LMFDB - Embedded newform 61.6.g.a.3.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [61,6,Mod(3,61)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(61, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("61.3");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 61 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	61.g (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.78341300859$
Analytic rank:	$0$
Dimension:	$104$
Relative dimension:	$26$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			3.18
Character	$\chi$	$=$	61.3
Dual form			61.6.g.a.41.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.92707 + 1.27598i) q^{2} +(-5.88917 + 18.1250i) q^{3} +(-12.0948 - 8.78737i) q^{4} +(-23.8009 - 17.2924i) q^{5} +(-46.2544 + 63.6637i) q^{6} +(16.7659 - 5.44756i) q^{7} +(-113.951 - 156.840i) q^{8} +(-97.2426 - 70.6509i) q^{9} +O(q^{10})$	\(q+(3.92707 + 1.27598i) q^{2} +(-5.88917 + 18.1250i) q^{3} +(-12.0948 - 8.78737i) q^{4} +(-23.8009 - 17.2924i) q^{5} +(-46.2544 + 63.6637i) q^{6} +(16.7659 - 5.44756i) q^{7} +(-113.951 - 156.840i) q^{8} +(-97.2426 - 70.6509i) q^{9} +(-71.4031 - 98.2779i) q^{10} -288.788i q^{11} +(230.500 - 167.468i) q^{12} -1126.17 q^{13} +72.7918 q^{14} +(453.592 - 329.554i) q^{15} +(-99.5341 - 306.334i) q^{16} +(1331.94 - 1833.25i) q^{17} +(-291.729 - 401.531i) q^{18} +(-57.5328 + 177.068i) q^{19} +(135.912 + 418.295i) q^{20} +335.963i q^{21} +(368.489 - 1134.09i) q^{22} +(-2530.97 + 3483.58i) q^{23} +(3513.79 - 1141.70i) q^{24} +(-698.221 - 2148.90i) q^{25} +(-4422.56 - 1436.98i) q^{26} +(-1893.36 + 1375.61i) q^{27} +(-250.649 - 81.4409i) q^{28} +1349.79i q^{29} +(2201.79 - 715.406i) q^{30} +(-8883.29 + 2886.36i) q^{31} +4873.66i q^{32} +(5234.29 + 1700.72i) q^{33} +(7569.81 - 5499.79i) q^{34} +(-493.244 - 160.265i) q^{35} +(555.293 + 1709.01i) q^{36} +(2138.29 - 694.773i) q^{37} +(-451.871 + 621.946i) q^{38} +(6632.23 - 20411.9i) q^{39} +5703.40i q^{40} +(-1063.39 - 3272.78i) q^{41} +(-428.684 + 1319.35i) q^{42} +(4908.36 + 6755.77i) q^{43} +(-2537.69 + 3492.83i) q^{44} +(1092.74 + 3363.11i) q^{45} +(-14384.3 + 10450.8i) q^{46} +6339.78 q^{47} +6138.49 q^{48} +(-13345.7 + 9696.24i) q^{49} -9329.82i q^{50} +(25383.7 + 34937.7i) q^{51} +(13620.8 + 9896.11i) q^{52} +(-14832.9 - 20415.7i) q^{53} +(-9190.61 + 2986.21i) q^{54} +(-4993.83 + 6873.42i) q^{55} +(-2764.88 - 2008.80i) q^{56} +(-2870.53 - 2085.56i) q^{57} +(-1722.31 + 5300.72i) q^{58} +(26952.5 + 8757.39i) q^{59} -8382.01 q^{60} +(28547.4 - 5444.43i) q^{61} -38568.3 q^{62} +(-2015.23 - 654.789i) q^{63} +(-9403.79 + 28941.9i) q^{64} +(26803.9 + 19474.2i) q^{65} +(18385.3 + 13357.7i) q^{66} +(38721.6 - 53295.8i) q^{67} +(-32219.0 + 10468.6i) q^{68} +(-48234.7 - 66389.3i) q^{69} +(-1732.51 - 1258.74i) q^{70} +(-22973.2 - 31619.9i) q^{71} +23302.2i q^{72} +(-15895.3 + 11548.6i) q^{73} +9283.74 q^{74} +43060.9 q^{75} +(2251.81 - 1636.03i) q^{76} +(-1573.19 - 4841.79i) q^{77} +(52090.5 - 71696.4i) q^{78} +(-18794.5 - 25868.4i) q^{79} +(-2928.25 + 9012.22i) q^{80} +(-22808.4 - 70197.1i) q^{81} -14209.3i q^{82} +(4837.25 - 14887.5i) q^{83} +(2952.24 - 4063.40i) q^{84} +(-63402.6 + 20600.8i) q^{85} +(10655.2 + 32793.4i) q^{86} +(-24464.9 - 7949.14i) q^{87} +(-45293.4 + 32907.6i) q^{88} +(-57922.5 - 18820.2i) q^{89} +14601.5i q^{90} +(-18881.3 + 6134.90i) q^{91} +(61223.1 - 19892.6i) q^{92} -178008. i q^{93} +(24896.8 + 8089.45i) q^{94} +(4431.25 - 3219.49i) q^{95} +(-88335.1 - 28701.8i) q^{96} +(-6007.38 - 18488.8i) q^{97} +(-64781.9 + 21048.9i) q^{98} +(-20403.1 + 28082.5i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 5 q^{2} + 15 q^{3} + 465 q^{4} - 122 q^{5} + 445 q^{6} + 230 q^{7} - 5 q^{8} - 2841 q^{9}+O(q^{10}) $ 104 * q - 5 * q^2 + 15 * q^3 + 465 * q^4 - 122 * q^5 + 445 * q^6 + 230 * q^7 - 5 * q^8 - 2841 * q^9	\( 104 q - 5 q^{2} + 15 q^{3} + 465 q^{4} - 122 q^{5} + 445 q^{6} + 230 q^{7} - 5 q^{8} - 2841 q^{9} - 595 q^{10} + 1982 q^{12} + 2372 q^{13} - 4474 q^{14} - 1149 q^{15} - 8631 q^{16} + 950 q^{17} + 4340 q^{18} - 5597 q^{19} - 6627 q^{20} - 8639 q^{22} + 9065 q^{23} + 17220 q^{24} - 7694 q^{25} + 14810 q^{26} + 4500 q^{27} + 19835 q^{28} - 44585 q^{30} + 10905 q^{31} - 19205 q^{33} - 15376 q^{34} - 43790 q^{35} - 25135 q^{36} - 5 q^{37} + 17555 q^{38} + 29401 q^{39} - 21014 q^{41} + 62197 q^{42} - 31625 q^{43} + 146190 q^{44} + 153742 q^{45} + 13387 q^{46} + 27326 q^{47} - 82968 q^{48} + 14694 q^{49} + 34090 q^{51} + 90072 q^{52} - 40270 q^{53} - 13760 q^{54} + 25140 q^{55} - 97860 q^{56} + 114893 q^{57} - 18003 q^{58} - 117435 q^{59} - 536650 q^{60} - 121867 q^{61} - 157388 q^{62} - 160825 q^{63} + 132509 q^{64} - 155852 q^{65} + 308443 q^{66} + 101665 q^{67} + 303780 q^{68} + 281945 q^{69} + 264985 q^{70} + 160970 q^{71} + 127669 q^{73} - 133952 q^{74} - 139592 q^{75} - 641111 q^{76} + 128917 q^{77} + 1670 q^{78} + 187940 q^{79} + 785373 q^{80} - 453473 q^{81} - 301209 q^{83} + 100475 q^{84} - 340045 q^{85} - 462669 q^{86} + 189245 q^{87} - 881635 q^{88} - 201970 q^{89} + 93865 q^{91} - 622085 q^{92} - 285265 q^{94} - 113308 q^{95} + 1215465 q^{96} - 342131 q^{97} - 616150 q^{98} + 714235 q^{99}+O(q^{100}) \) 104 * q - 5 * q^2 + 15 * q^3 + 465 * q^4 - 122 * q^5 + 445 * q^6 + 230 * q^7 - 5 * q^8 - 2841 * q^9 - 595 * q^10 + 1982 * q^12 + 2372 * q^13 - 4474 * q^14 - 1149 * q^15 - 8631 * q^16 + 950 * q^17 + 4340 * q^18 - 5597 * q^19 - 6627 * q^20 - 8639 * q^22 + 9065 * q^23 + 17220 * q^24 - 7694 * q^25 + 14810 * q^26 + 4500 * q^27 + 19835 * q^28 - 44585 * q^30 + 10905 * q^31 - 19205 * q^33 - 15376 * q^34 - 43790 * q^35 - 25135 * q^36 - 5 * q^37 + 17555 * q^38 + 29401 * q^39 - 21014 * q^41 + 62197 * q^42 - 31625 * q^43 + 146190 * q^44 + 153742 * q^45 + 13387 * q^46 + 27326 * q^47 - 82968 * q^48 + 14694 * q^49 + 34090 * q^51 + 90072 * q^52 - 40270 * q^53 - 13760 * q^54 + 25140 * q^55 - 97860 * q^56 + 114893 * q^57 - 18003 * q^58 - 117435 * q^59 - 536650 * q^60 - 121867 * q^61 - 157388 * q^62 - 160825 * q^63 + 132509 * q^64 - 155852 * q^65 + 308443 * q^66 + 101665 * q^67 + 303780 * q^68 + 281945 * q^69 + 264985 * q^70 + 160970 * q^71 + 127669 * q^73 - 133952 * q^74 - 139592 * q^75 - 641111 * q^76 + 128917 * q^77 + 1670 * q^78 + 187940 * q^79 + 785373 * q^80 - 453473 * q^81 - 301209 * q^83 + 100475 * q^84 - 340045 * q^85 - 462669 * q^86 + 189245 * q^87 - 881635 * q^88 - 201970 * q^89 + 93865 * q^91 - 622085 * q^92 - 285265 * q^94 - 113308 * q^95 + 1215465 * q^96 - 342131 * q^97 - 616150 * q^98 + 714235 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/61\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$	3.92707	+	1.27598i	0.694215	+	0.225564i	0.634808	−	0.772670i	$-0.281079\pi$
$2$	3.92707	+	1.27598i	0.694215	+	0.225564i	0.0594067	+	0.998234i	$0.481079\pi$
$3$	−5.88917	+	18.1250i	−0.377791	+	1.16272i	0.563786	+	0.825921i	$0.309344\pi$
$3$	−5.88917	+	18.1250i	−0.377791	+	1.16272i	−0.941577	+	0.336799i	$0.890656\pi$
$4$	−12.0948	−	8.78737i	−0.377962	−	0.274605i
$5$	−23.8009	−	17.2924i	−0.425763	−	0.309335i	0.354189	−	0.935174i	$-0.384757\pi$
$5$	−23.8009	−	17.2924i	−0.425763	−	0.309335i	−0.779953	+	0.625839i	$0.784757\pi$
$6$	−46.2544	+	63.6637i	−0.524536	+	0.721962i
$7$	16.7659	−	5.44756i	0.129325	−	0.0420201i	−0.243640	−	0.969866i	$-0.578341\pi$
$7$	16.7659	−	5.44756i	0.129325	−	0.0420201i	0.372964	+	0.927846i	$0.378341\pi$
$8$	−113.951	−	156.840i	−0.629494	−	0.866424i
$9$	−97.2426	−	70.6509i	−0.400175	−	0.290744i
$10$	−71.4031	−	98.2779i	−0.225796	−	0.310782i
$11$		−	288.788i		−	0.719610i	−0.933027	−	0.359805i	$-0.882843\pi$
$11$		−	288.788i		−	0.719610i	0.933027	−	0.359805i	$-0.117157\pi$
$12$	230.500	−	167.468i	0.462080	−	0.335721i
$13$	−1126.17			−1.84819			−0.924096	−	0.382161i	$-0.875180\pi$
$13$	−1126.17			−1.84819			−0.924096	+	0.382161i	$0.875180\pi$
$14$	72.7918			0.0992573
$15$	453.592	−	329.554i	0.520520	−	0.378180i
$16$	−99.5341	−	306.334i	−0.0972013	−	0.299155i
$17$	1331.94	−	1833.25i	1.11779	−	1.53851i	0.308387	−	0.951261i	$-0.400211\pi$
$17$	1331.94	−	1833.25i	1.11779	−	1.53851i	0.809406	−	0.587249i	$-0.199789\pi$
$18$	−291.729	−	401.531i	−0.212226	−	0.292104i
$19$	−57.5328	+	177.068i	−0.0365621	+	0.112527i	−0.967672	−	0.252212i	$-0.918842\pi$
$19$	−57.5328	+	177.068i	−0.0365621	+	0.112527i	0.931110	+	0.364739i	$0.118842\pi$
$20$	135.912	+	418.295i	0.0759772	+	0.233834i
$21$			335.963i			0.166243i
$22$	368.489	−	1134.09i	0.162318	−	0.499564i
$23$	−2530.97	+	3483.58i	−0.997626	+	1.37311i	−0.0708546	+	0.997487i	$0.522573\pi$
$23$	−2530.97	+	3483.58i	−0.997626	+	1.37311i	−0.926771	+	0.375627i	$0.877427\pi$
$24$	3513.79	−	1141.70i	1.24523	−	0.404598i
$25$	−698.221	−	2148.90i	−0.223431	−	0.687649i
$26$	−4422.56	−	1436.98i	−1.28304	−	0.416886i
$27$	−1893.36	+	1375.61i	−0.499832	+	0.363149i
$28$	−250.649	−	81.4409i	−0.0604187	−	0.0196312i
$29$			1349.79i			0.298037i	0.988834	+	0.149019i	$0.0476115\pi$
$29$			1349.79i			0.298037i	−0.988834	+	0.149019i	$0.952389\pi$
$30$	2201.79	−	715.406i	0.446656	−	0.145127i
$31$	−8883.29	+	2886.36i	−1.66024	+	0.539443i	−0.980922	−	0.194404i	$-0.937723\pi$
$31$	−8883.29	+	2886.36i	−1.66024	+	0.539443i	−0.679314	+	0.733848i	$0.737723\pi$
$32$			4873.66i			0.841356i
$33$	5234.29	+	1700.72i	0.836706	+	0.271862i
$34$	7569.81	−	5499.79i	1.12302	−	0.815923i
$35$	−493.244	−	160.265i	−0.0680600	−	0.0221140i
$36$	555.293	+	1709.01i	0.0714111	+	0.219781i
$37$	2138.29	−	694.773i	0.256781	−	0.0834331i	−0.177798	−	0.984067i	$-0.556897\pi$
$37$	2138.29	−	694.773i	0.256781	−	0.0834331i	0.434579	+	0.900634i	$0.356897\pi$
$38$	−451.871	+	621.946i	−0.0507639	+	0.0698705i
$39$	6632.23	−	20411.9i	0.698229	−	2.14893i
$40$			5703.40i			0.563616i
$41$	−1063.39	−	3272.78i	−0.0987945	−	0.304058i	0.889429	−	0.457072i	$-0.151102\pi$
$41$	−1063.39	−	3272.78i	−0.0987945	−	0.304058i	−0.988224	+	0.153014i	$0.951102\pi$
$42$	−428.684	+	1319.35i	−0.0374985	+	0.115408i
$43$	4908.36	+	6755.77i	0.404823	+	0.557191i	0.961946	−	0.273239i	$-0.0880949\pi$
$43$	4908.36	+	6755.77i	0.404823	+	0.557191i	−0.557123	+	0.830430i	$0.688095\pi$
$44$	−2537.69	+	3492.83i	−0.197609	+	0.271985i
$45$	1092.74	+	3363.11i	0.0804426	+	0.247577i
$46$	−14384.3	+	10450.8i	−1.00229	+	0.728207i
$47$	6339.78			0.418629			0.209315	−	0.977848i	$-0.432877\pi$
$47$	6339.78			0.418629			0.209315	+	0.977848i	$0.432877\pi$
$48$	6138.49			0.384555
$49$	−13345.7	+	9696.24i	−0.794058	+	0.576917i
$50$		−	9329.82i		−	0.527774i
$51$	25383.7	+	34937.7i	1.36656	+	1.88092i
$52$	13620.8	+	9896.11i	0.698546	+	0.507523i
$53$	−14832.9	−	20415.7i	−0.725329	−	0.998330i	−0.999330	−	0.0366008i	$-0.988347\pi$
$53$	−14832.9	−	20415.7i	−0.725329	−	0.998330i	0.274001	−	0.961730i	$-0.411653\pi$
$54$	−9190.61	+	2986.21i	−0.428904	+	0.139359i
$55$	−4993.83	+	6873.42i	−0.222601	+	0.306384i
$56$	−2764.88	−	2008.80i	−0.117816	−	0.0855986i
$57$	−2870.53	−	2085.56i	−0.117024	−	0.0850230i
$58$	−1722.31	+	5300.72i	−0.0672265	+	0.206902i
$59$	26952.5	+	8757.39i	1.00802	+	0.327525i	0.766065	−	0.642763i	$-0.222212\pi$
$59$	26952.5	+	8757.39i	1.00802	+	0.327525i	0.241953	+	0.970288i	$0.422212\pi$
$60$	−8382.01			−0.300587
$61$	28547.4	−	5444.43i	0.982295	−	0.187339i
$61$	28547.4	−	5444.43i	0.982295	−	0.187339i
$62$	−38568.3			−1.27424
$63$	−2015.23	−	654.789i	−0.0639697	−	0.0207850i
$64$	−9403.79	+	28941.9i	−0.286981	+	0.883237i
$65$	26803.9	+	19474.2i	0.786892	+	0.571711i
$66$	18385.3	+	13357.7i	0.519531	+	0.377461i
$67$	38721.6	−	53295.8i	1.05382	−	1.45046i	0.168372	−	0.985724i	$-0.446149\pi$
$67$	38721.6	−	53295.8i	1.05382	−	1.45046i	0.885449	−	0.464736i	$-0.153851\pi$
$68$	−32219.0	+	10468.6i	−0.844966	+	0.274546i
$69$	−48234.7	−	66389.3i	−1.21965	−	1.67871i
$70$	−1732.51	−	1258.74i	−0.0422601	−	0.0307038i
$71$	−22973.2	−	31619.9i	−0.540849	−	0.744414i	0.447886	−	0.894090i	$-0.352177\pi$
$71$	−22973.2	−	31619.9i	−0.540849	−	0.744414i	−0.988735	+	0.149676i	$0.952177\pi$
$72$			23302.2i			0.529744i
$73$	−15895.3	+	11548.6i	−0.349109	+	0.253642i	−0.748495	−	0.663140i	$-0.769223\pi$
$73$	−15895.3	+	11548.6i	−0.349109	+	0.253642i	0.399386	+	0.916783i	$0.369223\pi$
$74$	9283.74			0.197081
$75$	43060.9			0.883954
$76$	2251.81	−	1636.03i	0.0447195	−	0.0324906i
$77$	−1573.19	−	4841.79i	−0.0302381	−	0.0930634i
$78$	52090.5	−	71696.4i	0.969442	−	1.33432i
$79$	−18794.5	−	25868.4i	−0.338816	−	0.466340i	0.605279	−	0.796013i	$-0.293061\pi$
$79$	−18794.5	−	25868.4i	−0.338816	−	0.466340i	−0.944095	+	0.329673i	$0.893061\pi$
$80$	−2928.25	+	9012.22i	−0.0511544	+	0.157437i
$81$	−22808.4	−	70197.1i	−0.386262	−	1.18879i
$82$		−	14209.3i		−	0.233366i
$83$	4837.25	−	14887.5i	0.0770731	−	0.237207i	−0.905096	−	0.425208i	$-0.860201\pi$
$83$	4837.25	−	14887.5i	0.0770731	−	0.237207i	0.982169	+	0.188001i	$0.0602009\pi$
$84$	2952.24	−	4063.40i	0.0456513	−	0.0628336i
$85$	−63402.6	+	20600.8i	−0.951831	+	0.309269i
$86$	10655.2	+	32793.4i	0.155352	+	0.478124i
$87$	−24464.9	−	7949.14i	−0.346534	−	0.112596i
$88$	−45293.4	+	32907.6i	−0.623488	+	0.452990i
$89$	−57922.5	−	18820.2i	−0.775126	−	0.251854i	−0.105368	−	0.994433i	$-0.533602\pi$
$89$	−57922.5	−	18820.2i	−0.775126	−	0.251854i	−0.669758	+	0.742580i	$0.733602\pi$
$90$			14601.5i			0.190016i
$91$	−18881.3	+	6134.90i	−0.239017	+	0.0776612i
$92$	61223.1	−	19892.6i	0.754129	−	0.245031i
$93$		−	178008.i		−	2.13419i
$94$	24896.8	+	8089.45i	0.290619	+	0.0944277i
$95$	4431.25	−	3219.49i	0.0503752	−	0.0365998i
$96$	−88335.1	−	28701.8i	−0.978262	−	0.317857i
$97$	−6007.38	−	18488.8i	−0.0648270	−	0.199517i	0.913397	−	0.407071i	$-0.133450\pi$
$97$	−6007.38	−	18488.8i	−0.0648270	−	0.199517i	−0.978224	+	0.207554i	$0.933450\pi$
$98$	−64781.9	+	21048.9i	−0.681378	+	0.221393i
$99$	−20403.1	+	28082.5i	−0.209223	+	0.287970i
$100$	−10438.4	+	32126.1i	−0.104384	+	0.321261i
$101$			152693.i			1.48942i	0.667390	+	0.744708i	$0.267411\pi$
$101$			152693.i			1.48942i	−0.667390	+	0.744708i	$0.732589\pi$
$102$	55103.8	+	169592.i	0.524423	+	1.61401i
$103$	−8787.88	+	27046.3i	−0.0816189	+	0.251197i	−0.983536	−	0.180712i	$-0.942160\pi$
$103$	−8787.88	+	27046.3i	−0.0816189	+	0.251197i	0.901917	+	0.431909i	$0.142160\pi$
$104$	128328.	+	176629.i	1.16343	+	1.60132i
$105$	5809.60	−	7996.23i	0.0514249	−	0.0707803i
$106$	−32199.7	−	99100.3i	−0.278347	−	0.856664i
$107$	13848.9	−	10061.8i	0.116938	−	0.0849602i	−0.527779	−	0.849382i	$-0.676975\pi$
$107$	13848.9	−	10061.8i	0.116938	−	0.0849602i	0.644717	+	0.764421i	$0.276975\pi$
$108$	34987.8			0.288640
$109$	159312.			1.28435			0.642173	−	0.766560i	$-0.278033\pi$
$109$	159312.			1.28435			0.642173	+	0.766560i	$0.278033\pi$
$110$	−28381.5	+	20620.4i	−0.223642	+	0.162485i
$111$			42848.2i			0.330084i
$112$	−3337.55	−	4593.75i	−0.0251410	−	0.0346037i
$113$	−147758.	−	107352.i	−1.08856	−	0.790887i	−0.109407	−	0.993997i	$-0.534895\pi$
$113$	−147758.	−	107352.i	−1.08856	−	0.790887i	−0.979156	+	0.203110i	$0.934895\pi$
$114$	−8611.64	−	11852.9i	−0.0620617	−	0.0854207i
$115$	120479.	−	39145.9i	0.849505	−	0.276021i
$116$	11861.1	−	16325.4i	0.0818427	−	0.112647i
$117$	109512.	+	79565.2i	0.739601	+	0.537351i
$118$	94670.0	+	68781.8i	0.625904	+	0.454746i
$119$	12344.3	−	37991.9i	0.0799098	−	0.245937i
$120$	−103374.	−	33588.3i	−0.655328	−	0.212929i
$121$	77652.5			0.482161
$122$	119055.	+	15045.3i	0.724181	+	0.0915171i
$123$	65581.6			0.390858
$124$	132805.	+	43151.0i	0.775640	+	0.252021i
$125$	−48951.1	+	150656.i	−0.280213	+	0.862406i
$126$	−7078.47	−	5142.81i	−0.0397203	−	0.0288585i
$127$	467.902	+	339.951i	0.00257422	+	0.00187028i	0.589072	−	0.808081i	$-0.299494\pi$
$127$	467.902	+	339.951i	0.00257422	+	0.00187028i	−0.586497	+	0.809951i	$0.699494\pi$
$128$	17810.5	−	24514.0i	0.0960839	−	0.132248i
$129$	−151355.	+	49178.1i	−0.800795	+	0.260194i
$130$	80412.3	+	110678.i	0.417315	+	0.574385i
$131$	149555.	+	108658.i	0.761418	+	0.553203i	0.899345	−	0.437240i	$-0.144044\pi$
$131$	149555.	+	108658.i	0.761418	+	0.553203i	−0.137927	+	0.990442i	$0.544044\pi$
$132$	−48362.7	−	66565.5i	−0.241588	−	0.332517i
$133$			3282.11i			0.0160888i
$134$	220067.	−	159888.i	1.05875	−	0.769227i
$135$	68851.2			0.325145
$136$	−439302.			−2.03665
$137$	−183086.	+	133020.i	−0.833401	+	0.605501i	−0.920519	−	0.390697i	$-0.872234\pi$
$137$	−183086.	+	133020.i	−0.833401	+	0.605501i	0.0871187	+	0.996198i	$0.472234\pi$
$138$	−104709.	−	322262.i	−0.468045	−	1.44049i
$139$	−36374.2	+	50064.8i	−0.159682	+	0.219784i	−0.881360	−	0.472446i	$-0.843371\pi$
$139$	−36374.2	+	50064.8i	−0.159682	+	0.219784i	0.721678	+	0.692229i	$0.243371\pi$
$140$	4557.38	+	6272.69i	0.0196515	+	0.0270479i
$141$	−37336.1	+	114909.i	−0.158154	+	0.486749i
$142$	−49871.0	−	153487.i	−0.207552	−	0.638779i
$143$			325225.i			1.32998i
$144$	−11963.9	+	36820.9i	−0.0480800	+	0.147975i
$145$	23341.0	−	32126.2i	0.0921935	−	0.126893i
$146$	−77157.6	+	25070.0i	−0.299569	+	0.0973358i
$147$	−97149.2	−	298994.i	−0.370805	−	1.14122i
$148$	−31967.4	−	10386.8i	−0.119965	−	0.0389789i
$149$	−254218.	+	184700.i	−0.938081	+	0.681556i	−0.947958	−	0.318395i	$-0.896856\pi$
$149$	−254218.	+	184700.i	−0.938081	+	0.681556i	0.00987671	+	0.999951i	$0.496856\pi$
$150$	169103.	+	54944.9i	0.613654	+	0.199388i
$151$		−	208924.i		−	0.745670i	−0.927898	−	0.372835i	$-0.878386\pi$
$151$		−	208924.i		−	0.745670i	0.927898	−	0.372835i	$-0.121614\pi$
$152$	34327.1	−	11153.5i	0.120511	−	0.0391565i
$153$	−259042.	+	84167.9i	−0.894627	+	0.290682i
$154$		−	21021.4i		−	0.0714266i
$155$	261342.	+	84915.3i	0.873737	+	0.283894i
$156$	−259582.	+	188598.i	−0.854012	+	0.620476i
$157$	−171068.	−	55583.4i	−0.553885	−	0.179968i	0.0186826	−	0.999825i	$-0.494053\pi$
$157$	−171068.	−	55583.4i	−0.553885	−	0.179968i	−0.572568	+	0.819857i	$0.694053\pi$
$158$	−40799.8	−	125569.i	−0.130021	−	0.400165i
$159$	457388.	−	148614.i	1.43480	−	0.466195i
$160$	84277.1	−	115997.i	0.260261	−	0.358219i
$161$	−23456.9	+	72192.9i	−0.0713191	+	0.219498i
$162$		−	304772.i		−	0.912405i
$163$	−156063.	−	480311.i	−0.460076	−	1.41597i	−0.865071	−	0.501650i	$-0.832727\pi$
$163$	−156063.	−	480311.i	−0.460076	−	1.41597i	0.404995	−	0.914319i	$-0.367273\pi$
$164$	−15897.7	+	48927.9i	−0.0461555	+	0.142052i
$165$	−95171.2	−	130992.i	−0.272142	−	0.374572i
$166$	37992.4	−	52292.1i	0.107011	−	0.147288i
$167$	12109.5	+	37269.2i	0.0335997	+	0.103409i	0.966450	−	0.256855i	$-0.0826864\pi$
$167$	12109.5	+	37269.2i	0.0335997	+	0.103409i	−0.932850	+	0.360265i	$0.882686\pi$
$168$	52692.3	−	38283.2i	0.144037	−	0.104649i
$169$	896974.			2.41581
$170$	−275273.			−0.730535
$171$	18104.6	−	13153.8i	0.0473477	−	0.0344002i
$172$		−	124841.i		−	0.321764i
$173$	−95019.0	−	130782.i	−0.241377	−	0.332226i	0.671091	−	0.741375i	$-0.265826\pi$
$173$	−95019.0	−	130782.i	−0.241377	−	0.332226i	−0.912468	+	0.409148i	$0.865826\pi$
$174$	−85932.6	−	62433.7i	−0.215171	−	0.156331i
$175$	−23412.6	−	32224.7i	−0.0577902	−	0.0795414i
$176$	−88465.7	+	28744.3i	−0.215275	+	0.0699471i
$177$	−317456.	+	436940.i	−0.761640	+	1.04831i
$178$	−203452.	−	147816.i	−0.481294	−	0.349681i
$179$	473317.	+	343885.i	1.10413	+	0.802197i	0.981729	−	0.190284i	$-0.0609409\pi$
$179$	473317.	+	343885.i	1.10413	+	0.802197i	0.122400	+	0.992481i	$0.460941\pi$
$180$	16336.4	−	50278.4i	0.0375817	−	0.115665i
$181$	33588.5	+	10913.5i	0.0762068	+	0.0247611i	0.346872	−	0.937912i	$-0.387244\pi$
$181$	33588.5	+	10913.5i	0.0762068	+	0.0247611i	−0.270666	+	0.962673i	$0.587244\pi$
$182$	−81976.2			−0.183446
$183$	−69440.2	+	549485.i	−0.153279	+	1.21291i
$184$	834769.			1.81770
$185$	−62907.5	−	20439.9i	−0.135137	−	0.0439086i
$186$	227135.	−	699051.i	0.481396	−	1.48158i
$187$	−529422.	−	384647.i	−1.10713	−	0.804376i
$188$	−76678.3	−	55710.0i	−0.158226	−	0.114958i
$189$	−24250.1	+	33377.5i	−0.0493810	+	0.0679671i
$190$	21509.9	−	6988.97i	0.0432268	−	0.0140452i
$191$	25054.7	+	34484.8i	0.0496941	+	0.0683981i	0.833141	−	0.553061i	$-0.186540\pi$
$191$	25054.7	+	34484.8i	0.0496941	+	0.0683981i	−0.783447	+	0.621459i	$0.786540\pi$
$192$	−469192.	−	340888.i	−0.918539	−	0.667357i
$193$	−496117.	−	682847.i	−0.958718	−	1.31956i	−0.947544	−	0.319625i	$-0.896443\pi$
$193$	−496117.	−	682847.i	−0.958718	−	1.31956i	−0.0111744	−	0.999938i	$-0.503557\pi$
$194$		−	80272.3i		−	0.153130i
$195$	−510823.	+	371135.i	−0.962020	+	0.698949i
$196$	246618.			0.458548
$197$	389148.			0.714413			0.357206	−	0.934026i	$-0.383729\pi$
$197$	389148.			0.714413			0.357206	+	0.934026i	$0.383729\pi$
$198$	−115957.	+	84248.0i	−0.210201	+	0.152720i
$199$	60706.5	+	186835.i	0.108668	+	0.334447i	0.990574	−	0.136979i	$-0.0437394\pi$
$199$	60706.5	+	186835.i	0.108668	+	0.334447i	−0.881906	+	0.471426i	$0.843739\pi$
$200$	−257470.	+	354378.i	−0.455148	+	0.626457i
$201$	737948.	+	1.01570e6i	1.28836	+	1.77327i
$202$	−194834.	+	599637.i	−0.335959	+	1.03397i
$203$	7353.06	+	22630.4i	0.0125236	+	0.0385436i
$204$		−	645621.i		−	1.08618i
$205$	−31284.4	+	96283.6i	−0.0519929	+	0.160018i
$206$	−69021.2	+	94999.6i	−0.113322	+	0.155975i
$207$	492237.	−	159937.i	0.798451	−	0.259432i
$208$	112093.	+	344986.i	0.179647	+	0.552895i
$209$	51135.0	+	16614.8i	0.0809753	+	0.0263105i
$210$	33017.8	−	23988.8i	0.0516654	−	0.0375371i
$211$	−666765.	−	216645.i	−1.03102	−	0.334998i	−0.255826	−	0.966723i	$-0.582347\pi$
$211$	−666765.	−	216645.i	−1.03102	−	0.334998i	−0.775193	+	0.631725i	$0.782347\pi$
$212$			377265.i			0.576510i
$213$	708404.	−	230175.i	1.06987	−	0.347623i
$214$	67224.1	−	21842.4i	0.100344	−	0.0326037i
$215$		−	245671.i		−	0.362458i
$216$	431499.	+	140203.i	0.629282	+	0.204466i
$217$	−133213.	+	96784.6i	−0.192042	+	0.139527i
$218$	625629.	+	203279.i	0.891612	+	0.289702i
$219$	−115708.	−	356113.i	−0.163025	−	0.501739i
$220$	120799.	−	39249.8i	0.168269	−	0.0546740i
$221$	−1.49999e6	+	2.06456e6i	−2.06590	+	2.84346i
$222$	−54673.6	+	168268.i	−0.0744552	+	0.229150i
$223$		−	293806.i		−	0.395638i	−0.980239	−	0.197819i	$-0.936614\pi$
$223$		−	293806.i		−	0.395638i	0.980239	−	0.197819i	$-0.0633859\pi$
$224$	26549.6	+	81711.1i	0.0353539	+	0.108808i
$225$	−83925.1	+	258295.i	−0.110519	+	0.340142i
$226$	−443275.	−	610116.i	−0.577301	−	0.794586i
$227$	−249782.	+	343796.i	−0.321734	+	0.442829i	−0.938996	−	0.343929i	$-0.888242\pi$
$227$	−249782.	+	343796.i	−0.321734	+	0.442829i	0.617262	+	0.786758i	$0.288242\pi$
$228$	16391.8	+	50448.9i	0.0208829	+	0.0642709i
$229$	−288053.	+	209283.i	−0.362981	+	0.263721i	−0.754294	−	0.656536i	$-0.772021\pi$
$229$	−288053.	+	209283.i	−0.362981	+	0.263721i	0.391313	+	0.920257i	$0.372021\pi$
$230$	523078.			0.651999
$231$	97022.2			0.119630
$232$	211700.	−	153809.i	0.258227	−	0.187613i
$233$		−	1.10286e6i		−	1.33085i	−0.746464	−	0.665426i	$-0.768250\pi$
$233$		−	1.10286e6i		−	1.33085i	0.746464	−	0.665426i	$-0.231750\pi$
$234$	328538.	+	452194.i	0.392235	+	0.539865i
$235$	−150892.	−	109630.i	−0.178237	−	0.129497i
$236$	−249030.	−	342760.i	−0.291053	−	0.400600i
$237$	579550.	−	188307.i	0.670224	−	0.217769i
$238$	96954.1	−	133446.i	0.110949	−	0.152708i
$239$	−689255.	−	500773.i	−0.780522	−	0.567082i	0.124614	−	0.992205i	$-0.460231\pi$
$239$	−689255.	−	500773.i	−0.780522	−	0.567082i	−0.905136	+	0.425123i	$0.860231\pi$
$240$	−146102.	−	106149.i	−0.163729	−	0.118956i
$241$	25403.8	−	78184.7i	0.0281744	−	0.0867120i	−0.935981	−	0.352052i	$-0.885484\pi$
$241$	25403.8	−	78184.7i	0.0281744	−	0.0867120i	0.964155	+	0.265340i	$0.0854841\pi$
$242$	304947.	+	99083.2i	0.334723	+	0.108758i
$243$	837947.			0.910334
$244$	−393117.	−	185008.i	−0.422715	−	0.198937i
$245$	485311.			0.516541
$246$	257544.	+	83681.0i	0.271340	+	0.0881636i
$247$	64791.9	−	199409.i	0.0675738	−	0.207971i
$248$	1.46495e6	+	1.06435e6i	1.51250	+	1.09889i
$249$	241349.	+	175350.i	0.246688	+	0.179229i
$250$	−384469.	+	529177.i	−0.389056	+	0.535489i
$251$	−372217.	+	120940.i	−0.372916	+	0.121168i	−0.489478	−	0.872016i	$-0.662813\pi$
$251$	−372217.	+	120940.i	−0.372916	+	0.121168i	0.116562	+	0.993183i	$0.462813\pi$
$252$	18619.9	+	25628.1i	0.0184704	+	0.0254224i
$253$	1.00602e6	+	730914.i	0.988107	+	0.717902i
$254$	1403.71	+	1932.05i	0.00136519	+	0.00187903i
$255$		−	1.27049e6i		−	1.22355i
$256$	889045.	−	645929.i	0.847859	−	0.616006i
$257$	−1.27526e6			−1.20439			−0.602193	−	0.798351i	$-0.705706\pi$
$257$	−1.27526e6			−1.20439			−0.602193	+	0.798351i	$0.705706\pi$
$258$	−657131.			−0.614615
$259$	32065.5	−	23297.0i	0.0297022	−	0.0215799i
$260$	−153061.	−	471073.i	−0.140420	−	0.432170i
$261$	95363.8	−	131257.i	0.0866527	−	0.119267i
$262$	448668.	+	617538.i	0.403805	+	0.555790i
$263$	−327959.	+	1.00935e6i	−0.292368	+	0.899816i	0.691725	+	0.722161i	$0.256851\pi$
$263$	−327959.	+	1.00935e6i	−0.292368	+	0.899816i	−0.984093	+	0.177655i	$0.943149\pi$
$264$	−329710.	−	1.01474e6i	−0.291153	−	0.896078i
$265$			742407.i			0.649423i
$266$	−4187.91	+	12889.1i	−0.00362906	+	0.0111691i
$267$	682231.	−	939010.i	0.585670	−	0.806106i
$268$	−936660.	+	304339.i	−0.796608	+	0.258834i
$269$	369135.	+	1.13608e6i	0.311032	+	0.957257i	0.977357	+	0.211596i	$0.0678662\pi$
$269$	369135.	+	1.13608e6i	0.311032	+	0.957257i	−0.666325	+	0.745661i	$0.732134\pi$
$270$	270384.	+	87852.9i	0.225720	+	0.0733410i
$271$	768837.	−	558593.i	0.635932	−	0.462032i	−0.222518	−	0.974929i	$-0.571428\pi$
$271$	768837.	−	558593.i	0.635932	−	0.462032i	0.858450	+	0.512897i	$0.171428\pi$
$272$	−694162.	−	225547.i	−0.568904	−	0.184848i
$273$		−	378353.i		−	0.307249i
$274$	−888723.	+	288764.i	−0.715138	+	0.232363i
$275$	−620578.	+	201638.i	−0.494840	+	0.160783i
$276$			1.22682e6i			0.969412i
$277$	−682732.	−	221833.i	−0.534627	−	0.173711i	0.0292461	−	0.999572i	$-0.490689\pi$
$277$	−682732.	−	221833.i	−0.534627	−	0.173711i	−0.563873	+	0.825861i	$0.690689\pi$
$278$	−206726.	+	150195.i	−0.160429	+	0.116558i
$279$	1.06776e6	+	346936.i	0.821226	+	0.266832i
$280$	31069.6	+	95622.5i	0.0236832	+	0.0728895i
$281$	−989677.	+	321566.i	−0.747701	+	0.242943i	−0.657992	−	0.753025i	$-0.728594\pi$
$281$	−989677.	+	321566.i	−0.747701	+	0.242943i	−0.0897092	+	0.995968i	$0.528594\pi$
$282$	−293243.	+	403614.i	−0.219586	+	0.302234i
$283$	189618.	−	583583.i	0.140738	−	0.433148i	−0.855700	−	0.517472i	$-0.826873\pi$
$283$	189618.	−	583583.i	0.140738	−	0.433148i	0.996438	+	0.0843239i	$0.0268730\pi$
$284$			584310.i			0.429880i
$285$	32256.9	+	99276.6i	0.0235240	+	0.0723994i
$286$	−414982.	+	1.27718e6i	−0.299995	+	0.923290i
$287$	−35657.3	−	49078.1i	−0.0255531	−	0.0351709i
$288$	344328.	−	473927.i	0.244620	−	0.336690i
$289$	−1.14800e6	−	3.53319e6i	−0.808535	−	2.48842i
$290$	132654.	−	96379.0i	0.0926246	−	0.0672957i
$291$	370489.			0.256474
$292$	293731.			0.201601
$293$	−892695.	+	648581.i	−0.607483	+	0.441362i	−0.848527	−	0.529152i	$-0.822510\pi$
$293$	−892695.	+	648581.i	−0.607483	+	0.441362i	0.241044	+	0.970514i	$0.422510\pi$
$294$		−	1.29813e6i		−	0.875893i
$295$	−490057.	−	674506.i	−0.327862	−	0.451264i
$296$	−352627.	−	256199.i	−0.233930	−	0.169960i
$297$	397259.	+	546780.i	0.261326	+	0.359684i
$298$	−1.23401e6	+	400953.i	−0.804964	+	0.261549i
$299$	2.85031e6	−	3.92312e6i	1.84380	−	2.53778i
$300$	−520812.	−	378392.i	−0.334101	−	0.242739i
$301$	119095.	+	86527.9i	0.0757668	+	0.0550478i
$302$	266584.	−	820461.i	0.168196	−	0.517655i
$303$	−2.76757e6	−	899237.i	−1.73177	−	0.562688i
$304$	59968.4			0.0372167
$305$	−773601.	−	364070.i	−0.476176	−	0.224097i
$306$	−1.12467e6			−0.686630
$307$	2.52066e6	+	819011.i	1.52640	+	0.495957i	0.947585	−	0.319503i	$-0.103516\pi$
$307$	2.52066e6	+	819011.i	1.52640	+	0.495957i	0.578813	+	0.815460i	$0.303516\pi$
$308$	−23519.2	+	72384.6i	−0.0141268	+	0.0434780i
$309$	−438461.	−	318561.i	−0.261237	−	0.189800i
$310$	917960.	+	666937.i	0.542524	+	0.394167i
$311$	1.39874e6	−	1.92520e6i	0.820043	−	1.12869i	−0.169652	−	0.985504i	$-0.554264\pi$
$311$	1.39874e6	−	1.92520e6i	0.820043	−	1.12869i	0.989695	−	0.143189i	$-0.0457356\pi$
$312$	−3.95714e6	+	1.28575e6i	−2.30142	+	0.747775i
$313$	−754155.	−	1.03800e6i	−0.435111	−	0.598878i	0.534006	−	0.845481i	$-0.320686\pi$
$313$	−754155.	−	1.03800e6i	−0.435111	−	0.598878i	−0.969117	+	0.246602i	$0.920686\pi$
$314$	−600873.	−	436560.i	−0.343921	−	0.249873i
$315$	36641.5	+	50432.7i	0.0208064	+	0.0286376i
$316$			478028.i			0.269299i
$317$	2.13368e6	−	1.55021e6i	1.19256	−	0.866448i	0.199030	−	0.979993i	$-0.436221\pi$
$317$	2.13368e6	−	1.55021e6i	1.19256	−	0.866448i	0.993533	+	0.113546i	$0.0362208\pi$
$318$	1.98582e6			1.10122
$319$	389803.			0.214471
$320$	724293.	−	526229.i	0.395402	−	0.287277i
$321$	100812.	+	310266.i	0.0546070	+	0.168063i
$322$	−184234.	+	253576.i	−0.0990216	+	0.136292i
$323$	247980.	+	341315.i	0.132254	+	0.182033i
$324$	−340985.	+	1.04944e6i	−0.180457	+	0.555388i
$325$	786318.	+	2.42004e6i	0.412943	+	1.27091i
$326$		−	2.08535e6i		−	1.08676i
$327$	−938215.	+	2.88753e6i	−0.485214	+	1.49333i
$328$	−392127.	+	539717.i	−0.201253	+	0.277001i
$329$	106292.	−	34536.4i	0.0541391	−	0.0175908i
$330$	−206601.	−	635852.i	−0.104435	−	0.321419i
$331$	−1.42714e6	−	463705.i	−0.715971	−	0.232633i	−0.0716954	−	0.997427i	$-0.522841\pi$
$331$	−1.42714e6	−	463705.i	−0.715971	−	0.232633i	−0.644275	+	0.764794i	$0.722841\pi$
$332$	−189328.	+	137555.i	−0.0942690	+	0.0684904i
$333$	−257019.	−	83510.7i	−0.127015	−	0.0412697i
$334$			161811.i			0.0793671i
$335$	−1.84322e6	+	598898.i	−0.897357	+	0.291569i
$336$	102917.	−	33439.8i	0.0497324	−	0.0161590i
$337$		−	3.47535e6i		−	1.66696i	−0.552553	−	0.833478i	$-0.686346\pi$
$337$		−	3.47535e6i		−	1.66696i	0.552553	−	0.833478i	$-0.313654\pi$
$338$	3.52248e6	+	1.14452e6i	1.67709	+	0.544920i
$339$	2.81593e6	−	2.04589e6i	1.33083	−	0.966904i
$340$	947867.	+	307981.i	0.444683	+	0.144486i
$341$	833545.	+	2.56539e6i	0.388189	+	1.19472i
$342$	87882.2	−	28554.6i	0.0406289	−	0.0132011i
$343$	−345084.	+	474968.i	−0.158376	+	0.217986i
$344$	500262.	−	1.53965e6i	0.227930	−	0.701497i
$345$			2.41422e6i			1.09201i
$346$	−206270.	−	634835.i	−0.0926289	−	0.285082i
$347$	−898354.	+	2.76485e6i	−0.400520	+	1.23267i	0.524059	+	0.851682i	$0.324417\pi$
$347$	−898354.	+	2.76485e6i	−0.400520	+	1.23267i	−0.924579	+	0.380991i	$0.875583\pi$
$348$	226046.	+	311126.i	0.100057	+	0.137717i
$349$	−2.22521e6	+	3.06274e6i	−0.977930	+	1.34601i	−0.0399934	+	0.999200i	$0.512734\pi$
$349$	−2.22521e6	+	3.06274e6i	−0.977930	+	1.34601i	−0.937937	+	0.346806i	$0.887266\pi$
$350$	−50824.8	−	156423.i	−0.0221771	−	0.0682542i
$351$	2.13225e6	−	1.54917e6i	0.923785	−	0.671169i
$352$	1.40745e6			0.605449
$353$	−70223.1			−0.0299946			−0.0149973	−	0.999888i	$-0.504774\pi$
$353$	−70223.1			−0.0299946			−0.0149973	+	0.999888i	$0.504774\pi$
$354$	−1.80420e6	+	1.31083e6i	−0.765203	+	0.555952i
$355$			1.14984e6i			0.484248i
$356$	535180.	+	736612.i	0.223808	+	0.308045i
$357$	615906.	+	447482.i	0.255767	+	0.185825i
$358$	1.41996e6	+	1.95441e6i	0.585556	+	0.805949i
$359$	−2.93080e6	+	952275.i	−1.20019	+	0.389966i	−0.839831	−	0.542848i	$-0.817346\pi$
$359$	−2.93080e6	+	952275.i	−1.20019	+	0.389966i	−0.360360	+	0.932813i	$0.617346\pi$
$360$	402950.	−	554613.i	0.163868	−	0.225545i
$361$	1.97516e6	+	1.43504e6i	0.797692	+	0.579557i
$362$	117979.	+	85716.6i	0.0473187	+	0.0343790i
$363$	−457309.	+	1.40745e6i	−0.182156	+	0.560618i
$364$	282275.	+	91716.6i	0.111665	+	0.0362823i
$365$	578024.			0.227098
$366$	−973831.	+	2.06926e6i	−0.379998	+	0.807445i
$367$	−1.29600e6			−0.502272			−0.251136	−	0.967952i	$-0.580804\pi$
$367$	−1.29600e6			−0.502272			−0.251136	+	0.967952i	$0.580804\pi$
$368$	1.31906e6	+	428588.i	0.507744	+	0.164976i
$369$	−127818.	+	393383.i	−0.0488681	+	0.150401i
$370$	−220961.	−	160538.i	−0.0839097	−	0.0609640i
$371$	−359902.	−	261484.i	−0.135753	−	0.0986303i
$372$	−1.56422e6	+	2.15297e6i	−0.586059	+	0.806641i
$373$	321455.	−	104447.i	0.119632	−	0.0388709i	−0.248589	−	0.968609i	$-0.579967\pi$
$373$	321455.	−	104447.i	0.119632	−	0.0388709i	0.368221	+	0.929738i	$0.379967\pi$
$374$	−1.58827e6	−	2.18607e6i	−0.587146	−	0.808138i
$375$	−2.44236e6	−	1.77448e6i	−0.896875	−	0.651618i
$376$	−722422.	−	994328.i	−0.263525	−	0.362710i
$377$		−	1.52010e6i		−	0.550830i
$378$	−137821.	+	100133.i	−0.0496120	+	0.0360452i
$379$	3.61364e6			1.29225			0.646125	−	0.763232i	$-0.276389\pi$
$379$	3.61364e6			1.29225			0.646125	+	0.763232i	$0.276389\pi$
$380$	−81885.9			−0.0290904
$381$	−8917.17	+	6478.71i	−0.00314713	+	0.00228652i
$382$	54389.5	+	167394.i	0.0190703	+	0.0586922i
$383$	3.24875e6	−	4.47152e6i	1.13167	−	1.55761i	0.346807	−	0.937936i	$-0.387266\pi$
$383$	3.24875e6	−	4.47152e6i	1.13167	−	1.55761i	0.784861	−	0.619672i	$-0.212734\pi$
$384$	339428.	+	467183.i	0.117468	+	0.161681i
$385$	−46282.6	+	142443.i	−0.0159135	+	0.0489767i
$386$	−1.07699e6	−	3.31463e6i	−0.367911	−	1.13231i
$387$		−	1.00373e6i		−	0.340674i
$388$	−89810.2	+	276407.i	−0.0302863	+	0.0932117i
$389$	1.12299e6	−	1.54566e6i	0.376272	−	0.517894i	−0.578320	−	0.815810i	$-0.696291\pi$
$389$	1.12299e6	−	1.54566e6i	0.376272	−	0.517894i	0.954592	+	0.297916i	$0.0962914\pi$
$390$	−2.47960e6	+	805671.i	−0.825506	+	0.268223i
$391$	3.01520e6	+	9.27982e6i	0.997410	+	3.06971i
$392$	3.04151e6	+	988246.i	0.999709	+	0.324825i
$393$	−2.85019e6	+	2.07078e6i	−0.930876	+	0.676321i
$394$	1.52821e6	+	496546.i	0.495956	+	0.161146i
$395$			940694.i			0.303358i
$396$	493543.	−	160362.i	0.158157	−	0.0513882i
$397$	−5.10283e6	+	1.65801e6i	−1.62493	+	0.527972i	−0.973098	−	0.230390i	$-0.926000\pi$
$397$	−5.10283e6	+	1.65801e6i	−1.62493	+	0.527972i	−0.651833	+	0.758362i	$0.726000\pi$
$398$			811177.i			0.256689i
$399$	−59488.3	−	19328.9i	−0.0187068	−	0.00607820i
$400$	−588787.	+	427778.i	−0.183996	+	0.133681i
$401$	−2.51472e6	−	817083.i	−0.780960	−	0.253749i	−0.108710	−	0.994073i	$-0.534672\pi$
$401$	−2.51472e6	−	817083.i	−0.780960	−	0.253749i	−0.672250	+	0.740324i	$0.734672\pi$
$402$	1.60196e6	+	4.93033e6i	0.494410	+	1.52164i
$403$	1.00041e7	−	3.25054e6i	3.06843	−	0.996994i
$404$	1.34177e6	−	1.84679e6i	0.409002	−	0.562943i
$405$	−671013.	+	2.06516e6i	−0.203279	+	0.625629i
$406$			98253.5i			0.0295824i
$407$	−200642.	−	617513.i	−0.0600394	−	0.184782i
$408$	2.58712e6	−	7.96235e6i	0.769426	−	2.36805i
$409$	−2.70099e6	−	3.71760e6i	−0.798390	−	1.09889i	−0.993012	−	0.118012i	$-0.962348\pi$
$409$	−2.70099e6	−	3.71760e6i	−0.798390	−	1.09889i	0.194622	−	0.980878i	$-0.437652\pi$
$410$	−245712.	+	338194.i	−0.0721884	+	0.0993588i
$411$	−1.33276e6	−	4.10181e6i	−0.389177	−	1.19776i
$412$	343953.	−	249897.i	0.0998290	−	0.0725300i
$413$	499588.			0.144124
$414$	2.13713e6			0.612815
$415$	−372571.	+	270689.i	−0.106191	+	0.0771525i
$416$		−	5.48858e6i		−	1.55499i
$417$	−693211.	−	954123.i	−0.195220	−	0.268698i
$418$	179611.	+	130495.i	0.0502796	+	0.0365302i
$419$	−2.66242e6	−	3.66451e6i	−0.740871	−	1.01972i	−0.998568	−	0.0534952i	$-0.982964\pi$
$419$	−2.66242e6	−	3.66451e6i	−0.740871	−	1.01972i	0.257698	−	0.966226i	$-0.417036\pi$
$420$	−140532.	+	45661.5i	−0.0388733	+	0.0126307i
$421$	−48324.1	+	66512.4i	−0.0132880	+	0.0182893i	−0.815609	−	0.578603i	$-0.803598\pi$
$421$	−48324.1	+	66512.4i	−0.0132880	+	0.0182893i	0.802321	+	0.596892i	$0.203598\pi$
$422$	−2.34200e6	−	1.70156e6i	−0.640185	−	0.465121i
$423$	−616497.	−	447911.i	−0.167525	−	0.121714i
$424$	−1.51177e6	+	4.65276e6i	−0.408387	+	1.25689i
$425$	−4.86947e6	−	1.58219e6i	−1.30770	−	0.424899i
$426$	3.07565e6			0.821133
$427$	448963.	−	246795.i	0.119163	−	0.0655037i
$428$	−255916.			−0.0675285
$429$	−5.89472e6	−	1.91531e6i	−1.54639	−	0.502453i
$430$	313472.	−	964766.i	0.0817574	−	0.251623i
$431$	124476.	+	90437.3i	0.0322770	+	0.0234506i	0.603807	−	0.797131i	$-0.293650\pi$
$431$	124476.	+	90437.3i	0.0322770	+	0.0234506i	−0.571530	+	0.820581i	$0.693650\pi$
$432$	609850.	+	443082.i	0.157222	+	0.114229i
$433$	−2.31732e6	+	3.18951e6i	−0.593971	+	0.817532i	−0.995140	−	0.0984728i	$-0.968604\pi$
$433$	−2.31732e6	+	3.18951e6i	−0.593971	+	0.817532i	0.401168	+	0.916004i	$0.368604\pi$
$434$	−646631.	+	210103.i	−0.164791	+	0.0535437i
$435$	444828.	+	612253.i	0.112712	+	0.155134i
$436$	−1.92684e6	−	1.39993e6i	−0.485434	−	0.352688i
$437$	−471216.	−	648573.i	−0.118037	−	0.162463i
$438$		−	1.54612e6i		−	0.385087i
$439$	2.57123e6	−	1.86811e6i	0.636767	−	0.462638i	−0.221971	−	0.975053i	$-0.571249\pi$
$439$	2.57123e6	−	1.86811e6i	0.636767	−	0.462638i	0.858738	+	0.512415i	$0.171249\pi$
$440$	1.64707e6			0.405584
$441$	1.98282e6			0.485498
$442$	−8.52492e6	+	6.19372e6i	−2.07556	+	1.50798i
$443$	−1.05991e6	−	3.26206e6i	−0.256601	−	0.789737i	−0.993510	−	0.113745i	$-0.963715\pi$
$443$	−1.05991e6	−	3.26206e6i	−0.256601	−	0.789737i	0.736909	−	0.675992i	$-0.236285\pi$
$444$	376523.	−	518240.i	0.0906430	−	0.124759i
$445$	1.05316e6	+	1.44955e6i	0.252113	+	0.347004i
$446$	374891.	−	1.15380e6i	0.0892418	−	0.274658i
$447$	−1.85056e6	−	5.69543e6i	−0.438061	−	1.34821i
$448$			536464.i			0.126283i
$449$	−85513.0	+	263182.i	−0.0200178	+	0.0616084i	−0.960566	−	0.278051i	$-0.910312\pi$
$449$	−85513.0	+	263182.i	−0.0200178	+	0.0616084i	0.940549	+	0.339659i	$0.110312\pi$
$450$	−659160.	+	907256.i	−0.153447	+	0.211202i
$451$	−945139.	+	307094.i	−0.218804	+	0.0710936i
$452$	843752.	+	2.59680e6i	0.194253	+	0.597850i
$453$	3.78676e6	+	1.23039e6i	0.867006	+	0.281707i
$454$	−1.41959e6	+	1.03139e6i	−0.323239	+	0.234847i
$455$	555479.	+	180486.i	0.125788	+	0.0408710i
$456$			687864.i			0.154914i
$457$	−400542.	+	130144.i	−0.0897134	+	0.0291497i	−0.353530	−	0.935423i	$-0.615019\pi$
$457$	−400542.	+	130144.i	−0.0897134	+	0.0291497i	0.263816	+	0.964573i	$0.415019\pi$
$458$	−1.39825e6	+	454318.i	−0.311473	+	0.101204i
$459$			5.30323e6i			1.17492i
$460$	−1.80115e6	−	585231.i	−0.396877	−	0.128953i
$461$	2.30766e6	−	1.67662e6i	0.505732	−	0.367436i	−0.305470	−	0.952202i	$-0.598814\pi$
$461$	2.30766e6	−	1.67662e6i	0.505732	−	0.367436i	0.811202	+	0.584766i	$0.198814\pi$
$462$	381013.	+	123799.i	0.0830491	+	0.0269843i
$463$	451548.	+	1.38972e6i	0.0978930	+	0.301284i	0.987997	−	0.154474i	$-0.0493683\pi$
$463$	451548.	+	1.38972e6i	0.0978930	+	0.301284i	−0.890104	+	0.455758i	$0.849368\pi$
$464$	413487.	−	134350.i	0.0891593	−	0.0289696i
$465$	−3.07818e6	+	4.23675e6i	−0.660179	+	0.908658i
$466$	1.40723e6	−	4.33100e6i	0.300192	−	0.923897i
$467$			4.69546e6i			0.996291i	0.867094	+	0.498145i	$0.165985\pi$
$467$			4.69546e6i			0.996291i	−0.867094	+	0.498145i	$0.834015\pi$
$468$	−625356.	−	1.92465e6i	−0.131981	−	0.406197i
$469$	358870.	−	1.10449e6i	0.0753365	−	0.231862i
$470$	−452680.	−	623060.i	−0.0945250	−	0.130102i
$471$	2.01490e6	−	2.77327e6i	0.418506	−	0.576023i
$472$	−1.69775e6	−	5.22512e6i	−0.350766	−	1.07955i
$473$	1.95099e6	−	1.41747e6i	0.400960	−	0.291315i
$474$	2.51621e6			0.514400
$475$	420672.			0.0855479
$476$	−483151.	+	351030.i	−0.0977385	+	0.0710112i
$477$			3.03323e6i			0.610393i
$478$	−2.06778e6	−	2.84605e6i	−0.413936	−	0.569735i
$479$	4.83874e6	+	3.51555e6i	0.963592	+	0.700091i	0.953982	−	0.299863i	$-0.0969411\pi$
$479$	4.83874e6	+	3.51555e6i	0.963592	+	0.700091i	0.00960973	+	0.999954i	$0.496941\pi$
$480$	1.60613e6	+	2.21065e6i	0.318184	+	0.437943i
$481$	−2.40809e6	+	782435.i	−0.474580	+	0.154200i
$482$	199525.	−	274622.i	0.0391182	−	0.0538416i
$483$	−1.17036e6	−	850314.i	−0.228271	−	0.165848i
$484$	−939190.	−	682361.i	−0.182238	−	0.132404i
$485$	−176734.	+	543933.i	−0.0341167	+	0.105000i
$486$	3.29068e6	+	1.06921e6i	0.631968	+	0.205339i
$487$	−904490.			−0.172815			−0.0864075	−	0.996260i	$-0.527539\pi$
$487$	−904490.			−0.172815			−0.0864075	+	0.996260i	$0.527539\pi$
$488$	−4.10690e6	−	3.85697e6i	−0.780664	−	0.733156i
$489$	9.62472e6			1.82019
$490$	1.90585e6	+	619249.i	0.358591	+	0.116513i
$491$	−1.19603e6	+	3.68100e6i	−0.223892	+	0.689068i	0.774510	+	0.632561i	$0.217996\pi$
$491$	−1.19603e6	+	3.68100e6i	−0.223892	+	0.689068i	−0.998402	+	0.0565070i	$0.982004\pi$
$492$	−793196.	−	576290.i	−0.147730	−	0.107332i
$493$	2.47450e6	+	1.79783e6i	0.458533	+	0.333144i
$494$	508885.	−	700420.i	0.0938214	−	0.129134i
$495$	971226.	−	315570.i	0.178159	−	0.0578873i
$496$	1.76838e6	+	2.43397e6i	0.322754	+	0.444233i
$497$	−557417.	−	404987.i	−0.101225	−	0.0735446i
$498$	724051.	+	996571.i	0.130827	+	0.180067i
$499$		−	7.82043e6i		−	1.40598i	−0.711199	−	0.702990i	$-0.751848\pi$
$499$		−	7.82043e6i		−	1.40598i	0.711199	−	0.702990i	$-0.248152\pi$
$500$	1.91592e6	−	1.39200e6i	0.342731	−	0.249009i
$501$	−746821.			−0.132930
$502$	−1.61604e6			−0.286215
$503$	220737.	−	160375.i	0.0389004	−	0.0282628i	−0.568165	−	0.822915i	$-0.692347\pi$
$503$	220737.	−	160375.i	0.0389004	−	0.0282628i	0.607066	+	0.794652i	$0.292347\pi$
$504$	126940.	+	390682.i	0.0222599	+	0.0685089i
$505$	2.64043e6	−	3.63423e6i	0.460729	−	0.634139i
$506$	3.01807e6	+	4.15401e6i	0.524026	+	0.721259i
$507$	−5.28243e6	+	1.62577e7i	−0.912671	+	2.80891i
$508$	−2671.90	−	8223.26i	−0.000459368	−	0.00141379i
$509$		−	697354.i		−	0.119305i	−0.998219	−	0.0596525i	$-0.981001\pi$
$509$		−	697354.i		−	0.119305i	0.998219	−	0.0596525i	$-0.0189993\pi$
$510$	1.62113e6	−	4.98932e6i	0.275989	−	0.849408i
$511$	−203586.	+	280213.i	−0.0344903	+	0.0474718i
$512$	3.39336e6	−	1.10257e6i	0.572078	−	0.185880i
$513$	−134645.	−	414395.i	−0.0225890	−	0.0695219i
$514$	−5.00803e6	−	1.62721e6i	−0.836102	−	0.271666i
$515$	676854.	−	491763.i	0.112455	−	0.0817030i
$516$	2.26275e6	+	735212.i	0.374121	+	0.121559i
$517$		−	1.83085e6i		−	0.301250i
$518$	155650.	−	50573.8i	0.0254874	−	0.00828135i
$519$	2.93002e6	−	952020.i	0.477476	−	0.155141i
$520$		−	6.42301e6i		−	1.04167i
$521$	8.05280e6	+	2.61651e6i	1.29973	+	0.422307i	0.875487	−	0.483242i	$-0.160541\pi$
$521$	8.05280e6	+	2.61651e6i	1.29973	+	0.422307i	0.424241	+	0.905549i	$0.360541\pi$
$522$	541982.	−	393773.i	0.0870580	−	0.0632513i
$523$	6.02156e6	+	1.95652e6i	0.962620	+	0.312774i	0.747833	−	0.663887i	$-0.231094\pi$
$523$	6.02156e6	+	1.95652e6i	0.962620	+	0.312774i	0.214787	+	0.976661i	$0.431094\pi$
$524$	−854017.	−	2.62839e6i	−0.135875	−	0.418179i
$525$	721953.	−	234577.i	0.114317	−	0.0371438i
$526$	−2.57583e6	+	3.54533e6i	−0.405932	+	0.558718i
$527$	−6.54056e6	+	2.01298e7i	−1.02586	+	3.15728i
$528$		−	1.77272e6i		−	0.276730i
$529$	−3.74059e6	−	1.15124e7i	−0.581168	−	1.78865i
$530$	−947299.	+	2.91549e6i	−0.146486	+	0.450839i
$531$	−2.00221e6	−	2.75581e6i	−0.308158	−	0.424143i
$532$	28841.1	−	39696.4i	0.00441807	−	0.00608096i
$533$	1.19756e6	+	3.68572e6i	0.182591	+	0.561958i
$534$	3.87733e6	−	2.81705e6i	0.588410	−	0.427505i
$535$	−503607.			−0.0760690
$536$	−1.27712e7			−1.92009
$537$	−9.02037e6	+	6.55368e6i	−1.34986	+	0.980731i
$538$			4.93248e6i			0.734700i
$539$	2.80016e6	+	3.85409e6i	0.415155	+	0.571412i
$540$	−832740.	−	605021.i	−0.122892	−	0.0892866i
$541$	2.10236e6	+	2.89365e6i	0.308826	+	0.425062i	0.935015	−	0.354609i	$-0.115386\pi$
$541$	2.10236e6	+	2.89365e6i	0.308826	+	0.425062i	−0.626189	+	0.779671i	$0.715386\pi$
$542$	3.73203e6	−	1.21261e6i	0.545691	−	0.177306i
$543$	−395616.	+	544519.i	−0.0575804	+	0.0792526i
$544$	8.93465e6	+	6.49140e6i	1.29444	+	0.940462i
$545$	−3.79177e6	−	2.75488e6i	−0.546827	−	0.397293i
$546$	482772.	−	1.48582e6i	0.0693044	−	0.213297i
$547$	−9.02562e6	−	2.93260e6i	−1.28976	−	0.419068i	−0.417752	−	0.908561i	$-0.637182\pi$
$547$	−9.02562e6	−	2.93260e6i	−1.28976	−	0.419068i	−0.872008	+	0.489492i	$0.837182\pi$
$548$	3.38328e6			0.481268
$549$	−3.16068e6	−	1.48747e6i	−0.447558	−	0.210629i
$550$	−2.69434e6			−0.379792
$551$	−239004.	−	77657.0i	−0.0335371	−	0.0108969i
$552$	−4.91610e6	+	1.51302e7i	−0.686709	+	2.11347i
$553$	−456027.	−	331323.i	−0.0634129	−	0.0460722i
$554$	−2.39808e6	−	1.74231e6i	−0.331963	−	0.241185i
$555$	740947.	−	1.01983e6i	0.102107	−	0.140538i
$556$	879876.	−	285889.i	0.120708	−	0.0392202i
$557$	−4.54001e6	−	6.24879e6i	−0.620039	−	0.853410i	0.377317	−	0.926084i	$-0.376847\pi$
$557$	−4.54001e6	−	6.24879e6i	−0.620039	−	0.853410i	−0.997356	+	0.0726739i	$0.976847\pi$
$558$	3.75048e6	+	2.72488e6i	0.509919	+	0.370478i
$559$	−5.52766e6	−	7.60817e6i	−0.748190	−	1.02980i
$560$			167050.i			0.0225100i
$561$	1.00896e7	−	7.33052e6i	1.35353	−	0.983394i
$562$	−4.29685e6			−0.573864
$563$	−6.91864e6			−0.919920			−0.459960	−	0.887940i	$-0.652136\pi$
$563$	−6.91864e6			−0.919920			−0.459960	+	0.887940i	$0.652136\pi$
$564$	1.46132e6	−	1.06171e6i	0.193440	−	0.140542i
$565$	1.66039e6	+	5.11015e6i	0.218821	+	0.673462i
$566$	1.48928e6	−	2.04982e6i	0.195405	−	0.268953i
$567$	−764806.	−	1.05267e6i	−0.0999065	−	0.137509i
$568$	−2.34144e6	+	7.20621e6i	−0.304518	+	0.937209i
$569$	1.80447e6	+	5.55358e6i	0.233652	+	0.719106i	0.997297	+	0.0734702i	$0.0234074\pi$
$569$	1.80447e6	+	5.55358e6i	0.233652	+	0.719106i	−0.763646	+	0.645635i	$0.776593\pi$
$570$			431026.i			0.0555669i
$571$	−161790.	+	497939.i	−0.0207664	+	0.0639125i	−0.960903	−	0.276886i	$-0.910697\pi$
$571$	−161790.	+	497939.i	−0.0207664	+	0.0639125i	0.940136	+	0.340799i	$0.110697\pi$
$572$	2.85788e6	−	3.93353e6i	0.365219	−	0.502681i
$573$	−772589.	+	251029.i	−0.0983019	+	0.0319402i
$574$	−77406.1	−	238231.i	−0.00980608	−	0.0301800i
$575$	9.25306e6	+	3.00650e6i	1.16712	+	0.379221i
$576$	2.95922e6	−	2.15000e6i	0.371639	−	0.270012i
$577$	8.50379e6	+	2.76305e6i	1.06334	+	0.345501i	0.787891	−	0.615814i	$-0.211173\pi$
$577$	8.50379e6	+	2.76305e6i	1.06334	+	0.345501i	0.275451	+	0.961315i	$0.411173\pi$
$578$		−	1.53399e7i		−	1.90987i
$579$	1.52983e7	−	4.97073e6i	1.89648	−	0.616203i
$580$	−564609.	+	183453.i	−0.0696912	+	0.0226441i
$581$		−	275954.i		−	0.0339153i
$582$	1.45494e6	+	472737.i	0.178048	+	0.0578512i
$583$	−5.89581e6	+	4.28355e6i	−0.718409	+	0.521955i
$584$	3.62255e6	+	1.17704e6i	0.439523	+	0.142810i
$585$	−1.23062e6	−	3.78745e6i	−0.148673	−	0.457569i
$586$	−4.33326e6	+	1.40796e6i	−0.521279	+	0.169374i
$587$	−241708.	+	332683.i	−0.0289532	+	0.0398506i	−0.823248	−	0.567682i	$-0.807840\pi$
$587$	−241708.	+	332683.i	−0.0289532	+	0.0398506i	0.794295	+	0.607532i	$0.207840\pi$
$588$	−1.45238e6	+	4.46996e6i	−0.173235	+	0.533163i
$589$		−	1.73900e6i		−	0.206544i
$590$	−1.06383e6	−	3.27414e6i	−0.125818	−	0.387228i
$591$	−2.29176e6	+	7.05331e6i	−0.269898	+	0.830662i
$592$	−425666.	−	585879.i	−0.0499188	−	0.0687074i
$593$	−2.34036e6	+	3.22123e6i	−0.273304	+	0.376171i	−0.923502	−	0.383594i	$-0.874686\pi$
$593$	−2.34036e6	+	3.22123e6i	−0.273304	+	0.376171i	0.650197	+	0.759765i	$0.274686\pi$
$594$	862382.	+	2.65414e6i	0.100284	+	0.308644i
$595$	−950776.	+	690779.i	−0.110100	+	0.0799921i
$596$	4.69774e6			0.541718
$597$	−3.74391e6			−0.429922
$598$	1.61992e7	−	1.17694e7i	1.85243	−	1.34587i
$599$		−	2.33289e6i		−	0.265661i	−0.991139	−	0.132830i	$-0.957593\pi$
$599$		−	2.33289e6i		−	0.265661i	0.991139	−	0.132830i	$-0.0424066\pi$
$600$	−4.90681e6	−	6.75364e6i	−0.556444	−	0.765879i
$601$	3.09556e6	+	2.24905e6i	0.349585	+	0.253988i	0.748695	−	0.662915i	$-0.230681\pi$
$601$	3.09556e6	+	2.24905e6i	0.349585	+	0.253988i	−0.399110	+	0.916903i	$0.630681\pi$
$602$	357288.	+	491765.i	0.0401816	+	0.0553053i
$603$	−7.53079e6	+	2.44690e6i	−0.843426	+	0.274046i
$604$	−1.83590e6	+	2.52690e6i	−0.204765	+	0.281835i
$605$	−1.84820e6	−	1.34279e6i	−0.205286	−	0.149149i
$606$	−9.72102e6	−	7.06273e6i	−1.07530	−	0.781252i
$607$	2.67818e6	−	8.24258e6i	0.295031	−	0.908012i	−0.688180	−	0.725540i	$-0.741590\pi$
$607$	2.67818e6	−	8.24258e6i	0.295031	−	0.908012i	0.983211	−	0.182472i	$-0.0584098\pi$
$608$	−862967.	−	280395.i	−0.0946750	−	0.0307618i
$609$	−453480.			−0.0495467
$610$	−2.57344e6	−	2.41683e6i	−0.280020	−	0.262979i
$611$	−7.13969e6			−0.773707
$612$	3.87267e6	+	1.25831e6i	0.417958	+	0.135803i
$613$	−2.23146e6	+	6.86772e6i	−0.239849	+	0.738179i	0.756592	+	0.653887i	$0.226863\pi$
$613$	−2.23146e6	+	6.86772e6i	−0.239849	+	0.738179i	−0.996441	+	0.0842919i	$0.973137\pi$
$614$	8.85376e6	+	6.43263e6i	0.947778	+	0.688601i
$615$	−1.56090e6	−	1.13406e6i	−0.166413	−	0.120906i
$616$	−580117.	+	798463.i	−0.0615976	+	0.0847819i
$617$	−1.23364e7	+	4.00833e6i	−1.30459	+	0.423887i	−0.877176	−	0.480168i	$-0.840576\pi$
$617$	−1.23364e7	+	4.00833e6i	−1.30459	+	0.423887i	−0.427415	+	0.904056i	$0.640576\pi$
$618$	−1.31539e6	−	1.81048e6i	−0.138543	−	0.190688i
$619$	6.35149e6	+	4.61463e6i	0.666268	+	0.484072i	0.868774	−	0.495209i	$-0.164908\pi$
$619$	6.35149e6	+	4.61463e6i	0.666268	+	0.484072i	−0.202506	+	0.979281i	$0.564908\pi$
$620$	−2.41470e6	−	3.32354e6i	−0.252280	−	0.347234i
$621$		−	1.00773e7i		−	1.04861i
$622$	7.94949e6	−	5.77564e6i	0.823879	−	0.598583i
$623$	−1.07365e6			−0.110826
$624$	−6.91301e6			−0.710731
$625$	−1.94211e6	+	1.41103e6i	−0.198873	+	0.144489i
$626$	−1.63714e6	−	5.03861e6i	−0.166975	−	0.513895i
$627$	−602286.	+	828976.i	−0.0611834	+	0.0842118i
$628$	1.58060e6	+	2.17551e6i	0.159927	+	0.220121i
$629$	1.57437e6	−	4.84542e6i	0.158665	−	0.488321i
$630$	79542.6	+	244807.i	0.00798451	+	0.0245738i
$631$		−	1.20279e7i		−	1.20258i	−0.799029	−	0.601292i	$-0.794653\pi$
$631$		−	1.20279e7i		−	1.20258i	0.799029	−	0.601292i	$-0.205347\pi$
$632$	−1.91555e6	+	5.89545e6i	−0.190766	+	0.587116i
$633$	7.85339e6	−	1.08093e7i	0.779018	−	1.07223i
$634$	1.03572e7	−	3.36525e6i	1.02333	−	0.332502i
$635$	−5257.94	−	16182.3i	−0.000517465	−	0.00159259i
$636$	−6.83794e6	−	2.22178e6i	−0.670320	−	0.217800i
$637$	1.50296e7	−	1.09196e7i	1.46757	−	1.06625i
$638$	1.53078e6	+	497382.i	0.148889	+	0.0483769i
$639$			4.69788e6i			0.455145i
$640$	−847811.	+	275470.i	−0.0818180	+	0.0265843i
$641$	4.55063e6	−	1.47859e6i	0.437448	−	0.142136i	−0.0820098	−	0.996632i	$-0.526134\pi$
$641$	4.55063e6	−	1.47859e6i	0.437448	−	0.142136i	0.519458	+	0.854496i	$0.326134\pi$
$642$			1.34707e6i			0.128989i
$643$	−6.56109e6	−	2.13183e6i	−0.625819	−	0.203341i	−0.0210966	−	0.999777i	$-0.506716\pi$
$643$	−6.56109e6	−	2.13183e6i	−0.625819	−	0.203341i	−0.604722	+	0.796437i	$0.706716\pi$
$644$	918093.	−	667033.i	0.0872312	−	0.0633772i
$645$	4.45278e6	+	1.44680e6i	0.421437	+	0.136933i
$646$	538323.	+	1.65679e6i	0.0507530	+	0.156202i
$647$	−5.34636e6	+	1.73714e6i	−0.502109	+	0.163145i	−0.549110	−	0.835750i	$-0.685033\pi$
$647$	−5.34636e6	+	1.73714e6i	−0.502109	+	0.163145i	0.0470018	+	0.998895i	$0.485033\pi$
$648$	−8.41064e6	+	1.15763e7i	−0.786849	+	1.08301i
$649$	2.52903e6	−	7.78355e6i	0.235691	−	0.725381i
$650$			1.05070e7i			0.975428i
$651$	−969710.	−	2.98446e6i	−0.0896788	−	0.276003i
$652$	−2.33313e6	+	7.18064e6i	−0.214941	+	0.661522i
$653$	9.87772e6	+	1.35955e7i	0.906512	+	1.24771i	0.968344	+	0.249620i	$0.0803058\pi$
$653$	9.87772e6	+	1.35955e7i	0.906512	+	1.24771i	−0.0618316	+	0.998087i	$0.519694\pi$
$654$	−7.36888e6	+	1.01424e7i	−0.673685	+	0.927248i
$655$	−1.68059e6	−	5.17233e6i	−0.153059	−	0.471067i
$656$	−896721.	+	651506.i	−0.0813575	+	0.0591097i
$657$	2.36161e6			0.213450
$658$	461484.			0.0415520
$659$	−1.19222e7	+	8.66196e6i	−1.06940	+	0.776967i	−0.975805	−	0.218643i	$-0.929837\pi$
$659$	−1.19222e7	+	8.66196e6i	−1.06940	+	0.776967i	−0.0935986	+	0.995610i	$0.529837\pi$
$660$			2.42062e6i			0.216305i
$661$	7.33602e6	+	1.00972e7i	0.653066	+	0.898868i	0.999227	−	0.0393068i	$-0.0125150\pi$
$661$	7.33602e6	+	1.00972e7i	0.653066	+	0.898868i	−0.346161	+	0.938175i	$0.612515\pi$
$662$	−5.01279e6	−	3.64200e6i	−0.444564	−	0.322995i
$663$	−2.85865e7	−	3.93459e7i	−2.52567	−	3.47629i
$664$	−2.88616e6	+	937770.i	−0.254039	+	0.0825422i
$665$	56755.4	−	78117.1i	0.00497683	−	0.00685002i
$666$	−902776.	−	655905.i	−0.0788668	−	0.0573001i
$667$	−4.70210e6	−	3.41627e6i	−0.409239	−	0.297330i
$668$	181037.	−	557174.i	0.0156973	−	0.0483114i
$669$	5.32524e6	+	1.73027e6i	0.460017	+	0.149468i
$670$	−8.00264e6			−0.688726
$671$	−1.57229e6	−	8.24415e6i	−0.134811	−	0.706870i
$672$	−1.63737e6			−0.139870
$673$	−8.74279e6	−	2.84071e6i	−0.744068	−	0.241762i	−0.0876412	−	0.996152i	$-0.527933\pi$
$673$	−8.74279e6	−	2.84071e6i	−0.744068	−	0.241762i	−0.656427	+	0.754390i	$0.727933\pi$
$674$	4.43449e6	−	1.36480e7i	0.376005	−	1.15723i
$675$	4.27803e6	+	3.10817e6i	0.361397	+	0.262570i
$676$	−1.08487e7	−	7.88204e6i	−0.913085	−	0.663395i
$677$	−5.69250e6	+	7.83505e6i	−0.477344	+	0.657007i	−0.977992	−	0.208644i	$-0.933095\pi$
$677$	−5.69250e6	+	7.83505e6i	−0.477344	+	0.657007i	0.500648	+	0.865651i	$0.333095\pi$
$678$	1.36689e7	−	4.44129e6i	1.14198	−	0.371052i
$679$	−201438.	−	277256.i	−0.0167675	−	0.0230784i
$680$	1.04558e7	+	7.59657e6i	0.867130	+	0.630006i
$681$	−4.76029e6	−	6.55198e6i	−0.393338	−	0.541383i
$682$			1.11381e7i			0.916956i
$683$	−1.49361e7	+	1.08517e7i	−1.22514	+	0.890116i	−0.996516	−	0.0833985i	$-0.973423\pi$
$683$	−1.49361e7	+	1.08517e7i	−1.22514	+	0.890116i	−0.228624	+	0.973515i	$0.573423\pi$
$684$	−334559.			−0.0273421
$685$	6.65784e6			0.542134
$686$	−1.96122e6	+	1.42491e6i	−0.159117	+	0.115605i
$687$	−2.09686e6	−	6.45347e6i	−0.169503	−	0.521677i
$688$	1.58098e6	−	2.17603e6i	0.127337	−	0.175264i
$689$	1.67044e7	+	2.29916e7i	1.34055	+	1.84511i
$690$	−3.08050e6	+	9.48080e6i	−0.246319	+	0.758093i
$691$	−1.27343e6	−	3.91922e6i	−0.101457	−	0.312251i	0.887426	−	0.460950i	$-0.152491\pi$
$691$	−1.27343e6	−	3.91922e6i	−0.101457	−	0.312251i	−0.988882	+	0.148699i	$0.952491\pi$
$692$			2.41675e6i			0.191852i
$693$	−189095.	+	581975.i	−0.0149571	+	0.0460332i
$694$	−7.05580e6	+	9.71148e6i	−0.556093	+	0.765397i
$695$	1.73148e6	−	562591.i	0.135974	−	0.0441805i
$696$	1.54105e6	+	4.74288e6i	0.120585	+	0.371124i
$697$	−7.41620e6	−	2.40967e6i	−0.578229	−	0.187878i
$698$	−1.26466e7	+	9.18828e6i	−0.982504	+	0.713831i
$699$	1.99893e7	+	6.49492e6i	1.54741	+	0.502784i
$700$			595485.i			0.0459331i
$701$	1.13565e7	−	3.68996e6i	0.872871	−	0.283613i	0.161877	−	0.986811i	$-0.448245\pi$
$701$	1.13565e7	−	3.68996e6i	0.872871	−	0.283613i	0.710994	+	0.703198i	$0.248245\pi$
$702$	1.03502e7	−	3.36299e6i	0.792697	−	0.257563i
$703$			418594.i			0.0319452i
$704$	8.35808e6	+	2.71570e6i	0.635586	+	0.206515i
$705$	2.87567e6	−	2.08930e6i	0.217905	−	0.158317i
$706$	−275771.	−	89603.5i	−0.0208227	−	0.00676571i
$707$	831806.	+	2.56003e6i	0.0625855	+	0.192618i
$708$	7.67911e6	−	2.49510e6i	0.575742	−	0.187070i
$709$	−6.58539e6	+	9.06401e6i	−0.492001	+	0.677181i	−0.980755	−	0.195240i	$-0.937451\pi$
$709$	−6.58539e6	+	9.06401e6i	−0.492001	+	0.677181i	0.488755	+	0.872421i	$0.337451\pi$
$710$	−1.46718e6	+	4.51552e6i	−0.109229	+	0.336172i
$711$			3.84337e6i			0.285127i
$712$	3.64856e6	+	1.12291e7i	0.269725	+	0.830128i
$713$	1.24285e7	−	3.82510e7i	0.915577	−	2.81785i
$714$	1.84773e6	+	2.54318e6i	0.135642	+	0.186695i
$715$	5.62392e6	−	7.74066e6i	0.411409	−	0.566256i
$716$	−2.70282e6	−	8.31843e6i	−0.197031	−	0.606400i
$717$	1.31357e7	−	9.54362e6i	0.954232	−	0.693290i
$718$	−1.27246e7			−0.921153
$719$	1.75157e6			0.126359			0.0631794	−	0.998002i	$-0.479876\pi$
$719$	1.75157e6			0.126359			0.0631794	+	0.998002i	$0.479876\pi$
$720$	921472.	−	669488.i	0.0662446	−	0.0481296i
$721$			501328.i			0.0359156i
$722$	5.92552e6	+	8.15578e6i	0.423042	+	0.582267i
$723$	1.26749e6	+	920887.i	0.0901778	+	0.0655180i
$724$	−310344.	−	427151.i	−0.0220037	−	0.0302855i
$725$	2.90057e6	−	942451.i	0.204945	−	0.0665907i
$726$	−3.59177e6	+	4.94365e6i	−0.252911	+	0.348102i
$727$	1.97501e7	+	1.43493e7i	1.38590	+	1.00692i	0.996301	+	0.0859346i	$0.0273876\pi$
$727$	1.97501e7	+	1.43493e7i	1.38590	+	1.00692i	0.389603	+	0.920983i	$0.372612\pi$
$728$	3.11373e6	+	2.26226e6i	0.217747	+	0.158203i
$729$	607627.	−	1.87008e6i	0.0423466	−	0.130329i
$730$	2.26994e6	+	737549.i	0.157655	+	0.0512252i
$731$	1.89227e7			1.30975
$732$	5.66840e6	−	6.03571e6i	0.391005	−	0.416342i
$733$	1.35777e7			0.933394			0.466697	−	0.884417i	$-0.345444\pi$
$733$	1.35777e7			0.933394			0.466697	+	0.884417i	$0.345444\pi$
$734$	−5.08947e6	−	1.65367e6i	−0.348684	−	0.113294i
$735$	−2.85808e6	+	8.79627e6i	−0.195145	+	0.600593i
$736$	−1.69778e7	−	1.23351e7i	−1.15528	−	0.839359i
$737$	−1.53912e7	−	1.11823e7i	−1.04377	−	0.758340i
$738$	−1.00390e6	+	1.38175e6i	−0.0678500	+	0.0933875i
$739$	9.93099e6	−	3.22678e6i	0.668932	−	0.217349i	0.0451885	−	0.998978i	$-0.485611\pi$
$739$	9.93099e6	−	3.22678e6i	0.668932	−	0.217349i	0.623743	+	0.781629i	$0.285611\pi$
$740$	581240.	+	800008.i	0.0390190	+	0.0537050i
$741$	3.23272e6	+	2.34871e6i	0.216283	+	0.157139i
$742$	−1.07971e6	−	1.48609e6i	−0.0719942	−	0.0990916i
$743$			2.36918e7i			1.57444i	0.616671	+	0.787221i	$0.288481\pi$
$743$			2.36918e7i			1.57444i	−0.616671	+	0.787221i	$0.711519\pi$
$744$	−2.79187e7	+	2.02841e7i	−1.84911	+	1.34346i
$745$	9.24452e6			0.610230
$746$	1.39565e6			0.0918185
$747$	−1.52220e6	+	1.10595e6i	−0.0998093	+	0.0725157i
$748$	3.02320e6	+	9.30446e6i	0.197566	+	0.608047i
$749$	177376.	−	244137.i	0.0115529	−	0.0159012i
$750$	−7.32713e6	−	1.00849e7i	−0.475642	−	0.654665i
$751$	−4.90933e6	+	1.51094e7i	−0.317631	+	0.977566i	0.657028	+	0.753867i	$0.271814\pi$
$751$	−4.90933e6	+	1.51094e7i	−0.317631	+	0.977566i	−0.974658	+	0.223700i	$0.928186\pi$
$752$	−631024.	−	1.94209e6i	−0.0406913	−	0.125235i
$753$		−	7.45867e6i		−	0.479373i
$754$	1.93962e6	−	5.96953e6i	0.124247	−	0.382394i
$755$	−3.61280e6	+	4.97259e6i	−0.230662	+	0.317479i
$756$	586600.	−	190598.i	0.0373283	−	0.0121287i
$757$	−2.73015e6	−	8.40254e6i	−0.173160	−	0.532931i	0.826385	−	0.563106i	$-0.190394\pi$
$757$	−2.73015e6	−	8.40254e6i	−0.173160	−	0.532931i	−0.999545	+	0.0301747i	$0.990394\pi$
$758$	1.41910e7	+	4.61094e6i	0.897099	+	0.291485i
$759$	−1.91724e7	+	1.39296e7i	−1.20802	+	0.877675i
$760$	−1.00989e6	−	328132.i	−0.0634218	−	0.0206070i
$761$			2.17048e7i			1.35861i	0.733856	+	0.679305i	$0.237718\pi$
$761$			2.17048e7i			1.35861i	−0.733856	+	0.679305i	$0.762282\pi$
$762$	−43285.1	+	14064.2i	−0.00270054	+	0.000877459i
$763$	2.67100e6	−	867862.i	0.166097	−	0.0539683i
$764$		−	637251.i		−	0.0394982i
$765$	7.62090e6	+	2.47618e6i	0.470817	+	0.152978i
$766$	1.84637e7	−	1.34146e7i	1.13696	−	0.826051i
$767$	−3.03532e7	−	9.86234e6i	−1.86301	−	0.605329i
$768$	6.47173e6	+	1.99179e7i	0.395929	+	1.21854i
$769$	1.22886e7	−	3.99281e6i	0.749353	−	0.243480i	0.0906502	−	0.995883i	$-0.471105\pi$
$769$	1.22886e7	−	3.99281e6i	0.749353	−	0.243480i	0.658703	+	0.752403i	$0.271105\pi$
$770$	−363510.	+	500328.i	−0.0220948	+	0.0304108i
$771$	7.51022e6	−	2.31141e7i	0.455006	−	1.40036i
$772$			1.26185e7i			0.762014i
$773$	−8.73716e6	−	2.68902e7i	−0.525922	−	1.61862i	−0.762485	−	0.647006i	$-0.776021\pi$
$773$	−8.73716e6	−	2.68902e7i	−0.525922	−	1.61862i	0.236563	−	0.971616i	$-0.423979\pi$
$774$	1.28074e6	−	3.94172e6i	0.0768438	−	0.236501i
$775$	1.24050e7	+	1.70740e7i	0.741896	+	1.02113i
$776$	−2.21523e6	+	3.04901e6i	−0.132058	+	0.181762i
$777$	233418.	+	718388.i	0.0138702	+	0.0426881i
$778$	6.38231e6	−	4.63702e6i	0.378032	−	0.274656i
$779$	640683.			0.0378268
$780$	9.43960e6			0.555542
$781$	−9.13145e6	+	6.63439e6i	−0.535688	+	0.389200i
$782$			4.02899e7i			2.35602i
$783$	−1.85678e6	−	2.55564e6i	−0.108232	−	0.148969i
$784$	4.29865e6	+	3.12315e6i	0.249771	+	0.181469i
$785$	3.11041e6	+	4.28111e6i	0.180154	+	0.247960i
$786$	−1.38352e7	+	4.49532e6i	−0.798782	+	0.259540i
$787$	−1.44676e6	+	1.99130e6i	−0.0832647	+	0.114604i	−0.848617	−	0.529007i	$-0.822565\pi$
$787$	−1.44676e6	+	1.99130e6i	−0.0832647	+	0.114604i	0.765353	+	0.643611i	$0.222565\pi$
$788$	−4.70666e6	−	3.41959e6i	−0.270021	−	0.196182i
$789$	−1.63631e7	−	1.18885e7i	−0.935780	−	0.679884i
$790$	−1.20031e6	+	3.69417e6i	−0.0684267	+	0.210596i
$791$	−3.06209e6	−	994934.i	−0.174011	−	0.0565396i
$792$	6.72940e6			0.381209
$793$	−3.21493e7	+	6.13137e6i	−1.81547	+	0.346238i
$794$	−2.21548e7			−1.24714
$795$	−1.34561e7	−	4.37216e6i	−0.755097	−	0.245346i
$796$	907561.	−	2.79319e6i	0.0507684	−	0.156249i
$797$	−8.90647e6	−	6.47093e6i	−0.496661	−	0.360845i	0.311079	−	0.950384i	$-0.399310\pi$
$797$	−8.90647e6	−	6.47093e6i	−0.496661	−	0.360845i	−0.807740	+	0.589539i	$0.799310\pi$
$798$	−208951.	−	151812.i	−0.0116155	−	0.00843915i
$799$	8.44419e6	−	1.16224e7i	0.467941	−	0.644065i
$800$	1.04730e7	−	3.40289e6i	0.578558	−	0.187985i
$801$	4.30287e6	+	5.92240e6i	0.236961	+	0.326149i
$802$	−8.83291e6	−	6.41748e6i	−0.484917	−	0.352313i
$803$	3.33509e6	+	4.59036e6i	0.182524	+	0.251222i
$804$		−	1.87693e7i		−	1.02402i
$805$	1.80668e6	−	1.31263e6i	0.0982635	−	0.0713926i
$806$	4.34346e7			2.35504
$807$	−2.27654e7			−1.23053
$808$	2.39483e7	−	1.73995e7i	1.29047	−	0.937579i
$809$	−3.96465e6	−	1.22019e7i	−0.212978	−	0.655478i	−0.999291	−	0.0376498i	$-0.988013\pi$
$809$	−3.96465e6	−	1.22019e7i	−0.212978	−	0.655478i	0.786313	−	0.617828i	$-0.211987\pi$
$810$	−5.27023e6	+	7.25385e6i	−0.282239	+	0.388469i
$811$	145405.	+	200133.i	0.00776298	+	0.0106848i	0.812881	−	0.582430i	$-0.197898\pi$
$811$	145405.	+	200133.i	0.00776298	+	0.0106848i	−0.805118	+	0.593115i	$0.797898\pi$
$812$	109928.	−	338324.i	0.00585084	−	0.0180070i
$813$	5.59668e6	+	1.72248e7i	0.296964	+	0.913963i
$814$		−	2.68103e6i		−	0.141821i
$815$	−4.59129e6	+	1.41305e7i	−0.242125	+	0.745185i
$816$	8.17608e6	−	1.12534e7i	0.429853	−	0.591642i
$817$	−1.47862e6	+	480433.i	−0.0775000	+	0.0251813i
$818$	−5.86340e6	−	1.80457e7i	−0.306384	−	0.942954i
$819$	2.26950e6	+	737406.i	0.118228	+	0.0384147i
$820$	1.22446e6	−	889621.i	0.0635930	−	0.0462030i
$821$	−1.38328e7	−	4.49455e6i	−0.716230	−	0.232717i	−0.0718420	−	0.997416i	$-0.522888\pi$
$821$	−1.38328e7	−	4.49455e6i	−0.716230	−	0.232717i	−0.644388	+	0.764699i	$0.722888\pi$
$822$		−	1.78087e7i		−	0.919290i
$823$	−2.40300e7	+	7.80780e6i	−1.23667	+	0.401818i	−0.853126	−	0.521705i	$-0.825296\pi$
$823$	−2.40300e7	+	7.80780e6i	−1.23667	+	0.401818i	−0.383543	+	0.923523i	$0.625296\pi$
$824$	5.24331e6	−	1.70366e6i	0.269022	−	0.0874105i
$825$		−	1.24355e7i		−	0.636102i
$826$	1.96192e6	+	637466.i	0.100053	+	0.0325093i
$827$	1.16793e7	−	8.48548e6i	0.593816	−	0.431432i	−0.249863	−	0.968281i	$-0.580385\pi$
$827$	1.16793e7	−	8.48548e6i	0.593816	−	0.431432i	0.843678	+	0.536849i	$0.180385\pi$
$828$	−7.35892e6	−	2.39106e6i	−0.373025	−	0.121203i
$829$	−8.23553e6	−	2.53464e7i	−0.416203	−	1.28094i	−0.911170	−	0.412030i	$-0.864820\pi$
$829$	−8.23553e6	−	2.53464e7i	−0.416203	−	1.28094i	0.494967	−	0.868912i	$-0.335180\pi$
$830$	−1.80851e6	+	587620.i	−0.0911224	+	0.0296075i
$831$	8.04146e6	−	1.10681e7i	0.403954	−	0.555995i
$832$	1.05903e7	−	3.25936e7i	0.530396	−	1.63239i
$833$			3.73809e7i			1.86654i
$834$	−1.50484e6	−	4.63143e6i	−0.0749163	−	0.230569i
$835$	356256.	−	1.09644e6i	0.0176826	−	0.0544214i
$836$	−472467.	−	650295.i	−0.0233806	−	0.0321806i
$837$	1.28488e7	−	1.76848e7i	0.633940	−	0.872544i
$838$	−5.77968e6	−	1.77880e7i	−0.284311	−	0.875019i
$839$	−9.68956e6	+	7.03988e6i	−0.475225	+	0.345271i	−0.799474	−	0.600701i	$-0.794888\pi$
$839$	−9.68956e6	+	7.03988e6i	−0.475225	+	0.345271i	0.324249	+	0.945972i	$0.394888\pi$
$840$	−1.91613e6			−0.0936974
$841$	1.86892e7			0.911174
$842$	−274641.	+	199538.i	−0.0133501	+	0.00969943i
$843$		−	1.98317e7i		−	0.961148i
$844$	6.16063e6	+	8.47939e6i	0.297693	+	0.409740i
$845$	−2.13488e7	−	1.55108e7i	−1.02856	−	0.747295i
$846$	−1.84950e6	−	2.54562e6i	−0.0888441	−	0.122283i
$847$	1.30191e6	−	423017.i	0.0623553	−	0.0202605i
$848$	−4.77765e6	+	6.57587e6i	−0.228152	+	0.314025i
$849$	9.46076e6	+	6.87365e6i	0.450461	+	0.327279i
$850$	−1.71039e7	−	1.24267e7i	−0.811986	−	0.589942i
$851$	−2.99165e6	+	9.20736e6i	−0.141608	+	0.435824i
$852$	−1.05906e7	−	3.44110e6i	−0.499830	−	0.162405i
$853$	−2.11942e7			−0.997343			−0.498671	−	0.866791i	$-0.666179\pi$
$853$	−2.11942e7			−0.997343			−0.498671	+	0.866791i	$0.666179\pi$
$854$	2.07802e6	−	396310.i	0.0975000	−	0.0185948i
$855$	−658366.			−0.0308001
$856$	−3.15617e6	−	1.02550e6i	−0.147223	−	0.0478357i
$857$	779326.	−	2.39852e6i	0.0362466	−	0.111556i	−0.931296	−	0.364263i	$-0.881321\pi$
$857$	779326.	−	2.39852e6i	0.0362466	−	0.111556i	0.967543	+	0.252707i	$0.0813210\pi$
$858$	−2.07051e7	−	1.50431e7i	−0.960193	−	0.697621i
$859$	2.74159e6	+	1.99188e6i	0.126771	+	0.0921045i	0.649364	−	0.760478i	$-0.275035\pi$
$859$	2.74159e6	+	1.99188e6i	0.126771	+	0.0921045i	−0.522593	+	0.852582i	$0.675035\pi$
$860$	−2.15880e6	+	2.97133e6i	−0.0995328	+	0.136995i
$861$	1.09953e6	−	357260.i	0.0505476	−	0.0164239i
$862$	373431.	+	513983.i	0.0171176	+	0.0235603i
$863$	1.72047e7	+	1.24999e7i	0.786356	+	0.571321i	0.906880	−	0.421389i	$-0.138457\pi$
$863$	1.72047e7	+	1.24999e7i	0.786356	+	0.571321i	−0.120524	+	0.992710i	$0.538457\pi$
$864$	−6.70424e6	−	9.22759e6i	−0.305538	−	0.420537i
$865$			4.75584e6i			0.216116i
$866$	−1.31700e7	+	9.56859e6i	−0.596749	+	0.433564i
$867$	7.08000e7			3.19879
$868$	2.46166e6			0.110899
$869$	−7.47050e6	+	5.42763e6i	−0.335583	+	0.243815i
$870$	965647.	+	2.97196e6i	0.0432534	+	0.133120i
$871$	−4.36073e7	+	6.00203e7i	−1.94766	+	2.68073i
$872$	−1.81537e7	−	2.49864e7i	−0.808488	−	1.11279i
$873$	−722079.	+	2.22233e6i	−0.0320663	+	0.0986899i
$874$	−1.02293e6	−	3.14826e6i	−0.0452968	−	0.139409i
$875$			2.79255e6i			0.123305i
$876$	−1.72984e6	+	5.32389e6i	−0.0761631	+	0.234406i
$877$	1.22542e7	−	1.68664e7i	0.538003	−	0.740498i	−0.450320	−	0.892867i	$-0.648690\pi$
$877$	1.22542e7	−	1.68664e7i	0.538003	−	0.740498i	0.988324	+	0.152369i	$0.0486903\pi$
$878$	1.24811e7	−	4.05536e6i	0.546408	−	0.177539i
$879$	−6.49830e6	−	1.99997e7i	−0.283679	−	0.873075i
$880$	2.60262e6	+	845643.i	0.113293	+	0.0368112i
$881$	1.71394e7	−	1.24525e7i	0.743969	−	0.540525i	−0.149983	−	0.988689i	$-0.547922\pi$
$881$	1.71394e7	−	1.24525e7i	0.743969	−	0.540525i	0.893952	+	0.448164i	$0.147922\pi$
$882$	7.78669e6	+	2.53005e6i	0.337040	+	0.109511i
$883$			3.96893e7i			1.71306i	0.516100	+	0.856529i	$0.327383\pi$
$883$			3.96893e7i			1.71306i	−0.516100	+	0.856529i	$0.672617\pi$
$884$	3.62842e7	−	1.17894e7i	1.56166	−	0.507414i
$885$	1.51115e7	−	4.91001e6i	0.648557	−	0.210729i
$886$		−	1.41628e7i		−	0.606127i
$887$	−1.85160e7	−	6.01621e6i	−0.790202	−	0.256752i	−0.114012	−	0.993479i	$-0.536370\pi$
$887$	−1.85160e7	−	6.01621e6i	−0.790202	−	0.256752i	−0.676190	+	0.736727i	$0.736370\pi$
$888$	6.72029e6	−	4.88258e6i	0.285993	−	0.207786i
$889$	9696.70	+	3150.65i	0.000411500	+	0.000133704i
$890$	2.28624e6	+	7.03632e6i	0.0967490	+	0.297763i
$891$	−2.02721e7	+	6.58680e6i	−0.855468	+	0.277958i
$892$	−2.58178e6	+	3.55352e6i	−0.108644	+	0.149536i
$893$	−364745.	+	1.12257e6i	−0.0153060	+	0.0471069i
$894$		−	2.47277e7i		−	1.03476i
$895$	−5.31879e6	−	1.63696e7i	−0.221950	−	0.683092i
$896$	165067.	−	508023.i	0.00686893	−	0.0211404i
$897$	5.43206e7	+	7.47659e7i	2.25415	+	3.10258i
$898$	−671631.	+	924421.i	−0.0277933	+	0.0382542i
$899$	−3.89597e6	−	1.19906e7i	−0.160774	−	0.494812i
$900$	3.28479e6	−	2.38654e6i	0.135177	−	0.0982116i
$901$	−5.71836e7			−2.34671
$902$	−4.10348e6			−0.167933
$903$	−2.26969e6	+	1.64903e6i	−0.0926292	+	0.0672990i
$904$			3.54071e7i			1.44102i
$905$	−610714.	−	840576.i	−0.0247866	−	0.0341158i
$906$	1.33009e7	+	9.66368e6i	0.538345	+	0.391131i
$907$	−2.30217e6	−	3.16867e6i	−0.0929222	−	0.127896i	0.760025	−	0.649894i	$-0.225187\pi$
$907$	−2.30217e6	−	3.16867e6i	−0.0929222	−	0.127896i	−0.852947	+	0.521998i	$0.825187\pi$
$908$	6.04213e6	−	1.96321e6i	0.243207	−	0.0790226i
$909$	1.07879e7	−	1.48483e7i	0.433040	−	0.596028i
$910$	1.95111e6	+	1.41756e6i	0.0781048	+	0.0567465i
$911$	3.65956e6	+	2.65882e6i	0.146094	+	0.106144i	0.658431	−	0.752641i	$-0.271220\pi$
$911$	3.65956e6	+	2.65882e6i	0.146094	+	0.106144i	−0.512337	+	0.858784i	$0.671220\pi$
$912$	−353164.	+	1.08693e6i	−0.0140601	+	0.0432727i
$913$	−4.29934e6	−	1.39694e6i	−0.170696	−	0.0554626i
$914$	−1.73902e6			−0.0688555
$915$	1.11546e7	−	1.18775e7i	0.440456	−	0.468998i
$916$	5.32298e6			0.209612
$917$	3.09935e6	+	1.00704e6i	0.121716	+	0.0395478i
$918$	−6.76683e6	+	2.08262e7i	−0.265020	+	0.815648i
$919$	1.88063e7	+	1.36636e7i	0.734540	+	0.533675i	0.890997	−	0.454010i	$-0.150007\pi$
$919$	1.88063e7	+	1.36636e7i	0.734540	+	0.533675i	−0.156456	+	0.987685i	$0.550007\pi$
$920$	−1.98683e7	−	1.44351e7i	−0.773909	−	0.562278i
$921$	−2.96892e7	+	4.08637e7i	−1.15332	+	1.58741i
$922$	1.12017e7	−	3.63965e6i	0.433967	−	0.141004i
$923$	2.58718e7	+	3.56095e7i	0.999592	+	1.37582i
$924$	−1.17346e6	−	852571.i	−0.0452157	−	0.0328511i
$925$	−2.98600e6	−	4.10988e6i	−0.114745	−	0.157934i
$926$			6.03371e6i			0.231237i
$927$	2.76540e6	−	2.00918e6i	0.105696	−	0.0767927i
$928$	−6.57841e6			−0.250756
$929$	−1.86311e7			−0.708272			−0.354136	−	0.935194i	$-0.615225\pi$
$929$	−1.86311e7			−0.708272			−0.354136	+	0.935194i	$0.615225\pi$
$930$	−1.74943e7	+	1.27103e7i	−0.663267	+	0.481892i
$931$	−949074.	−	2.92095e6i	−0.0358861	−	0.110446i
$932$	−9.69123e6	+	1.33388e7i	−0.365459	+	0.503012i
$933$	2.66569e7	+	3.66901e7i	1.00255	+	1.37989i
$934$	−5.99133e6	+	1.84394e7i	−0.224727	+	0.691640i
$935$	5.94925e6	+	1.83099e7i	0.222553	+	0.684947i
$936$		−	2.62423e7i		−	0.979068i
$937$	−1.52480e6	+	4.69287e6i	−0.0567368	+	0.174618i	−0.975409	−	0.220403i	$-0.929263\pi$
$937$	−1.52480e6	+	4.69287e6i	−0.0567368	+	0.174618i	0.918672	+	0.395021i	$0.129263\pi$
$938$	2.81862e6	−	3.87950e6i	0.104599	−	0.143969i
$939$	2.32552e7	−	7.55607e6i	0.860709	−	0.279661i
$940$	861654.	+	2.65190e6i	0.0318063	+	0.0978897i
$941$	−1.71632e7	−	5.57665e6i	−0.631864	−	0.205305i	−0.0244631	−	0.999701i	$-0.507788\pi$
$941$	−1.71632e7	−	5.57665e6i	−0.631864	−	0.205305i	−0.607400	+	0.794396i	$0.707788\pi$
$942$	1.14513e7	−	8.31986e6i	0.420463	−	0.305484i
$943$	1.40924e7	+	4.57890e6i	0.516067	+	0.167680i
$944$		−	9.12813e6i		−	0.333390i
$945$	1.15435e6	−	375071.i	0.0420492	−	0.0136626i
$946$	9.47034e6	−	3.07710e6i	0.344063	−	0.111793i
$947$		−	4.37306e7i		−	1.58457i	−0.610153	−	0.792284i	$-0.708892\pi$
$947$		−	4.37306e7i		−	1.58457i	0.610153	−	0.792284i	$-0.291108\pi$
$948$	−8.66426e6	−	2.81519e6i	−0.313120	−	0.101739i
$949$	1.79008e7	−	1.30057e7i	0.645219	−	0.468779i
$950$	1.65201e6	+	536770.i	0.0593886	+	0.0192965i
$951$	1.55320e7	+	4.78025e7i	0.556897	+	1.71395i
$952$	−7.36528e6	+	2.39312e6i	−0.263389	+	0.0855801i
$953$	1.30729e6	−	1.79934e6i	0.0466274	−	0.0641771i	−0.785067	−	0.619411i	$-0.787371\pi$
$953$	1.30729e6	−	1.79934e6i	0.0466274	−	0.0641771i	0.831694	+	0.555234i	$0.187371\pi$
$954$	−3.87035e6	+	1.19117e7i	−0.137683	+	0.423744i
$955$		−	1.25402e6i		−	0.0444936i
$956$	3.93591e6	+	1.21135e7i	0.139284	+	0.428671i
$957$	−2.29562e6	+	7.06518e6i	−0.0810251	+	0.249370i
$958$	1.45163e7	+	1.99800e7i	0.511025	+	0.703365i
$959$	−2.34496e6	+	3.22757e6i	−0.0823360	+	0.113326i
$960$	5.27243e6	+	1.62269e7i	0.184643	+	0.568273i
$961$	4.74204e7	−	3.44529e7i	1.65637	−	1.20342i
$962$	−1.04551e7			−0.364243
$963$	−2.05757e6			−0.0714973
$964$	−994292.	+	722395.i	−0.0344605	+	0.0250370i
$965$			2.48314e7i			0.858387i
$966$	−3.51109e6	−	4.83260e6i	−0.121060	−	0.166624i
$967$	−1.04543e7	−	7.59549e6i	−0.359525	−	0.261210i	0.393329	−	0.919398i	$-0.371323\pi$
$967$	−1.04543e7	−	7.59549e6i	−0.359525	−	0.261210i	−0.752854	+	0.658188i	$0.771323\pi$
$968$	−8.84854e6	−	1.21790e7i	−0.303517	−	0.417756i
$969$	−7.64674e6	+	2.48458e6i	−0.261617	+	0.0850047i
$970$	−1.38810e6	+	1.91055e6i	−0.0473686	+	0.0651973i
$971$	−1.03165e7	−	7.49534e6i	−0.351142	−	0.255119i	0.398206	−	0.917296i	$-0.369633\pi$
$971$	−1.03165e7	−	7.49534e6i	−0.351142	−	0.255119i	−0.749348	+	0.662177i	$0.769633\pi$
$972$	−1.01348e7	−	7.36335e6i	−0.344072	−	0.249983i
$973$	−337114.	+	1.03753e6i	−0.0114155	+	0.0351333i
$974$	−3.55200e6	−	1.15411e6i	−0.119971	−	0.0389808i
$975$	−4.84940e7			−1.63372
$976$	−4.50926e6	−	8.20315e6i	−0.151524	−	0.275649i
$977$	8.26248e6			0.276933			0.138466	−	0.990367i	$-0.455783\pi$
$977$	8.26248e6			0.276933			0.138466	+	0.990367i	$0.455783\pi$
$978$	3.77970e7	+	1.22810e7i	1.26360	+	0.410569i
$979$	−5.43503e6	+	1.67273e7i	−0.181236	+	0.557788i
$980$	−5.86973e6	−	4.26461e6i	−0.195233	−	0.141845i
$981$	−1.54919e7	−	1.12555e7i	−0.513964	−	0.373416i
$982$	−9.39379e6	+	1.29294e7i	−0.310858	+	0.427859i
$983$	5.31028e7	−	1.72541e7i	1.75280	−	0.569520i	0.756389	−	0.654122i	$-0.226962\pi$
$983$	5.31028e7	−	1.72541e7i	1.75280	−	0.569520i	0.996415	+	0.0846019i	$0.0269618\pi$
$984$	−7.47307e6	−	1.02858e7i	−0.246043	−	0.338649i
$985$	−9.26207e6	−	6.72929e6i	−0.304171	−	0.220993i
$986$	7.42355e6	+	1.02176e7i	0.243175	+	0.334702i
$987$			2.12993e6i			0.0695942i
$988$	−2.53592e6	+	1.84246e6i	−0.0826502	+	0.0600489i
$989$	−3.59572e7			−1.16895
$990$	4.21674e6			0.136738
$991$	−3.83298e7	+	2.78482e7i	−1.23980	+	0.900770i	−0.997585	−	0.0694522i	$-0.977875\pi$
$991$	−3.83298e7	+	2.78482e7i	−1.23980	+	0.900770i	−0.242218	+	0.970222i	$0.577875\pi$
$992$	−1.40671e7	−	4.32941e7i	−0.453864	−	1.39685i
$993$	1.68093e7	−	2.31360e7i	0.540974	−	0.744587i
$994$	−1.67226e6	−	2.30167e6i	−0.0536832	−	0.0738885i
$995$	1.78596e6	−	5.49661e6i	0.0571891	−	0.176010i
$996$	−1.37820e6	−	4.24165e6i	−0.0440213	−	0.135483i
$997$		−	4.34738e7i		−	1.38513i	−0.721357	−	0.692563i	$-0.756481\pi$
$997$		−	4.34738e7i		−	1.38513i	0.721357	−	0.692563i	$-0.243519\pi$
$998$	9.97874e6	−	3.07114e7i	0.317139	−	0.976052i
$999$	−3.09282e6	+	4.25690e6i	−0.0980485	+	0.134952i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	61.6.g.a.3.18	✓	104
61.41	even	10	inner	61.6.g.a.41.18	yes	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.6.g.a.3.18	✓	104	1.1	even	1	trivial
61.6.g.a.41.18	yes	104	61.41	even	10	inner

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:	\( N \)	\(=\)	\( 61 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	61.g (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.92707 + 1.27598i) q^{2} +(-5.88917 + 18.1250i) q^{3} +(-12.0948 - 8.78737i) q^{4} +(-23.8009 - 17.2924i) q^{5} +(-46.2544 + 63.6637i) q^{6} +(16.7659 - 5.44756i) q^{7} +(-113.951 - 156.840i) q^{8} +(-97.2426 - 70.6509i) q^{9} +O(q^{10})\)	\(q+(3.92707 + 1.27598i) q^{2} +(-5.88917 + 18.1250i) q^{3} +(-12.0948 - 8.78737i) q^{4} +(-23.8009 - 17.2924i) q^{5} +(-46.2544 + 63.6637i) q^{6} +(16.7659 - 5.44756i) q^{7} +(-113.951 - 156.840i) q^{8} +(-97.2426 - 70.6509i) q^{9} +(-71.4031 - 98.2779i) q^{10} -288.788i q^{11} +(230.500 - 167.468i) q^{12} -1126.17 q^{13} +72.7918 q^{14} +(453.592 - 329.554i) q^{15} +(-99.5341 - 306.334i) q^{16} +(1331.94 - 1833.25i) q^{17} +(-291.729 - 401.531i) q^{18} +(-57.5328 + 177.068i) q^{19} +(135.912 + 418.295i) q^{20} +335.963i q^{21} +(368.489 - 1134.09i) q^{22} +(-2530.97 + 3483.58i) q^{23} +(3513.79 - 1141.70i) q^{24} +(-698.221 - 2148.90i) q^{25} +(-4422.56 - 1436.98i) q^{26} +(-1893.36 + 1375.61i) q^{27} +(-250.649 - 81.4409i) q^{28} +1349.79i q^{29} +(2201.79 - 715.406i) q^{30} +(-8883.29 + 2886.36i) q^{31} +4873.66i q^{32} +(5234.29 + 1700.72i) q^{33} +(7569.81 - 5499.79i) q^{34} +(-493.244 - 160.265i) q^{35} +(555.293 + 1709.01i) q^{36} +(2138.29 - 694.773i) q^{37} +(-451.871 + 621.946i) q^{38} +(6632.23 - 20411.9i) q^{39} +5703.40i q^{40} +(-1063.39 - 3272.78i) q^{41} +(-428.684 + 1319.35i) q^{42} +(4908.36 + 6755.77i) q^{43} +(-2537.69 + 3492.83i) q^{44} +(1092.74 + 3363.11i) q^{45} +(-14384.3 + 10450.8i) q^{46} +6339.78 q^{47} +6138.49 q^{48} +(-13345.7 + 9696.24i) q^{49} -9329.82i q^{50} +(25383.7 + 34937.7i) q^{51} +(13620.8 + 9896.11i) q^{52} +(-14832.9 - 20415.7i) q^{53} +(-9190.61 + 2986.21i) q^{54} +(-4993.83 + 6873.42i) q^{55} +(-2764.88 - 2008.80i) q^{56} +(-2870.53 - 2085.56i) q^{57} +(-1722.31 + 5300.72i) q^{58} +(26952.5 + 8757.39i) q^{59} -8382.01 q^{60} +(28547.4 - 5444.43i) q^{61} -38568.3 q^{62} +(-2015.23 - 654.789i) q^{63} +(-9403.79 + 28941.9i) q^{64} +(26803.9 + 19474.2i) q^{65} +(18385.3 + 13357.7i) q^{66} +(38721.6 - 53295.8i) q^{67} +(-32219.0 + 10468.6i) q^{68} +(-48234.7 - 66389.3i) q^{69} +(-1732.51 - 1258.74i) q^{70} +(-22973.2 - 31619.9i) q^{71} +23302.2i q^{72} +(-15895.3 + 11548.6i) q^{73} +9283.74 q^{74} +43060.9 q^{75} +(2251.81 - 1636.03i) q^{76} +(-1573.19 - 4841.79i) q^{77} +(52090.5 - 71696.4i) q^{78} +(-18794.5 - 25868.4i) q^{79} +(-2928.25 + 9012.22i) q^{80} +(-22808.4 - 70197.1i) q^{81} -14209.3i q^{82} +(4837.25 - 14887.5i) q^{83} +(2952.24 - 4063.40i) q^{84} +(-63402.6 + 20600.8i) q^{85} +(10655.2 + 32793.4i) q^{86} +(-24464.9 - 7949.14i) q^{87} +(-45293.4 + 32907.6i) q^{88} +(-57922.5 - 18820.2i) q^{89} +14601.5i q^{90} +(-18881.3 + 6134.90i) q^{91} +(61223.1 - 19892.6i) q^{92} -178008. i q^{93} +(24896.8 + 8089.45i) q^{94} +(4431.25 - 3219.49i) q^{95} +(-88335.1 - 28701.8i) q^{96} +(-6007.38 - 18488.8i) q^{97} +(-64781.9 + 21048.9i) q^{98} +(-20403.1 + 28082.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 5 q^{2} + 15 q^{3} + 465 q^{4} - 122 q^{5} + 445 q^{6} + 230 q^{7} - 5 q^{8} - 2841 q^{9}+O(q^{10}) \) 104 * q - 5 * q^2 + 15 * q^3 + 465 * q^4 - 122 * q^5 + 445 * q^6 + 230 * q^7 - 5 * q^8 - 2841 * q^9	\( 104 q - 5 q^{2} + 15 q^{3} + 465 q^{4} - 122 q^{5} + 445 q^{6} + 230 q^{7} - 5 q^{8} - 2841 q^{9} - 595 q^{10} + 1982 q^{12} + 2372 q^{13} - 4474 q^{14} - 1149 q^{15} - 8631 q^{16} + 950 q^{17} + 4340 q^{18} - 5597 q^{19} - 6627 q^{20} - 8639 q^{22} + 9065 q^{23} + 17220 q^{24} - 7694 q^{25} + 14810 q^{26} + 4500 q^{27} + 19835 q^{28} - 44585 q^{30} + 10905 q^{31} - 19205 q^{33} - 15376 q^{34} - 43790 q^{35} - 25135 q^{36} - 5 q^{37} + 17555 q^{38} + 29401 q^{39} - 21014 q^{41} + 62197 q^{42} - 31625 q^{43} + 146190 q^{44} + 153742 q^{45} + 13387 q^{46} + 27326 q^{47} - 82968 q^{48} + 14694 q^{49} + 34090 q^{51} + 90072 q^{52} - 40270 q^{53} - 13760 q^{54} + 25140 q^{55} - 97860 q^{56} + 114893 q^{57} - 18003 q^{58} - 117435 q^{59} - 536650 q^{60} - 121867 q^{61} - 157388 q^{62} - 160825 q^{63} + 132509 q^{64} - 155852 q^{65} + 308443 q^{66} + 101665 q^{67} + 303780 q^{68} + 281945 q^{69} + 264985 q^{70} + 160970 q^{71} + 127669 q^{73} - 133952 q^{74} - 139592 q^{75} - 641111 q^{76} + 128917 q^{77} + 1670 q^{78} + 187940 q^{79} + 785373 q^{80} - 453473 q^{81} - 301209 q^{83} + 100475 q^{84} - 340045 q^{85} - 462669 q^{86} + 189245 q^{87} - 881635 q^{88} - 201970 q^{89} + 93865 q^{91} - 622085 q^{92} - 285265 q^{94} - 113308 q^{95} + 1215465 q^{96} - 342131 q^{97} - 616150 q^{98} + 714235 q^{99}+O(q^{100}) \) 104 * q - 5 * q^2 + 15 * q^3 + 465 * q^4 - 122 * q^5 + 445 * q^6 + 230 * q^7 - 5 * q^8 - 2841 * q^9 - 595 * q^10 + 1982 * q^12 + 2372 * q^13 - 4474 * q^14 - 1149 * q^15 - 8631 * q^16 + 950 * q^17 + 4340 * q^18 - 5597 * q^19 - 6627 * q^20 - 8639 * q^22 + 9065 * q^23 + 17220 * q^24 - 7694 * q^25 + 14810 * q^26 + 4500 * q^27 + 19835 * q^28 - 44585 * q^30 + 10905 * q^31 - 19205 * q^33 - 15376 * q^34 - 43790 * q^35 - 25135 * q^36 - 5 * q^37 + 17555 * q^38 + 29401 * q^39 - 21014 * q^41 + 62197 * q^42 - 31625 * q^43 + 146190 * q^44 + 153742 * q^45 + 13387 * q^46 + 27326 * q^47 - 82968 * q^48 + 14694 * q^49 + 34090 * q^51 + 90072 * q^52 - 40270 * q^53 - 13760 * q^54 + 25140 * q^55 - 97860 * q^56 + 114893 * q^57 - 18003 * q^58 - 117435 * q^59 - 536650 * q^60 - 121867 * q^61 - 157388 * q^62 - 160825 * q^63 + 132509 * q^64 - 155852 * q^65 + 308443 * q^66 + 101665 * q^67 + 303780 * q^68 + 281945 * q^69 + 264985 * q^70 + 160970 * q^71 + 127669 * q^73 - 133952 * q^74 - 139592 * q^75 - 641111 * q^76 + 128917 * q^77 + 1670 * q^78 + 187940 * q^79 + 785373 * q^80 - 453473 * q^81 - 301209 * q^83 + 100475 * q^84 - 340045 * q^85 - 462669 * q^86 + 189245 * q^87 - 881635 * q^88 - 201970 * q^89 + 93865 * q^91 - 622085 * q^92 - 285265 * q^94 - 113308 * q^95 + 1215465 * q^96 - 342131 * q^97 - 616150 * q^98 + 714235 * q^99

Introduction

L-functions

Modular forms

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