LMFDB - Embedded newform 25.4.d.a.16.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,4,Mod(6,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("25.6");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	25.d (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.47504775014$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			16.6
Character	$\chi$	$=$	25.16
Dual form			25.4.d.a.11.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.27143 + 1.65029i) q^{2} +(0.411392 + 1.26614i) q^{3} +(-0.0362106 - 0.111445i) q^{4} +(9.59405 + 5.74058i) q^{5} +(-1.15504 + 3.55485i) q^{6} -35.1773 q^{7} +(7.04252 - 21.6747i) q^{8} +(20.4096 - 14.8284i) q^{9} +O(q^{10})$	\(q+(2.27143 + 1.65029i) q^{2} +(0.411392 + 1.26614i) q^{3} +(-0.0362106 - 0.111445i) q^{4} +(9.59405 + 5.74058i) q^{5} +(-1.15504 + 3.55485i) q^{6} -35.1773 q^{7} +(7.04252 - 21.6747i) q^{8} +(20.4096 - 14.8284i) q^{9} +(12.3186 + 28.8722i) q^{10} +(-14.3169 - 10.4018i) q^{11} +(0.126207 - 0.0916951i) q^{12} +(0.739994 - 0.537637i) q^{13} +(-79.9025 - 58.0526i) q^{14} +(-3.32144 + 14.5090i) q^{15} +(51.0076 - 37.0592i) q^{16} +(-28.4167 + 87.4576i) q^{17} +70.8301 q^{18} +(-19.0393 + 58.5968i) q^{19} +(0.292352 - 1.27708i) q^{20} +(-14.4717 - 44.5392i) q^{21} +(-15.3537 - 47.2539i) q^{22} +(86.9971 + 63.2071i) q^{23} +30.3403 q^{24} +(59.0915 + 110.151i) q^{25} +2.56810 q^{26} +(56.2512 + 40.8689i) q^{27} +(1.27379 + 3.92032i) q^{28} +(-34.5348 - 106.287i) q^{29} +(-31.4884 + 27.4748i) q^{30} +(61.0355 - 187.848i) q^{31} -5.30253 q^{32} +(7.28026 - 22.4063i) q^{33} +(-208.877 + 151.758i) q^{34} +(-337.492 - 201.938i) q^{35} +(-2.39160 - 1.73760i) q^{36} +(26.0940 - 18.9584i) q^{37} +(-139.948 + 101.678i) q^{38} +(0.985150 + 0.715753i) q^{39} +(191.991 - 167.520i) q^{40} +(-119.955 + 87.1521i) q^{41} +(40.6312 - 125.050i) q^{42} -162.956 q^{43} +(-0.640806 + 1.97220i) q^{44} +(280.935 - 25.1018i) q^{45} +(93.2976 + 287.140i) q^{46} +(-8.22946 - 25.3277i) q^{47} +(67.9061 + 49.3367i) q^{48} +894.440 q^{49} +(-47.5585 + 347.717i) q^{50} -122.424 q^{51} +(-0.0867125 - 0.0630003i) q^{52} +(-159.325 - 490.352i) q^{53} +(60.3250 + 185.661i) q^{54} +(-77.6443 - 181.983i) q^{55} +(-247.737 + 762.455i) q^{56} -82.0241 q^{57} +(96.9612 - 298.416i) q^{58} +(91.9115 - 66.7776i) q^{59} +(1.73722 - 0.155223i) q^{60} +(162.310 + 117.925i) q^{61} +(448.641 - 325.957i) q^{62} +(-717.954 + 521.624i) q^{63} +(-420.105 - 305.224i) q^{64} +(10.1859 - 0.910121i) q^{65} +(53.5135 - 38.8798i) q^{66} +(-102.839 + 316.507i) q^{67} +10.7757 q^{68} +(-44.2388 + 136.153i) q^{69} +(-433.333 - 1015.65i) q^{70} +(-99.3996 - 305.921i) q^{71} +(-177.666 - 546.801i) q^{72} +(252.369 + 183.357i) q^{73} +90.5574 q^{74} +(-115.156 + 120.133i) q^{75} +7.21973 q^{76} +(503.629 + 365.908i) q^{77} +(1.05650 + 3.25156i) q^{78} +(233.493 + 718.618i) q^{79} +(702.110 - 62.7344i) q^{80} +(181.882 - 559.774i) q^{81} -416.294 q^{82} +(113.867 - 350.448i) q^{83} +(-4.43963 + 3.22558i) q^{84} +(-774.689 + 675.944i) q^{85} +(-370.143 - 268.925i) q^{86} +(120.367 - 87.4515i) q^{87} +(-326.283 + 237.058i) q^{88} +(-711.811 - 517.161i) q^{89} +(679.547 + 406.606i) q^{90} +(-26.0310 + 18.9126i) q^{91} +(3.89388 - 11.9841i) q^{92} +262.951 q^{93} +(23.1053 - 71.1109i) q^{94} +(-519.043 + 452.884i) q^{95} +(-2.18142 - 6.71373i) q^{96} +(208.265 + 640.972i) q^{97} +(2031.65 + 1476.08i) q^{98} -446.445 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - q^{2} - 7 q^{3} - 31 q^{4} - 20 q^{5} + q^{6} - 16 q^{7} + 100 q^{8} - 34 q^{9}+O(q^{10}) $ 28 * q - q^2 - 7 * q^3 - 31 * q^4 - 20 * q^5 + q^6 - 16 * q^7 + 100 * q^8 - 34 * q^9	\( 28 q - q^{2} - 7 q^{3} - 31 q^{4} - 20 q^{5} + q^{6} - 16 q^{7} + 100 q^{8} - 34 q^{9} - 25 q^{10} - 89 q^{11} + 139 q^{12} + 33 q^{13} - 17 q^{14} + 225 q^{15} - 207 q^{16} - 191 q^{17} - 552 q^{18} - 115 q^{19} - 225 q^{20} - 144 q^{21} + 808 q^{22} + 433 q^{23} + 780 q^{24} + 90 q^{25} + 586 q^{26} + 35 q^{27} - 13 q^{28} - 5 q^{29} + 675 q^{30} - 639 q^{31} - 1386 q^{32} + 251 q^{33} - 777 q^{34} - 1030 q^{35} + 673 q^{36} + 699 q^{37} - 2355 q^{38} - 1133 q^{39} + 410 q^{40} + 341 q^{41} - 2407 q^{42} - 172 q^{43} + 548 q^{44} + 470 q^{45} - 1239 q^{46} + 2319 q^{47} + 4738 q^{48} + 1344 q^{49} + 2335 q^{50} + 2006 q^{51} + 2344 q^{52} - 927 q^{53} + 1615 q^{54} + 1225 q^{55} - 2910 q^{56} - 770 q^{57} + 2410 q^{58} - 1905 q^{59} - 12030 q^{60} + 1391 q^{61} - 3832 q^{62} - 6142 q^{63} - 3596 q^{64} + 1215 q^{65} + 3632 q^{66} - 3611 q^{67} + 3622 q^{68} + 2687 q^{69} + 560 q^{70} - 3719 q^{71} + 9025 q^{72} + 4593 q^{73} + 4848 q^{74} + 3815 q^{75} + 3520 q^{76} + 1368 q^{77} - 3679 q^{78} + 775 q^{79} + 9500 q^{80} - 3712 q^{81} - 6762 q^{82} - 2447 q^{83} - 7612 q^{84} - 8185 q^{85} + 3891 q^{86} - 85 q^{87} - 10960 q^{88} - 5075 q^{89} + 685 q^{90} + 376 q^{91} - 8456 q^{92} + 4366 q^{93} + 3573 q^{94} + 3265 q^{95} - 7754 q^{96} + 7439 q^{97} + 7082 q^{98} + 6572 q^{99}+O(q^{100}) \) 28 * q - q^2 - 7 * q^3 - 31 * q^4 - 20 * q^5 + q^6 - 16 * q^7 + 100 * q^8 - 34 * q^9 - 25 * q^10 - 89 * q^11 + 139 * q^12 + 33 * q^13 - 17 * q^14 + 225 * q^15 - 207 * q^16 - 191 * q^17 - 552 * q^18 - 115 * q^19 - 225 * q^20 - 144 * q^21 + 808 * q^22 + 433 * q^23 + 780 * q^24 + 90 * q^25 + 586 * q^26 + 35 * q^27 - 13 * q^28 - 5 * q^29 + 675 * q^30 - 639 * q^31 - 1386 * q^32 + 251 * q^33 - 777 * q^34 - 1030 * q^35 + 673 * q^36 + 699 * q^37 - 2355 * q^38 - 1133 * q^39 + 410 * q^40 + 341 * q^41 - 2407 * q^42 - 172 * q^43 + 548 * q^44 + 470 * q^45 - 1239 * q^46 + 2319 * q^47 + 4738 * q^48 + 1344 * q^49 + 2335 * q^50 + 2006 * q^51 + 2344 * q^52 - 927 * q^53 + 1615 * q^54 + 1225 * q^55 - 2910 * q^56 - 770 * q^57 + 2410 * q^58 - 1905 * q^59 - 12030 * q^60 + 1391 * q^61 - 3832 * q^62 - 6142 * q^63 - 3596 * q^64 + 1215 * q^65 + 3632 * q^66 - 3611 * q^67 + 3622 * q^68 + 2687 * q^69 + 560 * q^70 - 3719 * q^71 + 9025 * q^72 + 4593 * q^73 + 4848 * q^74 + 3815 * q^75 + 3520 * q^76 + 1368 * q^77 - 3679 * q^78 + 775 * q^79 + 9500 * q^80 - 3712 * q^81 - 6762 * q^82 - 2447 * q^83 - 7612 * q^84 - 8185 * q^85 + 3891 * q^86 - 85 * q^87 - 10960 * q^88 - 5075 * q^89 + 685 * q^90 + 376 * q^91 - 8456 * q^92 + 4366 * q^93 + 3573 * q^94 + 3265 * q^95 - 7754 * q^96 + 7439 * q^97 + 7082 * q^98 + 6572 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	2.27143	+	1.65029i	0.803070	+	0.583465i	0.911813	−	0.410605i	$-0.134683\pi$
$2$	2.27143	+	1.65029i	0.803070	+	0.583465i	−0.108743	+	0.994070i	$0.534683\pi$
$3$	0.411392	+	1.26614i	0.0791725	+	0.243668i	0.982807	−	0.184637i	$-0.0591109\pi$
$3$	0.411392	+	1.26614i	0.0791725	+	0.243668i	−0.903634	+	0.428305i	$0.859111\pi$
$4$	−0.0362106	−	0.111445i	−0.00452633	−	0.0139306i
$5$	9.59405	+	5.74058i	0.858118	+	0.513453i
$5$	9.59405	+	5.74058i	0.858118	+	0.513453i
$6$	−1.15504	+	3.55485i	−0.0785905	+	0.241877i
$7$	−35.1773			−1.89939			−0.949697	−	0.313171i	$-0.898609\pi$
$7$	−35.1773			−1.89939			−0.949697	+	0.313171i	$0.898609\pi$
$8$	7.04252	−	21.6747i	0.311239	−	0.957894i
$9$	20.4096	−	14.8284i	0.755911	−	0.549202i
$10$	12.3186	+	28.8722i	0.389547	+	0.913020i
$11$	−14.3169	−	10.4018i	−0.392427	−	0.285115i	0.374022	−	0.927420i	$-0.377978\pi$
$11$	−14.3169	−	10.4018i	−0.392427	−	0.285115i	−0.766449	+	0.642305i	$0.777978\pi$
$12$	0.126207	−	0.0916951i	0.00303608	−	0.00220584i
$13$	0.739994	−	0.537637i	0.0157875	−	0.0114703i	−0.579864	−	0.814714i	$-0.696894\pi$
$13$	0.739994	−	0.537637i	0.0157875	−	0.0114703i	0.595651	+	0.803243i	$0.296894\pi$
$14$	−79.9025	−	58.0526i	−1.52535	−	1.10823i
$15$	−3.32144	+	14.5090i	−0.0571727	+	0.249747i
$16$	51.0076	−	37.0592i	0.796993	−	0.579050i
$17$	−28.4167	+	87.4576i	−0.405416	+	1.24774i	0.515132	+	0.857111i	$0.327743\pi$
$17$	−28.4167	+	87.4576i	−0.405416	+	1.24774i	−0.920548	+	0.390630i	$0.872257\pi$
$18$	70.8301			0.927489
$19$	−19.0393	+	58.5968i	−0.229890	+	0.707528i	0.767869	+	0.640607i	$0.221317\pi$
$19$	−19.0393	+	58.5968i	−0.229890	+	0.707528i	−0.997758	+	0.0669205i	$0.978683\pi$
$20$	0.292352	−	1.27708i	0.00326859	−	0.0142782i
$21$	−14.4717	−	44.5392i	−0.150380	−	0.462821i
$22$	−15.3537	−	47.2539i	−0.148792	−	0.457935i
$23$	86.9971	+	63.2071i	0.788702	+	0.573026i	0.907578	−	0.419883i	$-0.137929\pi$
$23$	86.9971	+	63.2071i	0.788702	+	0.573026i	−0.118876	+	0.992909i	$0.537929\pi$
$24$	30.3403			0.258050
$25$	59.0915	+	110.151i	0.472732	+	0.881206i
$26$	2.56810			0.0193710
$27$	56.2512	+	40.8689i	0.400947	+	0.291305i
$28$	1.27379	+	3.92032i	0.00859728	+	0.0264597i
$29$	−34.5348	−	106.287i	−0.221136	−	0.680587i	−0.998661	−	0.0517349i	$-0.983525\pi$
$29$	−34.5348	−	106.287i	−0.221136	−	0.680587i	0.777525	−	0.628853i	$-0.216475\pi$
$30$	−31.4884	+	27.4748i	−0.191632	+	0.167206i
$31$	61.0355	−	187.848i	0.353623	−	1.08834i	−0.603181	−	0.797604i	$-0.706100\pi$
$31$	61.0355	−	187.848i	0.353623	−	1.08834i	0.956804	−	0.290735i	$-0.0938997\pi$
$32$	−5.30253			−0.0292926
$33$	7.28026	−	22.4063i	0.0384040	−	0.118195i
$34$	−208.877	+	151.758i	−1.05359	+	0.765478i
$35$	−337.492	−	201.938i	−1.62990	−	0.975250i
$36$	−2.39160	−	1.73760i	−0.0110722	−	0.00804443i
$37$	26.0940	−	18.9584i	0.115941	−	0.0842363i	−0.528304	−	0.849056i	$-0.677172\pi$
$37$	26.0940	−	18.9584i	0.115941	−	0.0842363i	0.644245	+	0.764819i	$0.277172\pi$
$38$	−139.948	+	101.678i	−0.597435	+	0.434062i
$39$	0.985150	+	0.715753i	0.00404488	+	0.00293878i
$40$	191.991	−	167.520i	0.758913	−	0.662179i
$41$	−119.955	+	87.1521i	−0.456921	+	0.331972i	−0.792322	−	0.610103i	$-0.791128\pi$
$41$	−119.955	+	87.1521i	−0.456921	+	0.331972i	0.335401	+	0.942075i	$0.391128\pi$
$42$	40.6312	−	125.050i	0.149274	−	0.459419i
$43$	−162.956			−0.577922			−0.288961	−	0.957341i	$-0.593310\pi$
$43$	−162.956			−0.577922			−0.288961	+	0.957341i	$0.593310\pi$
$44$	−0.640806	+	1.97220i	−0.00219557	+	0.00675727i
$45$	280.935	−	25.1018i	0.930650	−	0.0831547i
$46$	93.2976	+	287.140i	0.299043	+	0.920360i
$47$	−8.22946	−	25.3277i	−0.0255402	−	0.0786047i	0.937474	−	0.348055i	$-0.113158\pi$
$47$	−8.22946	−	25.3277i	−0.0255402	−	0.0786047i	−0.963014	+	0.269451i	$0.913158\pi$
$48$	67.9061	+	49.3367i	0.204196	+	0.148357i
$49$	894.440			2.60770
$50$	−47.5585	+	347.717i	−0.134516	+	0.983493i
$51$	−122.424			−0.336132
$52$	−0.0867125	−	0.0630003i	−0.000231247	−	0.000168011i
$53$	−159.325	−	490.352i	−0.412924	−	1.27085i	−0.914094	−	0.405501i	$-0.867097\pi$
$53$	−159.325	−	490.352i	−0.412924	−	1.27085i	0.501170	−	0.865349i	$-0.332903\pi$
$54$	60.3250	+	185.661i	0.152022	+	0.467876i
$55$	−77.6443	−	181.983i	−0.190356	−	0.446155i
$56$	−247.737	+	762.455i	−0.591165	+	1.81942i
$57$	−82.0241			−0.190603
$58$	96.9612	−	298.416i	0.219511	−	0.675585i
$59$	91.9115	−	66.7776i	0.202811	−	0.147351i	−0.481744	−	0.876312i	$-0.659996\pi$
$59$	91.9115	−	66.7776i	0.202811	−	0.147351i	0.684555	+	0.728961i	$0.259996\pi$
$60$	1.73722	−	0.155223i	0.00373791	−	0.000333987i
$61$	162.310	+	117.925i	0.340684	+	0.247521i	0.744950	−	0.667120i	$-0.232473\pi$
$61$	162.310	+	117.925i	0.340684	+	0.247521i	−0.404266	+	0.914641i	$0.632473\pi$
$62$	448.641	−	325.957i	0.918991	−	0.667686i
$63$	−717.954	+	521.624i	−1.43577	+	1.04315i
$64$	−420.105	−	305.224i	−0.820517	−	0.596141i
$65$	10.1859	−	0.910121i	0.0194370	−	0.00173672i
$66$	53.5135	−	38.8798i	0.0998038	−	0.0725117i
$67$	−102.839	+	316.507i	−0.187520	+	0.577126i	−0.999983	−	0.00588648i	$-0.998126\pi$
$67$	−102.839	+	316.507i	−0.187520	+	0.577126i	0.812463	+	0.583013i	$0.198126\pi$
$68$	10.7757			0.0192168
$69$	−44.2388	+	136.153i	−0.0771845	+	0.237549i
$70$	−433.333	−	1015.65i	−0.739903	−	1.73418i
$71$	−99.3996	−	305.921i	−0.166149	−	0.511354i	0.832970	−	0.553318i	$-0.186638\pi$
$71$	−99.3996	−	305.921i	−0.166149	−	0.511354i	−0.999119	+	0.0419642i	$0.986638\pi$
$72$	−177.666	−	546.801i	−0.290808	−	0.895015i
$73$	252.369	+	183.357i	0.404624	+	0.293977i	0.771422	−	0.636324i	$-0.219546\pi$
$73$	252.369	+	183.357i	0.404624	+	0.293977i	−0.366798	+	0.930301i	$0.619546\pi$
$74$	90.5574			0.142258
$75$	−115.156	+	120.133i	−0.177294	+	0.184957i
$76$	7.21973			0.0108968
$77$	503.629	+	365.908i	0.745374	+	0.541546i
$78$	1.05650	+	3.25156i	0.00153365	+	0.00472009i
$79$	233.493	+	718.618i	0.332532	+	1.02343i	0.967925	+	0.251239i	$0.0808380\pi$
$79$	233.493	+	718.618i	0.332532	+	1.02343i	−0.635393	+	0.772189i	$0.719162\pi$
$80$	702.110	−	62.7344i	0.981229	−	0.0876740i
$81$	181.882	−	559.774i	0.249495	−	0.767866i
$82$	−416.294			−0.560634
$83$	113.867	−	350.448i	0.150585	−	0.463453i	−0.847102	−	0.531431i	$-0.821655\pi$
$83$	113.867	−	350.448i	0.150585	−	0.463453i	0.997687	+	0.0679775i	$0.0216546\pi$
$84$	−4.43963	+	3.22558i	−0.00576671	+	0.00418976i
$85$	−774.689	+	675.944i	−0.988551	+	0.862547i
$86$	−370.143	−	268.925i	−0.464112	−	0.337197i
$87$	120.367	−	87.4515i	0.148329	−	0.107768i
$88$	−326.283	+	237.058i	−0.395249	+	0.287165i
$89$	−711.811	−	517.161i	−0.847773	−	0.615943i	0.0767580	−	0.997050i	$-0.475543\pi$
$89$	−711.811	−	517.161i	−0.847773	−	0.615943i	−0.924531	+	0.381107i	$0.875543\pi$
$90$	679.547	+	406.606i	0.795895	+	0.476222i
$91$	−26.0310	+	18.9126i	−0.0299867	+	0.0217866i
$92$	3.89388	−	11.9841i	0.00441267	−	0.0135808i
$93$	262.951			0.293191
$94$	23.1053	−	71.1109i	0.0253525	−	0.0780269i
$95$	−519.043	+	452.884i	−0.560555	+	0.489105i
$96$	−2.18142	−	6.71373i	−0.00231917	−	0.00713768i
$97$	208.265	+	640.972i	0.218001	+	0.670937i	0.998927	+	0.0463137i	$0.0147474\pi$
$97$	208.265	+	640.972i	0.218001	+	0.670937i	−0.780926	+	0.624623i	$0.785253\pi$
$98$	2031.65	+	1476.08i	2.09416	+	1.52150i
$99$	−446.445			−0.453226
$100$	10.1360	−	10.5741i	0.0101360	−	0.0105741i
$101$	1209.88			1.19196			0.595978	−	0.803001i	$-0.296765\pi$
$101$	1209.88			1.19196			0.595978	+	0.803001i	$0.296765\pi$
$102$	−278.076	−	202.034i	−0.269938	−	0.196121i
$103$	−270.354	−	832.065i	−0.258629	−	0.795978i	−0.993093	−	0.117331i	$-0.962566\pi$
$103$	−270.354	−	832.065i	−0.258629	−	0.795978i	0.734464	−	0.678648i	$-0.237434\pi$
$104$	−6.44168	−	19.8254i	−0.00607364	−	0.0186927i
$105$	116.839	−	510.387i	0.108594	−	0.474368i
$106$	447.327	−	1376.73i	0.409889	−	1.26151i
$107$	808.795			0.730740			0.365370	−	0.930862i	$-0.380942\pi$
$107$	808.795			0.730740			0.365370	+	0.930862i	$0.380942\pi$
$108$	2.51774	−	7.74880i	0.00224324	−	0.00690397i
$109$	−1299.12	+	943.862i	−1.14158	+	0.829409i	−0.987339	−	0.158623i	$-0.949294\pi$
$109$	−1299.12	+	943.862i	−1.14158	+	0.829409i	−0.154245	+	0.988033i	$0.549294\pi$
$110$	123.961	−	541.496i	0.107447	−	0.469360i
$111$	34.7388	+	25.2392i	0.0297051	+	0.0215820i
$112$	−1794.31	+	1303.64i	−1.51380	+	1.09984i
$113$	−167.906	+	121.991i	−0.139781	+	0.101557i	−0.655478	−	0.755214i	$-0.727533\pi$
$113$	−167.906	+	121.991i	−0.139781	+	0.101557i	0.515697	+	0.856771i	$0.327533\pi$
$114$	−186.312	−	135.363i	−0.153067	−	0.111210i
$115$	471.809	+	1105.83i	0.382577	+	0.896685i
$116$	−10.5946	+	7.69745i	−0.00848006	+	0.00616112i
$117$	7.13066	−	21.9459i	0.00563445	−	0.0173410i
$118$	318.972			0.248846
$119$	999.622	−	3076.52i	0.770044	−	2.36995i
$120$	291.086	+	174.171i	0.221437	+	0.132496i
$121$	−314.526	−	968.013i	−0.236308	−	0.727282i
$122$	174.065	+	535.717i	0.129173	+	0.397554i
$123$	−159.695	−	116.025i	−0.117067	−	0.0850539i
$124$	−23.1448			−0.0167618
$125$	−65.4030	+	1396.01i	−0.0467986	+	0.998904i
$126$	−2491.61			−1.76167
$127$	−2107.06	−	1530.87i	−1.47221	−	1.06963i	−0.979964	−	0.199172i	$-0.936175\pi$
$127$	−2107.06	−	1530.87i	−1.47221	−	1.06963i	−0.492250	−	0.870454i	$-0.663825\pi$
$128$	−437.421	−	1346.24i	−0.302054	−	0.929627i
$129$	−67.0391	−	206.325i	−0.0457555	−	0.140821i
$130$	24.6384	+	14.7424i	0.0166226	+	0.00994609i
$131$	−545.199	+	1677.95i	−0.363620	+	1.11911i	0.587220	+	0.809427i	$0.300222\pi$
$131$	−545.199	+	1677.95i	−0.363620	+	1.11911i	−0.950840	+	0.309681i	$0.899778\pi$
$132$	−2.76069			−0.00182036
$133$	669.749	−	2061.28i	0.436651	−	1.34387i
$134$	−755.919	+	549.207i	−0.487324	+	0.354062i
$135$	305.066	+	715.013i	0.194488	+	0.455841i
$136$	1695.49	+	1231.85i	1.06902	+	0.776690i
$137$	−380.434	+	276.401i	−0.237245	+	0.172369i	−0.700055	−	0.714089i	$-0.746841\pi$
$137$	−380.434	+	276.401i	−0.237245	+	0.172369i	0.462810	+	0.886458i	$0.346841\pi$
$138$	−325.177	+	236.255i	−0.200586	+	0.145734i
$139$	2091.89	+	1519.85i	1.27649	+	0.927422i	0.999441	−	0.0334351i	$-0.0106447\pi$
$139$	2091.89	+	1519.85i	1.27649	+	0.927422i	0.277046	+	0.960857i	$0.410645\pi$
$140$	−10.2841	+	44.9241i	−0.00620834	+	0.0271198i
$141$	28.6827	−	20.8392i	0.0171314	−	0.0124467i
$142$	279.078	−	858.914i	0.164928	−	0.507595i
$143$	−16.1868			−0.00946580
$144$	491.514	−	1512.73i	0.284441	−	0.875420i
$145$	278.822	−	1217.97i	0.159689	−	0.697567i
$146$	270.646	+	832.963i	0.153417	+	0.472168i
$147$	367.966	+	1132.48i	0.206458	+	0.635412i
$148$	−3.05770	−	2.22155i	−0.00169825	−	0.00123385i
$149$	−1034.06			−0.568544			−0.284272	−	0.958744i	$-0.591752\pi$
$149$	−1034.06			−0.568544			−0.284272	+	0.958744i	$0.591752\pi$
$150$	−459.822	+	82.8327i	−0.250296	+	0.0450884i
$151$	2400.28			1.29359			0.646795	−	0.762664i	$-0.276109\pi$
$151$	2400.28			1.29359			0.646795	+	0.762664i	$0.276109\pi$
$152$	1135.98	+	825.339i	0.606186	+	0.440420i
$153$	716.887	+	2206.35i	0.378803	+	1.16584i
$154$	540.102	+	1662.26i	0.282615	+	0.869799i
$155$	1663.93	−	1451.84i	0.862261	−	0.752354i
$156$	0.0440941	−	0.135708i	2.26305e−5	−	6.96494e-5i
$157$	756.796			0.384706			0.192353	−	0.981326i	$-0.438388\pi$
$157$	756.796			0.384706			0.192353	+	0.981326i	$0.438388\pi$
$158$	−655.563	+	2017.62i	−0.330087	+	1.01590i
$159$	555.307	−	403.454i	0.276973	−	0.201233i
$160$	−50.8728	−	30.4396i	−0.0251365	−	0.0150404i
$161$	−3060.32	−	2223.45i	−1.49806	−	1.08840i
$162$	1336.92	−	971.328i	0.648384	−	0.471079i
$163$	−1324.05	+	961.975i	−0.636241	+	0.462256i	−0.858557	−	0.512719i	$-0.828638\pi$
$163$	−1324.05	+	961.975i	−0.636241	+	0.462256i	0.222316	+	0.974975i	$0.428638\pi$
$164$	14.0563	+	10.2125i	0.00669275	+	0.00486257i
$165$	198.473	−	173.175i	0.0936429	−	0.0817068i
$166$	836.980	−	608.102i	0.391339	−	0.284324i
$167$	599.880	−	1846.24i	0.277965	−	0.855488i	−0.710455	−	0.703743i	$-0.751511\pi$
$167$	599.880	−	1846.24i	0.277965	−	0.855488i	0.988420	−	0.151745i	$-0.0484893\pi$
$168$	−1067.29			−0.490138
$169$	−678.652	+	2088.68i	−0.308899	+	0.950694i
$170$	−2875.15	+	256.898i	−1.29714	+	0.115901i
$171$	480.316	+	1478.26i	0.214799	+	0.661084i
$172$	5.90075	+	18.1607i	0.00261586	+	0.00805080i
$173$	−1401.67	−	1018.37i	−0.615995	−	0.447546i	0.235526	−	0.971868i	$-0.424319\pi$
$173$	−1401.67	−	1018.37i	−0.615995	−	0.447546i	−0.851520	+	0.524322i	$0.824319\pi$
$174$	417.724			0.181998
$175$	−2078.68	−	3874.80i	−0.897904	−	1.67376i
$176$	−1115.75			−0.477858
$177$	122.361	+	88.9006i	0.0519618	+	0.0377524i
$178$	−763.361	−	2349.38i	−0.321440	−	0.989291i
$179$	699.541	+	2152.97i	0.292101	+	0.898996i	0.984180	+	0.177173i	$0.0566953\pi$
$179$	699.541	+	2152.97i	0.292101	+	0.898996i	−0.692078	+	0.721822i	$0.743305\pi$
$180$	−12.9703	−	30.3997i	−0.00537082	−	0.0125881i
$181$	−476.487	+	1466.47i	−0.195674	+	0.602222i	0.804294	+	0.594231i	$0.202544\pi$
$181$	−476.487	+	1466.47i	−0.195674	+	0.602222i	−0.999968	+	0.00799089i	$0.997456\pi$
$182$	−90.3386			−0.0367931
$183$	−82.5363	+	254.021i	−0.0333402	+	0.102611i
$184$	1982.67	−	1440.50i	0.794372	−	0.577145i
$185$	359.180	−	32.0931i	0.142743	−	0.0127542i
$186$	597.273	+	433.944i	0.235453	+	0.171066i
$187$	1316.56	−	956.535i	0.514846	−	0.374058i
$188$	−2.52464	+	1.83426i	−0.000979408	+	0.000711581i
$189$	−1978.77	−	1437.66i	−0.761555	−	0.553302i
$190$	−1926.36	+	172.122i	−0.735540	+	0.0657214i
$191$	−1677.10	+	1218.48i	−0.635342	+	0.461603i	−0.858247	−	0.513237i	$-0.828446\pi$
$191$	−1677.10	+	1218.48i	−0.635342	+	0.461603i	0.222905	+	0.974840i	$0.428446\pi$
$192$	213.627	−	657.477i	0.0802980	−	0.247132i
$193$	1987.27			0.741177			0.370588	−	0.928797i	$-0.379156\pi$
$193$	1987.27			0.741177			0.370588	+	0.928797i	$0.379156\pi$
$194$	−584.731	+	1799.62i	−0.216398	+	0.666005i
$195$	5.34274	+	12.5223i	0.00196206	+	0.00459867i
$196$	−32.3882	−	99.6807i	−0.0118033	−	0.0363268i
$197$	−1049.88	−	3231.19i	−0.379699	−	1.16859i	−0.940253	−	0.340476i	$-0.889412\pi$
$197$	−1049.88	−	3231.19i	−0.379699	−	1.16859i	0.560554	−	0.828118i	$-0.310588\pi$
$198$	−1014.07	−	736.762i	−0.363972	−	0.264441i
$199$	−625.803			−0.222925			−0.111462	−	0.993769i	$-0.535553\pi$
$199$	−625.803			−0.222925			−0.111462	+	0.993769i	$0.535553\pi$
$200$	2803.63	−	505.048i	0.991234	−	0.178562i
$201$	−443.048			−0.155474
$202$	2748.15	+	1996.65i	0.957224	+	0.695464i
$203$	1214.84	+	3738.89i	0.420025	+	1.29270i
$204$	4.43304	+	13.6435i	0.00152144	+	0.00468252i
$205$	−1651.15	+	147.533i	−0.562544	+	0.0502640i
$206$	759.056	−	2336.13i	0.256728	−	0.790127i
$207$	2712.84			0.910896
$208$	17.8209	−	54.8471i	0.00594067	−	0.0182835i
$209$	882.096	−	640.881i	0.291942	−	0.212108i
$210$	1107.68	−	966.488i	0.363985	−	0.317590i
$211$	2265.63	+	1646.08i	0.739206	+	0.537065i	0.892462	−	0.451122i	$-0.148976\pi$
$211$	2265.63	+	1646.08i	0.739206	+	0.537065i	−0.153256	+	0.988186i	$0.548976\pi$
$212$	−48.8780	+	35.5119i	−0.0158347	+	0.0115046i
$213$	346.445	−	251.707i	0.111446	−	0.0809703i
$214$	1837.12	+	1334.74i	0.586835	+	0.426361i
$215$	−1563.41	−	935.465i	−0.495925	−	0.296736i
$216$	1281.97	−	931.406i	0.403829	−	0.293399i
$217$	−2147.06	+	6607.98i	−0.671669	+	2.06718i
$218$	−4508.49			−1.40070
$219$	−128.332	+	394.965i	−0.0395976	+	0.121869i
$220$	−17.4695	+	15.2428i	−0.00535360	+	0.00467121i
$221$	25.9923	+	79.9960i	0.00791145	+	0.0243489i
$222$	37.2546	+	114.658i	0.0112629	+	0.0346637i
$223$	679.760	+	493.875i	0.204126	+	0.148306i	0.685152	−	0.728400i	$-0.259736\pi$
$223$	679.760	+	493.875i	0.204126	+	0.148306i	−0.481026	+	0.876706i	$0.659736\pi$
$224$	186.529			0.0556382
$225$	2839.40	+	1371.90i	0.841303	+	0.406489i
$226$	−582.706			−0.171509
$227$	−3614.46	−	2626.06i	−1.05683	−	0.767831i	−0.0833296	−	0.996522i	$-0.526555\pi$
$227$	−3614.46	−	2626.06i	−1.05683	−	0.767831i	−0.973499	+	0.228691i	$0.926555\pi$
$228$	2.97014	+	9.14116i	0.000862731	+	0.00265521i
$229$	−1471.68	−	4529.36i	−0.424678	−	1.30703i	−0.903302	−	0.429005i	$-0.858864\pi$
$229$	−1471.68	−	4529.36i	−0.424678	−	1.30703i	0.478624	−	0.878020i	$-0.341136\pi$
$230$	−753.251	+	3290.42i	−0.215947	+	0.943321i
$231$	−256.100	+	788.194i	−0.0729443	+	0.224499i
$232$	−2546.95			−0.720757
$233$	−291.004	+	895.617i	−0.0818210	+	0.251819i	−0.983596	−	0.180387i	$-0.942265\pi$
$233$	−291.004	+	895.617i	−0.0818210	+	0.251819i	0.901775	+	0.432206i	$0.142265\pi$
$234$	52.4138	−	38.0809i	0.0146427	−	0.0106386i
$235$	66.4417	−	290.237i	0.0184433	−	0.0805658i
$236$	−10.7702	−	7.82500i	−0.00297068	−	0.00215832i
$237$	−813.810	+	591.268i	−0.223049	+	0.162055i
$238$	7347.71	−	5338.42i	2.00118	−	1.45394i
$239$	1520.98	+	1105.06i	0.411649	+	0.299081i	0.774269	−	0.632856i	$-0.218118\pi$
$239$	1520.98	+	1105.06i	0.411649	+	0.299081i	−0.362620	+	0.931937i	$0.618118\pi$
$240$	368.273	+	863.158i	0.0990497	+	0.232153i
$241$	−2792.94	+	2029.19i	−0.746511	+	0.542372i	−0.894744	−	0.446580i	$-0.852642\pi$
$241$	−2792.94	+	2029.19i	−0.746511	+	0.542372i	0.148232	+	0.988953i	$0.452642\pi$
$242$	883.076	−	2717.83i	0.234571	−	0.721936i
$243$	2660.89			0.702455
$244$	7.26481	−	22.3588i	0.00190607	−	0.00586629i
$245$	8581.30	+	5134.60i	2.23771	+	1.33893i
$246$	−171.260	−	527.084i	−0.0443868	−	0.136608i
$247$	17.4149	+	53.5975i	0.00448617	+	0.0138070i
$248$	−3641.70	−	2645.85i	−0.932452	−	0.677466i
$249$	490.558			0.124851
$250$	−2452.38	+	3063.00i	−0.620408	+	0.774885i
$251$	514.962			0.129498			0.0647492	−	0.997902i	$-0.479375\pi$
$251$	514.962			0.129498			0.0647492	+	0.997902i	$0.479375\pi$
$252$	84.1299	+	61.1239i	0.0210305	+	0.0152795i
$253$	−588.058	−	1809.86i	−0.146130	−	0.449742i
$254$	−2259.65	−	6954.50i	−0.558202	−	1.71797i
$255$	−1174.54	−	702.783i	−0.288441	−	0.172588i
$256$	−55.6075	+	171.142i	−0.0135761	+	0.0417828i
$257$	−6747.95			−1.63784			−0.818921	−	0.573906i	$-0.805428\pi$
$257$	−6747.95			−1.63784			−0.818921	+	0.573906i	$0.805428\pi$
$258$	188.221	−	579.286i	0.0454192	−	0.139786i
$259$	−917.916	+	666.905i	−0.220218	+	0.159998i
$260$	−0.470266	−	1.10221i	−0.000112172	−	0.000262908i
$261$	−2280.92	−	1657.18i	−0.540939	−	0.393015i
$262$	−4007.48	+	2911.60i	−0.944973	+	0.686563i
$263$	1099.66	−	798.950i	0.257825	−	0.187321i	−0.451363	−	0.892341i	$-0.649062\pi$
$263$	1099.66	−	798.950i	0.257825	−	0.187321i	0.709188	+	0.705020i	$0.249062\pi$
$264$	−434.379	−	315.594i	−0.101266	−	0.0735739i
$265$	1286.33	−	5619.08i	0.298184	−	1.30256i
$266$	4922.98	−	3576.76i	1.13476	−	0.824455i
$267$	361.962	−	1114.01i	0.0829653	−	0.255341i
$268$	38.9969			0.00888849
$269$	−1900.91	+	5850.40i	−0.430857	+	1.32604i	0.466416	+	0.884565i	$0.345545\pi$
$269$	−1900.91	+	5850.40i	−0.430857	+	1.32604i	−0.897273	+	0.441476i	$0.854455\pi$
$270$	−487.043	+	2127.55i	−0.109780	+	0.479549i
$271$	−1056.23	−	3250.75i	−0.236759	−	0.728668i	−0.996883	−	0.0788907i	$-0.974862\pi$
$271$	−1056.23	−	3250.75i	−0.236759	−	0.728668i	0.760125	−	0.649777i	$-0.225138\pi$
$272$	1791.64	+	5514.10i	0.399390	+	1.22920i
$273$	−34.6549	−	25.1782i	−0.00768282	−	0.00558189i
$274$	−1320.27			−0.291096
$275$	299.763	−	2191.67i	0.0657324	−	0.480593i
$276$	16.7755			0.00365857
$277$	744.320	+	540.780i	0.161451	+	0.117301i	0.665577	−	0.746329i	$-0.268185\pi$
$277$	744.320	+	540.780i	0.161451	+	0.117301i	−0.504126	+	0.863630i	$0.668185\pi$
$278$	2243.39	+	6904.43i	0.483990	+	1.48957i
$279$	−1539.78	−	4738.97i	−0.330410	−	1.01690i
$280$	−6753.73	+	5892.88i	−1.44147	+	1.25774i
$281$	2002.21	−	6162.18i	0.425061	−	1.30820i	−0.477875	−	0.878428i	$-0.658593\pi$
$281$	2002.21	−	6162.18i	0.425061	−	1.30820i	0.902936	−	0.429775i	$-0.141407\pi$
$282$	99.5414			0.0210199
$283$	−2106.97	+	6484.57i	−0.442566	+	1.36208i	0.442566	+	0.896736i	$0.354068\pi$
$283$	−2106.97	+	6484.57i	−0.442566	+	1.36208i	−0.885131	+	0.465341i	$0.845932\pi$
$284$	−30.4939	+	22.1551i	−0.00637142	+	0.00462911i
$285$	−786.943	−	470.866i	−0.163560	−	0.0978656i
$286$	−36.7671	−	26.7129i	−0.00760170	−	0.00552296i
$287$	4219.67	−	3065.77i	0.867873	−	0.630546i
$288$	−108.223	+	78.6283i	−0.0221426	+	0.0160876i
$289$	−2866.63	−	2082.73i	−0.583478	−	0.423922i
$290$	2643.33	−	2306.40i	0.535247	−	0.467023i
$291$	−725.880	+	527.382i	−0.146226	+	0.106240i
$292$	11.2957	−	34.7647i	0.00226381	−	0.00696729i
$293$	6109.09			1.21808			0.609039	−	0.793140i	$-0.291555\pi$
$293$	6109.09			1.21808			0.609039	+	0.793140i	$0.291555\pi$
$294$	−1033.11	+	3179.60i	−0.204940	+	0.630741i
$295$	1265.15	−	113.042i	0.249694	−	0.0223104i
$296$	−227.149	−	699.094i	−0.0446040	−	0.137277i
$297$	−380.231	−	1170.23i	−0.0742870	−	0.228632i
$298$	−2348.78	−	1706.49i	−0.456581	−	0.331725i
$299$	98.3599			0.0190244
$300$	17.5581	+	8.48346i	0.00337905	+	0.00163264i
$301$	5732.36			1.09770
$302$	5452.06	+	3961.15i	1.03884	+	0.754764i
$303$	497.735	+	1531.87i	0.0943701	+	0.290441i
$304$	1200.40	+	3694.46i	0.226473	+	0.697013i
$305$	880.253	+	2063.14i	0.165256	+	0.387328i
$306$	−2012.76	+	6194.63i	−0.376019	+	1.15727i
$307$	3762.44			0.699459			0.349730	−	0.936851i	$-0.386273\pi$
$307$	3762.44			0.699459			0.349730	+	0.936851i	$0.386273\pi$
$308$	22.5418	−	69.3765i	0.00417026	−	0.0128347i
$309$	942.285	−	684.610i	0.173478	−	0.126039i
$310$	6175.46	−	551.785i	1.13143	−	0.101094i
$311$	1143.48	+	830.787i	0.208491	+	0.151478i	0.687131	−	0.726534i	$-0.258870\pi$
$311$	1143.48	+	830.787i	0.208491	+	0.151478i	−0.478639	+	0.878012i	$0.658870\pi$
$312$	22.4517	−	16.3121i	0.00407396	−	0.00295990i
$313$	7790.44	−	5660.09i	1.40684	−	1.02213i	0.413070	−	0.910699i	$-0.364456\pi$
$313$	7790.44	−	5660.09i	1.40684	−	1.02213i	0.993772	−	0.111432i	$-0.0355436\pi$
$314$	1719.01	+	1248.93i	0.308946	+	0.224463i
$315$	−9882.51	+	883.014i	−1.76767	+	0.157943i
$316$	71.6313	−	52.0432i	0.0127518	−	0.00926474i
$317$	−1972.31	+	6070.14i	−0.349451	+	1.07550i	0.609707	+	0.792627i	$0.291287\pi$
$317$	−1972.31	+	6070.14i	−0.349451	+	1.07550i	−0.959158	+	0.282872i	$0.908713\pi$
$318$	1927.15			0.339841
$319$	−611.150	+	1880.93i	−0.107266	+	0.330130i
$320$	−2278.34	−	5339.98i	−0.398010	−	0.932856i
$321$	332.732	+	1024.04i	0.0578545	+	0.178058i
$322$	−3281.95	−	10100.8i	−0.568000	−	1.74813i
$323$	−4583.71	−	3330.26i	−0.789611	−	0.573686i
$324$	−68.9700			−0.0118261
$325$	102.949	+	49.7412i	0.0175709	+	0.00848967i
$326$	−4595.01			−0.780656
$327$	−1729.50	−	1256.56i	−0.292483	−	0.212501i
$328$	1044.21	+	3213.75i	0.175783	+	0.541004i
$329$	289.490	+	890.958i	0.0485109	+	0.149301i
$330$	736.604	−	65.8164i	0.122875	−	0.0109790i
$331$	−489.422	+	1506.29i	−0.0812721	+	0.250130i	−0.983434	−	0.181269i	$-0.941980\pi$
$331$	−489.422	+	1506.29i	−0.0812721	+	0.250130i	0.902162	+	0.431398i	$0.141980\pi$
$332$	−43.1788			−0.00713778
$333$	251.445	−	773.867i	0.0413786	−	0.127350i
$334$	4409.41	−	3203.63i	0.722372	−	0.524834i
$335$	−2803.58	+	2446.22i	−0.457241	+	0.398960i
$336$	−2388.75	−	1735.53i	−0.387848	−	0.281788i
$337$	8028.18	−	5832.81i	1.29769	−	0.942829i	0.297763	−	0.954640i	$-0.403759\pi$
$337$	8028.18	−	5832.81i	1.29769	−	0.942829i	0.999930	+	0.0118103i	$0.00375942\pi$
$338$	−4988.42	+	3624.30i	−0.802764	+	0.583242i
$339$	−223.532	−	162.406i	−0.0358130	−	0.0260197i
$340$	103.382	+	61.8587i	0.0164903	+	0.00986694i
$341$	−2827.80	+	2054.52i	−0.449073	+	0.326271i
$342$	−1348.55	+	4150.42i	−0.213220	+	0.656225i
$343$	−19398.1			−3.05365
$344$	−1147.62	+	3532.03i	−0.179871	+	0.553588i
$345$	−1206.03	+	1052.30i	−0.188204	+	0.164215i
$346$	−1503.18	−	4626.32i	−0.233559	−	0.718822i
$347$	−796.491	−	2451.35i	−0.123222	−	0.379237i	0.870351	−	0.492431i	$-0.163892\pi$
$347$	−796.491	−	2451.35i	−0.123222	−	0.379237i	−0.993573	+	0.113194i	$0.963892\pi$
$348$	−14.1046	−	10.2476i	−0.00217266	−	0.00157853i
$349$	−1767.48			−0.271091			−0.135546	−	0.990771i	$-0.543279\pi$
$349$	−1767.48			−0.271091			−0.135546	+	0.990771i	$0.543279\pi$
$350$	1672.98	−	12231.7i	0.255499	−	1.86804i
$351$	63.5983			0.00967129
$352$	75.9157	+	55.1560i	0.0114952	+	0.00835178i
$353$	−566.833	−	1744.53i	−0.0854659	−	0.263037i	0.899186	−	0.437566i	$-0.144160\pi$
$353$	−566.833	−	1744.53i	−0.0854659	−	0.263037i	−0.984652	+	0.174530i	$0.944160\pi$
$354$	131.223	+	403.862i	0.0197017	+	0.0606357i
$355$	802.517	−	3505.63i	0.119981	−	0.524111i
$356$	−31.8598	+	98.0543i	−0.00474316	+	0.0145979i
$357$	4306.53			0.638447
$358$	−1964.06	+	6044.75i	−0.289954	+	0.892387i
$359$	6790.42	−	4933.53i	0.998287	−	0.725298i	0.0365664	−	0.999331i	$-0.488358\pi$
$359$	6790.42	−	4933.53i	0.998287	−	0.725298i	0.961720	+	0.274034i	$0.0883580\pi$
$360$	1434.41	−	6265.94i	0.210001	−	0.917345i
$361$	2477.95	+	1800.34i	0.361270	+	0.262478i
$362$	−3502.41	+	2544.65i	−0.508515	+	0.369458i
$363$	1096.24	−	796.466i	0.158506	−	0.115162i
$364$	3.05031	+	2.21618i	0.000439230	+	0.000319119i
$365$	1368.67	+	3207.88i	0.196272	+	0.460022i
$366$	−606.682	+	440.780i	−0.0866442	+	0.0629507i
$367$	759.595	−	2337.79i	0.108040	−	0.332512i	−0.882392	−	0.470514i	$-0.844068\pi$
$367$	759.595	−	2337.79i	0.108040	−	0.332512i	0.990432	+	0.138003i	$0.0440683\pi$
$368$	6779.91			0.960401
$369$	−1155.89	+	3557.48i	−0.163072	+	0.501883i
$370$	868.812	+	519.852i	0.122074	+	0.0730428i
$371$	5604.62	+	17249.2i	0.784306	+	2.41384i
$372$	−9.52161	−	29.3045i	−0.00132708	−	0.00408432i
$373$	−1530.26	−	1111.80i	−0.212423	−	0.154334i	0.476486	−	0.879182i	$-0.341910\pi$
$373$	−1530.26	−	1111.80i	−0.212423	−	0.154334i	−0.688909	+	0.724848i	$0.741910\pi$
$374$	4569.02			0.631707
$375$	−1794.45	+	491.499i	−0.247106	+	0.0676825i
$376$	−606.925			−0.0832441
$377$	−82.6995	−	60.0847i	−0.0112977	−	0.00820828i
$378$	−2122.07	−	6531.06i	−0.288750	−	0.888681i
$379$	2080.40	+	6402.81i	0.281960	+	0.867784i	0.987293	+	0.158908i	$0.0507974\pi$
$379$	2080.40	+	6402.81i	0.281960	+	0.867784i	−0.705333	+	0.708876i	$0.749203\pi$
$380$	69.2665	+	41.4455i	0.00935078	+	0.00559502i
$381$	1071.46	−	3297.61i	0.144075	−	0.443416i
$382$	−5820.24			−0.779553
$383$	2238.88	−	6890.56i	0.298698	−	0.919298i	−0.683256	−	0.730179i	$-0.739437\pi$
$383$	2238.88	−	6890.56i	0.298698	−	0.919298i	0.981954	−	0.189119i	$-0.0605633\pi$
$384$	1524.58	−	1107.67i	0.202606	−	0.147202i
$385$	2731.32	+	6401.66i	0.361560	+	0.847425i
$386$	4513.95	+	3279.57i	0.595217	+	0.432451i
$387$	−3325.88	+	2416.39i	−0.436857	+	0.317396i
$388$	63.8916	−	46.4200i	0.00835981	−	0.00607376i
$389$	5160.54	+	3749.35i	0.672622	+	0.488688i	0.870902	−	0.491457i	$-0.163536\pi$
$389$	5160.54	+	3749.35i	0.672622	+	0.488688i	−0.198280	+	0.980145i	$0.563536\pi$
$390$	−8.52977	+	37.2605i	−0.00110749	+	0.00483785i
$391$	−8000.12	+	5812.42i	−1.03474	+	0.751782i
$392$	6299.11	−	19386.7i	0.811616	−	2.49790i
$393$	−2348.80			−0.301480
$394$	2947.68	−	9072.01i	0.376908	−	1.16000i
$395$	−1885.14	+	8234.84i	−0.240131	+	1.04896i
$396$	16.1660	+	49.7539i	0.00205145	+	0.00631371i
$397$	3678.84	+	11322.3i	0.465077	+	1.43136i	0.858886	+	0.512167i	$0.171157\pi$
$397$	3678.84	+	11322.3i	0.465077	+	1.43136i	−0.393809	+	0.919192i	$0.628843\pi$
$398$	−1421.47	−	1032.76i	−0.179024	−	0.130069i
$399$	2885.38			0.362030
$400$	7096.21	+	3428.64i	0.887026	+	0.428580i
$401$	−4441.67			−0.553133			−0.276567	−	0.960995i	$-0.589197\pi$
$401$	−4441.67			−0.553133			−0.276567	+	0.960995i	$0.589197\pi$
$402$	−1006.35	−	731.156i	−0.124856	−	0.0907133i
$403$	−55.8282	−	171.821i	−0.00690074	−	0.0212383i
$404$	−43.8105	−	134.835i	−0.00539518	−	0.0166047i
$405$	4958.41	−	4326.39i	0.608359	−	0.530815i
$406$	−3410.83	+	10497.4i	−0.416937	+	1.28320i
$407$	−570.787			−0.0695156
$408$	−862.172	+	2653.49i	−0.104617	+	0.321979i
$409$	−3729.50	+	2709.64i	−0.450885	+	0.327587i	−0.789945	−	0.613177i	$-0.789891\pi$
$409$	−3729.50	+	2709.64i	−0.450885	+	0.327587i	0.339060	+	0.940765i	$0.389891\pi$
$410$	−3993.94	−	2389.77i	−0.481090	−	0.287859i
$411$	−506.469	−	367.971i	−0.0607841	−	0.0441622i
$412$	−82.9396	+	60.2591i	−0.00991782	+	0.00720572i
$413$	−3233.19	+	2349.05i	−0.385218	+	0.279877i
$414$	6162.01	+	4476.96i	0.731513	+	0.531475i
$415$	3104.22	−	2708.55i	0.367181	−	0.320379i
$416$	−3.92384	+	2.85084i	−0.000462457	+	0.000335995i
$417$	−1063.74	+	3273.87i	−0.124920	+	0.384465i
$418$	3061.25			0.358208
$419$	4510.35	−	13881.4i	0.525883	−	1.61850i	−0.236681	−	0.971588i	$-0.576059\pi$
$419$	4510.35	−	13881.4i	0.525883	−	1.61850i	0.762563	−	0.646913i	$-0.223941\pi$
$420$	−61.1108	+	5.46032i	−0.00709976	+	0.000634372i
$421$	−4518.66	−	13907.0i	−0.523102	−	1.60994i	−0.768038	−	0.640404i	$-0.778767\pi$
$421$	−4518.66	−	13907.0i	−0.523102	−	1.60994i	0.244936	−	0.969539i	$-0.421233\pi$
$422$	2429.71	+	7477.88i	0.280276	+	0.862601i
$423$	−543.530	−	394.898i	−0.0624760	−	0.0453915i
$424$	−11750.3			−1.34586
$425$	−11312.7	+	2037.88i	−1.29117	+	0.232592i
$426$	1202.31			0.136742
$427$	−5709.63	−	4148.29i	−0.647093	−	0.470140i
$428$	−29.2870	−	90.1360i	−0.00330757	−	0.0101796i
$429$	−6.65913	−	20.4947i	−0.000749431	−	0.00230651i
$430$	−2007.39	−	4704.92i	−0.225128	−	0.527654i
$431$	3801.49	−	11699.8i	0.424853	−	1.30756i	−0.478282	−	0.878206i	$-0.658740\pi$
$431$	3801.49	−	11699.8i	0.424853	−	1.30756i	0.903135	−	0.429356i	$-0.141260\pi$
$432$	4383.81			0.488232
$433$	−846.039	+	2603.84i	−0.0938985	+	0.288990i	−0.986965	−	0.160935i	$-0.948549\pi$
$433$	−846.039	+	2603.84i	−0.0938985	+	0.288990i	0.893067	+	0.449925i	$0.148549\pi$
$434$	−15782.0	+	11466.3i	−1.74553	+	1.26820i
$435$	1656.83	−	148.039i	0.182618	−	0.0163171i
$436$	152.230	+	110.602i	0.0167214	+	0.0121488i
$437$	−5360.10	+	3894.34i	−0.586746	+	0.426296i
$438$	−943.302	+	685.349i	−0.102906	+	0.0747654i
$439$	4137.42	+	3006.01i	0.449814	+	0.326809i	0.789522	−	0.613722i	$-0.210328\pi$
$439$	4137.42	+	3006.01i	0.449814	+	0.326809i	−0.339708	+	0.940531i	$0.610328\pi$
$440$	−4491.23	+	401.296i	−0.486616	+	0.0434797i
$441$	18255.2	−	13263.2i	1.97119	−	1.43215i
$442$	−72.9769	+	224.600i	−0.00785329	+	0.0241700i
$443$	7152.19			0.767067			0.383534	−	0.923527i	$-0.374707\pi$
$443$	7152.19			0.767067			0.383534	+	0.923527i	$0.374707\pi$
$444$	1.55487	−	4.78539i	0.000166195	−	0.000511496i
$445$	−3860.34	−	9047.87i	−0.411231	−	0.963843i
$446$	728.989	+	2243.60i	0.0773961	+	0.238201i
$447$	−425.403	−	1309.25i	−0.0450131	−	0.138536i
$448$	14778.1	+	10736.9i	1.55849	+	1.13231i
$449$	−12142.0			−1.27620			−0.638102	−	0.769951i	$-0.720280\pi$
$449$	−12142.0			−1.27620			−0.638102	+	0.769951i	$0.720280\pi$
$450$	4185.45	+	7801.99i	0.438454	+	0.817310i
$451$	2623.92			0.273959
$452$	19.6752	+	14.2949i	0.00204745	+	0.00148756i
$453$	987.457	+	3039.08i	0.102417	+	0.315206i
$454$	−3876.22	−	11929.8i	−0.400705	−	1.23324i
$455$	−358.312	+	32.0156i	−0.0369185	+	0.00329871i
$456$	−577.657	+	1777.85i	−0.0593230	+	0.182577i
$457$	18430.7			1.88654			0.943272	−	0.332021i	$-0.107731\pi$
$457$	18430.7			1.88654			0.943272	+	0.332021i	$0.107731\pi$
$458$	4131.94	−	12716.8i	0.421557	−	1.29742i
$459$	−5172.78	+	3758.24i	−0.526023	+	0.382178i
$460$	106.154	−	92.6233i	0.0107597	−	0.00938822i
$461$	−12452.8	−	9047.51i	−1.25810	−	0.914066i	−0.259441	−	0.965759i	$-0.583538\pi$
$461$	−12452.8	−	9047.51i	−1.25810	−	0.914066i	−0.998663	+	0.0516933i	$0.983538\pi$
$462$	−1882.46	+	1367.69i	−0.189567	+	0.137728i
$463$	−8117.71	+	5897.86i	−0.814820	+	0.592002i	−0.915224	−	0.402945i	$-0.867987\pi$
$463$	−8117.71	+	5897.86i	−0.814820	+	0.592002i	0.100404	+	0.994947i	$0.467987\pi$
$464$	−5700.45	−	4141.62i	−0.570338	−	0.414375i
$465$	2522.76	+	1509.49i	0.251592	+	0.150540i
$466$	−2139.02	+	1554.09i	−0.212635	+	0.154489i
$467$	−2401.74	+	7391.78i	−0.237985	+	0.732443i	0.758726	+	0.651410i	$0.225822\pi$
$467$	−2401.74	+	7391.78i	−0.237985	+	0.732443i	−0.996711	+	0.0810335i	$0.974178\pi$
$468$	−2.70397			−0.000267074
$469$	3617.61	−	11133.8i	0.356174	−	1.09619i
$470$	629.891	−	549.603i	0.0618186	−	0.0539390i
$471$	311.340	+	958.207i	0.0304582	+	0.0937406i
$472$	−800.093	−	2462.43i	−0.0780239	−	0.240133i
$473$	2333.03	+	1695.04i	0.226792	+	0.164774i
$474$	−2824.27			−0.273677
$475$	−7579.54	+	1365.38i	−0.732154	+	0.131891i
$476$	−379.059			−0.0365003
$477$	−10522.9	−	7645.35i	−1.01009	−	0.733871i
$478$	1631.13	+	5020.12i	0.156080	+	0.480366i
$479$	3179.32	+	9784.95i	0.303271	+	0.933373i	0.980317	+	0.197432i	$0.0632602\pi$
$479$	3179.32	+	9784.95i	0.303271	+	0.933373i	−0.677045	+	0.735941i	$0.736740\pi$
$480$	17.6120	−	76.9344i	0.00167474	−	0.00731575i
$481$	9.11667	−	28.0582i	0.000864209	−	0.00265976i
$482$	−9692.71			−0.915956
$483$	1556.20	−	4789.49i	0.146604	−	0.451200i
$484$	−96.4908	+	70.1047i	−0.00906187	+	0.00658384i
$485$	−1681.45	+	7345.08i	−0.157424	+	0.687676i
$486$	6044.02	+	4391.24i	0.564120	+	0.409857i
$487$	−954.833	+	693.727i	−0.0888452	+	0.0645498i	−0.631321	−	0.775522i	$-0.717487\pi$
$487$	−954.833	+	693.727i	−0.0888452	+	0.0645498i	0.542476	+	0.840071i	$0.317487\pi$
$488$	3699.07	−	2687.53i	0.343133	−	0.249301i
$489$	−1762.69	−	1280.67i	−0.163010	−	0.118434i
$490$	11018.2	+	25824.5i	1.01582	+	2.38088i
$491$	6115.75	−	4443.35i	0.562118	−	0.408403i	−0.270115	−	0.962828i	$-0.587062\pi$
$491$	6115.75	−	4443.35i	0.562118	−	0.408403i	0.832234	+	0.554425i	$0.187062\pi$
$492$	−7.14774	+	21.9985i	−0.000654970	+	0.00201579i
$493$	10277.0			0.938849
$494$	−48.8947	+	150.482i	−0.00445319	+	0.0137055i
$495$	−4283.21	−	2562.85i	−0.388921	−	0.232710i
$496$	−3848.22	−	11843.6i	−0.348367	−	1.07216i
$497$	3496.61	+	10761.5i	0.315582	+	0.971262i
$498$	1114.27	+	809.562i	0.100264	+	0.0728461i
$499$	12772.6			1.14585			0.572926	−	0.819607i	$-0.305808\pi$
$499$	12772.6			1.14585			0.572926	+	0.819607i	$0.305808\pi$
$500$	157.946	−	43.2616i	0.0141272	−	0.00386944i
$501$	2584.38			0.230462
$502$	1169.70	+	849.835i	0.103996	+	0.0755578i
$503$	−2453.43	−	7550.87i	−0.217481	−	0.669337i	−0.998968	−	0.0454162i	$-0.985539\pi$
$503$	−2453.43	−	7550.87i	−0.217481	−	0.669337i	0.781487	−	0.623921i	$-0.214461\pi$
$504$	6249.82	+	19235.0i	0.552359	+	1.69999i
$505$	11607.6	+	6945.41i	1.02284	+	0.612013i
$506$	1651.05	−	5081.42i	0.145056	−	0.446436i
$507$	−2923.74			−0.256110
$508$	−94.3094	+	290.254i	−0.00823681	+	0.0253503i
$509$	4959.08	−	3602.98i	0.431841	−	0.313751i	−0.350543	−	0.936546i	$-0.614003\pi$
$509$	4959.08	−	3602.98i	0.431841	−	0.313751i	0.782385	+	0.622795i	$0.214003\pi$
$510$	−1508.08	−	3534.64i	−0.130939	−	0.306895i
$511$	−8877.65	−	6449.99i	−0.768541	−	0.558377i
$512$	−9570.21	+	6953.16i	−0.826069	+	0.600174i
$513$	−3465.77	+	2518.03i	−0.298280	+	0.216713i
$514$	−15327.5	−	11136.1i	−1.31530	−	0.955623i
$515$	2182.74	−	9534.86i	0.186763	−	0.815837i
$516$	−20.5663	+	14.9423i	−0.00175462	+	0.00127480i
$517$	−145.634	+	448.215i	−0.0123887	+	0.0381286i
$518$	−3185.56			−0.270204
$519$	712.762	−	2193.66i	0.0602828	−	0.185532i
$520$	52.0078	−	227.185i	0.00438595	−	0.0191591i
$521$	4976.40	+	15315.8i	0.418465	+	1.28790i	0.909115	+	0.416546i	$0.136759\pi$
$521$	4976.40	+	15315.8i	0.418465	+	1.28790i	−0.490650	+	0.871357i	$0.663241\pi$
$522$	−2446.10	−	7528.33i	−0.205102	−	0.631238i
$523$	11959.8	+	8689.31i	0.999934	+	0.726495i	0.962074	−	0.272788i	$-0.0879458\pi$
$523$	11959.8	+	8689.31i	0.999934	+	0.726495i	0.0378603	+	0.999283i	$0.487946\pi$
$524$	206.741			0.0172357
$525$	4050.88	−	4225.95i	0.336752	−	0.351306i
$526$	3816.29			0.316347
$527$	14694.3	+	10676.0i	1.21460	+	0.882459i
$528$	−459.012	−	1412.69i	−0.0378332	−	0.116439i
$529$	−186.450	−	573.835i	−0.0153243	−	0.0471632i
$530$	12194.9	−	10640.5i	0.999458	−	0.872064i
$531$	885.669	−	2725.81i	0.0723818	−	0.222768i
$532$	−253.971			−0.0206974
$533$	−41.9095	+	128.984i	−0.00340582	+	0.0104820i
$534$	2660.60	−	1933.04i	0.215609	−	0.156649i
$535$	7759.62	+	4642.95i	0.627061	+	0.375201i
$536$	6135.93	+	4458.01i	0.494462	+	0.359248i
$537$	−2438.16	+	1771.43i	−0.195930	+	0.142352i
$538$	−13972.6	+	10151.7i	−1.11971	+	0.813514i
$539$	−12805.6	−	9303.81i	−1.02333	−	0.743494i
$540$	68.6379	−	59.8891i	0.00546982	−	0.00477262i
$541$	−13411.8	+	9744.27i	−1.06584	+	0.774379i	−0.975160	−	0.221501i	$-0.928904\pi$
$541$	−13411.8	+	9744.27i	−1.06584	+	0.774379i	−0.0906808	+	0.995880i	$0.528904\pi$
$542$	2965.52	−	9126.92i	0.235018	−	0.723312i
$543$	−2052.78			−0.162234
$544$	150.681	−	463.747i	0.0118757	−	0.0365496i
$545$	−17882.1	+	1597.79i	−1.40548	+	0.125581i
$546$	−37.1646	−	114.381i	−0.00291300	−	0.00896530i
$547$	−4427.27	−	13625.7i	−0.346063	−	1.06507i	−0.961012	−	0.276506i	$-0.910823\pi$
$547$	−4427.27	−	13625.7i	−0.346063	−	1.06507i	0.614949	−	0.788567i	$-0.289177\pi$
$548$	44.5792	+	32.3887i	0.00347505	+	0.00252477i
$549$	5061.34			0.393466
$550$	4297.78	−	4483.53i	0.333196	−	0.347597i
$551$	6885.61			0.532372
$552$	2639.52	+	1917.72i	0.203524	+	0.147869i
$553$	−8213.64	−	25279.0i	−0.631609	−	1.94389i
$554$	798.225	+	2456.68i	0.0612154	+	0.188402i
$555$	188.398	+	441.567i	0.0144091	+	0.0337720i
$556$	93.6304	−	288.165i	0.00714175	−	0.0219800i
$557$	−21387.7			−1.62698			−0.813488	−	0.581582i	$-0.802434\pi$
$557$	−21387.7			−1.62698			−0.813488	+	0.581582i	$0.802434\pi$
$558$	4323.15	−	13305.3i	0.327981	−	1.00942i
$559$	−120.587	+	87.6115i	−0.00912394	+	0.00662893i
$560$	−24698.3	+	2206.82i	−1.86374	+	0.166527i
$561$	1752.73	+	1273.43i	0.131908	+	0.0958364i
$562$	14717.2	−	10692.7i	1.10464	−	0.802570i
$563$	−191.087	+	138.833i	−0.0143044	+	0.0103927i	−0.594914	−	0.803789i	$-0.702814\pi$
$563$	−191.087	+	138.833i	−0.0143044	+	0.0103927i	0.580610	+	0.814182i	$0.302814\pi$
$564$	−3.36104	−	2.44194i	−0.000250932	−	0.000182313i
$565$	−2311.20	+	206.508i	−0.172093	+	0.0153768i
$566$	−15487.2	+	11252.1i	−1.15014	+	0.835622i
$567$	−6398.10	+	19691.3i	−0.473889	+	1.45848i
$568$	−7330.75			−0.541534
$569$	1183.91	−	3643.69i	0.0872267	−	0.268456i	−0.897923	−	0.440152i	$-0.854925\pi$
$569$	1183.91	−	3643.69i	0.0872267	−	0.268456i	0.985150	+	0.171696i	$0.0549246\pi$
$570$	−1010.42	−	2368.22i	−0.0742488	−	0.174024i
$571$	−510.448	−	1571.00i	−0.0374108	−	0.115139i	0.930607	−	0.366020i	$-0.119280\pi$
$571$	−510.448	−	1571.00i	−0.0374108	−	0.115139i	−0.968018	+	0.250881i	$0.919280\pi$
$572$	0.586135	+	1.80394i	4.28453e−5	+	0.000131864i
$573$	−2232.71	−	1622.16i	−0.162780	−	0.118266i
$574$	14644.1			1.06486
$575$	−1821.52	+	13317.8i	−0.132109	+	0.965897i
$576$	−13100.2			−0.947640
$577$	−12673.0	−	9207.47i	−0.914357	−	0.664319i	0.0277561	−	0.999615i	$-0.491164\pi$
$577$	−12673.0	−	9207.47i	−0.914357	−	0.664319i	−0.942113	+	0.335296i	$0.891164\pi$
$578$	−3074.23	−	9461.52i	−0.221231	−	0.680878i
$579$	817.550	+	2516.16i	0.0586808	+	0.180601i
$580$	−145.833	+	13.0304i	−0.0104403	+	0.000932856i
$581$	−4005.54	+	12327.8i	−0.286020	+	0.880280i
$582$	−2519.11			−0.179417
$583$	−2819.52	+	8677.59i	−0.200296	+	0.616447i
$584$	5751.51	−	4178.72i	0.407533	−	0.296090i
$585$	194.394	−	169.616i	0.0137388	−	0.0119876i
$586$	13876.3	+	10081.8i	0.978202	+	0.710705i
$587$	16446.4	−	11949.0i	1.15641	−	0.840183i	0.167093	−	0.985941i	$-0.446562\pi$
$587$	16446.4	−	11949.0i	1.15641	−	0.840183i	0.989320	+	0.145758i	$0.0465620\pi$
$588$	112.885	−	82.0158i	0.00791718	−	0.00575217i
$589$	9845.23	+	7152.98i	0.688736	+	0.500396i
$590$	3060.23	+	1831.09i	0.213539	+	0.127771i
$591$	3659.22	−	2658.58i	0.254687	−	0.185041i
$592$	628.409	−	1934.05i	0.0436275	−	0.134272i
$593$	−6889.02			−0.477063			−0.238531	−	0.971135i	$-0.576666\pi$
$593$	−6889.02			−0.477063			−0.238531	+	0.971135i	$0.576666\pi$
$594$	1067.55	−	3285.58i	0.0737410	−	0.226951i
$595$	27251.4	−	23777.9i	1.87765	−	1.63832i
$596$	37.4438	+	115.240i	0.00257342	+	0.00792016i
$597$	−257.451	−	792.352i	−0.0176495	−	0.0543196i
$598$	223.417	+	162.322i	0.0152779	+	0.0111001i
$599$	16163.0			1.10251			0.551255	−	0.834337i	$-0.314149\pi$
$599$	16163.0			1.10251			0.551255	+	0.834337i	$0.314149\pi$
$600$	1792.85	+	3342.01i	0.121988	+	0.227395i
$601$	−22882.8			−1.55310			−0.776548	−	0.630058i	$-0.783031\pi$
$601$	−22882.8			−1.55310			−0.776548	+	0.630058i	$0.783031\pi$
$602$	13020.6	+	9460.04i	0.881531	+	0.640469i
$603$	2594.39	+	7984.73i	0.175210	+	0.539242i
$604$	−86.9156	−	267.499i	−0.00585521	−	0.0180205i
$605$	2539.37	−	11092.7i	0.170645	−	0.745427i
$606$	−1397.46	+	4300.94i	−0.0936764	+	0.288306i
$607$	16840.3			1.12608			0.563038	−	0.826431i	$-0.309632\pi$
$607$	16840.3			1.12608			0.563038	+	0.826431i	$0.309632\pi$
$608$	100.956	−	310.712i	0.00673408	−	0.0207254i
$609$	−4234.17	+	3076.30i	−0.281736	+	0.204693i
$610$	−1405.34	+	6138.93i	−0.0932796	+	0.407472i
$611$	−19.7069	−	14.3179i	−0.00130483	−	0.000948018i
$612$	219.927	−	159.787i	0.0145262	−	0.0105539i
$613$	−14979.4	+	10883.2i	−0.986970	+	0.717076i	−0.959255	−	0.282540i	$-0.908823\pi$
$613$	−14979.4	+	10883.2i	−0.986970	+	0.717076i	−0.0277146	+	0.999616i	$0.508823\pi$
$614$	8546.11	+	6209.11i	0.561715	+	0.408110i
$615$	−866.068	−	2029.89i	−0.0567858	−	0.133094i
$616$	11477.7	−	8339.07i	0.750733	−	0.545439i
$617$	4279.38	−	13170.6i	0.279224	−	0.859363i	−0.708847	−	0.705363i	$-0.750784\pi$
$617$	4279.38	−	13170.6i	0.279224	−	0.859363i	0.988071	−	0.154001i	$-0.0492158\pi$
$618$	3270.13			0.212854
$619$	−9044.03	+	27834.7i	−0.587254	+	1.80738i	0.00276987	+	0.999996i	$0.499118\pi$
$619$	−9044.03	+	27834.7i	−0.587254	+	1.80738i	−0.590024	+	0.807386i	$0.700882\pi$
$620$	−222.053	−	132.865i	−0.0143836	−	0.00860641i
$621$	2310.49	+	7110.96i	0.149302	+	0.459505i
$622$	1226.29	+	3774.14i	0.0790512	+	0.243295i
$623$	25039.6	+	18192.3i	1.61025	+	1.16992i
$624$	76.7753			0.00492544
$625$	−8641.39	+	13017.9i	−0.553049	+	0.833149i
$626$	27036.2			1.72617
$627$	1174.33	+	853.200i	0.0747978	+	0.0543438i
$628$	−27.4041	−	84.3410i	−0.00174131	−	0.00535919i
$629$	916.552	+	2820.86i	0.0581007	+	0.178815i
$630$	−23904.6	−	14303.3i	−1.51172	−	0.904534i
$631$	589.537	−	1814.41i	0.0371935	−	0.114470i	−0.930736	−	0.365692i	$-0.880832\pi$
$631$	589.537	−	1814.41i	0.0371935	−	0.114470i	0.967930	+	0.251222i	$0.0808324\pi$
$632$	17220.2			1.08383
$633$	−1152.09	+	3545.78i	−0.0723406	+	0.222642i
$634$	−14497.4	+	10533.0i	−0.908149	+	0.659809i
$635$	−11427.2	−	26783.0i	−0.714130	−	1.67378i
$636$	−65.0709	−	47.2768i	−0.00405697	−	0.00294756i
$637$	661.880	−	480.884i	0.0411690	−	0.0299110i
$638$	−4492.25	+	3263.81i	−0.278761	+	0.202532i
$639$	−6565.03	−	4769.78i	−0.406430	−	0.295289i
$640$	3531.58	−	15427.0i	0.218122	−	0.952820i
$641$	2282.93	−	1658.65i	0.140671	−	0.102204i	−0.515224	−	0.857056i	$-0.672291\pi$
$641$	2282.93	−	1658.65i	0.140671	−	0.102204i	0.655895	+	0.754852i	$0.272291\pi$
$642$	−934.191	+	2875.14i	−0.0574293	+	0.176749i
$643$	−16146.1			−0.990263			−0.495132	−	0.868818i	$-0.664880\pi$
$643$	−16146.1			−0.990263			−0.495132	+	0.868818i	$0.664880\pi$
$644$	−136.976	+	421.569i	−0.00838140	+	0.0257953i
$645$	541.249	−	2364.34i	0.0330414	−	0.144334i
$646$	−4915.67	−	15128.9i	−0.299387	−	0.921420i
$647$	742.836	+	2286.22i	0.0451374	+	0.138919i	0.971085	−	0.238732i	$-0.0767319\pi$
$647$	742.836	+	2286.22i	0.0451374	+	0.138919i	−0.925948	+	0.377651i	$0.876732\pi$
$648$	−10852.0	−	7884.45i	−0.657881	−	0.477979i
$649$	−2010.49			−0.121601
$650$	151.753	+	282.878i	0.00915728	+	0.0170698i
$651$	−9249.89			−0.556884
$652$	155.152	+	112.724i	0.00931934	+	0.00677089i
$653$	1898.71	+	5843.63i	0.113786	+	0.350197i	0.991692	−	0.128636i	$-0.0410599\pi$
$653$	1898.71	+	5843.63i	0.113786	+	0.350197i	−0.877906	+	0.478833i	$0.841060\pi$
$654$	−1854.76	−	5708.36i	−0.110897	−	0.341306i
$655$	−14863.1	+	12968.6i	−0.886639	+	0.773625i
$656$	−2888.81	+	8890.83i	−0.171934	+	0.529160i
$657$	7869.65			0.467312
$658$	−812.782	+	2501.49i	−0.0481543	+	0.148204i
$659$	−12203.4	+	8866.29i	−0.721361	+	0.524099i	−0.886819	−	0.462117i	$-0.847090\pi$
$659$	−12203.4	+	8866.29i	−0.721361	+	0.524099i	0.165458	+	0.986217i	$0.447090\pi$
$660$	−26.4862	−	15.8480i	−0.00156208	−	0.000934670i
$661$	9585.70	+	6964.42i	0.564055	+	0.409810i	0.832941	−	0.553362i	$-0.186655\pi$
$661$	9585.70	+	6964.42i	0.564055	+	0.409810i	−0.268886	+	0.963172i	$0.586655\pi$
$662$	−3597.49	+	2613.73i	−0.211209	+	0.153452i
$663$	−90.5928	+	65.8195i	−0.00530669	+	0.00385553i
$664$	−6793.92	−	4936.07i	−0.397071	−	0.288489i
$665$	18258.5	−	15931.2i	1.06471	−	0.929002i
$666$	1848.24	−	1342.83i	0.107534	−	0.0781283i
$667$	3713.68	−	11429.5i	0.215583	−	0.663498i
$668$	−227.476			−0.0131756
$669$	−345.664	+	1063.84i	−0.0199763	+	0.0614807i
$670$	−10405.1	+	929.707i	−0.599976	+	0.0536085i
$671$	−1097.14	−	3376.65i	−0.0631216	−	0.194268i
$672$	76.7365	+	236.171i	0.00440502	+	0.0135573i
$673$	−554.394	−	402.791i	−0.0317538	−	0.0230705i	0.571795	−	0.820396i	$-0.306247\pi$
$673$	−554.394	−	402.791i	−0.0317538	−	0.0230705i	−0.603549	+	0.797326i	$0.706247\pi$
$674$	27861.2			1.59225
$675$	−1177.77	+	8611.12i	−0.0671594	+	0.491026i
$676$	257.346			0.0146419
$677$	−2082.35	−	1512.91i	−0.118214	−	0.0858877i	0.527107	−	0.849799i	$-0.323277\pi$
$677$	−2082.35	−	1512.91i	−0.118214	−	0.0858877i	−0.645322	+	0.763911i	$0.723277\pi$
$678$	−239.721	−	737.785i	−0.0135788	−	0.0417913i
$679$	−7326.18	−	22547.7i	−0.414069	−	1.27437i
$680$	9195.10	+	21551.5i	0.518553	+	1.21538i
$681$	1837.99	−	5656.74i	0.103424	−	0.318306i
$682$	−9813.68			−0.551005
$683$	5622.62	−	17304.6i	0.314998	−	0.969463i	−0.660758	−	0.750599i	$-0.729765\pi$
$683$	5622.62	−	17304.6i	0.314998	−	0.969463i	0.975755	−	0.218864i	$-0.0702351\pi$
$684$	147.352	−	107.057i	0.00823705	−	0.00598457i
$685$	−5236.60	+	467.896i	−0.292088	+	0.0260984i
$686$	−44061.4	−	32012.5i	−2.45229	−	1.78170i
$687$	5129.35	−	3726.69i	0.284857	−	0.206961i
$688$	−8312.01	+	6039.03i	−0.460600	+	0.334645i
$689$	−381.531	−	277.199i	−0.0210961	−	0.0153272i
$690$	−4476.00	+	399.936i	−0.246954	+	0.0220657i
$691$	−11038.0	+	8019.59i	−0.607679	+	0.441504i	−0.848596	−	0.529041i	$-0.822552\pi$
$691$	−11038.0	+	8019.59i	−0.607679	+	0.441504i	0.240917	+	0.970546i	$0.422552\pi$
$692$	−62.7371	+	193.085i	−0.00344640	+	0.0106069i
$693$	15704.7			0.860855
$694$	2236.26	−	6882.49i	0.122316	−	0.376449i
$695$	11344.9	+	26590.1i	0.619188	+	1.45125i
$696$	−1047.80	−	3224.79i	−0.0570641	−	0.175625i
$697$	−4213.40	−	12967.5i	−0.228973	−	0.704706i
$698$	−4014.69	−	2916.84i	−0.217705	−	0.158172i
$699$	−1253.69			−0.0678382
$700$	−356.557	+	371.967i	−0.0192522	+	0.0200843i
$701$	24439.6			1.31679			0.658395	−	0.752673i	$-0.271236\pi$
$701$	24439.6			1.31679			0.658395	+	0.752673i	$0.271236\pi$
$702$	144.459	+	104.955i	0.00776673	+	0.00564286i
$703$	614.092	+	1889.98i	0.0329458	+	0.101397i
$704$	2839.70	+	8739.71i	0.152025	+	0.467884i
$705$	394.813	−	35.2770i	0.0210915	−	0.00188455i
$706$	1591.46	−	4898.01i	0.0848376	−	0.261103i
$707$	−42560.2			−2.26399
$708$	5.47674	−	16.8557i	0.000290718	−	0.000894738i
$709$	2038.30	−	1480.91i	0.107969	−	0.0784441i	−0.532491	−	0.846436i	$-0.678744\pi$
$709$	2038.30	−	1480.91i	0.107969	−	0.0784441i	0.640460	+	0.767992i	$0.278744\pi$
$710$	7608.15	−	6638.39i	0.402153	−	0.350893i
$711$	15421.5	+	11204.4i	0.813433	+	0.590993i
$712$	−16222.2	+	11786.1i	−0.853868	+	0.620371i
$713$	17183.2	−	12484.4i	0.902549	−	0.655740i
$714$	9781.96	+	7107.01i	0.512718	+	0.372511i
$715$	−155.297	−	92.9217i	−0.00812277	−	0.00486024i
$716$	214.606	−	155.920i	0.0112014	−	0.00813830i
$717$	−773.433	+	2380.38i	−0.0402851	+	0.123985i
$718$	23565.7			1.22488
$719$	−2456.12	+	7559.16i	−0.127396	+	0.392085i	−0.994330	−	0.106338i	$-0.966087\pi$
$719$	−2456.12	+	7559.16i	−0.127396	+	0.392085i	0.866934	+	0.498423i	$0.166087\pi$
$720$	13399.5	−	11691.6i	0.693571	−	0.605166i
$721$	9510.32	+	29269.8i	0.491238	+	1.51188i
$722$	2657.41	+	8178.67i	0.136979	+	0.421577i
$723$	−3718.23	−	2701.45i	−0.191262	−	0.138960i
$724$	180.685			0.00927500
$725$	9666.91	−	10084.7i	0.495200	−	0.516602i
$726$	3804.43			0.194484
$727$	9686.48	+	7037.64i	0.494156	+	0.359026i	0.806781	−	0.590851i	$-0.201208\pi$
$727$	9686.48	+	7037.64i	0.494156	+	0.359026i	−0.312624	+	0.949877i	$0.601208\pi$
$728$	226.601	+	697.405i	0.0115362	+	0.0355049i
$729$	−3816.13	−	11744.8i	−0.193880	−	0.596700i
$730$	−2185.10	+	9545.15i	−0.110786	+	0.483948i
$731$	4630.69	−	14251.8i	0.234298	−	0.721096i
$732$	31.2980			0.00158034
$733$	97.0939	−	298.824i	0.00489256	−	0.0150577i	−0.948580	−	0.316536i	$-0.897480\pi$
$733$	97.0939	−	298.824i	0.00489256	−	0.0150577i	0.953473	+	0.301478i	$0.0974801\pi$
$734$	5583.39	−	4056.57i	0.280772	−	0.203993i
$735$	−2970.82	+	12977.4i	−0.149089	+	0.651265i
$736$	−461.305	−	335.158i	−0.0231032	−	0.0167854i
$737$	4764.59	−	3461.67i	0.238135	−	0.173015i
$738$	−8496.39	+	6172.99i	−0.423789	+	0.307901i
$739$	−26770.8	−	19450.2i	−1.33259	−	0.968181i	−0.999682	−	0.0252200i	$-0.991971\pi$
$739$	−26770.8	−	19450.2i	−1.33259	−	0.968181i	−0.332904	−	0.942961i	$-0.608029\pi$
$740$	−16.5827	−	38.8666i	−0.000823774	−	0.00193076i
$741$	−60.6974	+	44.0992i	−0.00300914	+	0.00218627i
$742$	−15735.7	+	48429.6i	−0.778540	+	2.39610i
$743$	−6266.35			−0.309408			−0.154704	−	0.987961i	$-0.549442\pi$
$743$	−6266.35			−0.309408			−0.154704	+	0.987961i	$0.549442\pi$
$744$	1851.84	−	5699.37i	0.0912522	−	0.280845i
$745$	−9920.77	−	5936.08i	−0.487878	−	0.291921i
$746$	−1641.08	−	5050.73i	−0.0805419	−	0.247883i
$747$	−2872.61	−	8840.97i	−0.140700	−	0.433031i
$748$	−154.274	−	112.087i	−0.00754121	−	0.00547901i
$749$	−28451.2			−1.38796
$750$	−4887.07	−	1844.95i	−0.237934	−	0.0898239i
$751$	−25936.6			−1.26024			−0.630119	−	0.776498i	$-0.716994\pi$
$751$	−25936.6			−1.26024			−0.630119	+	0.776498i	$0.716994\pi$
$752$	−1358.39	−	986.926i	−0.0658714	−	0.0478584i
$753$	211.851	+	652.012i	0.0102527	+	0.0315546i
$754$	−88.6887	−	272.956i	−0.00428363	−	0.0131836i
$755$	23028.4	+	13779.0i	1.11005	+	0.664197i
$756$	−88.5671	+	272.582i	−0.00426079	+	0.0131134i
$757$	30135.4			1.44688			0.723440	−	0.690387i	$-0.242560\pi$
$757$	30135.4			1.44688			0.723440	+	0.690387i	$0.242560\pi$
$758$	−5841.00	+	17976.8i	−0.279888	+	0.861405i
$759$	2049.60	−	1489.12i	0.0980182	−	0.0712144i
$760$	6160.74	+	14439.5i	0.294044	+	0.689180i
$761$	7771.50	+	5646.33i	0.370193	+	0.268961i	0.757291	−	0.653078i	$-0.226522\pi$
$761$	7771.50	+	5646.33i	0.370193	+	0.268961i	−0.387098	+	0.922039i	$0.626522\pi$
$762$	7875.74	−	5722.06i	0.374420	−	0.272032i
$763$	45699.3	−	33202.5i	2.16832	−	1.57538i
$764$	196.522	+	142.782i	0.00930618	+	0.00676133i
$765$	−5787.89	+	25283.2i	−0.273545	+	1.19492i
$766$	16456.9	−	11956.6i	0.776254	−	0.563981i
$767$	32.1118	−	98.8301i	0.00151172	−	0.00465260i
$768$	−239.566			−0.0112560
$769$	1023.27	−	3149.30i	0.0479844	−	0.147681i	−0.924193	−	0.381925i	$-0.875261\pi$
$769$	1023.27	−	3149.30i	0.0479844	−	0.147681i	0.972178	+	0.234244i	$0.0752614\pi$
$770$	−4360.59	+	19048.3i	−0.204084	+	0.891499i
$771$	−2776.06	−	8543.82i	−0.129672	−	0.399090i
$772$	−71.9604	−	221.471i	−0.00335481	−	0.0103250i
$773$	−13063.2	−	9490.98i	−0.607828	−	0.441613i	0.240821	−	0.970570i	$-0.422583\pi$
$773$	−13063.2	−	9490.98i	−0.607828	−	0.441613i	−0.848649	+	0.528957i	$0.822583\pi$
$774$	−11542.2			−0.536016
$775$	24298.3	−	4377.11i	1.12622	−	0.202878i
$776$	15359.6			0.710536
$777$	−1222.02	−	887.847i	−0.0564216	−	0.0409927i
$778$	5534.28	+	17032.8i	0.255030	+	0.784902i
$779$	−2822.99	−	8688.27i	−0.129838	−	0.399601i
$780$	1.20208	−	1.04886i	5.51813e−5	−	4.81477e-5i
$781$	−1759.04	+	5413.77i	−0.0805933	+	0.248041i
$782$	−27763.8			−1.26961
$783$	2401.22	−	7390.19i	0.109595	−	0.337297i
$784$	45623.2	−	33147.2i	2.07832	−	1.50999i
$785$	7260.74	+	4344.45i	0.330123	+	0.197529i
$786$	−5335.13	−	3876.20i	−0.242109	−	0.175903i
$787$	−24144.9	+	17542.3i	−1.09361	+	0.794557i	−0.980006	−	0.198968i	$-0.936241\pi$
$787$	−24144.9	+	17542.3i	−1.09361	+	0.794557i	−0.113608	+	0.993526i	$0.536241\pi$
$788$	−322.083	+	234.007i	−0.0145606	+	0.0105789i
$789$	1463.97	+	1063.64i	0.0660568	+	0.0479930i
$790$	−17871.8	+	15593.8i	−0.804873	+	0.702281i
$791$	5906.48	−	4291.31i	0.265500	−	0.192897i
$792$	−3144.10	+	9676.54i	−0.141061	+	0.434142i
$793$	183.510			0.00821769
$794$	−10328.8	+	31788.9i	−0.461658	+	1.42084i
$795$	7643.71	−	682.974i	0.340999	−	0.0304687i
$796$	22.6607	+	69.7425i	0.00100903	+	0.00310548i
$797$	−4935.39	−	15189.6i	−0.219348	−	0.675084i	−0.998816	−	0.0486423i	$-0.984511\pi$
$797$	−4935.39	−	15189.6i	−0.219348	−	0.675084i	0.779468	−	0.626442i	$-0.215489\pi$
$798$	6553.94	+	4761.71i	0.290735	+	0.211232i
$799$	2448.95			0.108433
$800$	−313.335	−	584.078i	−0.0138476	−	0.0258129i
$801$	−22196.5			−0.979118
$802$	−10088.9	−	7330.03i	−0.444205	−	0.322734i
$803$	−1705.89	−	5250.20i	−0.0749684	−	0.230729i
$804$	16.0430	+	49.3754i	0.000703724	+	0.00216584i
$805$	−16596.9	−	38899.9i	−0.726665	−	1.70316i
$806$	156.745	−	482.412i	0.00685002	−	0.0210822i
$807$	−8189.42			−0.357226
$808$	8520.60	−	26223.7i	0.370982	−	1.14177i
$809$	10510.1	−	7636.00i	0.456754	−	0.331851i	−0.335503	−	0.942039i	$-0.608906\pi$
$809$	10510.1	−	7636.00i	0.456754	−	0.331851i	0.792257	+	0.610188i	$0.208906\pi$
$810$	18402.4	−	1644.28i	0.798267	−	0.0713261i
$811$	9766.25	+	7095.59i	0.422860	+	0.307226i	0.778787	−	0.627288i	$-0.215835\pi$
$811$	9766.25	+	7095.59i	0.422860	+	0.307226i	−0.355928	+	0.934513i	$0.615835\pi$
$812$	372.690	−	270.775i	0.0161070	−	0.0117024i
$813$	3681.36	−	2674.67i	0.158808	−	0.115381i
$814$	−1296.50	−	941.962i	−0.0558259	−	0.0405599i
$815$	−18225.2	+	1628.45i	−0.783316	+	0.0699902i
$816$	−6244.53	+	4536.92i	−0.267895	+	0.194637i
$817$	3102.57	−	9548.73i	0.132858	−	0.408896i
$818$	−12943.0			−0.553228
$819$	−250.837	+	771.998i	−0.0107020	+	0.0329375i
$820$	76.2310	+	178.670i	0.00324647	+	0.00760907i
$821$	−8336.47	−	25657.0i	−0.354378	−	1.09066i	−0.956369	−	0.292161i	$-0.905626\pi$
$821$	−8336.47	−	25657.0i	−0.354378	−	1.09066i	0.601991	−	0.798503i	$-0.294374\pi$
$822$	−543.148	−	1671.64i	−0.0230468	−	0.0709307i
$823$	−12794.0	−	9295.35i	−0.541882	−	0.393701i	0.282901	−	0.959149i	$-0.408703\pi$
$823$	−12794.0	−	9295.35i	−0.541882	−	0.393701i	−0.824784	+	0.565448i	$0.808703\pi$
$824$	−19938.7			−0.842958
$825$	2898.28	−	522.097i	0.122309	−	0.0220328i
$826$	−11220.6			−0.472656
$827$	−9014.41	−	6549.35i	−0.379035	−	0.275385i	0.381913	−	0.924198i	$-0.375266\pi$
$827$	−9014.41	−	6549.35i	−0.379035	−	0.275385i	−0.760947	+	0.648814i	$0.775266\pi$
$828$	−98.2336	−	302.332i	−0.00412301	−	0.0126893i
$829$	8090.34	+	24899.5i	0.338950	+	1.04318i	0.964744	+	0.263191i	$0.0847750\pi$
$829$	8090.34	+	24899.5i	0.338950	+	1.04318i	−0.625794	+	0.779988i	$0.715225\pi$
$830$	11520.9	−	1029.40i	0.481802	−	0.0430496i
$831$	−378.493	+	1164.88i	−0.0158000	+	0.0486274i
$832$	−474.975			−0.0197918
$833$	−25417.0	+	78225.6i	−1.05720	+	3.25373i
$834$	−7819.04	+	5680.86i	−0.324642	+	0.235866i
$835$	16353.8	−	14269.3i	0.677779	−	0.591387i
$836$	−103.364	−	75.0984i	−0.00427622	−	0.00310686i
$837$	11110.5	−	8072.23i	0.458822	−	0.333354i
$838$	33153.3	−	24087.2i	1.36666	−	0.992936i
$839$	289.711	+	210.487i	0.0119213	+	0.00866130i	0.593730	−	0.804664i	$-0.297655\pi$
$839$	289.711	+	210.487i	0.0119213	+	0.00866130i	−0.581809	+	0.813326i	$0.697655\pi$
$840$	−10239.6	−	6126.86i	−0.420596	−	0.251663i
$841$	9626.80	−	6994.28i	0.394719	−	0.286780i
$842$	12686.8	−	39045.8i	0.519257	−	1.59811i
$843$	8625.85			0.352420
$844$	101.407	−	312.098i	0.00413575	−	0.0127285i
$845$	−18501.2	+	16143.0i	−0.753209	+	0.657202i
$846$	−582.893	−	1793.96i	−0.0236883	−	0.0729050i
$847$	11064.2	+	34052.0i	0.448843	+	1.38140i
$848$	−26298.8	−	19107.2i	−1.06498	−	0.773755i
$849$	−9077.14			−0.366934
$850$	−29059.1	−	14040.3i	−1.17261	−	0.566564i
$851$	3468.41			0.139713
$852$	−40.5964	−	29.4950i	−0.00163241	−	0.00118601i
$853$	9458.51	+	29110.3i	0.379664	+	1.16848i	0.940278	+	0.340407i	$0.110565\pi$
$853$	9458.51	+	29110.3i	0.379664	+	1.16848i	−0.560614	+	0.828077i	$0.689435\pi$
$854$	−6123.14	−	18845.1i	−0.245351	−	0.755111i
$855$	−3877.90	+	16939.8i	−0.155113	+	0.677577i
$856$	5695.96	−	17530.4i	0.227434	−	0.699971i
$857$	913.409			0.0364078			0.0182039	−	0.999834i	$-0.494205\pi$
$857$	913.409			0.0364078			0.0182039	+	0.999834i	$0.494205\pi$
$858$	18.6964	−	57.5417i	0.000743922	−	0.00228956i
$859$	−36013.6	+	26165.4i	−1.43046	+	1.03929i	−0.440535	+	0.897736i	$0.645211\pi$
$859$	−36013.6	+	26165.4i	−1.43046	+	1.03929i	−0.989930	+	0.141558i	$0.954789\pi$
$860$	−47.6406	+	208.108i	−0.00188899	+	0.00825165i
$861$	5617.63	+	4081.44i	0.222356	+	0.161551i
$862$	27942.8	−	20301.7i	1.10410	−	0.802178i
$863$	−31291.0	+	22734.2i	−1.23425	+	0.896734i	−0.997201	−	0.0747640i	$-0.976180\pi$
$863$	−31291.0	+	22734.2i	−1.23425	+	0.896734i	−0.237047	+	0.971498i	$0.576180\pi$
$864$	−298.274	−	216.709i	−0.0117448	−	0.00853308i
$865$	−7601.64	−	17816.7i	−0.298802	−	0.700332i
$866$	−6218.80	+	4518.22i	−0.244022	+	0.177293i
$867$	1457.71	−	4486.36i	0.0571007	−	0.175738i
$868$	814.172			0.0318373
$869$	4132.04	−	12717.1i	0.161300	−	0.496431i
$870$	4007.66	+	2397.98i	0.156175	+	0.0934472i
$871$	94.0654	+	289.503i	0.00365934	+	0.0112623i
$872$	11308.8	+	34805.1i	0.439181	+	1.35166i
$873$	13755.2	+	9993.75i	0.533269	+	0.387442i
$874$	−18601.8			−0.719927
$875$	2300.70	−	49107.9i	0.0888889	−	1.89731i
$876$	48.6638			0.00187694
$877$	23348.3	+	16963.6i	0.898993	+	0.653157i	0.938207	−	0.346074i	$-0.112485\pi$
$877$	23348.3	+	16963.6i	0.898993	+	0.653157i	−0.0392139	+	0.999231i	$0.512485\pi$
$878$	4437.06	+	13655.9i	0.170551	+	0.524901i
$879$	2513.23	+	7734.94i	0.0964383	+	0.296807i
$880$	−10704.6	−	6405.07i	−0.410058	−	0.245358i
$881$	3324.08	−	10230.5i	0.127118	−	0.391229i	−0.867163	−	0.498025i	$-0.834059\pi$
$881$	3324.08	−	10230.5i	0.127118	−	0.391229i	0.994281	+	0.106795i	$0.0340589\pi$
$882$	63353.2			2.41861
$883$	6523.57	−	20077.5i	0.248625	−	0.765188i	−0.746394	−	0.665504i	$-0.768217\pi$
$883$	6523.57	−	20077.5i	0.248625	−	0.765188i	0.995019	−	0.0996842i	$-0.0317833\pi$
$884$	7.97395	−	5.79341i	0.000303386	−	0.000220423i
$885$	663.598	+	1555.34i	0.0252052	+	0.0590759i
$886$	16245.7	+	11803.2i	0.616009	+	0.447557i
$887$	−20311.0	+	14756.8i	−0.768857	+	0.558607i	−0.901614	−	0.432541i	$-0.857617\pi$
$887$	−20311.0	+	14756.8i	−0.768857	+	0.558607i	0.132757	+	0.991149i	$0.457617\pi$
$888$	791.700	−	575.204i	0.0299186	−	0.0217371i
$889$	74120.6	+	53851.7i	2.79631	+	2.03164i
$890$	6163.11	−	26922.2i	0.232121	−	1.01397i
$891$	−8426.65	+	6122.32i	−0.316839	+	0.230197i
$892$	30.4252	−	93.6392i	0.00114205	−	0.00351488i
$893$	1640.80			0.0614865
$894$	1194.38	−	3675.91i	0.0446822	−	0.137518i
$895$	−5647.84	+	24671.4i	−0.210935	+	0.921425i
$896$	15387.3	+	47357.2i	0.573720	+	1.76573i
$897$	40.4645	+	124.537i	0.00150621	+	0.00463564i
$898$	−27579.6	−	20037.8i	−1.02488	−	0.744620i
$899$	−22073.7			−0.818909
$900$	50.0747	−	366.114i	0.00185462	−	0.0135598i
$901$	47412.5			1.75310
$902$	5960.03	+	4330.21i	0.220008	+	0.159845i
$903$	2358.25	+	7257.95i	0.0869077	+	0.267474i
$904$	1461.63	+	4498.43i	0.0537755	+	0.165504i
$905$	−12989.8	+	11334.1i	−0.477124	+	0.416308i
$906$	−2772.42	+	8532.63i	−0.101664	+	0.312889i
$907$	5609.06			0.205343			0.102671	−	0.994715i	$-0.467261\pi$
$907$	5609.06			0.205343			0.102671	+	0.994715i	$0.467261\pi$
$908$	−161.779	+	497.904i	−0.00591280	+	0.0181977i
$909$	24693.2	−	17940.6i	0.901012	−	0.654624i
$910$	−866.713	−	518.596i	−0.0315728	−	0.0188915i
$911$	−42353.8	−	30771.8i	−1.54033	−	1.11912i	−0.950126	−	0.311865i	$-0.899046\pi$
$911$	−42353.8	−	30771.8i	−1.54033	−	1.11912i	−0.590207	−	0.807252i	$-0.700954\pi$
$912$	−4183.85	+	3039.75i	−0.151909	+	0.110368i
$913$	−5275.52	+	3832.89i	−0.191231	+	0.138938i
$914$	41863.9	+	30415.9i	1.51503	+	1.10073i
$915$	−2250.08	+	1963.28i	−0.0812956	+	0.0709333i
$916$	−451.484	+	328.022i	−0.0162854	+	0.0118320i
$917$	19178.6	−	59025.7i	0.690658	−	2.12563i
$918$	−17951.7			−0.645420
$919$	8652.28	−	26629.0i	0.310568	−	0.955832i	−0.666972	−	0.745083i	$-0.732410\pi$
$919$	8652.28	−	26629.0i	0.310568	−	0.955832i	0.977540	−	0.210749i	$-0.0675901\pi$
$920$	27291.1	−	2438.49i	0.978002	−	0.0873856i
$921$	1547.84	+	4763.76i	0.0553780	+	0.170436i
$922$	−13354.7	−	41101.5i	−0.477020	−	1.46812i
$923$	−238.030	−	172.939i	−0.00848845	−	0.00616722i
$924$	97.1137			0.00345758
$925$	3630.22	+	1754.00i	0.129039	+	0.0623471i
$926$	−28171.9			−0.999770
$927$	−17856.0	−	12973.2i	−0.632653	−	0.459649i
$928$	183.122	+	563.591i	0.00647766	+	0.0199362i
$929$	−648.811	−	1996.83i	−0.0229137	−	0.0705210i	0.938946	−	0.344065i	$-0.111804\pi$
$929$	−648.811	−	1996.83i	−0.0229137	−	0.0705210i	−0.961859	+	0.273544i	$0.911804\pi$
$930$	3239.17	+	7591.97i	0.114211	+	0.267689i
$931$	−17029.5	+	52411.3i	−0.599483	+	1.84502i
$932$	110.349			0.00387834
$933$	−581.470	+	1789.58i	−0.0204035	+	0.0627955i
$934$	−17653.9	+	12826.3i	−0.618473	+	0.449347i
$935$	18122.2	−	1619.24i	0.633860	−	0.0566361i
$936$	−425.453	−	309.109i	−0.0148572	−	0.0107944i
$937$	−21350.1	+	15511.8i	−0.744374	+	0.540819i	−0.894078	−	0.447912i	$-0.852168\pi$
$937$	−21350.1	+	15511.8i	−0.744374	+	0.540819i	0.149704	+	0.988731i	$0.452168\pi$
$938$	26591.2	−	19319.6i	0.925621	−	0.672503i
$939$	10371.4	+	7535.24i	0.360444	+	0.261878i
$940$	−34.7513	+	3.10507i	−0.00120581	+	0.000107741i
$941$	−31862.4	+	23149.4i	−1.10381	+	0.801965i	−0.981678	−	0.190549i	$-0.938973\pi$
$941$	−31862.4	+	23149.4i	−1.10381	+	0.801965i	−0.122132	+	0.992514i	$0.538973\pi$
$942$	−874.130	+	2690.30i	−0.0302343	+	0.0930516i
$943$	−15944.3			−0.550603
$944$	2213.46	−	6812.33i	0.0763156	−	0.234875i
$945$	−10731.4	−	25152.2i	−0.369409	−	0.865822i
$946$	2501.99	+	7700.33i	0.0859902	+	0.264651i
$947$	8956.50	+	27565.3i	0.307336	+	0.945883i	0.978795	+	0.204841i	$0.0656678\pi$
$947$	8956.50	+	27565.3i	0.307336	+	0.945883i	−0.671459	+	0.741041i	$0.734332\pi$
$948$	95.3623	+	69.2848i	0.00326711	+	0.00237370i
$949$	285.331			0.00976000
$950$	−19469.6	−	9407.06i	−0.664925	−	0.321269i
$951$	−8497.02			−0.289732
$952$	−59642.7	−	43332.9i	−2.03049	−	1.47524i
$953$	−1541.94	−	4745.61i	−0.0524118	−	0.161307i	0.921425	−	0.388557i	$-0.127026\pi$
$953$	−1541.94	−	4745.61i	−0.0524118	−	0.161307i	−0.973836	+	0.227250i	$0.927026\pi$
$954$	−11285.0	−	34731.7i	−0.382983	−	1.17870i
$955$	−23084.9	+	2062.67i	−0.782210	+	0.0698914i
$956$	68.0773	−	209.520i	0.00230312	−	0.00708826i
$957$	−2632.93			−0.0889347
$958$	−8926.38	+	27472.6i	−0.301042	+	0.926512i
$959$	13382.6	−	9723.04i	0.450623	−	0.327396i
$960$	5823.85	−	5081.52i	0.195796	−	0.170839i
$961$	−7460.13	−	5420.10i	−0.250416	−	0.181938i
$962$	67.0120	−	48.6871i	0.00224590	−	0.00163174i
$963$	16507.2	−	11993.2i	0.552375	−	0.401324i
$964$	327.277	+	237.781i	0.0109345	+	0.00794440i
$965$	19066.0	+	11408.1i	0.636017	+	0.380560i
$966$	11438.8	−	8310.80i	0.380992	−	0.276807i
$967$	−9029.12	+	27788.8i	−0.300266	+	0.924123i	0.681136	+	0.732157i	$0.261486\pi$
$967$	−9029.12	+	27788.8i	−0.300266	+	0.924123i	−0.981402	+	0.191966i	$0.938514\pi$
$968$	−23196.4			−0.770208
$969$	2330.86	−	7173.64i	0.0772734	−	0.237823i
$970$	−15940.8	+	13908.9i	−0.527657	+	0.460400i
$971$	−6020.49	−	18529.2i	−0.198977	−	0.612389i	−0.999907	−	0.0136307i	$-0.995661\pi$
$971$	−6020.49	−	18529.2i	−0.198977	−	0.612389i	0.800930	−	0.598758i	$-0.204339\pi$
$972$	−96.3526	−	296.543i	−0.00317954	−	0.00978562i
$973$	−73586.9	−	53464.0i	−2.42455	−	1.76154i
$974$	−3313.68			−0.109011
$975$	−20.6268	+	150.810i	−0.000677525	+	0.00495362i
$976$	12649.3			0.414850
$977$	22059.7	+	16027.3i	0.722368	+	0.524831i	0.887140	−	0.461501i	$-0.152689\pi$
$977$	22059.7	+	16027.3i	0.722368	+	0.524831i	−0.164772	+	0.986332i	$0.552689\pi$
$978$	−1890.35	−	5817.90i	−0.0618065	−	0.190221i
$979$	4811.50	+	14808.3i	0.157075	+	0.483426i
$980$	261.491	−	1142.27i	0.00852349	−	0.0372331i
$981$	−12518.4	+	38527.7i	−0.407423	+	1.25392i
$982$	21224.3			0.689709
$983$	14798.2	−	45544.1i	0.480151	−	1.47775i	−0.358732	−	0.933441i	$-0.616791\pi$
$983$	14798.2	−	45544.1i	0.480151	−	1.47775i	0.838883	−	0.544312i	$-0.183209\pi$
$984$	−3639.46	+	2644.22i	−0.117908	+	0.0856653i
$985$	8476.34	−	37027.1i	0.274192	−	1.19775i
$986$	23343.4	+	16960.0i	0.753961	+	0.547785i
$987$	−1008.98	+	733.067i	−0.0325392	+	0.0236411i
$988$	5.34256	−	3.88160i	0.000172034	−	0.000124990i
$989$	−14176.7	−	10300.0i	−0.455808	−	0.331164i
$990$	−5499.55	−	12889.9i	−0.176553	−	0.413804i
$991$	41709.3	−	30303.6i	1.33697	−	0.971367i	0.337423	−	0.941353i	$-0.390445\pi$
$991$	41709.3	−	30303.6i	1.33697	−	0.971367i	0.999549	−	0.0300142i	$-0.00955526\pi$
$992$	−323.643	+	996.071i	−0.0103585	+	0.0318803i
$993$	−2108.51			−0.0673832
$994$	−9817.20	+	30214.2i	−0.313262	+	0.964122i
$995$	−6003.99	−	3592.47i	−0.191296	−	0.114461i
$996$	−17.7634	−	54.6702i	−0.000565116	−	0.00173925i
$997$	−1454.84	−	4477.53i	−0.0462138	−	0.142231i	0.925287	−	0.379268i	$-0.123824\pi$
$997$	−1454.84	−	4477.53i	−0.0462138	−	0.142231i	−0.971501	+	0.237036i	$0.923824\pi$
$998$	29012.0	+	21078.4i	0.920199	+	0.668563i
$999$	2242.63			0.0710247

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.4.d.a.16.6	yes	28
3.2	odd	2		225.4.h.b.91.2		28
5.2	odd	4		125.4.e.b.49.4		56
5.3	odd	4		125.4.e.b.49.11		56
5.4	even	2		125.4.d.a.76.2		28
25.2	odd	20		125.4.e.b.74.11		56
25.6	even	5		625.4.a.c.1.4		14
25.11	even	5	inner	25.4.d.a.11.6	✓	28
25.14	even	10		125.4.d.a.51.2		28
25.19	even	10		625.4.a.d.1.11		14
25.23	odd	20		125.4.e.b.74.4		56
75.11	odd	10		225.4.h.b.136.2		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.4.d.a.11.6	✓	28	25.11	even	5	inner
25.4.d.a.16.6	yes	28	1.1	even	1	trivial
125.4.d.a.51.2		28	25.14	even	10
125.4.d.a.76.2		28	5.4	even	2
125.4.e.b.49.4		56	5.2	odd	4
125.4.e.b.49.11		56	5.3	odd	4
125.4.e.b.74.4		56	25.23	odd	20
125.4.e.b.74.11		56	25.2	odd	20
225.4.h.b.91.2		28	3.2	odd	2
225.4.h.b.136.2		28	75.11	odd	10
625.4.a.c.1.4		14	25.6	even	5
625.4.a.d.1.11		14	25.19	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	25.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.27143 + 1.65029i) q^{2} +(0.411392 + 1.26614i) q^{3} +(-0.0362106 - 0.111445i) q^{4} +(9.59405 + 5.74058i) q^{5} +(-1.15504 + 3.55485i) q^{6} -35.1773 q^{7} +(7.04252 - 21.6747i) q^{8} +(20.4096 - 14.8284i) q^{9} +O(q^{10})\)	\(q+(2.27143 + 1.65029i) q^{2} +(0.411392 + 1.26614i) q^{3} +(-0.0362106 - 0.111445i) q^{4} +(9.59405 + 5.74058i) q^{5} +(-1.15504 + 3.55485i) q^{6} -35.1773 q^{7} +(7.04252 - 21.6747i) q^{8} +(20.4096 - 14.8284i) q^{9} +(12.3186 + 28.8722i) q^{10} +(-14.3169 - 10.4018i) q^{11} +(0.126207 - 0.0916951i) q^{12} +(0.739994 - 0.537637i) q^{13} +(-79.9025 - 58.0526i) q^{14} +(-3.32144 + 14.5090i) q^{15} +(51.0076 - 37.0592i) q^{16} +(-28.4167 + 87.4576i) q^{17} +70.8301 q^{18} +(-19.0393 + 58.5968i) q^{19} +(0.292352 - 1.27708i) q^{20} +(-14.4717 - 44.5392i) q^{21} +(-15.3537 - 47.2539i) q^{22} +(86.9971 + 63.2071i) q^{23} +30.3403 q^{24} +(59.0915 + 110.151i) q^{25} +2.56810 q^{26} +(56.2512 + 40.8689i) q^{27} +(1.27379 + 3.92032i) q^{28} +(-34.5348 - 106.287i) q^{29} +(-31.4884 + 27.4748i) q^{30} +(61.0355 - 187.848i) q^{31} -5.30253 q^{32} +(7.28026 - 22.4063i) q^{33} +(-208.877 + 151.758i) q^{34} +(-337.492 - 201.938i) q^{35} +(-2.39160 - 1.73760i) q^{36} +(26.0940 - 18.9584i) q^{37} +(-139.948 + 101.678i) q^{38} +(0.985150 + 0.715753i) q^{39} +(191.991 - 167.520i) q^{40} +(-119.955 + 87.1521i) q^{41} +(40.6312 - 125.050i) q^{42} -162.956 q^{43} +(-0.640806 + 1.97220i) q^{44} +(280.935 - 25.1018i) q^{45} +(93.2976 + 287.140i) q^{46} +(-8.22946 - 25.3277i) q^{47} +(67.9061 + 49.3367i) q^{48} +894.440 q^{49} +(-47.5585 + 347.717i) q^{50} -122.424 q^{51} +(-0.0867125 - 0.0630003i) q^{52} +(-159.325 - 490.352i) q^{53} +(60.3250 + 185.661i) q^{54} +(-77.6443 - 181.983i) q^{55} +(-247.737 + 762.455i) q^{56} -82.0241 q^{57} +(96.9612 - 298.416i) q^{58} +(91.9115 - 66.7776i) q^{59} +(1.73722 - 0.155223i) q^{60} +(162.310 + 117.925i) q^{61} +(448.641 - 325.957i) q^{62} +(-717.954 + 521.624i) q^{63} +(-420.105 - 305.224i) q^{64} +(10.1859 - 0.910121i) q^{65} +(53.5135 - 38.8798i) q^{66} +(-102.839 + 316.507i) q^{67} +10.7757 q^{68} +(-44.2388 + 136.153i) q^{69} +(-433.333 - 1015.65i) q^{70} +(-99.3996 - 305.921i) q^{71} +(-177.666 - 546.801i) q^{72} +(252.369 + 183.357i) q^{73} +90.5574 q^{74} +(-115.156 + 120.133i) q^{75} +7.21973 q^{76} +(503.629 + 365.908i) q^{77} +(1.05650 + 3.25156i) q^{78} +(233.493 + 718.618i) q^{79} +(702.110 - 62.7344i) q^{80} +(181.882 - 559.774i) q^{81} -416.294 q^{82} +(113.867 - 350.448i) q^{83} +(-4.43963 + 3.22558i) q^{84} +(-774.689 + 675.944i) q^{85} +(-370.143 - 268.925i) q^{86} +(120.367 - 87.4515i) q^{87} +(-326.283 + 237.058i) q^{88} +(-711.811 - 517.161i) q^{89} +(679.547 + 406.606i) q^{90} +(-26.0310 + 18.9126i) q^{91} +(3.89388 - 11.9841i) q^{92} +262.951 q^{93} +(23.1053 - 71.1109i) q^{94} +(-519.043 + 452.884i) q^{95} +(-2.18142 - 6.71373i) q^{96} +(208.265 + 640.972i) q^{97} +(2031.65 + 1476.08i) q^{98} -446.445 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{2} - 7 q^{3} - 31 q^{4} - 20 q^{5} + q^{6} - 16 q^{7} + 100 q^{8} - 34 q^{9}+O(q^{10}) \) 28 * q - q^2 - 7 * q^3 - 31 * q^4 - 20 * q^5 + q^6 - 16 * q^7 + 100 * q^8 - 34 * q^9	\( 28 q - q^{2} - 7 q^{3} - 31 q^{4} - 20 q^{5} + q^{6} - 16 q^{7} + 100 q^{8} - 34 q^{9} - 25 q^{10} - 89 q^{11} + 139 q^{12} + 33 q^{13} - 17 q^{14} + 225 q^{15} - 207 q^{16} - 191 q^{17} - 552 q^{18} - 115 q^{19} - 225 q^{20} - 144 q^{21} + 808 q^{22} + 433 q^{23} + 780 q^{24} + 90 q^{25} + 586 q^{26} + 35 q^{27} - 13 q^{28} - 5 q^{29} + 675 q^{30} - 639 q^{31} - 1386 q^{32} + 251 q^{33} - 777 q^{34} - 1030 q^{35} + 673 q^{36} + 699 q^{37} - 2355 q^{38} - 1133 q^{39} + 410 q^{40} + 341 q^{41} - 2407 q^{42} - 172 q^{43} + 548 q^{44} + 470 q^{45} - 1239 q^{46} + 2319 q^{47} + 4738 q^{48} + 1344 q^{49} + 2335 q^{50} + 2006 q^{51} + 2344 q^{52} - 927 q^{53} + 1615 q^{54} + 1225 q^{55} - 2910 q^{56} - 770 q^{57} + 2410 q^{58} - 1905 q^{59} - 12030 q^{60} + 1391 q^{61} - 3832 q^{62} - 6142 q^{63} - 3596 q^{64} + 1215 q^{65} + 3632 q^{66} - 3611 q^{67} + 3622 q^{68} + 2687 q^{69} + 560 q^{70} - 3719 q^{71} + 9025 q^{72} + 4593 q^{73} + 4848 q^{74} + 3815 q^{75} + 3520 q^{76} + 1368 q^{77} - 3679 q^{78} + 775 q^{79} + 9500 q^{80} - 3712 q^{81} - 6762 q^{82} - 2447 q^{83} - 7612 q^{84} - 8185 q^{85} + 3891 q^{86} - 85 q^{87} - 10960 q^{88} - 5075 q^{89} + 685 q^{90} + 376 q^{91} - 8456 q^{92} + 4366 q^{93} + 3573 q^{94} + 3265 q^{95} - 7754 q^{96} + 7439 q^{97} + 7082 q^{98} + 6572 q^{99}+O(q^{100}) \) 28 * q - q^2 - 7 * q^3 - 31 * q^4 - 20 * q^5 + q^6 - 16 * q^7 + 100 * q^8 - 34 * q^9 - 25 * q^10 - 89 * q^11 + 139 * q^12 + 33 * q^13 - 17 * q^14 + 225 * q^15 - 207 * q^16 - 191 * q^17 - 552 * q^18 - 115 * q^19 - 225 * q^20 - 144 * q^21 + 808 * q^22 + 433 * q^23 + 780 * q^24 + 90 * q^25 + 586 * q^26 + 35 * q^27 - 13 * q^28 - 5 * q^29 + 675 * q^30 - 639 * q^31 - 1386 * q^32 + 251 * q^33 - 777 * q^34 - 1030 * q^35 + 673 * q^36 + 699 * q^37 - 2355 * q^38 - 1133 * q^39 + 410 * q^40 + 341 * q^41 - 2407 * q^42 - 172 * q^43 + 548 * q^44 + 470 * q^45 - 1239 * q^46 + 2319 * q^47 + 4738 * q^48 + 1344 * q^49 + 2335 * q^50 + 2006 * q^51 + 2344 * q^52 - 927 * q^53 + 1615 * q^54 + 1225 * q^55 - 2910 * q^56 - 770 * q^57 + 2410 * q^58 - 1905 * q^59 - 12030 * q^60 + 1391 * q^61 - 3832 * q^62 - 6142 * q^63 - 3596 * q^64 + 1215 * q^65 + 3632 * q^66 - 3611 * q^67 + 3622 * q^68 + 2687 * q^69 + 560 * q^70 - 3719 * q^71 + 9025 * q^72 + 4593 * q^73 + 4848 * q^74 + 3815 * q^75 + 3520 * q^76 + 1368 * q^77 - 3679 * q^78 + 775 * q^79 + 9500 * q^80 - 3712 * q^81 - 6762 * q^82 - 2447 * q^83 - 7612 * q^84 - 8185 * q^85 + 3891 * q^86 - 85 * q^87 - 10960 * q^88 - 5075 * q^89 + 685 * q^90 + 376 * q^91 - 8456 * q^92 + 4366 * q^93 + 3573 * q^94 + 3265 * q^95 - 7754 * q^96 + 7439 * q^97 + 7082 * q^98 + 6572 * q^99

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