125.158i	−1.88171	−	0.544166i
$231$	0.00506033	+	0.00367654i	2.19062e−5	+	1.59158e-5i
$232$	−39.7576	−	39.7576i	−0.171369	−	0.171369i
$233$	−127.549	+	20.2018i	−0.547421	+	0.0867029i	−0.424018	−	0.905654i	$-0.639381\pi$
$233$	−127.549	+	20.2018i	−0.547421	+	0.0867029i	−0.123403	+	0.992357i	$0.539381\pi$
$234$	−132.057	−	42.9079i	−0.564346	−	0.183367i
$235$	223.456	+	405.278i	0.950878	+	1.72459i
$236$	19.2376	+	59.2073i	0.0815154	+	0.250879i
$237$	5.89506	−	3.00368i	0.0248737	−	0.0126738i
$238$	−4.49962	−	8.83101i	−0.0189060	−	0.0371051i
$239$	−128.322	+	41.6942i	−0.536910	+	0.174453i	−0.564906	−	0.825155i	$-0.691088\pi$
$239$	−128.322	+	41.6942i	−0.536910	+	0.174453i	0.0279957	+	0.999608i	$0.491088\pi$
$240$	31.6793	+	164.960i	0.131997	+	0.687333i
$241$	−85.2518	+	262.378i	−0.353742	+	1.08871i	0.602994	+	0.797746i	$0.293974\pi$
$241$	−85.2518	+	262.378i	−0.353742	+	1.08871i	−0.956735	+	0.290959i	$0.906026\pi$
$242$	−43.2584	−	273.123i	−0.178754	−	1.12861i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$	20.5512	−	28.2863i	0.0842262	−	0.115927i
$245$	−192.072	+	149.367i	−0.783965	+	0.609660i
$246$	150.964	−	109.682i	0.613674	−	0.445860i
$247$	−128.998	−	20.4312i	−0.522257	−	0.0827174i
$248$	−154.595	−	78.7702i	−0.623367	−	0.317622i
$249$			45.6123i			0.183182i
$250$	16.8793	−	285.170i	0.0675173	−	1.14068i
$251$	34.2338			0.136390			0.0681949	−	0.997672i	$-0.478276\pi$
$251$	34.2338			0.136390			0.0681949	+	0.997672i	$0.478276\pi$
$252$	−0.966997	+	1.89784i	−0.00383729	+	0.00753111i
$253$	−0.0383618	+	0.242207i	−0.000151628	+	0.000957339i
$254$	−227.500	−	313.126i	−0.895668	−	1.23278i
$255$	39.7101	+	51.0634i	0.155726	+	0.200249i
$256$	−174.000	−	126.419i	−0.679689	−	0.493823i
$257$	19.6597	+	19.6597i	0.0764967	+	0.0764967i	0.744320	−	0.667823i	$-0.232774\pi$
$257$	19.6597	+	19.6597i	0.0764967	+	0.0764967i	−0.667823	+	0.744320i	$0.732774\pi$
$258$	220.981	−	34.9999i	0.856515	−	0.135659i
$259$	1.28936	+	0.418940i	0.00497824	+	0.00161753i
$260$	−121.605	+	23.3533i	−0.467711	+	0.0898204i
$261$	8.21265	+	25.2759i	0.0314661	+	0.0968427i
$262$	−476.846	+	242.965i	−1.82002	+	0.927349i
$263$	118.691	+	232.944i	0.451296	+	0.885719i	0.998803	+	0.0489173i	$0.0155771\pi$
$263$	118.691	+	232.944i	0.451296	+	0.885719i	−0.547507	+	0.836801i	$0.684423\pi$
$264$	0.0650265	−	0.0211284i	0.000246313	−	8.00318e-5i
$265$	−360.063	+	198.527i	−1.35873	+	0.749157i
$266$	−2.64429	+	8.13827i	−0.00994092	+	0.0305950i
$267$	−7.48133	−	47.2353i	−0.0280200	−	0.176911i
$268$	25.3165	−	25.3165i	0.0944647	−	0.0944647i
$269$	203.225	−	279.715i	0.755482	−	1.03983i	−0.242095	−	0.970253i	$-0.577834\pi$
$269$	203.225	−	279.715i	0.755482	−	1.03983i	0.997576	−	0.0695788i	$-0.0221655\pi$
$270$	16.4946	−	57.0380i	0.0610911	−	0.211252i
$271$	352.035	−	255.768i	1.29902	−	0.943794i	0.299076	−	0.954229i	$-0.403322\pi$
$271$	352.035	−	255.768i	1.29902	−	0.943794i	0.999946	+	0.0104349i	$0.00332161\pi$
$272$	−143.092	−	22.6636i	−0.526074	−	0.0833220i
$273$	18.1475	+	9.24659i	0.0664742	+	0.0338703i
$274$		−	531.127i		−	1.93842i
$275$	−0.155160	+	0.0101472i	−0.000564220	+	3.68991e-5i
$276$	−83.5072			−0.302562
$277$	162.173	−	318.282i	0.585461	−	1.14903i	−0.388316	−	0.921526i	$-0.626943\pi$
$277$	162.173	−	318.282i	0.585461	−	1.14903i	0.973777	−	0.227506i	$-0.0730570\pi$
$278$	−64.8607	+	409.515i	−0.233312	+	1.47307i
$279$	48.2058	+	66.3495i	0.172780	+	0.237812i
$280$	−0.601535	−	18.4157i	−0.00214834	−	0.0657702i
$281$	82.4210	+	59.8824i	0.293313	+	0.213104i	0.724703	−	0.689061i	$-0.241977\pi$
$281$	82.4210	+	59.8824i	0.293313	+	0.213104i	−0.431390	+	0.902165i	$0.641977\pi$
$282$	259.072	+	259.072i	0.918695	+	0.918695i
$283$	246.147	−	38.9858i	0.869776	−	0.137759i	0.294434	−	0.955672i	$-0.404869\pi$
$283$	246.147	−	38.9858i	0.869776	−	0.137759i	0.575342	+	0.817913i	$0.304869\pi$
$284$	54.6849	+	17.7682i	0.192552	+	0.0625641i
$285$	6.93113	−	55.4167i	0.0243198	−	0.194444i
$286$	0.0889578	+	0.273784i	0.000311041	+	0.000957286i
$287$	−24.3880	+	12.4263i	−0.0849755	+	0.0432972i
$288$	25.7949	+	50.6253i	0.0895656	+	0.175782i
$289$	221.795	−	72.0654i	0.767455	−	0.249361i
$290$	73.8780	+	69.2043i	0.254752	+	0.238636i
$291$	100.547	−	309.452i	0.345523	−	1.06341i
$292$	−20.2959	−	128.143i	−0.0695064	−	0.438846i
$293$	284.513	−	284.513i	0.971035	−	0.971035i	−0.0285567	−	0.999592i	$-0.509091\pi$
$293$	284.513	−	284.513i	0.971035	−	0.971035i	0.999592	+	0.0285567i	$0.00909113\pi$
$294$	−113.222	+	155.836i	−0.385108	+	0.530056i
$295$	86.5222	+	239.395i	0.293296	+	0.811510i
$296$	11.9892	−	8.71066i	0.0405040	−	0.0294279i
$297$	−0.0319205	−	0.00505571i	−0.000107476	−	1.70226e-5i
$298$	108.201	+	55.1314i	0.363092	+	0.185005i
$299$			798.510i			2.67060i
$300$	−11.6784	−	51.6459i	−0.0389281	−	0.172153i
$301$	−32.8182			−0.109030
$302$	−31.6960	+	62.2068i	−0.104954	+	0.205983i
$303$	−29.9476	+	189.082i	−0.0988369	+	0.624032i
$304$	73.5210	+	101.193i	0.241845	+	0.332871i
$305$	80.2109	−	118.341i	0.262987	−	0.388004i
$306$	41.4300	+	30.1007i	0.135392	+	0.0983683i
$307$	−249.442	−	249.442i	−0.812516	−	0.812516i	0.172494	−	0.985010i	$-0.444817\pi$
$307$	−249.442	−	249.442i	−0.812516	−	0.812516i	−0.985010	+	0.172494i	$0.944817\pi$
$308$	0.00436159		0.000690808i	1.41610e−5		2.24288e-6i
$309$	−100.210	−	32.5602i	−0.324304	−	0.105373i
$310$	282.813	+	132.655i	0.912301	+	0.427919i
$311$	−130.551	−	401.795i	−0.419779	−	1.29195i	−0.907906	−	0.419174i	$-0.862320\pi$
$311$	−130.551	−	401.795i	−0.419779	−	1.29195i	0.488127	−	0.872772i	$-0.337680\pi$
$312$	198.371	−	101.075i	0.635805	−	0.323959i
$313$	−181.676	−	356.558i	−0.580433	−	1.13916i	−0.975395	−	0.220467i	$-0.929242\pi$
$313$	−181.676	−	356.558i	−0.580433	−	1.13916i	0.394961	−	0.918698i	$-0.370758\pi$
$314$	−578.127	+	187.845i	−1.84117	+	0.598232i
$315$	−3.69850	+	7.88501i	−0.0117413	+	0.0250318i
$316$	1.44342	−	4.44239i	0.00456779	−	0.0140582i
$317$	−7.04741	−	44.4956i	−0.0222316	−	0.140365i	0.974076	−	0.226221i	$-0.0726373\pi$
$317$	−7.04741	−	44.4956i	−0.0222316	−	0.140365i	−0.996307	+	0.0858567i	$0.972637\pi$
$318$	−230.169	+	230.169i	−0.723801	+	0.723801i
$319$	0.0323866	−	0.0445764i	0.000101526	−	0.000139738i
$320$	−141.967	−	96.2243i	−0.443647	−	0.300701i
$321$	67.6133	−	49.1239i	0.210633	−	0.153034i
$322$	51.6731	+	8.18422i	0.160475	+	0.0254168i
$323$	42.9185	+	21.8681i	0.132875	+	0.0677031i
$324$		−	11.0054i		−	0.0339674i
$325$	−493.847	+	111.671i	−1.51953	+	0.343604i
$326$	377.676			1.15851
$327$	−9.75098	+	19.1374i	−0.0298195	+	0.0585241i
$328$	−46.8048	+	295.514i	−0.142698	+	0.900957i
$329$	−31.5889	−	43.4783i	−0.0960147	−	0.132153i
$330$	−0.115769	+	0.0418412i	−0.000350815	+	0.000126791i
$331$	83.8645	+	60.9311i	0.253367	+	0.184082i	0.707218	−	0.706996i	$-0.249950\pi$
$331$	83.8645	+	60.9311i	0.253367	+	0.184082i	−0.453851	+	0.891078i	$0.649950\pi$
$332$	22.7704	+	22.7704i	0.0685855	+	0.0685855i
$333$	−6.91859	+	1.09580i	−0.0207765	+	0.00329068i
$334$	453.880	+	147.474i	1.35892	+	0.441540i
$335$	100.082	−	106.841i	0.298752	−	0.318928i
$336$	−6.02765	−	18.5512i	−0.0179394	−	0.0552119i
$337$	210.731	−	107.373i	0.625316	−	0.318614i	−0.112464	−	0.993656i	$-0.535874\pi$
$337$	210.731	−	107.373i	0.625316	−	0.318614i	0.737780	+	0.675041i	$0.235874\pi$
$338$	250.219	+	491.083i	0.740293	+	1.45291i
$339$	146.197	−	47.5022i	0.431259	−	0.140125i
$340$	45.3156	+	5.66776i	0.133281	+	0.0166699i
$341$	0.0525423	−	0.161708i	0.000154083	−	0.000474218i
$342$	−6.91651	−	43.6691i	−0.0202237	−	0.127687i
$343$	40.0966	−	40.0966i	0.116900	−	0.116900i
$344$	−210.861	+	290.225i	−0.612968	+	0.843678i
$345$	−341.270	+	11.1474i	−0.989188	+	0.0323112i
$346$	−412.143	+	299.439i	−1.19116	+	0.865432i
$347$	18.9291	+	2.99808i	0.0545509	+	0.00864001i	0.183650	−	0.982992i	$-0.441209\pi$
$347$	18.9291	+	2.99808i	0.0545509	+	0.00864001i	−0.129099	+	0.991632i	$0.541209\pi$
$348$	16.7180	+	8.51827i	0.0480404	+	0.0244778i
$349$			520.676i			1.49191i	0.665998	+	0.745954i	$0.268006\pi$
$349$			520.676i			1.49191i	−0.665998	+	0.745954i	$0.731994\pi$
$350$	2.16484	+	33.1024i	0.00618526	+	0.0945782i
$351$	−105.236			−0.299817
$352$	0.0534786	−	0.104958i	0.000151928	−	0.000298175i
$353$	−51.9023	+	327.698i	−0.147032	+	0.928324i	0.798311	+	0.602246i	$0.205727\pi$
$353$	−51.9023	+	327.698i	−0.147032	+	0.928324i	−0.945343	+	0.326078i	$0.894273\pi$
$354$	118.451	+	163.033i	0.334606	+	0.460546i
$355$	225.853	+	65.3137i	0.636207	+	0.183982i
$356$	−27.3154	−	19.8458i	−0.0767287	−	0.0557467i
$357$	−5.31156	−	5.31156i	−0.0148783	−	0.0148783i
$358$	−140.697	+	22.2841i	−0.393007	+	0.0622462i
$359$	−35.6103	−	11.5705i	−0.0991931	−	0.0322298i	0.259000	−	0.965877i	$-0.416607\pi$
$359$	−35.6103	−	11.5705i	−0.0991931	−	0.0322298i	−0.358193	+	0.933648i	$0.616607\pi$
$360$	45.9672	+	83.3696i	0.127687	+	0.231582i
$361$	98.7040	+	303.780i	0.273418	+	0.841495i
$362$	323.894	−	165.032i	0.894736	−	0.455891i
$363$	−95.1465	−	186.735i	−0.262111	−	0.514423i
$364$	13.6756	−	4.44346i	0.0375702	−	0.0122073i
$365$	−100.049	−	520.975i	−0.274107	−	1.42733i
$366$	34.9744	−	107.640i	0.0955583	−	0.294098i
$367$	108.856	+	687.289i	0.296610	+	1.87272i	0.462562	+	0.886587i	$0.346930\pi$
$367$	108.856	+	687.289i	0.296610	+	1.87272i	−0.165952	+	0.986134i	$0.553070\pi$
$368$	540.749	−	540.749i	1.46943	−	1.46943i
$369$	83.1270	−	114.414i	0.225276	−	0.310066i
$370$	−21.0617	+	16.3789i	−0.0569236	+	0.0442673i
$371$	38.6277	−	28.0647i	0.104118	−	0.0756460i
$372$	57.1879	+	9.05767i	0.153731	+	0.0243486i
$373$	−364.034	−	185.485i	−0.975962	−	0.497278i	−0.108131	−	0.994137i	$-0.534487\pi$
$373$	−364.034	−	185.485i	−0.975962	−	0.497278i	−0.867831	+	0.496859i	$0.834487\pi$
$374$		−	0.106171i		−	0.000283878i
$375$	−54.6206	−	209.503i	−0.145655	−	0.558675i
$376$	−587.460			−1.56239
$377$	81.4531	−	159.861i	0.216056	−	0.424034i
$378$	−1.07860	+	6.81001i	−0.00285344	+	0.0180159i
$379$	−314.962	−	433.508i	−0.831034	−	1.14382i	−0.987730	−	0.156173i	$-0.950084\pi$
$379$	−314.962	−	433.508i	−0.831034	−	1.14382i	0.156696	−	0.987647i	$-0.449916\pi$
$380$	−24.2048	−	31.1250i	−0.0636967	−	0.0819080i
$381$	−237.316	−	172.420i	−0.622878	−	0.452547i
$382$	187.508	+	187.508i	0.490859	+	0.490859i
$383$	352.341	−	55.8054i	0.919952	−	0.145706i	0.321541	−	0.946896i	$-0.395799\pi$
$383$	352.341	−	55.8054i	0.919952	−	0.145706i	0.598411	+	0.801190i	$0.295799\pi$
$384$	−253.923	−	82.5046i	−0.661258	−	0.214856i
$385$	0.0177323	−	0.00340536i	4.60580e−5	−	8.84509e-6i
$386$	108.153	+	332.862i	0.280190	+	0.862336i
$387$	151.086	−	76.9820i	0.390402	−	0.198920i
$388$	−104.289	−	204.678i	−0.268786	−	0.527521i
$389$	−84.7780	+	27.5460i	−0.217938	+	0.0708125i	−0.415951	−	0.909387i	$-0.636551\pi$
$389$	−84.7780	+	27.5460i	−0.217938	+	0.0708125i	0.198013	+	0.980199i	$0.436551\pi$
$390$	−351.014	+	193.538i	−0.900037	+	0.496250i
$391$	91.0050	−	280.084i	0.232749	−	0.716329i
$392$	−48.3155	−	305.052i	−0.123254	−	0.778194i
$393$	−286.807	+	286.807i	−0.729790	+	0.729790i
$394$	−30.0367	+	41.3420i	−0.0762354	+	0.104929i
$395$	5.30583	−	18.3475i	0.0134325	−	0.0464493i
$396$	−0.0184591	+	0.0134113i	−4.66139e−5	+	3.38670e-5i
$397$	−21.9127	−	3.47062i	−0.0551956	−	0.00874213i	0.128776	−	0.991674i	$-0.458895\pi$
$397$	−21.9127	−	3.47062i	−0.0551956	−	0.00874213i	−0.183971	+	0.982932i	$0.558895\pi$
$398$	−351.294	−	178.993i	−0.882647	−	0.449731i
$399$			6.48536i			0.0162540i
$400$	410.056	+	258.809i	1.02514	+	0.647022i
$401$	−325.099			−0.810720			−0.405360	−	0.914157i	$-0.632854\pi$
$401$	−325.099			−0.810720			−0.405360	+	0.914157i	$0.632854\pi$
$402$	52.6157	−	103.264i	0.130885	−	0.256876i
$403$	86.6109	−	546.840i	0.214915	−	1.35692i
$404$	79.4423	+	109.343i	0.196639	+	0.270651i
$405$	−1.46911	−	44.9760i	−0.00362743	−	0.111052i
$406$	−9.51005	−	6.90946i	−0.0234238	−	0.0170184i
$407$	0.0102690	+	0.0102690i	2.52310e−5	+	2.52310e-5i
$408$	−81.0999	+	12.8450i	−0.198774	+	0.0314828i
$409$	390.581	+	126.908i	0.954966	+	0.310287i	0.744732	−	0.667364i	$-0.232577\pi$
$409$	390.581	+	126.908i	0.954966	+	0.310287i	0.210234	+	0.977651i	$0.432577\pi$
$410$	66.8525	−	534.508i	0.163055	−	1.30368i
$411$	−124.391	−	382.836i	−0.302654	−	0.931474i
$412$	−66.2811	+	33.7719i	−0.160876	+	0.0819706i
$413$	−13.4198	−	26.3378i	−0.0324934	−	0.0637718i
$414$	−257.086	+	83.5325i	−0.620982	+	0.201769i
$415$	96.0957	+	90.0164i	0.231556	+	0.216907i
$416$	118.530	−	364.799i	0.284929	−	0.876920i
$417$	49.1575	+	310.368i	0.117884	+	0.744288i
$418$	−0.0648165	+	0.0648165i	−0.000155063	+	0.000155063i
$419$	187.367	−	257.888i	0.447176	−	0.615484i	−0.524612	−	0.851341i	$-0.675790\pi$
$419$	187.367	−	257.888i	0.447176	−	0.615484i	0.971788	+	0.235857i	$0.0757897\pi$
$420$	2.08997	+	5.78267i	0.00497613	+	0.0137683i
$421$	−392.656	+	285.282i	−0.932676	+	0.677629i	−0.946646	−	0.322274i	$-0.895553\pi$
$421$	−392.656	+	285.282i	−0.932676	+	0.677629i	0.0139708	+	0.999902i	$0.495553\pi$
$422$	196.145	+	31.0663i	0.464798	+	0.0736167i
$423$	247.414	+	126.064i	0.584903	+	0.298023i
$424$		−	521.920i		−	1.23094i
$425$	185.948	+	17.1133i	0.437525	+	0.0402667i
$426$	186.127			0.436919
$427$	−7.53692	+	14.7920i	−0.0176509	+	0.0346418i
$428$	9.23019	−	58.2771i	0.0215659	−	0.136161i
$429$	0.128241	+	0.176509i	0.000298931	+	0.000411443i
$430$	362.371	−	534.634i	0.842723	−	1.24333i
$431$	440.095	+	319.748i	1.02110	+	0.741874i	0.966508	−	0.256635i	$-0.0826138\pi$
$431$	440.095	+	319.748i	1.02110	+	0.741874i	0.0545932	+	0.998509i	$0.482614\pi$
$432$	71.2655	+	71.2655i	0.164966	+	0.164966i
$433$	−276.236	+	43.7515i	−0.637958	+	0.101043i	−0.467031	−	0.884241i	$-0.654676\pi$
$433$	−276.236	+	43.7515i	−0.637958	+	0.101043i	−0.170927	+	0.985284i	$0.554676\pi$
$434$	−34.4994	−	11.2095i	−0.0794916	−	0.0258284i
$435$	69.4590	+	32.5800i	0.159676	+	0.0748966i
$436$	4.68584	+	14.4215i	0.0107473	+	0.0330769i
$437$	−226.548	+	115.432i	−0.518416	+	0.264146i
$438$	−190.665	−	374.201i	−0.435308	−	0.854340i
$439$	346.056	−	112.440i	0.788282	−	0.256128i	0.112910	−	0.993605i	$-0.463983\pi$
$439$	346.056	−	112.440i	0.788282	−	0.256128i	0.675372	+	0.737477i	$0.263983\pi$
$440$	0.0838175	−	0.178695i	0.000190494	−	0.000406124i
$441$	−45.1130	+	138.843i	−0.102297	+	0.314838i
$442$	−54.0817	−	341.458i	−0.122357	−	0.772530i
$443$	268.560	−	268.560i	0.606231	−	0.606231i	−0.335728	−	0.941959i	$-0.608982\pi$
$443$	268.560	−	268.560i	0.606231	−	0.606231i	0.941959	+	0.335728i	$0.108982\pi$
$444$	−2.90683	+	4.00091i	−0.00654692	+	0.00901106i
$445$	−114.279	−	77.4578i	−0.256808	−	0.174062i
$446$	−530.023	+	385.084i	−1.18839	+	0.863418i
$447$	90.9034	+	14.3977i	0.203363	+	0.0322096i
$448$	17.7451	+	9.04159i	0.0396097	+	0.0201821i
$449$			295.781i			0.658756i	0.944198	+	0.329378i	$0.106839\pi$
$449$			295.781i			0.658756i	−0.944198	+	0.329378i	$0.893161\pi$
$450$	−87.6150	−	147.316i	−0.194700	−	0.327369i
$451$	−0.293204			−0.000650119
$452$	49.2699	−	96.6977i	0.109004	−	0.213933i
$453$	−8.27747	+	52.2619i	−0.0182726	+	0.115368i
$454$	164.966	+	227.057i	0.363362	+	0.500125i
$455$	55.2949	−	19.9847i	0.121527	−	0.0439224i
$456$	57.3528	+	41.6692i	0.125774	+	0.0913799i
$457$	−56.6276	−	56.6276i	−0.123912	−	0.123912i	0.642432	−	0.766343i	$-0.277926\pi$
$457$	−56.6276	−	56.6276i	−0.123912	−	0.123912i	−0.766343	+	0.642432i	$0.777926\pi$
$458$	−582.580	+	92.2716i	−1.27201	+	0.201466i
$459$	36.9124	+	11.9936i	0.0804191	+	0.0261298i
$460$	−164.803	+	175.932i	−0.358266	+	0.382462i
$461$	42.3641	+	130.383i	0.0918962	+	0.282827i	0.986432	−	0.164168i	$-0.0524940\pi$
$461$	42.3641	+	130.383i	0.0918962	+	0.282827i	−0.894536	+	0.446996i	$0.852494\pi$
$462$	0.0127366	−	0.00648964i	2.75685e−5	−	1.40468e-5i
$463$	−353.634	−	694.046i	−0.763788	−	1.49902i	−0.863691	−	0.504022i	$-0.831853\pi$
$463$	−353.634	−	694.046i	−0.763788	−	1.49902i	0.0999024	−	0.994997i	$-0.468147\pi$
$464$	−163.417	+	53.0975i	−0.352193	+	0.114434i
$465$	234.919	+	29.3821i	0.505203	+	0.0631873i
$466$	−91.1994	+	280.683i	−0.195707	+	0.602324i
$467$	97.1411	+	613.325i	0.208011	+	1.31333i	0.841786	+	0.539812i	$0.181505\pi$
$467$	97.1411	+	613.325i	0.208011	+	1.31333i	−0.633775	+	0.773518i	$0.718495\pi$
$468$	−52.5354	+	52.5354i	−0.112255	+	0.112255i
$469$	−9.99233	+	13.7533i	−0.0213056	+	0.0293246i
$470$	1057.09	−	34.5292i	2.24914	−	0.0734665i
$471$	−372.720	+	270.797i	−0.791337	+	0.574940i
$472$	−319.140	−	50.5468i	−0.676143	−	0.107091i
$473$	−0.313235	−	0.159601i	−0.000662230	−	0.000337423i
$474$		−	15.1203i		−	0.0318993i
$475$	−103.073	−	123.968i	−0.216995	−	0.260985i
$476$	−5.30324			−0.0111413
$477$	−112.000	+	219.811i	−0.234800	+	0.460821i
$478$	−48.2368	+	304.555i	−0.100914	+	0.637144i
$479$	91.0201	+	125.278i	0.190021	+	0.261542i	0.893389	−	0.449285i	$-0.148321\pi$
$479$	91.0201	+	125.278i	0.190021	+	0.261542i	−0.703368	+	0.710826i	$0.748321\pi$
$480$	157.564	+	45.5652i	0.328258	+	0.0949276i
$481$	38.2574	+	27.7956i	0.0795372	+	0.0577871i
$482$	445.819	+	445.819i	0.924936	+	0.924936i
$483$	39.1627	−	6.20276i	0.0810822	−	0.0128422i
$484$	−140.720	−	45.7227i	−0.290744	−	0.0944684i
$485$	−453.521	−	822.540i	−0.935094	−	1.69596i
$486$	−11.0088	−	33.8815i	−0.0226518	−	0.0697150i
$487$	−520.789	+	265.355i	−1.06938	+	0.544877i	−0.897850	−	0.440302i	$-0.854872\pi$
$487$	−520.789	+	265.355i	−1.06938	+	0.544877i	−0.171531	+	0.985179i	$0.554872\pi$
$488$	82.3866	+	161.693i	0.168825	+	0.331338i
$489$	272.228	−	88.4523i	0.556704	−	0.180884i
$490$	104.870	+	546.080i	0.214021	+	1.11445i
$491$	−134.728	+	414.650i	−0.274395	+	0.844500i	0.714984	+	0.699141i	$0.246434\pi$
$491$	−134.728	+	414.650i	−0.274395	+	0.844500i	−0.989379	+	0.145360i	$0.953566\pi$
$492$	−15.6192	−	98.6159i	−0.0317464	−	0.200439i
$493$	−46.7895	+	46.7895i	−0.0949077	+	0.0949077i
$494$	−175.442	+	241.475i	−0.355145	+	0.488816i
$495$	−0.0736468	+	0.0572724i	−0.000148781	+	0.000115702i
$496$	−428.972	+	311.666i	−0.864863	+	0.628359i
$497$	−26.9656	−	4.27093i	−0.0542567	−	0.00859341i
$498$	92.8785	+	47.3240i	0.186503	+	0.0950281i
$499$		−	245.479i		−	0.491942i	−0.969277	−	0.245971i	$-0.920893\pi$
$499$		−	245.479i		−	0.491942i	0.969277	−	0.245971i	$-0.0791067\pi$
$500$	−131.855	−	77.3199i	−0.263710	−	0.154640i
$501$	361.695			0.721946
$502$	35.5185	−	69.7091i	0.0707541	−	0.138863i
$503$	53.0716	−	335.081i	0.105510	−	0.666164i	−0.877075	−	0.480353i	$-0.840509\pi$
$503$	53.0716	−	335.081i	0.105510	−	0.666164i	0.982585	−	0.185812i	$-0.0594914\pi$
$504$	−6.49814	−	8.94392i	−0.0128931	−	0.0177459i
$505$	339.254	+	436.249i	0.671790	+	0.863859i
$506$	0.453395	+	0.329411i	0.000896038	+	0.000651010i
$507$	295.370	+	295.370i	0.582584	+	0.582584i
$508$	−204.547	+	32.3971i	−0.402652	+	0.0637738i
$509$	249.032	+	80.9153i	0.489257	+	0.158969i	0.543248	−	0.839572i	$-0.317194\pi$
$509$	249.032	+	80.9153i	0.489257	+	0.158969i	−0.0539913	+	0.998541i	$0.517194\pi$
$510$	145.179	−	27.8804i	0.284664	−	0.0546675i
$511$	19.0365	+	58.5882i	0.0372533	+	0.114654i
$512$	111.432	−	56.7775i	0.217641	−	0.110894i
$513$	−15.2128	−	29.8568i	−0.0296546	−	0.0582004i
$514$	60.4296	−	19.6348i	0.117567	−	0.0382000i
$515$	−266.363	+	146.864i	−0.517211	+	0.285173i
$516$	36.9938	−	113.855i	0.0716934	−	0.220650i
$517$	−0.0900580	−	0.568604i	−0.000174193	−	0.00109981i
$518$	2.19082	−	2.19082i	0.00422938	−	0.00422938i
$519$	−226.943	+	312.360i	−0.437270	+	0.601850i
$520$	178.544	−	617.401i	0.343353	−	1.18731i
$521$	−88.1610	+	64.0527i	−0.169215	+	0.122942i	−0.669170	−	0.743110i	$-0.733350\pi$
$521$	−88.1610	+	64.0527i	−0.169215	+	0.122942i	0.499955	+	0.866052i	$0.333350\pi$
$522$	59.9893	+	9.50137i	0.114922	+	0.0182019i
$523$	480.996	+	245.079i	0.919686	+	0.468603i	0.848700	−	0.528874i	$-0.177386\pi$
$523$	480.996	+	245.079i	0.919686	+	0.468603i	0.0709854	+	0.997477i	$0.477386\pi$
$524$			286.358i			0.546485i
$525$	9.31305	+	23.3531i	0.0177391	+	0.0444822i
$526$	597.480			1.13589
$527$	−92.7021	+	181.938i	−0.175905	+	0.345234i
$528$	0.0326868	−	0.206377i	6.19069e−5	−	0.000390865i
$529$	602.789	+	829.667i	1.13949	+	1.56837i
$530$	30.6770	+	939.159i	0.0578811	+	1.77200i
$531$	123.562	+	89.7728i	0.232696	+	0.169064i
$532$	3.23760	+	3.23760i	0.00608571	+	0.00608571i
$533$	−942.981	+	149.354i	−1.76920	+	0.280213i
$534$	−103.945	−	33.7739i	−0.194654	−	0.0632470i
$535$	29.9417	−	239.394i	0.0559659	−	0.447465i
$536$	57.4240	+	176.733i	0.107134	+	0.329725i
$537$	−96.1949	+	49.0138i	−0.179134	+	0.0912733i
$538$	−358.721	−	704.030i	−0.666768	−	1.30861i
$539$	0.287854	−	0.0935293i	0.000534051	−	0.000173524i
$540$	−23.1862	−	21.7194i	−0.0429373	−	0.0402210i
$541$	118.206	−	363.800i	0.218495	−	0.672459i	−0.780392	−	0.625291i	$-0.784980\pi$
$541$	118.206	−	363.800i	0.218495	−	0.672459i	0.998887	−	0.0471681i	$-0.0150196\pi$
$542$	−155.565	−	982.202i	−0.287021	−	1.81218i
$543$	194.812	−	194.812i	0.358770	−	0.358770i
$544$	−83.1511	+	114.448i	−0.152851	+	0.210382i
$545$	21.0748	+	58.3112i	0.0386694	+	0.106993i
$546$	37.6570	−	27.3594i	0.0689688	−	0.0501088i
$547$	637.836	+	101.023i	1.16606	+	0.184686i	0.709302	−	0.704904i	$-0.249010\pi$
$547$	637.836	+	101.023i	1.16606	+	0.184686i	0.456759	+	0.889590i	$0.349010\pi$
$548$	−253.216	−	129.020i	−0.462073	−	0.235438i
$549$		−	85.7779i		−	0.156244i
$550$	−0.140321	+	0.326475i	−0.000255128	+	0.000593591i
$551$	57.1294			0.103683
$552$	196.772	−	386.186i	0.356470	−	0.699612i
$553$	−0.346954	+	2.19058i	−0.000627403	+	0.00396127i
$554$	−479.847	−	660.452i	−0.866149	−	1.19215i
$555$	−11.3453	+	16.7386i	−0.0204420	+	0.0301596i
$556$	179.481	+	130.401i	0.322808	+	0.234534i
$557$	−410.789	−	410.789i	−0.737503	−	0.737503i	0.234591	−	0.972094i	$-0.424625\pi$
$557$	−410.789	−	410.789i	−0.737503	−	0.737503i	−0.972094	+	0.234591i	$0.924625\pi$
$558$	185.120	−	29.3201i	0.331756	−	0.0525450i
$559$	−1088.70	−	353.741i	−1.94759	−	0.632810i
$560$	−50.9792	−	23.9120i	−0.0910343	−	0.0427000i
$561$	−0.0248653	−	0.0765276i	−4.43232e−5	−	0.000136413i
$562$	207.450	−	105.701i	0.369128	−	0.188080i
$563$	391.296	+	767.961i	0.695019	+	1.36405i	0.920862	+	0.389888i	$0.127486\pi$
$563$	391.296	+	767.961i	0.695019	+	1.36405i	−0.225843	+	0.974164i	$0.572514\pi$
$564$	186.446	−	60.5800i	0.330578	−	0.107411i
$565$	188.444	−	401.753i	0.333529	−	0.711067i
$566$	175.999	−	541.668i	0.310951	−	0.957010i
$567$	0.817463	+	5.16126i	0.00144173	+	0.00910274i
$568$	−211.027	+	211.027i	−0.371526	+	0.371526i
$569$	363.153	−	499.837i	0.638230	−	0.878448i	−0.360290	−	0.932840i	$-0.617322\pi$
$569$	363.153	−	499.837i	0.638230	−	0.878448i	0.998520	+	0.0543924i	$0.0173222\pi$
$570$	−105.652	−	71.6099i	−0.185354	−	0.125631i
$571$	407.201	−	295.849i	0.713136	−	0.518124i	−0.171048	−	0.985263i	$-0.554715\pi$
$571$	407.201	−	295.849i	0.713136	−	0.518124i	0.884184	+	0.467139i	$0.154715\pi$
$572$	0.152136	+	0.0240960i	0.000265973	+	4.21259e-5i
$573$	179.070	+	91.2410i	0.312514	+	0.159234i
$574$			62.5529i			0.108977i
$575$	−650.015	+	740.985i	−1.13046	+	1.28867i
$576$	−102.903			−0.178650
$577$	0.100405	−	0.197056i	0.000174012	−	0.000341518i	−0.890920	−	0.454161i	$-0.849939\pi$
$577$	0.100405	−	0.197056i	0.000174012	−	0.000341518i	0.891094	+	0.453820i	$0.149939\pi$
$578$	83.3738	−	526.402i	0.144245	−	0.910729i
$579$	155.914	+	214.597i	0.269281	+	0.370633i
$580$	50.9395	−	18.4106i	0.0878268	−	0.0317423i
$581$	−12.3701	−	8.98737i	−0.0212910	−	0.0154688i
$582$	−525.805	−	525.805i	−0.903445	−	0.903445i
$583$	0.505168	−	0.0800107i	0.000866497	−	0.000137240i
$584$	640.432	+	208.089i	1.09663	+	0.356317i
$585$	−207.684	+	221.710i	−0.355015	+	0.378991i
$586$	−284.153	−	874.534i	−0.484903	−	1.49238i
$587$	−492.447	+	250.914i	−0.838921	+	0.427452i	−0.819996	−	0.572369i	$-0.806024\pi$
$587$	−492.447	+	250.914i	−0.838921	+	0.427452i	−0.0189253	+	0.999821i	$0.506024\pi$
$588$	46.7918	+	91.8340i	0.0795779	+	0.156180i
$589$	167.666	−	54.4781i	0.284663	−	0.0924925i
$590$	577.241	+	72.1973i	0.978374	+	0.122368i
$591$	−11.9681	+	36.8339i	−0.0202506	+	0.0623248i
$592$	−7.08469	−	44.7310i	−0.0119674	−	0.0755591i
$593$	−128.971	+	128.971i	−0.217489	+	0.217489i	−0.807439	−	0.589951i	$-0.799147\pi$
$593$	−128.971	+	128.971i	−0.217489	+	0.217489i	0.589951	+	0.807439i	$0.299147\pi$
$594$	−0.0434131	+	0.0597530i	−7.30860e−5	+	0.000100594i
$595$	−21.6728	+	0.707928i	−0.0364249	+	0.00118979i
$596$	52.5680	−	38.1929i	0.0882014	−	0.0640820i
$597$	−295.133	−	46.7444i	−0.494359	−	0.0782988i
$598$	1625.97	+	828.476i	2.71902	+	1.38541i
$599$		−	594.925i		−	0.993197i	−0.867980	−	0.496599i	$-0.834582\pi$
$599$		−	594.925i		−	0.993197i	0.867980	−	0.496599i	$-0.165418\pi$
$600$	266.359	+	67.6876i	0.443932	+	0.112813i
$601$	−36.1356			−0.0601258			−0.0300629	−	0.999548i	$-0.509571\pi$
$601$	−36.1356			−0.0601258			−0.0300629	+	0.999548i	$0.509571\pi$
$602$	−34.0497	+	66.8264i	−0.0565610	+	0.111007i
$603$	13.7407	−	86.7553i	0.0227872	−	0.143873i
$604$	21.9577	+	30.2222i	0.0363539	+	0.0500368i
$605$	−581.186	−	168.071i	−0.960638	−	0.277803i
$606$	353.948	+	257.159i	0.584073	+	0.424354i
$607$	167.285	+	167.285i	0.275593	+	0.275593i	0.831347	−	0.555754i	$-0.187570\pi$
$607$	167.285	+	167.285i	0.275593	+	0.275593i	−0.555754	+	0.831347i	$0.687570\pi$
$608$	120.633	−	19.1064i	0.198409	−	0.0314250i
$609$	−8.47305	−	2.75306i	−0.0139130	−	0.00452062i
$610$	−157.753	−	286.113i	−0.258611	−	0.469037i
$611$	−579.276	−	1782.83i	−0.948079	−	2.91789i
$612$	24.4146	−	12.4399i	0.0398932	−	0.0203266i
$613$	227.589	+	446.668i	0.371271	+	0.728660i	0.998751	−	0.0499731i	$-0.0159136\pi$
$613$	227.589	+	446.668i	0.371271	+	0.728660i	−0.627480	+	0.778633i	$0.715914\pi$
$614$	−766.733	+	249.127i	−1.24875	+	0.405744i
$615$	−76.9955	−	400.930i	−0.125196	−	0.651918i
$616$	−0.00708270	+	0.0217983i	−1.14979e−5	+	3.53869e-5i
$617$	155.986	+	984.855i	0.252813	+	1.59620i	0.708270	+	0.705941i	$0.249476\pi$
$617$	155.986	+	984.855i	0.252813	+	1.59620i	−0.455457	+	0.890258i	$0.650524\pi$
$618$	−170.272	+	170.272i	−0.275521	+	0.275521i
$619$	−319.162	+	439.288i	−0.515608	+	0.709674i	−0.984852	−	0.173395i	$-0.944526\pi$
$619$	−319.162	+	439.288i	−0.515608	+	0.709674i	0.469244	+	0.883068i	$0.344526\pi$
$620$	131.944	−	102.608i	0.212812	−	0.165496i
$621$	−165.744	+	120.420i	−0.266899	+	0.193913i
$622$	−953.611	−	151.037i	−1.53314	−	0.242825i
$623$	14.2843	+	7.27822i	0.0229283	+	0.0116825i
$624$		−	680.384i		−	1.09036i
$625$	−549.175	−	298.383i	−0.878679	−	0.477413i
$626$	−914.540			−1.46093
$627$	−0.0315395	+	0.0618998i	−5.03023e−5	+	9.87238e-5i
$628$	−50.8816	+	321.254i	−0.0810217	+	0.511551i
$629$	−10.2513	−	14.1097i	−0.0162978	−	0.0224320i
$630$	12.2186	+	15.7120i	0.0193947	+	0.0249397i
$631$	386.134	+	280.543i	0.611941	+	0.444601i	0.850097	−	0.526626i	$-0.176543\pi$
$631$	386.134	+	280.543i	0.611941	+	0.444601i	−0.238157	+	0.971227i	$0.576543\pi$
$632$	17.1430	+	17.1430i	0.0271250	+	0.0271250i
$633$	148.657	−	23.5449i	0.234845	−	0.0371957i
$634$	−97.9166	−	31.8150i	−0.154443	−	0.0501814i
$635$	−831.601	+	159.703i	−1.30961	+	0.251500i
$636$	53.8215	+	165.645i	0.0846249	+	0.260449i
$637$	878.132	−	447.431i	1.37854	−	0.702403i
$638$	−0.0571672	−	0.112197i	−8.96037e−5	−	0.000175857i
$639$	134.160	−	43.5914i	0.209954	−	0.0682181i
$640$	−674.941	+	372.140i	−1.05459	+	0.581468i
$641$	199.106	−	612.784i	0.310617	−	0.955981i	−0.666904	−	0.745144i	$-0.732381\pi$
$641$	199.106	−	612.784i	0.310617	−	0.955981i	0.977521	−	0.210838i	$-0.0676191\pi$
$642$	−29.8786	−	188.646i	−0.0465398	−	0.293841i
$643$	51.9074	−	51.9074i	0.0807269	−	0.0807269i	−0.665590	−	0.746317i	$-0.731820\pi$
$643$	51.9074	−	51.9074i	0.0807269	−	0.0807269i	0.746317	+	0.665590i	$0.231820\pi$
$644$	16.4541	−	22.6472i	0.0255499	−	0.0351664i
$645$	135.984	−	470.232i	0.210829	−	0.729041i
$646$	89.0583	−	64.7047i	0.137861	−	0.100162i
$647$	−9.24610	−	1.46444i	−0.0142907	−	0.00226343i	0.149285	−	0.988794i	$-0.452303\pi$
$647$	−9.24610	−	1.46444i	−0.0142907	−	0.00226343i	−0.163576	+	0.986531i	$0.552303\pi$
$648$	50.8955	+	25.9326i	0.0785424	+	0.0400194i
$649$		−	0.316645i		−	0.000487897i
$650$	−284.988	+	1121.46i	−0.438443	+	1.72533i
$651$	−27.4924			−0.0422310
$652$	91.7439	−	180.058i	0.140712	−	0.276162i
$653$	−94.7276	+	598.086i	−0.145065	+	0.915906i	0.802572	+	0.596556i	$0.203465\pi$
$653$	−94.7276	+	598.086i	−0.145065	+	0.915906i	−0.947637	+	0.319350i	$0.896535\pi$
$654$	28.8518	+	39.7111i	0.0441159	+	0.0607203i
$655$	38.2258	+	1170.26i	0.0583600	+	1.78666i
$656$	739.727	+	537.443i	1.12763	+	0.819274i
$657$	−225.070	−	225.070i	−0.342572	−	0.342572i
$658$	−121.308	+	19.2132i	−0.184358	+	0.0291994i
$659$	−628.783	−	204.304i	−0.954147	−	0.310021i	−0.209748	−	0.977756i	$-0.567264\pi$
$659$	−628.783	−	204.304i	−0.954147	−	0.310021i	−0.744400	+	0.667734i	$0.767264\pi$
$660$	−0.00817440	+	0.0653570i	−1.23854e−5	+	9.90257e-5i
$661$	60.5592	+	186.382i	0.0916176	+	0.281970i	0.986357	−	0.164618i	$-0.0526391\pi$
$661$	60.5592	+	186.382i	0.0916176	+	0.281970i	−0.894740	+	0.446588i	$0.852639\pi$
$662$	211.083	−	107.552i	0.318857	−	0.162466i
$663$	−118.952	−	233.457i	−0.179415	−	0.352122i
$664$	−158.958	+	51.6487i	−0.239395	+	0.0777842i
$665$	13.6633	+	12.7989i	0.0205463	+	0.0192465i
$666$	−4.94689	+	15.2250i	−0.00742777	+	0.0228603i
$667$	−54.6400	−	344.984i	−0.0819191	−	0.517217i
$668$	180.564	−	180.564i	0.270305	−	0.270305i
$669$	−291.853	+	401.701i	−0.436252	+	0.600450i
$670$	−113.718	−	314.643i	−0.169729	−	0.469617i
$671$	−0.143873	+	0.104530i	−0.000214416	+	0.000155782i
$672$	−18.8122	−	2.97956i	−0.0279943	−	0.00443387i
$673$	434.847	+	221.566i	0.646132	+	0.329221i	0.746163	−	0.665764i	$-0.231894\pi$
$673$	434.847	+	221.566i	0.646132	+	0.329221i	−0.100031	+	0.994984i	$0.531894\pi$
$674$		−	540.507i		−	0.801939i
$675$	−97.6545	−	85.6656i	−0.144673	−	0.126912i
$676$	294.907			0.436253
$677$	362.790	−	712.015i	0.535879	−	1.05172i	−0.451340	−	0.892352i	$-0.649054\pi$
$677$	362.790	−	712.015i	0.535879	−	1.05172i	0.987219	−	0.159370i	$-0.0509461\pi$
$678$	54.9562	−	346.980i	0.0810563	−	0.511770i
$679$	64.1118	+	88.2423i	0.0944209	+	0.129959i
$680$	−132.990	+	196.210i	−0.195574	+	0.288545i
$681$	172.085	+	125.027i	0.252694	+	0.183593i
$682$	−0.274767	−	0.274767i	−0.000402884	−	0.000402884i
$683$	−599.825	+	95.0029i	−0.878221	+	0.139096i	−0.579234	−	0.815161i	$-0.696648\pi$
$683$	−599.825	+	95.0029i	−0.878221	+	0.139096i	−0.298986	+	0.954257i	$0.596648\pi$
$684$	−22.4995	−	7.31052i	−0.0328940	−	0.0106879i
$685$	−1052.04	−	493.465i	−1.53583	−	0.720388i
$686$	−40.0459	−	123.248i	−0.0583759	−	0.179662i
$687$	−398.313	+	202.951i	−0.579786	+	0.295416i
$688$	497.714	+	976.820i	0.723422	+	1.41980i
$689$	1583.93	−	514.650i	2.29888	−	0.746952i
$690$	−331.378	+	706.481i	−0.480258	+	1.02388i
$691$	109.021	−	335.531i	0.157772	−	0.485573i	−0.840659	−	0.541565i	$-0.817832\pi$
$691$	109.021	−	335.531i	0.157772	−	0.485573i	0.998431	+	0.0559919i	$0.0178321\pi$
$692$	42.6417	+	269.229i	0.0616209	+	0.389059i
$693$	0.00766067	−	0.00766067i	1.10544e−5	−	1.10544e-5i
$694$	25.7444	−	35.4341i	0.0370957	−	0.0510578i
$695$	750.895	+	508.951i	1.08042	+	0.732304i
$696$	−78.7869	+	57.2420i	−0.113200	+	0.0822443i
$697$	347.781	+	55.0831i	0.498968	+	0.0790288i
$698$	1060.23	+	540.215i	1.51896	+	0.773947i
$699$			223.675i			0.319993i
$700$	16.3075	+	7.00904i	0.0232964	+	0.0100129i
$701$	452.456			0.645443			0.322722	−	0.946494i	$-0.395402\pi$
$701$	452.456			0.645443			0.322722	+	0.946494i	$0.395402\pi$
$702$	−109.185	+	214.287i	−0.155534	+	0.305253i
$703$	−2.35553	+	14.8722i	−0.00335069	+	0.0211554i
$704$	0.125398	+	0.172596i	0.000178123	+	0.000245165i
$705$	753.865	−	272.462i	1.06931	−	0.386471i
$706$	613.430	+	445.683i	0.868880	+	0.631279i
$707$	−45.3782	−	45.3782i	−0.0641841	−	0.0641841i
$708$	106.500	−	16.8679i	0.150424	−	0.0238248i
$709$	−977.831	−	317.716i	−1.37917	−	0.448119i	−0.476773	−	0.879027i	$-0.658194\pi$
$709$	−977.831	−	317.716i	−1.37917	−	0.448119i	−0.902396	+	0.430907i	$0.858194\pi$
$710$	367.325	−	392.132i	0.517359	−	0.552298i
$711$	−3.54120	−	10.8987i	−0.00498059	−	0.0153287i
$712$	156.143	−	79.5589i	0.219302	−	0.111740i
$713$	−489.333	−	960.370i	−0.686302	−	1.34694i
$714$	−16.3266	+	5.30484i	−0.0228664	+	0.00742975i
$715$	0.624954	+	0.0781649i	0.000874062	+	0.000109322i
$716$	−23.5536	+	72.4905i	−0.0328961	+	0.101244i
$717$	36.5583	+	230.820i	0.0509879	+	0.321925i
$718$	−60.5072	+	60.5072i	−0.0842719	+	0.0842719i
$719$	232.296	−	319.728i	0.323082	−	0.444684i	−0.616323	−	0.787493i	$-0.711378\pi$
$719$	232.296	−	319.728i	0.323082	−	0.444684i	0.939405	+	0.342809i	$0.111378\pi$
$720$	290.785	−	9.49829i	0.403868	−	0.0131921i
$721$	28.5756	−	20.7614i	0.0396332	−	0.0287952i
$722$	720.983	+	114.192i	0.998591	+	0.158161i
$723$	425.758	+	216.934i	0.588876	+	0.300048i
$724$		−	194.506i		−	0.268655i
$725$	205.718	−	82.0386i	0.283748	−	0.113157i
$726$	−478.959			−0.659724
$727$	−355.893	+	698.480i	−0.489537	+	0.960770i	0.505647	+	0.862741i	$0.331254\pi$
$727$	−355.893	+	698.480i	−0.489537	+	0.960770i	−0.995184	+	0.0980293i	$0.968746\pi$
$728$	−11.6752	+	73.7140i	−0.0160373	+	0.101256i
$729$	−15.8702	−	21.8435i	−0.0217698	−	0.0299636i
$730$	−1164.64	−	336.799i	−1.59540	−	0.461369i
$731$	341.557	+	248.155i	0.467246	+	0.339474i
$732$	−42.8217	−	42.8217i	−0.0584996	−	0.0584996i
$733$	555.779	−	88.0268i	0.758226	−	0.120091i	0.234661	−	0.972077i	$-0.424602\pi$
$733$	555.779	−	88.0268i	0.758226	−	0.120091i	0.523564	+	0.851986i	$0.324602\pi$
$734$	1512.44	+	491.422i	2.06055	+	0.669512i
$735$	203.483	+	369.053i	0.276848	+	0.502113i
$736$	−230.753	−	710.184i	−0.313523	−	0.964924i
$737$	−0.162257	+	0.0826741i	−0.000220159	+	0.000112176i
$738$	−146.731	−	287.976i	−0.198823	−	0.390212i
$739$	−466.613	+	151.612i	−0.631412	+	0.205158i	−0.607200	−	0.794549i	$-0.707708\pi$
$739$	−466.613	+	151.612i	−0.631412	+	0.205158i	−0.0242115	+	0.999707i	$0.507708\pi$
$740$	2.69242	+	14.0199i	0.00363841	+	0.0189459i
$741$	−69.9044	+	215.144i	−0.0943379	+	0.290342i
$742$	−17.0697	−	107.774i	−0.0230050	−	0.145248i
$743$	352.944	−	352.944i	0.475025	−	0.475025i	−0.428511	−	0.903537i	$-0.640962\pi$
$743$	352.944	−	352.944i	0.475025	−	0.475025i	0.903537	+	0.428511i	$0.140962\pi$
$744$	−176.642	+	243.127i	−0.237422	+	0.326784i
$745$	209.732	−	163.101i	0.281519	−	0.218927i
$746$	−755.390	+	548.823i	−1.01259	+	0.735688i
$747$	78.0301	+	12.3588i	0.104458	+	0.0165445i
$748$	−0.0506170	−	0.0257907i	−6.76698e−5	−	3.44795e-5i
$749$			28.0160i			0.0374046i
$750$	−483.274	−	106.143i	−0.644365	−	0.141524i
$751$	−274.633			−0.365690			−0.182845	−	0.983142i	$-0.558531\pi$
$751$	−274.633			−0.365690			−0.182845	+	0.983142i	$0.558531\pi$
$752$	−815.044	+	1599.61i	−1.08384	+	2.12715i
$753$	9.27574	−	58.5647i	0.0123184	−	0.0777752i
$754$	−241.009	−	331.720i	−0.319640	−	0.439947i
$755$	93.7693	+	120.578i	0.124198	+	0.159707i
$756$	2.98467	+	2.16849i	0.00394798	+	0.00286838i
$757$	−253.627	−	253.627i	−0.335042	−	0.335042i	0.519456	−	0.854497i	$-0.326135\pi$
$757$	−253.627	−	253.627i	−0.335042	−	0.335042i	−0.854497	+	0.519456i	$0.826135\pi$
$758$	−1209.52	+	191.569i	−1.59567	+	0.252729i
$759$	0.403955	+	0.131253i	0.000532221	+	0.000172929i
$760$	200.975	−	38.5957i	0.264441	−	0.0507838i
$761$	319.924	+	984.624i	0.420399	+	1.29386i	0.907332	+	0.420416i	$0.138116\pi$
$761$	319.924	+	984.624i	0.420399	+	1.29386i	−0.486932	+	0.873440i	$0.661884\pi$
$762$	−597.315	+	304.347i	−0.783878	+	0.399406i
$763$	−3.26874	−	6.41527i	−0.00428407	−	0.00840795i
$764$	134.944	−	43.8459i	0.176628	−	0.0573899i
$765$	98.1150	−	54.0973i	0.128255	−	0.0707154i
$766$	251.929	−	775.359i	0.328890	−	1.01222i
$767$	−161.294	−	1018.37i	−0.210292	−	1.32773i
$768$	−263.414	+	263.414i	−0.342987	+	0.342987i
$769$	155.218	−	213.640i	0.201845	−	0.277815i	−0.696080	−	0.717964i	$-0.745074\pi$
$769$	155.218	−	213.640i	0.201845	−	0.277815i	0.897925	+	0.440149i	$0.145074\pi$
$770$	0.0114636	−	0.0396409i	1.48878e−5	−	5.14816e-5i
$771$	38.9591	−	28.3055i	0.0505306	−	0.0367127i
$772$	184.965	+	29.2955i	0.239592	+	0.0379476i
$773$	649.288	+	330.829i	0.839959	+	0.427980i	0.820374	−	0.571828i	$-0.193765\pi$
$773$	649.288	+	330.829i	0.839959	+	0.427980i	0.0195852	+	0.999808i	$0.493765\pi$
$774$		−	387.521i		−	0.500673i
$775$	525.519	−	436.941i	0.678089	−	0.563795i
$776$	1192.29			1.53646
$777$	1.06605	−	2.09224i	0.00137200	−	0.00269271i
$778$	−31.8685	+	201.210i	−0.0409621	+	0.258625i
$779$	−178.690	−	245.946i	−0.229384	−	0.315720i
$780$	7.00194	+	214.360i	0.00897685	+	0.274821i
$781$	−0.236604	−	0.171903i	−0.000302950	−	0.000220106i
$782$	−475.905	−	475.905i	−0.608574	−	0.608574i
$783$	45.4655	−	7.20102i	0.0580657	−	0.00919671i
$784$	−897.669	−	291.670i	−1.14499	−	0.372029i
$785$	−165.054	+	1319.66i	−0.210260	+	1.68110i
$786$	286.445	+	881.586i	0.364433	+	1.12161i
$787$	−481.835	+	245.507i	−0.612243	+	0.311953i	−0.732477	−	0.680792i	$-0.761636\pi$
$787$	−481.835	+	245.507i	−0.612243	+	0.311953i	0.120234	+	0.992746i	$0.461636\pi$
$788$	12.4134	+	24.3628i	0.0157531	+	0.0309172i
$789$	430.663	−	139.931i	0.545834	−	0.177352i
$790$	−31.8553	−	29.8401i	−0.0403232	−	0.0377722i
$791$	−15.9238	+	49.0084i	−0.0201312	+	0.0619575i
$792$	−0.0185258	−	0.116967i	−2.33912e−5	−	0.000147686i
$793$	−409.468	+	409.468i	−0.516353	+	0.516353i
$794$	−29.8021	+	41.0191i	−0.0375341	+	0.0516613i
$795$	242.065	+	669.761i	0.304484	+	0.842466i
$796$	−170.671	+	123.999i	−0.214410	+	0.155778i
$797$	−464.919	−	73.6360i	−0.583337	−	0.0923915i	−0.142210	−	0.989836i	$-0.545421\pi$
$797$	−464.919	−	73.6360i	−0.583337	−	0.0923915i	−0.441126	+	0.897445i	$0.645421\pi$
$798$	13.2059	+	6.72873i	0.0165487	+	0.00843200i
$799$			691.363i			0.865285i
$800$	406.951	−	242.031i	0.508688	−	0.302538i
$801$	−82.8337			−0.103413
$802$	−337.299	+	661.986i	−0.420572	+	0.825419i
$803$	−0.103231	+	0.651776i	−0.000128557	+	0.000811676i
$804$	−36.4501	−	50.1693i	−0.0453359	−	0.0623996i
$805$	64.2201	−	94.7489i	0.0797766	−	0.117701i
$806$	−1023.65	−	743.724i	−1.27003	−	0.922734i
$807$	−423.451	−	423.451i	−0.524722	−	0.524722i
$808$	−692.859	+	109.738i	−0.857499	+	0.135814i
$809$	−29.6560	−	9.63580i	−0.0366575	−	0.0119108i	0.290631	−	0.956835i	$-0.406135\pi$
$809$	−29.6560	−	9.63580i	−0.0366575	−	0.0119108i	−0.327288	+	0.944925i	$0.606135\pi$
$810$	−93.1072	−	43.6723i	−0.114947	−	0.0539165i
$811$	153.370	+	472.026i	0.189113	+	0.582029i	0.999995	−	0.00318021i	$-0.00101230\pi$
$811$	153.370	+	472.026i	0.189113	+	0.582029i	−0.810882	+	0.585209i	$0.801012\pi$
$812$	−5.60425	+	2.85551i	−0.00690179	+	0.00351664i
$813$	−342.165	−	671.536i	−0.420867	−	0.825998i
$814$	0.0315648	−	0.0102560i	3.87774e−5	−	1.25995e-5i
$815$	350.895	−	748.090i	0.430546	−	0.917902i
$816$	−77.5423	+	238.651i	−0.0950274	+	0.292464i
$817$	−57.0209	−	360.016i	−0.0697930	−	0.440656i
$818$	663.656	−	663.656i	0.811315	−	0.811315i
$819$	20.7355	−	28.5399i	0.0253180	−	0.0348473i
$820$	−238.588	−	161.713i	−0.290961	−	0.197211i
$821$	61.8613	−	44.9449i	0.0753488	−	0.0547441i	−0.549473	−	0.835511i	$-0.685172\pi$
$821$	61.8613	−	44.9449i	0.0753488	−	0.0547441i	0.624822	+	0.780767i	$0.285172\pi$
$822$	−908.613	−	143.910i	−1.10537	−	0.175073i
$823$	−921.277	−	469.414i	−1.11941	−	0.570370i	−0.206469	−	0.978453i	$-0.566197\pi$
$823$	−921.277	−	469.414i	−1.11941	−	0.570370i	−0.912945	+	0.408084i	$0.866197\pi$
$824$		−	386.100i		−	0.468568i
$825$	−0.0246819	+	0.268186i	−2.99175e−5	+	0.000325074i
$826$	−67.5539			−0.0817844
$827$	517.902	−	1016.44i	0.626242	−	1.22907i	−0.332046	−	0.943263i	$-0.607739\pi$
$827$	517.902	−	1016.44i	0.626242	−	1.22907i	0.958288	−	0.285806i	$-0.0922612\pi$
$828$	−22.6265	+	142.858i	−0.0273267	+	0.172534i
$829$	448.180	+	616.867i	0.540627	+	0.744109i	0.988703	−	0.149886i	$-0.0478907\pi$
$829$	448.180	+	616.867i	0.540627	+	0.744109i	−0.448076	+	0.893995i	$0.647891\pi$
$830$	282.999	−	102.281i	0.340963	−	0.123231i
$831$	−500.552	−	363.672i	−0.602349	−	0.437632i
$832$	491.215	+	491.215i	0.590403	+	0.590403i
$833$	−359.006	+	56.8609i	−0.430979	+	0.0682604i
$834$	682.993	+	221.918i	0.818937	+	0.266089i
$835$	713.809	−	762.016i	0.854862	−	0.912594i
$836$	0.0151563	+	0.0466464i	1.81296e−5	+	5.57972e-5i
$837$	126.567	−	64.4893i	0.151215	−	0.0770481i
$838$	−330.729	−	649.093i	−0.394665	−	0.774574i
$839$	−10.6786	+	3.46968i	−0.0127277	+	0.00413549i	−0.315374	−	0.948967i	$-0.602130\pi$
$839$	−10.6786	+	3.46968i	−0.0127277	+	0.00413549i	0.302646	+	0.953103i	$0.402130\pi$
$840$	−31.6671	−	3.96071i	−0.0376990	−	0.00471513i
$841$	235.632	−	725.200i	0.280180	−	0.862306i
$842$	173.516	+	1095.54i	0.206076	+	1.30112i
$843$	124.774	−	124.774i	0.148012	−	0.148012i
$844$	62.4578	−	85.9658i	0.0740021	−	0.101855i
$845$	1205.20	−	39.3671i	1.42627	−	0.0465882i
$846$	513.398	−	373.005i	0.606853	−	0.440904i
$847$	69.3902	+	10.9903i	0.0819247	+	0.0129756i
$848$	−1421.15	−	724.114i	−1.67589	−	0.853908i
$849$		−	431.653i		−	0.508425i
$850$	227.774	−	360.884i	0.267969	−	0.424569i
$851$	92.0609			0.108180
$852$	45.2135	−	88.7366i	0.0530675	−	0.104151i
$853$	61.8304	−	390.382i	0.0724859	−	0.457658i	−0.924572	−	0.381007i	$-0.875577\pi$
$853$	61.8304	−	390.382i	0.0724859	−	0.457658i	0.997058	−	0.0766507i	$-0.0244226\pi$
$854$	22.3007	+	30.6943i	0.0261132	+	0.0359418i
$855$	−92.9247	−	26.8725i	−0.108684	−	0.0314299i
$856$	247.758	+	180.007i	0.289437	+	0.210288i
$857$	−298.212	−	298.212i	−0.347973	−	0.347973i	0.511381	−	0.859354i	$-0.329134\pi$
$857$	−298.212	−	298.212i	−0.347973	−	0.347973i	−0.859354	+	0.511381i	$0.829134\pi$
$858$	0.492473	−	0.0780000i	0.000573977	−	9.09091e-5i
$859$	−943.939	−	306.704i	−1.09888	−	0.357048i	−0.297209	−	0.954812i	$-0.596056\pi$
$859$	−943.939	−	306.704i	−1.09888	−	0.357048i	−0.801672	+	0.597764i	$0.796056\pi$
$860$	−166.862	−	302.633i	−0.194025	−	0.351899i
$861$	14.6500	+	45.0881i	0.0170151	+	0.0523671i
$862$	1107.70	−	564.401i	1.28503	−	0.654758i
$863$	64.0274	+	125.661i	0.0741916	+	0.145609i	0.925123	−	0.379668i	$-0.123962\pi$
$863$	64.0274	+	125.661i	0.0741916	+	0.145609i	−0.850931	+	0.525277i	$0.823962\pi$
$864$	93.5953	−	30.4110i	0.108328	−	0.0351979i
$865$	210.204	+	1094.57i	0.243010	+	1.26540i
$866$	−197.513	+	607.882i	−0.228075	+	0.701942i
$867$	−63.1884	−	398.956i	−0.0728817	−	0.460157i
$868$	−13.7246	+	13.7246i	−0.0158118	+	0.0158118i
$869$	−0.0139647	+	0.0192208i	−1.60699e−5	+	2.21183e-5i
$870$	138.407	−	107.634i	0.159089	−	0.123717i
$871$	−479.727	+	348.542i	−0.550777	+	0.400163i
$872$	−77.7350	−	12.3120i	−0.0891457	−	0.0141193i
$873$	−502.144	−	255.855i	−0.575194	−	0.293076i
$874$			581.075i			0.664845i
$875$	67.5797	+	26.4671i	0.0772339	+	0.0302481i
$876$	−224.717			−0.256526
$877$	138.241	−	271.313i	0.157629	−	0.309364i	−0.798663	−	0.601779i	$-0.794459\pi$
$877$	138.241	−	271.313i	0.157629	−	0.309364i	0.956292	+	0.292415i	$0.0944588\pi$
$878$	130.084	−	821.320i	0.148160	−	0.935444i
$879$	−409.635	−	563.814i	−0.466024	−	0.641427i
$880$	−0.370285	−	0.476151i	−0.000420778	−	0.000541081i
$881$	651.161	+	473.096i	0.739116	+	0.536999i	0.892434	−	0.451178i	$-0.148996\pi$
$881$	651.161	+	473.096i	0.739116	+	0.536999i	−0.153318	+	0.988177i	$0.548996\pi$
$882$	235.916	+	235.916i	0.267478	+	0.267478i
$883$	351.604	−	55.6887i	0.398193	−	0.0630676i	0.0458732	−	0.998947i	$-0.485393\pi$
$883$	351.604	−	55.6887i	0.398193	−	0.0630676i	0.352320	+	0.935880i	$0.385393\pi$
$884$	−175.928	−	57.1626i	−0.199014	−	0.0646635i
$885$	432.983	−	83.1511i	0.489247	−	0.0939561i
$886$	−268.220	−	825.497i	−0.302732	−	0.931713i
$887$	−375.883	+	191.522i	−0.423769	+	0.215921i	−0.652851	−	0.757486i	$-0.726427\pi$
$887$	−375.883	+	191.522i	−0.423769	+	0.215921i	0.229083	+	0.973407i	$0.426427\pi$
$888$	−11.6531	−	22.8704i	−0.0131228	−	0.0257550i
$889$	93.5209	−	30.3868i	0.105198	−	0.0341809i
$890$	−276.292	+	152.338i	−0.310441	+	0.171167i
$891$	−0.0172979	+	0.0532373i	−1.94140e−5	+	5.97501e-5i
$892$	54.8380	+	346.233i	0.0614775	+	0.388154i
$893$	422.073	−	422.073i	0.472646	−	0.472646i
$894$	123.632	−	170.165i	0.138291	−	0.190341i
$895$	−86.5801	+	299.392i	−0.0967375	+	0.334516i
$896$	72.4079	−	52.6074i	0.0808124	−	0.0587136i
$897$	1366.03	+	216.358i	1.52289	+	0.241202i
$898$	602.288	+	306.881i	0.670700	+	0.341739i
$899$			242.180i			0.269388i
$900$	−91.5164	+	5.98503i	−0.101685	+	0.00665003i
$901$	−614.231			−0.681722
$902$	−0.304207	+	0.597040i	−0.000337258	+	0.000661906i
$903$	−8.89216	+	56.1429i	−0.00984736	+	0.0621738i
$904$	331.090	+	455.706i	0.366250	+	0.504099i
$905$	−25.9646	−	794.892i	−0.0286902	−	0.878334i
$906$	97.8308	+	71.0782i	0.107981	+	0.0784528i
$907$	860.780	+	860.780i	0.949041	+	0.949041i	0.998763	−	0.0497225i	$-0.0158337\pi$
$907$	860.780	+	860.780i	0.949041	+	0.949041i	−0.0497225	+	0.998763i	$0.515834\pi$
$908$	148.323	−	23.4920i	0.163351	−	0.0258723i
$909$	315.353	+	102.464i	0.346923	+	0.112722i
$910$	16.6759	−	133.330i	0.0183252	−	0.146516i
$911$	4.89509	+	15.0655i	0.00537332	+	0.0165374i	0.953707	−	0.300737i	$-0.0972325\pi$
$911$	4.89509	+	15.0655i	0.00537332	+	0.0165374i	−0.948334	+	0.317274i	$0.897233\pi$
$912$	193.034	−	98.3558i	0.211660	−	0.107846i
$913$	−0.0743593	−	0.145938i	−8.14451e−5	−	0.000159845i
$914$	−174.061	+	56.5559i	−0.190439	+	0.0618774i
$915$	−180.716	−	169.284i	−0.197504	−	0.185010i
$916$	−97.5281	+	300.161i	−0.106472	+	0.327686i
$917$	−21.2701	−	134.294i	−0.0231953	−	0.146450i
$918$	62.7196	−	62.7196i	0.0683220	−	0.0683220i
$919$	513.924	−	707.355i	0.559220	−	0.769701i	−0.432007	−	0.901870i	$-0.642194\pi$
$919$	513.924	−	707.355i	0.559220	−	0.769701i	0.991227	+	0.132170i	$0.0421943\pi$
$920$	−425.283	−	1176.70i	−0.462264	−	1.27902i
$921$	−494.315	+	359.141i	−0.536715	+	0.389946i
$922$	309.449	+	49.0119i	0.335628	+	0.0531582i
$923$	−848.514	−	432.339i	−0.919300	−	0.468407i
$924$		−	0.00764866i		−	8.27777e-6i
$925$	12.8747	+	56.9361i	0.0139186	+	0.0615525i
$926$	−1780.16			−1.92242
$927$	−82.8538	+	162.610i	−0.0893784	+	0.175415i
$928$	−26.2469	+	165.716i	−0.0282833	+	0.178574i
$929$	−88.8115	−	122.239i	−0.0955991	−	0.131581i	0.758538	−	0.651629i	$-0.225914\pi$
$929$	−88.8115	−	122.239i	−0.0955991	−	0.131581i	−0.854137	+	0.520048i	$0.825914\pi$
$930$	303.565	−	447.873i	0.326414	−	0.481584i
$931$	253.884	+	184.458i	0.272701	+	0.198129i
$932$	111.662	+	111.662i	0.119809	+	0.119809i
$933$	−722.735	+	114.470i	−0.774635	+	0.122690i
$934$	1349.68	+	438.537i	1.44505	+	0.469525i
$935$	−0.210300	−	0.0986422i	−0.000224920	−	0.000105500i
$936$	−119.163	−	366.746i	−0.127311	−	0.391822i
$937$	1096.04	−	558.460i	1.16973	−	0.596009i	0.242375	−	0.970183i	$-0.422074\pi$
$937$	1096.04	−	558.460i	1.16973	−	0.596009i	0.927359	+	0.374174i	$0.122074\pi$
$938$	17.6379	+	34.6164i	0.0188038	+	0.0369044i
$939$	−659.199	+	214.187i	−0.702023	+	0.228101i
$940$	240.324	−	512.359i	0.255664	−	0.545063i
$941$	−485.873	+	1495.36i	−0.516337	+	1.58912i	0.264499	+	0.964386i	$0.414793\pi$
$941$	−485.873	+	1495.36i	−0.516337	+	1.58912i	−0.780836	+	0.624736i	$0.785207\pi$
$942$	164.706	+	1039.91i	0.174847	+	1.10394i
$943$	−1314.27	+	1314.27i	−1.39372	+	1.39372i
$944$	−580.411	+	798.867i	−0.614842	+	0.846258i
$945$	12.4870	+	8.46358i	0.0132137	+	0.00895617i
$946$	−0.649979	+	0.472237i	−0.000687081	+	0.000499194i
$947$	−697.211	−	110.427i	−0.736231	−	0.116608i	−0.222952	−	0.974829i	$-0.571569\pi$
$947$	−697.211	−	110.427i	−0.736231	−	0.116608i	−0.513279	+	0.858222i	$0.671569\pi$
$948$	−7.20862	−	3.67298i	−0.00760403	−	0.00387445i
$949$			2148.78i			2.26426i
$950$	−359.372	+	81.2630i	−0.378286	+	0.0855400i
$951$	−78.0293			−0.0820497
$952$	12.4962	−	24.5253i	0.0131263	−	0.0257618i
$953$	−209.882	+	1325.15i	−0.220233	+	1.39050i	0.591422	+	0.806362i	$0.298567\pi$
$953$	−209.882	+	1325.15i	−0.220233	+	1.39050i	−0.811656	+	0.584136i	$0.801433\pi$
$954$	331.391	+	456.121i	0.347370	+	0.478114i
$955$	545.624	−	197.199i	0.571334	−	0.206491i
$956$	133.480	+	96.9787i	0.139623	+	0.101442i
$957$	−0.0674828	−	0.0674828i	−7.05149e−5	−	7.05149e-5i
$958$	349.535	−	55.3610i	0.364860	−	0.0577881i
$959$	128.335	+	41.6985i	0.133822	+	0.0434813i
$960$	−203.080	+	216.795i	−0.211541	+	0.225828i
$961$	−66.0248	−	203.203i	−0.0687042	−	0.211450i
$962$	96.2922	−	49.0633i	0.100096	−	0.0510014i
$963$	−65.7176	−	128.978i	−0.0682426	−	0.133934i
$964$	320.842	−	104.248i	0.332824	−	0.108141i
$965$	759.808	+	95.0315i	0.787366	+	0.0984783i
$966$	28.0019	−	86.1810i	0.0289875	−	0.0892143i
$967$	−95.8233	−	605.004i	−0.0990933	−	0.625651i	−0.986386	−	0.164445i	$-0.947417\pi$
$967$	−95.8233	−	605.004i	−0.0990933	−	0.625651i	0.887293	−	0.461206i	$-0.152583\pi$
$968$	543.033	−	543.033i	0.560984	−	0.560984i
$969$	49.0392	−	67.4967i	0.0506081	−	0.0696560i
$970$	−2145.45	+	70.0795i	−2.21180	+	0.0722470i
$971$	−769.428	+	559.022i	−0.792408	+	0.575718i	−0.908677	−	0.417500i	$-0.862906\pi$
$971$	−769.428	+	559.022i	−0.792408	+	0.575718i	0.116269	+	0.993218i	$0.462906\pi$
$972$	−18.8273	−	2.98195i	−0.0193696	−	0.00306785i
$973$	−93.8578	−	47.8229i	−0.0964623	−	0.0491500i
$974$			1335.78i			1.37143i
$975$	57.2298	+	875.095i	0.0586973	+	0.897533i
$976$	554.582			0.568220
$977$	127.996	−	251.207i	0.131010	−	0.257121i	−0.816178	−	0.577800i	$-0.803911\pi$
$977$	127.996	−	251.207i	0.131010	−	0.257121i	0.947188	+	0.320679i	$0.103911\pi$
$978$	102.332	−	646.100i	0.104634	−	0.660634i
$979$	0.100942	+	0.138935i	0.000103107	+	0.000141915i
$980$	285.820	+	82.6551i	0.291653	+	0.0843419i
$981$	30.0968	+	21.8666i	0.0306797	+	0.0222901i
$982$	704.552	+	704.552i	0.717466	+	0.717466i
$983$	1526.38	−	241.755i	1.55278	−	0.245936i	0.679691	−	0.733498i	$-0.262114\pi$
$983$	1526.38	−	241.755i	1.55278	−	0.245936i	0.873088	+	0.487562i	$0.162114\pi$
$984$	492.861	+	160.140i	0.500875	+	0.162744i
$985$	53.9824	+	97.9065i	0.0548044	+	0.0993975i
$986$	46.7303	+	143.821i	0.0473938	+	0.145863i
$987$	−82.9386	+	42.2593i	−0.0840310	+	0.0428159i
$988$	72.5058	+	142.301i	0.0733864	+	0.144029i
$989$	−2119.47	+	688.656i	−2.14304	+	0.696316i
$990$	0.0402109	+	0.209386i	4.06171e−5	+	0.000211501i
$991$	−34.0145	+	104.686i	−0.0343234	+	0.105636i	−0.966750	−	0.255722i	$-0.917687\pi$
$991$	−34.0145	+	104.686i	−0.0343234	+	0.105636i	0.932427	+	0.361358i	$0.117687\pi$
$992$	80.9948	+	511.381i	0.0816480	+	0.515505i
$993$	126.960	−	126.960i	0.127855	−	0.127855i
$994$	−36.6742	+	50.4778i	−0.0368956	+	0.0507825i
$995$	−680.929	+	529.533i	−0.684351	+	0.532194i
$996$	45.1236	−	32.7842i	0.0453048	−	0.0329159i
$997$	−315.326	−	49.9427i	−0.316274	−	0.0500929i	−0.00372083	−	0.999993i	$-0.501184\pi$
$997$	−315.326	−	49.9427i	−0.316274	−	0.0500929i	−0.312554	+	0.949900i	$0.601184\pi$
$998$	−499.859	−	254.691i	−0.500861	−	0.255201i
$999$			12.1327i			0.0121449i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.3.k.a.67.8	yes	80
3.2	odd	2		225.3.r.b.217.3		80
5.2	odd	4		375.3.k.b.268.8		80
5.3	odd	4		375.3.k.c.268.3		80
5.4	even	2		375.3.k.a.232.3		80
25.3	odd	20	inner	75.3.k.a.28.8	✓	80
25.4	even	10		375.3.k.b.7.8		80
25.21	even	5		375.3.k.c.7.3		80
25.22	odd	20		375.3.k.a.118.3		80
75.53	even	20		225.3.r.b.28.3		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.k.a.28.8	✓	80	25.3	odd	20	inner
75.3.k.a.67.8	yes	80	1.1	even	1	trivial
225.3.r.b.28.3		80	75.53	even	20
225.3.r.b.217.3		80	3.2	odd	2
375.3.k.a.118.3		80	25.22	odd	20
375.3.k.a.232.3		80	5.4	even	2
375.3.k.b.7.8		80	25.4	even	10
375.3.k.b.268.8		80	5.2	odd	4
375.3.k.c.7.3		80	25.21	even	5
375.3.k.c.268.3		80	5.3	odd	4

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	75.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.03753 - 2.03626i) q^{2} +(0.270952 - 1.71073i) q^{3} +(-0.718759 - 0.989286i) q^{4} +(-3.06942 - 3.94698i) q^{5} +(-3.20237 - 2.32666i) q^{6} +(0.410561 + 0.410561i) q^{7} +(6.26868 - 0.992861i) q^{8} +(-2.85317 - 0.927051i) q^{9} +O(q^{10})\)	\(q+(1.03753 - 2.03626i) q^{2} +(0.270952 - 1.71073i) q^{3} +(-0.718759 - 0.989286i) q^{4} +(-3.06942 - 3.94698i) q^{5} +(-3.20237 - 2.32666i) q^{6} +(0.410561 + 0.410561i) q^{7} +(6.26868 - 0.992861i) q^{8} +(-2.85317 - 0.927051i) q^{9} +(-11.2217 + 2.15504i) q^{10} +(0.00192198 + 0.00591526i) q^{11} +(-1.88715 + 0.961550i) q^{12} +(9.19450 + 18.0452i) q^{13} +(1.26198 - 0.410042i) q^{14} +(-7.58387 + 4.18149i) q^{15} +(5.99369 - 18.4467i) q^{16} +(-1.16847 - 7.37741i) q^{17} +(-4.84796 + 4.84796i) q^{18} +(-3.79052 + 5.21721i) q^{19} +(-1.69852 + 5.87346i) q^{20} +(0.813601 - 0.591115i) q^{21} +(0.0140391 + 0.00222358i) q^{22} +(35.1301 + 17.8997i) q^{23} -10.9930i q^{24} +(-6.15733 + 24.2299i) q^{25} +46.2843 q^{26} +(-2.35900 + 4.62981i) q^{27} +(0.111068 - 0.701257i) q^{28} +(-5.20713 - 7.16700i) q^{29} +(0.646138 + 19.7812i) q^{30} +(-22.1165 - 16.0686i) q^{31} +(-13.3922 - 13.3922i) q^{32} +(0.0106402 - 0.00168524i) q^{33} +(-16.2346 - 5.27496i) q^{34} +(0.360293 - 2.88066i) q^{35} +(1.13362 + 3.48893i) q^{36} +(2.08045 - 1.06004i) q^{37} +(6.69083 + 13.1315i) q^{38} +(33.3617 - 10.8399i) q^{39} +(-23.1600 - 21.6948i) q^{40} +(-14.5675 + 44.8341i) q^{41} +(-0.359533 - 2.27000i) q^{42} +(-39.9674 + 39.9674i) q^{43} +(0.00447044 - 0.00615304i) q^{44} +(5.09852 + 14.1069i) q^{45} +(72.8969 - 52.9627i) q^{46} +(-91.4202 - 14.4795i) q^{47} +(-29.9332 - 15.2517i) q^{48} -48.6629i q^{49} +(42.9500 + 37.6771i) q^{50} -12.9373 q^{51} +(11.2433 - 22.0661i) q^{52} +(12.8641 - 81.2210i) q^{53} +(6.97997 + 9.60710i) q^{54} +(0.0174481 - 0.0257425i) q^{55} +(2.98131 + 2.16605i) q^{56} +(7.89816 + 7.89816i) q^{57} +(-19.9964 + 3.16712i) q^{58} +(-48.4185 - 15.7321i) q^{59} +(9.58767 + 4.49714i) q^{60} +(8.83561 + 27.1932i) q^{61} +(-55.6663 + 28.3634i) q^{62} +(-0.790790 - 1.55201i) q^{63} +(32.6221 - 10.5996i) q^{64} +(43.0024 - 91.6789i) q^{65} +(0.00760787 - 0.0234146i) q^{66} +(4.58023 + 28.9184i) q^{67} +(-6.45852 + 6.45852i) q^{68} +(40.1401 - 55.2481i) q^{69} +(-5.49197 - 3.72242i) q^{70} +(-38.0412 + 27.6386i) q^{71} +(-18.8060 - 2.97858i) q^{72} +(94.5348 + 48.1679i) q^{73} -5.33616i q^{74} +(39.7824 + 17.0987i) q^{75} +7.88578 q^{76} +(-0.00163948 + 0.00321767i) q^{77} +(12.5409 - 79.1798i) q^{78} +(2.24525 + 3.09032i) q^{79} +(-91.2059 + 32.9636i) q^{80} +(7.28115 + 5.29007i) q^{81} +(76.1798 + 76.1798i) q^{82} +(-26.0100 + 4.11959i) q^{83} +(-1.16956 - 0.380015i) q^{84} +(-25.5320 + 27.2563i) q^{85} +(39.9169 + 122.851i) q^{86} +(-13.6717 + 6.96606i) q^{87} +(0.0179213 + 0.0351726i) q^{88} +(26.2598 - 8.53234i) q^{89} +(34.0152 + 4.25439i) q^{90} +(-3.63376 + 11.1836i) q^{91} +(-7.54216 - 47.6193i) q^{92} +(-33.4815 + 33.4815i) q^{93} +(-124.335 + 171.133i) q^{94} +(32.2269 - 1.05267i) q^{95} +(-26.5390 + 19.2817i) q^{96} +(185.544 + 29.3872i) q^{97} +(-99.0904 - 50.4891i) q^{98} -0.0186590i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8}+O(q^{10}) \) 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8	\( 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8} - 4 q^{10} - 24 q^{12} + 32 q^{13} - 24 q^{15} + 80 q^{16} - 100 q^{17} - 48 q^{18} - 100 q^{19} - 244 q^{20} - 100 q^{22} - 96 q^{23} - 16 q^{25} - 40 q^{26} + 196 q^{28} + 200 q^{29} + 264 q^{30} + 636 q^{32} + 216 q^{33} + 100 q^{34} + 260 q^{35} - 120 q^{36} - 184 q^{37} - 564 q^{38} - 948 q^{40} + 160 q^{41} - 12 q^{42} - 472 q^{43} - 700 q^{44} - 36 q^{45} - 288 q^{47} - 48 q^{48} + 16 q^{50} + 620 q^{52} + 304 q^{53} + 604 q^{55} + 72 q^{57} + 1272 q^{58} + 800 q^{59} + 84 q^{60} - 240 q^{61} + 1212 q^{62} - 12 q^{63} + 100 q^{64} + 272 q^{65} - 80 q^{67} + 104 q^{68} - 260 q^{70} + 36 q^{72} - 116 q^{73} - 24 q^{75} - 88 q^{77} - 120 q^{78} + 200 q^{79} - 164 q^{80} + 180 q^{81} - 168 q^{82} - 1264 q^{83} - 1200 q^{84} - 212 q^{85} - 876 q^{87} - 212 q^{88} - 1500 q^{89} - 444 q^{90} - 1504 q^{92} - 648 q^{93} - 200 q^{94} - 784 q^{95} + 60 q^{96} - 260 q^{97} - 92 q^{98}+O(q^{100}) \) 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8 - 4 * q^10 - 24 * q^12 + 32 * q^13 - 24 * q^15 + 80 * q^16 - 100 * q^17 - 48 * q^18 - 100 * q^19 - 244 * q^20 - 100 * q^22 - 96 * q^23 - 16 * q^25 - 40 * q^26 + 196 * q^28 + 200 * q^29 + 264 * q^30 + 636 * q^32 + 216 * q^33 + 100 * q^34 + 260 * q^35 - 120 * q^36 - 184 * q^37 - 564 * q^38 - 948 * q^40 + 160 * q^41 - 12 * q^42 - 472 * q^43 - 700 * q^44 - 36 * q^45 - 288 * q^47 - 48 * q^48 + 16 * q^50 + 620 * q^52 + 304 * q^53 + 604 * q^55 + 72 * q^57 + 1272 * q^58 + 800 * q^59 + 84 * q^60 - 240 * q^61 + 1212 * q^62 - 12 * q^63 + 100 * q^64 + 272 * q^65 - 80 * q^67 + 104 * q^68 - 260 * q^70 + 36 * q^72 - 116 * q^73 - 24 * q^75 - 88 * q^77 - 120 * q^78 + 200 * q^79 - 164 * q^80 + 180 * q^81 - 168 * q^82 - 1264 * q^83 - 1200 * q^84 - 212 * q^85 - 876 * q^87 - 212 * q^88 - 1500 * q^89 - 444 * q^90 - 1504 * q^92 - 648 * q^93 - 200 * q^94 - 784 * q^95 + 60 * q^96 - 260 * q^97 - 92 * q^98

Introduction

L-functions

Modular forms

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