LMFDB - Embedded newform 76.4.d.a.75.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,4,Mod(75,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("76.75");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	76.d (of order $2$, degree $1$, 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:	$4.48414516044$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			75.8
Character	$\chi$	$=$	76.75
Dual form			76.4.d.a.75.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.25296 + 1.71002i) q^{2} -8.24449 q^{3} +(2.15167 - 7.70521i) q^{4} -10.8316 q^{5} +(18.5745 - 14.0982i) q^{6} -8.32669i q^{7} +(8.32842 + 21.0389i) q^{8} +40.9716 q^{9} +O(q^{10})$	\(q+(-2.25296 + 1.71002i) q^{2} -8.24449 q^{3} +(2.15167 - 7.70521i) q^{4} -10.8316 q^{5} +(18.5745 - 14.0982i) q^{6} -8.32669i q^{7} +(8.32842 + 21.0389i) q^{8} +40.9716 q^{9} +(24.4032 - 18.5223i) q^{10} +53.9788i q^{11} +(-17.7394 + 63.5255i) q^{12} -43.7588i q^{13} +(14.2388 + 18.7597i) q^{14} +89.3011 q^{15} +(-54.7406 - 33.1582i) q^{16} +91.7057 q^{17} +(-92.3075 + 70.0622i) q^{18} +(54.7519 + 62.1388i) q^{19} +(-23.3061 + 83.4599i) q^{20} +68.6493i q^{21} +(-92.3047 - 121.612i) q^{22} -172.737i q^{23} +(-68.6636 - 173.455i) q^{24} -7.67618 q^{25} +(74.8283 + 98.5868i) q^{26} -115.189 q^{27} +(-64.1589 - 17.9163i) q^{28} -3.12725i q^{29} +(-201.192 + 152.707i) q^{30} +113.134 q^{31} +(180.030 - 18.9033i) q^{32} -445.027i q^{33} +(-206.609 + 156.818i) q^{34} +90.1914i q^{35} +(88.1575 - 315.695i) q^{36} -159.274i q^{37} +(-229.612 - 46.3695i) q^{38} +360.769i q^{39} +(-90.2102 - 227.886i) q^{40} +205.704i q^{41} +(-117.392 - 154.664i) q^{42} +28.4169i q^{43} +(415.918 + 116.145i) q^{44} -443.789 q^{45} +(295.384 + 389.170i) q^{46} +62.4555i q^{47} +(451.308 + 273.372i) q^{48} +273.666 q^{49} +(17.2941 - 13.1264i) q^{50} -756.067 q^{51} +(-337.171 - 94.1545i) q^{52} +650.269i q^{53} +(259.516 - 196.975i) q^{54} -584.677i q^{55} +(175.185 - 69.3482i) q^{56} +(-451.402 - 512.303i) q^{57} +(5.34765 + 7.04557i) q^{58} +792.302 q^{59} +(192.147 - 688.084i) q^{60} +30.4890 q^{61} +(-254.887 + 193.461i) q^{62} -341.158i q^{63} +(-373.275 + 350.442i) q^{64} +473.978i q^{65} +(761.005 + 1002.63i) q^{66} -278.499 q^{67} +(197.321 - 706.612i) q^{68} +1424.13i q^{69} +(-154.229 - 203.198i) q^{70} -74.0407 q^{71} +(341.229 + 862.000i) q^{72} +1117.76 q^{73} +(272.361 + 358.838i) q^{74} +63.2862 q^{75} +(596.601 - 288.173i) q^{76} +449.464 q^{77} +(-616.921 - 812.798i) q^{78} +51.9803 q^{79} +(592.929 + 359.157i) q^{80} -156.561 q^{81} +(-351.758 - 463.444i) q^{82} -1138.79i q^{83} +(528.957 + 147.711i) q^{84} -993.321 q^{85} +(-48.5934 - 64.0222i) q^{86} +25.7826i q^{87} +(-1135.66 + 449.558i) q^{88} -1036.42i q^{89} +(999.839 - 758.887i) q^{90} -364.365 q^{91} +(-1330.98 - 371.674i) q^{92} -932.733 q^{93} +(-106.800 - 140.710i) q^{94} +(-593.051 - 673.063i) q^{95} +(-1484.25 + 155.848i) q^{96} -145.329i q^{97} +(-616.560 + 467.974i) q^{98} +2211.60i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 10 q^{4} - 4 q^{5} - 6 q^{6} + 192 q^{9}+O(q^{10}) $ 28 * q + 10 * q^4 - 4 * q^5 - 6 * q^6 + 192 * q^9	$ 28 q + 10 q^{4} - 4 q^{5} - 6 q^{6} + 192 q^{9} - 134 q^{16} - 80 q^{17} - 300 q^{20} - 26 q^{24} + 496 q^{25} - 90 q^{26} + 254 q^{28} - 16 q^{30} - 556 q^{36} - 626 q^{38} - 850 q^{42} + 976 q^{44} - 612 q^{45} + 188 q^{49} + 354 q^{54} - 580 q^{57} + 2534 q^{58} - 948 q^{61} - 1068 q^{62} - 1634 q^{64} + 1244 q^{66} + 1630 q^{68} - 184 q^{73} + 2276 q^{74} + 1688 q^{76} + 308 q^{77} + 3376 q^{80} - 2284 q^{81} - 740 q^{82} + 684 q^{85} + 1810 q^{92} + 824 q^{93} - 5222 q^{96}+O(q^{100}) $ 28 * q + 10 * q^4 - 4 * q^5 - 6 * q^6 + 192 * q^9 - 134 * q^16 - 80 * q^17 - 300 * q^20 - 26 * q^24 + 496 * q^25 - 90 * q^26 + 254 * q^28 - 16 * q^30 - 556 * q^36 - 626 * q^38 - 850 * q^42 + 976 * q^44 - 612 * q^45 + 188 * q^49 + 354 * q^54 - 580 * q^57 + 2534 * q^58 - 948 * q^61 - 1068 * q^62 - 1634 * q^64 + 1244 * q^66 + 1630 * q^68 - 184 * q^73 + 2276 * q^74 + 1688 * q^76 + 308 * q^77 + 3376 * q^80 - 2284 * q^81 - 740 * q^82 + 684 * q^85 + 1810 * q^92 + 824 * q^93 - 5222 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−2.25296	+	1.71002i	−0.796542	+	0.604583i
$2$	−2.25296	+	1.71002i	−0.796542	+	0.604583i
$3$	−8.24449			−1.58665			−0.793326	−	0.608797i	$-0.791653\pi$
$3$	−8.24449			−1.58665			−0.793326	+	0.608797i	$0.791653\pi$
$4$	2.15167	−	7.70521i	0.268959	−	0.963152i
$5$	−10.8316			−0.968809			−0.484404	−	0.874844i	$-0.660964\pi$
$5$	−10.8316			−0.968809			−0.484404	+	0.874844i	$0.660964\pi$
$6$	18.5745	−	14.0982i	1.26384	−	0.959263i
$7$		−	8.32669i		−	0.449599i	−0.974405	−	0.224799i	$-0.927827\pi$
$7$		−	8.32669i		−	0.449599i	0.974405	−	0.224799i	$-0.0721727\pi$
$8$	8.32842	+	21.0389i	0.368068	+	0.929799i
$9$	40.9716			1.51747
$10$	24.4032	−	18.5223i	0.771697	−	0.585725i
$11$			53.9788i			1.47956i	0.672846	+	0.739782i	$0.265072\pi$
$11$			53.9788i			1.47956i	−0.672846	+	0.739782i	$0.734928\pi$
$12$	−17.7394	+	63.5255i	−0.426745	+	1.52819i
$13$		−	43.7588i		−	0.933577i	−0.884369	−	0.466788i	$-0.845411\pi$
$13$		−	43.7588i		−	0.933577i	0.884369	−	0.466788i	$-0.154589\pi$
$14$	14.2388	+	18.7597i	0.271820	+	0.358124i
$15$	89.3011			1.53716
$16$	−54.7406	−	33.1582i	−0.855322	−	0.518097i
$17$	91.7057			1.30835			0.654174	−	0.756344i	$-0.273017\pi$
$17$	91.7057			1.30835			0.654174	+	0.756344i	$0.273017\pi$
$18$	−92.3075	+	70.0622i	−1.20873	+	0.917435i
$19$	54.7519	+	62.1388i	0.661103	+	0.750296i
$19$	54.7519	+	62.1388i	0.661103	+	0.750296i
$20$	−23.3061	+	83.4599i	−0.260570	+	0.933110i
$21$			68.6493i			0.713357i
$22$	−92.3047	−	121.612i	−0.894519	−	1.17854i
$23$		−	172.737i		−	1.56601i	−0.622017	−	0.783004i	$-0.713686\pi$
$23$		−	172.737i		−	1.56601i	0.622017	−	0.783004i	$-0.286314\pi$
$24$	−68.6636	−	173.455i	−0.583996	−	1.47527i
$25$	−7.67618			−0.0614095
$26$	74.8283	+	98.5868i	0.564424	+	0.743633i
$27$	−115.189			−0.821041
$28$	−64.1589	−	17.9163i	−0.433032	−	0.120924i
$29$		−	3.12725i		−	0.0200247i	−0.999950	−	0.0100123i	$-0.996813\pi$
$29$		−	3.12725i		−	0.0200247i	0.999950	−	0.0100123i	$-0.00318708\pi$
$30$	−201.192	+	152.707i	−1.22442	+	0.929343i
$31$	113.134			0.655467			0.327734	−	0.944770i	$-0.393715\pi$
$31$	113.134			0.655467			0.327734	+	0.944770i	$0.393715\pi$
$32$	180.030	−	18.9033i	0.994533	−	0.104427i
$33$		−	445.027i		−	2.34756i
$34$	−206.609	+	156.818i	−1.04215	+	0.791004i
$35$			90.1914i			0.435575i
$36$	88.1575	−	315.695i	0.408137	−	1.46155i
$37$		−	159.274i		−	0.707688i	−0.935304	−	0.353844i	$-0.884874\pi$
$37$		−	159.274i		−	0.707688i	0.935304	−	0.353844i	$-0.115126\pi$
$38$	−229.612	−	46.3695i	−0.980212	−	0.197951i
$39$			360.769i			1.48126i
$40$	−90.2102	−	227.886i	−0.356587	−	0.900797i
$41$			205.704i			0.783551i	0.920061	+	0.391776i	$0.128139\pi$
$41$			205.704i			0.783551i	−0.920061	+	0.391776i	$0.871861\pi$
$42$	−117.392	−	154.664i	−0.431284	−	0.568219i
$43$			28.4169i			0.100780i	0.998730	+	0.0503899i	$0.0160464\pi$
$43$			28.4169i			0.100780i	−0.998730	+	0.0503899i	$0.983954\pi$
$44$	415.918	+	116.145i	1.42505	+	0.397942i
$45$	−443.789			−1.47014
$46$	295.384	+	389.170i	0.946782	+	1.24739i
$47$			62.4555i			0.193831i	0.995293	+	0.0969156i	$0.0308977\pi$
$47$			62.4555i			0.193831i	−0.995293	+	0.0969156i	$0.969102\pi$
$48$	451.308	+	273.372i	1.35710	+	0.822040i
$49$	273.666			0.797861
$50$	17.2941	−	13.1264i	0.0489152	−	0.0371271i
$51$	−756.067			−2.07589
$52$	−337.171	−	94.1545i	−0.899176	−	0.251094i
$53$			650.269i			1.68531i	0.538456	+	0.842654i	$0.319008\pi$
$53$			650.269i			1.68531i	−0.538456	+	0.842654i	$0.680992\pi$
$54$	259.516	−	196.975i	0.653994	−	0.496387i
$55$		−	584.677i		−	1.43342i
$56$	175.185	−	69.3482i	0.418037	−	0.165483i
$57$	−451.402	−	512.303i	−1.04894	−	1.19046i
$58$	5.34765	+	7.04557i	0.0121066	+	0.0159505i
$59$	792.302			1.74829			0.874144	−	0.485667i	$-0.161423\pi$
$59$	792.302			1.74829			0.874144	+	0.485667i	$0.161423\pi$
$60$	192.147	−	688.084i	0.413434	−	1.48052i
$61$	30.4890			0.0639953			0.0319976	−	0.999488i	$-0.489813\pi$
$61$	30.4890			0.0639953			0.0319976	+	0.999488i	$0.489813\pi$
$62$	−254.887	+	193.461i	−0.522107	+	0.396284i
$63$		−	341.158i		−	0.682251i
$64$	−373.275	+	350.442i	−0.729052	+	0.684458i
$65$			473.978i			0.904457i
$66$	761.005	+	1002.63i	1.41929	+	1.86993i
$67$	−278.499			−0.507822			−0.253911	−	0.967228i	$-0.581717\pi$
$67$	−278.499			−0.507822			−0.253911	+	0.967228i	$0.581717\pi$
$68$	197.321	−	706.612i	0.351892	−	1.26014i
$69$			1424.13i			2.48471i
$70$	−154.229	−	203.198i	−0.263341	−	0.346954i
$71$	−74.0407			−0.123761			−0.0618804	−	0.998084i	$-0.519710\pi$
$71$	−74.0407			−0.123761			−0.0618804	+	0.998084i	$0.519710\pi$
$72$	341.229	+	862.000i	0.558531	+	1.41094i
$73$	1117.76			1.79210			0.896052	−	0.443950i	$-0.146423\pi$
$73$	1117.76			1.79210			0.896052	+	0.443950i	$0.146423\pi$
$74$	272.361	+	358.838i	0.427856	+	0.563703i
$75$	63.2862			0.0974355
$76$	596.601	−	288.173i	0.900458	−	0.434943i
$77$	449.464			0.665211
$78$	−616.921	−	812.798i	−0.895546	−	1.17989i
$79$	51.9803			0.0740284			0.0370142	−	0.999315i	$-0.488215\pi$
$79$	51.9803			0.0740284			0.0370142	+	0.999315i	$0.488215\pi$
$80$	592.929	+	359.157i	0.828644	+	0.501937i
$81$	−156.561			−0.214761
$82$	−351.758	−	463.444i	−0.473722	−	0.624132i
$83$		−	1138.79i		−	1.50600i	−0.658020	−	0.753001i	$-0.728606\pi$
$83$		−	1138.79i		−	1.50600i	0.658020	−	0.753001i	$-0.271394\pi$
$84$	528.957	+	147.711i	0.687071	+	0.191864i
$85$	−993.321			−1.26754
$86$	−48.5934	−	64.0222i	−0.0609298	−	0.0802754i
$87$			25.7826i			0.0317722i
$88$	−1135.66	+	449.558i	−1.37570	+	0.544580i
$89$		−	1036.42i		−	1.23439i	−0.786810	−	0.617195i	$-0.788269\pi$
$89$		−	1036.42i		−	1.23439i	0.786810	−	0.617195i	$-0.211731\pi$
$90$	999.839	−	758.887i	1.17103	−	0.888819i
$91$	−364.365			−0.419735
$92$	−1330.98	−	371.674i	−1.50830	−	0.421192i
$93$	−932.733			−1.04000
$94$	−106.800	−	140.710i	−0.117187	−	0.154395i
$95$	−593.051	−	673.063i	−0.640482	−	0.726893i
$96$	−1484.25	+	155.848i	−1.57798	+	0.165690i
$97$		−	145.329i		−	0.152123i	−0.997103	−	0.0760616i	$-0.975765\pi$
$97$		−	145.329i		−	0.152123i	0.997103	−	0.0760616i	$-0.0242346\pi$
$98$	−616.560	+	467.974i	−0.635530	+	0.482373i
$99$			2211.60i			2.24519i
$100$	−16.5166	+	59.1466i	−0.0165166	+	0.0591466i
$101$	−120.050			−0.118272			−0.0591359	−	0.998250i	$-0.518835\pi$
$101$	−120.050			−0.118272			−0.0591359	+	0.998250i	$0.518835\pi$
$102$	1703.39	−	1292.89i	1.65354	−	1.25505i
$103$	467.567			0.447289			0.223644	−	0.974671i	$-0.428205\pi$
$103$	467.567			0.447289			0.223644	+	0.974671i	$0.428205\pi$
$104$	920.638	−	364.441i	0.868039	−	0.343619i
$105$		−	743.582i		−	0.691107i
$106$	−1111.97	−	1465.03i	−1.01891	−	1.34242i
$107$	−402.048			−0.363247			−0.181624	−	0.983368i	$-0.558135\pi$
$107$	−402.048			−0.363247			−0.181624	+	0.983368i	$0.558135\pi$
$108$	−247.849	+	887.554i	−0.220826	+	0.790787i
$109$		−	1409.93i		−	1.23896i	−0.785013	−	0.619479i	$-0.787344\pi$
$109$		−	1409.93i		−	1.23896i	0.785013	−	0.619479i	$-0.212656\pi$
$110$	999.809	+	1317.26i	0.866618	+	1.14178i
$111$			1313.13i			1.12286i
$112$	−276.098	+	455.808i	−0.232936	+	0.384552i
$113$			2163.38i			1.80100i	0.434854	+	0.900501i	$0.356800\pi$
$113$			2163.38i			1.80100i	−0.434854	+	0.900501i	$0.643200\pi$
$114$	1893.04	+	382.293i	1.55526	+	0.314079i
$115$			1871.02i			1.51716i
$116$	−24.0961	−	6.72882i	−0.0192868	−	0.00538582i
$117$		−	1792.87i		−	1.41667i
$118$	−1785.03	+	1354.85i	−1.39259	+	1.05699i
$119$		−	763.605i		−	0.588231i
$120$	743.737	+	1878.80i	0.565780	+	1.42925i
$121$	−1582.71			−1.18911
$122$	−68.6905	+	52.1367i	−0.0509749	+	0.0386905i
$123$		−	1695.93i		−	1.24322i
$124$	243.428	−	871.722i	0.176294	−	0.631314i
$125$	1437.10			1.02830
$126$	583.386	+	768.615i	0.412478	+	0.543442i
$127$	1117.34			0.780695			0.390348	−	0.920668i	$-0.372355\pi$
$127$	1117.34			0.780695			0.390348	+	0.920668i	$0.372355\pi$
$128$	241.711	−	1427.84i	0.166909	−	0.985972i
$129$		−	234.283i		−	0.159903i
$130$	−810.511	−	1067.85i	−0.546819	−	0.720438i
$131$			1499.93i			1.00037i	0.865917	+	0.500187i	$0.166736\pi$
$131$			1499.93i			1.00037i	−0.865917	+	0.500187i	$0.833264\pi$
$132$	−3429.03	−	957.553i	−2.26105	−	0.631396i
$133$	517.410	−	455.902i	0.337332	−	0.297231i
$134$	627.447	−	476.238i	0.404501	−	0.307020i
$135$	1247.68			0.795431
$136$	763.764	+	1929.39i	0.481560	+	1.21650i
$137$	845.590			0.527326			0.263663	−	0.964615i	$-0.415069\pi$
$137$	845.590			0.527326			0.263663	+	0.964615i	$0.415069\pi$
$138$	−2435.29	−	3208.51i	−1.50221	−	1.97918i
$139$		−	1116.12i		−	0.681063i	−0.940233	−	0.340532i	$-0.889393\pi$
$139$		−	1116.12i		−	0.681063i	0.940233	−	0.340532i	$-0.110607\pi$
$140$	694.944	+	194.062i	0.419525	+	0.117152i
$141$		−	514.914i		−	0.307543i
$142$	166.811	−	126.611i	0.0985807	−	0.0748237i
$143$	2362.04			1.38129
$144$	−2242.81	−	1358.54i	−1.29792	−	0.786195i
$145$			33.8731i			0.0194001i
$146$	−2518.26	+	1911.39i	−1.42749	+	1.08348i
$147$	−2256.24			−1.26593
$148$	−1227.24	−	342.705i	−0.681611	−	0.190339i
$149$	2000.12			1.09971			0.549854	−	0.835261i	$-0.314683\pi$
$149$	2000.12			1.09971			0.549854	+	0.835261i	$0.314683\pi$
$150$	−142.581	+	108.221i	−0.0776115	+	0.0589078i
$151$	2532.76			1.36499			0.682494	−	0.730891i	$-0.260895\pi$
$151$	2532.76			1.36499			0.682494	+	0.730891i	$0.260895\pi$
$152$	−851.338	+	1669.44i	−0.454294	+	0.890852i
$153$	3757.33			1.98537
$154$	−1012.63	+	768.592i	−0.529868	+	0.402175i
$155$	−1225.42			−0.635022
$156$	2779.80	+	776.256i	1.42668	+	0.398399i
$157$	2373.98			1.20678			0.603389	−	0.797447i	$-0.293817\pi$
$157$	2373.98			1.20678			0.603389	+	0.797447i	$0.293817\pi$
$158$	−117.110	+	88.8873i	−0.0589667	+	0.0447563i
$159$		−	5361.13i		−	2.67400i
$160$	−1950.01	+	204.753i	−0.963512	+	0.101170i
$161$	−1438.33			−0.704075
$162$	352.725	−	267.721i	0.171066	−	0.129841i
$163$			858.761i			0.412659i	0.978483	+	0.206329i	$0.0661518\pi$
$163$			858.761i			0.412659i	−0.978483	+	0.206329i	$0.933848\pi$
$164$	1585.00	+	442.608i	0.754679	+	0.210743i
$165$			4820.36i			2.27433i
$166$	1947.35	+	2565.64i	0.910503	+	1.19959i
$167$	−3711.38			−1.71973			−0.859866	−	0.510520i	$-0.829453\pi$
$167$	−3711.38			−1.71973			−0.859866	+	0.510520i	$0.829453\pi$
$168$	−1444.31	+	571.740i	−0.663279	+	0.262564i
$169$	282.171			0.128435
$170$	2237.91	−	1698.60i	1.00965	−	0.766332i
$171$	2243.27	+	2545.93i	1.00320	+	1.13855i
$172$	218.958	+	61.1438i	0.0970663	+	0.0271057i
$173$		−	1139.19i		−	0.500642i	−0.968163	−	0.250321i	$-0.919464\pi$
$173$		−	1139.19i		−	0.500642i	0.968163	−	0.250321i	$-0.0805361\pi$
$174$	−44.0887	−	58.0871i	−0.0192089	−	0.0253079i
$175$			63.9172i			0.0276096i
$176$	1789.84	−	2954.83i	0.766558	−	1.26550i
$177$	−6532.13			−2.77393
$178$	1772.30	+	2335.02i	0.746291	+	0.983244i
$179$	441.493			0.184350			0.0921752	−	0.995743i	$-0.470618\pi$
$179$	441.493			0.184350			0.0921752	+	0.995743i	$0.470618\pi$
$180$	−954.888	+	3419.49i	−0.395406	+	1.41596i
$181$		−	3285.85i		−	1.34936i	−0.738108	−	0.674682i	$-0.764281\pi$
$181$		−	3285.85i		−	1.34936i	0.738108	−	0.674682i	$-0.235719\pi$
$182$	820.901	−	623.072i	0.334337	−	0.253765i
$183$	−251.366			−0.101538
$184$	3634.21	−	1438.63i	1.45607	−	0.576397i
$185$			1725.19i			0.685614i
$186$	2101.41	−	1594.99i	0.828403	−	0.628765i
$187$			4950.16i			1.93578i
$188$	481.233	+	134.384i	0.186689	+	0.0521327i
$189$			959.141i			0.369139i
$190$	2487.07	+	502.257i	0.949638	+	0.191776i
$191$			2470.17i			0.935785i	0.883785	+	0.467893i	$0.154987\pi$
$191$			2470.17i			0.935785i	−0.883785	+	0.467893i	$0.845013\pi$
$192$	3077.46	−	2889.22i	1.15675	−	1.08600i
$193$			945.372i			0.352588i	0.984338	+	0.176294i	$0.0564109\pi$
$193$			945.372i			0.352588i	−0.984338	+	0.176294i	$0.943589\pi$
$194$	248.516	+	327.421i	0.0919710	+	0.121173i
$195$		−	3907.71i		−	1.43506i
$196$	588.840	−	2108.66i	0.214592	−	0.768461i
$197$	−4310.10			−1.55879			−0.779396	−	0.626531i	$-0.784474\pi$
$197$	−4310.10			−1.55879			−0.779396	+	0.626531i	$0.784474\pi$
$198$	−3781.87	−	4982.64i	−1.35740	−	1.78839i
$199$			3934.47i			1.40155i	0.713385	+	0.700773i	$0.247161\pi$
$199$			3934.47i			1.40155i	−0.713385	+	0.700773i	$0.752839\pi$
$200$	−63.9305	−	161.499i	−0.0226028	−	0.0570985i
$201$	2296.08			0.805737
$202$	270.469	−	205.288i	0.0942085	−	0.0715051i
$203$	−26.0396			−0.00900307
$204$	−1626.81	+	5825.66i	−0.558330	+	1.99940i
$205$		−	2228.11i		−	0.759111i
$206$	−1053.41	+	799.548i	−0.356284	+	0.270423i
$207$		−	7077.32i		−	2.37637i
$208$	−1450.96	+	2395.38i	−0.483683	+	0.798509i
$209$	−3354.18	+	2955.44i	−1.11011	+	0.978144i
$210$	1271.54	+	1675.26i	0.417831	+	0.550496i
$211$	−618.267			−0.201722			−0.100861	−	0.994901i	$-0.532160\pi$
$211$	−618.267			−0.201722			−0.100861	+	0.994901i	$0.532160\pi$
$212$	5010.46	+	1399.17i	1.62321	+	0.453279i
$213$	610.428			0.196365
$214$	905.799	−	687.510i	0.289342	−	0.219613i
$215$		−	307.801i		−	0.0976364i
$216$	−959.341	−	2423.45i	−0.302199	−	0.763403i
$217$		−	942.032i		−	0.294697i
$218$	2411.00	+	3176.51i	0.749053	+	0.986882i
$219$	−9215.34			−2.84345
$220$	−4505.06	−	1258.03i	−1.38060	−	0.385530i
$221$		−	4012.93i		−	1.22144i
$222$	−2245.48	−	2958.43i	−0.678859	−	0.894402i
$223$	2321.60			0.697157			0.348578	−	0.937280i	$-0.386665\pi$
$223$	2321.60			0.697157			0.348578	+	0.937280i	$0.386665\pi$
$224$	−157.402	−	1499.05i	−0.0469503	−	0.447141i
$225$	−314.506			−0.0931868
$226$	−3699.41	−	4874.00i	−1.08886	−	1.43457i
$227$	−2363.51			−0.691064			−0.345532	−	0.938407i	$-0.612301\pi$
$227$	−2363.51			−0.691064			−0.345532	+	0.938407i	$0.612301\pi$
$228$	−4918.67	+	2375.84i	−1.42871	+	0.690104i
$229$	−211.020			−0.0608934			−0.0304467	−	0.999536i	$-0.509693\pi$
$229$	−211.020			−0.0608934			−0.0304467	+	0.999536i	$0.509693\pi$
$230$	−3199.48	−	4215.34i	−0.917250	−	1.20848i
$231$	−3705.60			−1.05546
$232$	65.7940	−	26.0450i	0.0186189	−	0.00737043i
$233$	−2572.64			−0.723343			−0.361672	−	0.932306i	$-0.617794\pi$
$233$	−2572.64			−0.723343			−0.361672	+	0.932306i	$0.617794\pi$
$234$	3065.84	+	4039.26i	0.856496	+	1.12844i
$235$		−	676.494i		−	0.187785i
$236$	1704.78	−	6104.86i	0.470218	−	1.68387i
$237$	−428.551			−0.117457
$238$	1305.78	+	1720.37i	0.355635	+	0.468551i
$239$		−	4787.32i		−	1.29567i	−0.761779	−	0.647837i	$-0.775674\pi$
$239$		−	4787.32i		−	1.29567i	0.761779	−	0.647837i	$-0.224326\pi$
$240$	−4888.40	−	2961.06i	−1.31477	−	0.796399i
$241$			3421.02i			0.914386i	0.889368	+	0.457193i	$0.151145\pi$
$241$			3421.02i			0.914386i	−0.889368	+	0.457193i	$0.848855\pi$
$242$	3565.78	−	2706.46i	0.947178	−	0.718917i
$243$	4400.86			1.16179
$244$	65.6023	−	234.924i	0.0172121	−	0.0616372i
$245$	−2964.25			−0.772975
$246$	2900.07	+	3820.86i	0.751632	+	0.990280i
$247$	2719.12	−	2395.88i	0.700458	−	0.617190i
$248$	942.228	+	2380.22i	0.241256	+	0.609453i
$249$			9388.72i			2.38950i
$250$	−3237.72	+	2457.46i	−0.819087	+	0.621694i
$251$			30.6786i			0.00771481i	0.999993	+	0.00385740i	$0.00122785\pi$
$251$			30.6786i			0.00771481i	−0.999993	+	0.00385740i	$0.998772\pi$
$252$	−2628.69	−	734.060i	−0.657112	−	0.183498i
$253$	9324.14			2.31701
$254$	−2517.33	+	1910.68i	−0.621857	+	0.471995i
$255$	8189.42			2.01114
$256$	1897.07	+	3630.20i	0.463152	+	0.886279i
$257$		−	1378.16i		−	0.334504i	−0.985914	−	0.167252i	$-0.946511\pi$
$257$		−	1378.16i		−	0.334504i	0.985914	−	0.167252i	$-0.0534893\pi$
$258$	400.628	+	527.830i	0.0966744	+	0.127369i
$259$	−1326.22			−0.318176
$260$	3652.10	+	1019.85i	0.871130	+	0.243262i
$261$		−	128.128i		−	0.0303868i
$262$	−2564.90	−	3379.27i	−0.604809	−	0.796841i
$263$		−	440.404i		−	0.103257i	−0.998666	−	0.0516283i	$-0.983559\pi$
$263$		−	440.404i		−	0.103257i	0.998666	−	0.0516283i	$-0.0164411\pi$
$264$	9362.91	−	3706.38i	2.18275	−	0.864059i
$265$		−	7043.46i		−	1.63274i
$266$	−386.105	+	1911.91i	−0.0889985	+	0.440702i
$267$			8544.79i			1.95855i
$268$	−599.238	+	2145.89i	−0.136583	+	0.489109i
$269$			3105.10i			0.703797i	0.936038	+	0.351899i	$0.114464\pi$
$269$			3105.10i			0.703797i	−0.936038	+	0.351899i	$0.885536\pi$
$270$	−2810.98	+	2133.56i	−0.633595	+	0.480904i
$271$		−	1143.66i		−	0.256355i	−0.991751	−	0.128178i	$-0.959087\pi$
$271$		−	1143.66i		−	0.256355i	0.991751	−	0.128178i	$-0.0409128\pi$
$272$	−5020.03	−	3040.80i	−1.11906	−	0.677850i
$273$	3004.01			0.665974
$274$	−1905.08	+	1445.98i	−0.420037	+	0.318812i
$275$		−	414.351i		−	0.0908593i
$276$	10973.2	+	3064.26i	2.39315	+	0.668286i
$277$	−6934.06			−1.50407			−0.752035	−	0.659124i	$-0.770927\pi$
$277$	−6934.06			−1.50407			−0.752035	+	0.659124i	$0.770927\pi$
$278$	1908.58	+	2514.57i	0.411759	+	0.542496i
$279$	4635.29			0.994650
$280$	−1897.53	+	751.152i	−0.404997	+	0.160321i
$281$		−	5954.29i		−	1.26407i	−0.774941	−	0.632034i	$-0.782220\pi$
$281$		−	5954.29i		−	1.26407i	0.774941	−	0.632034i	$-0.217780\pi$
$282$	880.512	+	1160.08i	0.185935	+	0.244971i
$283$			460.810i			0.0967927i	0.998828	+	0.0483963i	$0.0154111\pi$
$283$			460.810i			0.0967927i	−0.998828	+	0.0483963i	$0.984589\pi$
$284$	−159.311	+	570.499i	−0.0332866	+	0.119200i
$285$	4889.41	+	5549.06i	1.01622	+	1.15333i
$286$	−5321.59	+	4039.14i	−1.10025	+	0.835102i
$287$	1712.83			0.352284
$288$	7376.10	−	774.500i	1.50917	−	0.158465i
$289$	3496.94			0.711772
$290$	−57.9237	−	76.3149i	−0.0117290	−	0.0154530i
$291$			1198.17i			0.241367i
$292$	2405.05	−	8612.56i	0.482003	−	1.72607i
$293$			6752.13i			1.34629i	0.739509	+	0.673146i	$0.235058\pi$
$293$			6752.13i			1.34629i	−0.739509	+	0.673146i	$0.764942\pi$
$294$	5083.22	−	3858.21i	1.00837	−	0.765359i
$295$	−8581.91			−1.69376
$296$	3350.95	−	1326.50i	0.658008	−	0.260477i
$297$		−	6217.75i		−	1.21478i
$298$	−4506.20	+	3420.25i	−0.875963	+	0.664864i
$299$	−7558.76			−1.46199
$300$	136.171	−	487.634i	0.0262062	−	0.0938452i
$301$	236.619			0.0453105
$302$	−5706.21	+	4331.07i	−1.08727	+	0.825248i
$303$	989.754			0.187656
$304$	−936.743	−	5216.99i	−0.176730	−	0.984259i
$305$	−330.245			−0.0619992
$306$	−8465.12	+	6425.11i	−1.58143	+	1.20032i
$307$	3859.20			0.717447			0.358723	−	0.933444i	$-0.383212\pi$
$307$	3859.20			0.717447			0.358723	+	0.933444i	$0.383212\pi$
$308$	967.100	−	3463.22i	0.178914	−	0.640699i
$309$	−3854.85			−0.709692
$310$	2760.83	−	2095.50i	0.505822	−	0.383924i
$311$			79.1103i			0.0144242i	0.999974	+	0.00721211i	$0.00229571\pi$
$311$			79.1103i			0.0144242i	−0.999974	+	0.00721211i	$0.997704\pi$
$312$	−7590.19	+	3004.63i	−1.37728	+	0.545205i
$313$	5303.24			0.957690			0.478845	−	0.877899i	$-0.341056\pi$
$313$	5303.24			0.957690			0.478845	+	0.877899i	$0.341056\pi$
$314$	−5348.48	+	4059.55i	−0.961249	+	0.729597i
$315$			3695.29i			0.660971i
$316$	111.845	−	400.519i	0.0199106	−	0.0713006i
$317$		−	7950.65i		−	1.40869i	−0.709860	−	0.704343i	$-0.751242\pi$
$317$		−	7950.65i		−	1.40869i	0.709860	−	0.704343i	$-0.248758\pi$
$318$	9167.64	+	12078.4i	1.61665	+	2.12995i
$319$	168.805			0.0296278
$320$	4043.17	−	3795.86i	0.706312	−	0.663109i
$321$	3314.68			0.576347
$322$	3240.50	−	2459.57i	0.560826	−	0.425672i
$323$	5021.06	+	5698.48i	0.864952	+	0.981647i
$324$	−336.867	+	1206.33i	−0.0577618	+	0.206847i
$325$			335.900i			0.0573304i
$326$	−1468.50	−	1934.76i	−0.249486	−	0.328700i
$327$			11624.1i			1.96580i
$328$	−4327.80	+	1713.19i	−0.728545	+	0.288400i
$329$	520.047			0.0871463
$330$	−8242.91	−	10860.1i	−1.37502	−	1.81160i
$331$	−2166.70			−0.359796			−0.179898	−	0.983685i	$-0.557577\pi$
$331$	−2166.70			−0.359796			−0.179898	+	0.983685i	$0.557577\pi$
$332$	−8774.60	−	2450.30i	−1.45051	−	0.405053i
$333$		−	6525.71i		−	1.07389i
$334$	8361.60	−	6346.53i	1.36984	−	1.03972i
$335$	3016.59			0.491982
$336$	2276.29	−	3757.90i	0.369588	−	0.610150i
$337$		−	6552.73i		−	1.05920i	−0.848248	−	0.529600i	$-0.822342\pi$
$337$		−	6552.73i		−	1.05920i	0.848248	−	0.529600i	$-0.177658\pi$
$338$	−635.720	+	482.517i	−0.102304	+	0.0776494i
$339$		−	17835.9i		−	2.85757i
$340$	−2137.30	+	7653.75i	−0.340916	+	1.22083i
$341$			6106.84i			0.969806i
$342$	−9407.59	−	1899.83i	−1.48744	−	0.300384i
$343$		−	5134.79i		−	0.808316i
$344$	−597.862	+	236.668i	−0.0937050	+	0.0370938i
$345$		−	15425.6i		−	2.40721i
$346$	1948.04	+	2566.55i	0.302679	+	0.398782i
$347$		−	3764.47i		−	0.582383i	−0.956665	−	0.291192i	$-0.905948\pi$
$347$		−	3764.47i		−	0.582383i	0.956665	−	0.291192i	$-0.0940518\pi$
$348$	198.660	+	55.4756i	0.0306014	+	0.00854542i
$349$	4243.17			0.650808			0.325404	−	0.945575i	$-0.394500\pi$
$349$	4243.17			0.650808			0.325404	+	0.945575i	$0.394500\pi$
$350$	−109.300	−	144.003i	−0.0166923	−	0.0219922i
$351$			5040.52i			0.766504i
$352$	1020.38	+	9717.78i	0.154507	+	1.47148i
$353$	5116.61			0.771473			0.385736	−	0.922609i	$-0.373947\pi$
$353$	5116.61			0.771473			0.385736	+	0.922609i	$0.373947\pi$
$354$	14716.6	−	11170.1i	2.20955	−	1.67707i
$355$	801.980			0.119901
$356$	−7985.87	−	2230.05i	−1.18890	−	0.332000i
$357$			6295.53i			0.933319i
$358$	−994.666	+	754.961i	−0.146843	+	0.111455i
$359$			9232.77i			1.35734i	0.734441	+	0.678672i	$0.237444\pi$
$359$			9232.77i			1.35734i	−0.734441	+	0.678672i	$0.762556\pi$
$360$	−3696.06	−	9336.85i	−0.541109	−	1.36693i
$361$	−863.458	+	6804.43i	−0.125887	+	0.992045i
$362$	5618.86	+	7402.89i	0.815803	+	1.07483i
$363$	13048.6			1.88671
$364$	−783.995	+	2807.51i	−0.112892	+	0.404268i
$365$	−12107.1			−1.73621
$366$	566.318	−	429.841i	0.0808795	−	0.0613883i
$367$		−	386.149i		−	0.0549232i	−0.999623	−	0.0274616i	$-0.991258\pi$
$367$		−	386.149i		−	0.0549232i	0.999623	−	0.0274616i	$-0.00874240\pi$
$368$	−5727.65	+	9455.74i	−0.811344	+	1.33944i
$369$			8428.03i			1.18901i
$370$	−2950.11	−	3886.79i	−0.414511	−	0.546121i
$371$	5414.58			0.757712
$372$	−2006.94	+	7186.90i	−0.279717	+	1.00168i
$373$			5244.60i			0.728030i	0.931393	+	0.364015i	$0.118594\pi$
$373$			5244.60i			0.728030i	−0.931393	+	0.364015i	$0.881406\pi$
$374$	−8464.87	−	11152.5i	−1.17034	−	1.54193i
$375$	−11848.1			−1.63156
$376$	−1314.00	+	520.156i	−0.180224	+	0.0713430i
$377$	−136.845			−0.0186946
$378$	−1640.15	−	2160.91i	−0.223175	−	0.294035i
$379$	6933.67			0.939733			0.469867	−	0.882737i	$-0.344302\pi$
$379$	6933.67			0.939733			0.469867	+	0.882737i	$0.344302\pi$
$380$	−6462.15	+	3121.38i	−0.872372	+	0.421377i
$381$	−9211.93			−1.23869
$382$	−4224.03	−	5565.19i	−0.565760	−	0.745392i
$383$	−14266.3			−1.90333			−0.951666	−	0.307135i	$-0.900630\pi$
$383$	−14266.3			−1.90333			−0.951666	+	0.307135i	$0.900630\pi$
$384$	−1992.78	+	11771.8i	−0.264827	+	1.56440i
$385$	−4868.42			−0.644462
$386$	−1616.60	−	2129.89i	−0.213168	−	0.280851i
$387$			1164.29i			0.152930i
$388$	−1119.79	−	312.701i	−0.146518	−	0.0409149i
$389$	3977.48			0.518422			0.259211	−	0.965821i	$-0.416537\pi$
$389$	3977.48			0.518422			0.259211	+	0.965821i	$0.416537\pi$
$390$	6682.25	+	8803.91i	0.867613	+	1.14309i
$391$		−	15841.0i		−	2.04888i
$392$	2279.21	+	5757.65i	0.293667	+	0.741850i
$393$		−	12366.1i		−	1.58725i
$394$	9710.50	−	7370.35i	1.24164	−	0.942419i
$395$	−563.031			−0.0717194
$396$	17040.8	+	4758.63i	2.16246	+	0.603864i
$397$	5351.99			0.676596			0.338298	−	0.941039i	$-0.390149\pi$
$397$	5351.99			0.676596			0.338298	+	0.941039i	$0.390149\pi$
$398$	−6728.02	−	8864.22i	−0.847350	−	1.11639i
$399$	−4265.78	+	3758.68i	−0.535229	+	0.471602i
$400$	420.199	+	254.528i	0.0525249	+	0.0318160i
$401$		−	392.753i		−	0.0489106i	−0.999701	−	0.0244553i	$-0.992215\pi$
$401$		−	392.753i		−	0.0489106i	0.999701	−	0.0244553i	$-0.00778514\pi$
$402$	−5172.98	+	3926.34i	−0.641803	+	0.487135i
$403$		−	4950.61i		−	0.611929i
$404$	−258.309	+	925.014i	−0.0318103	+	0.113914i
$405$	1695.80			0.208062
$406$	58.6663	−	44.5282i	0.00717132	−	0.00544310i
$407$	8597.41			1.04707
$408$	−6296.84	−	15906.9i	−0.764069	−	1.93016i
$409$			13687.4i			1.65476i	0.561642	+	0.827380i	$0.310170\pi$
$409$			13687.4i			1.65476i	−0.561642	+	0.827380i	$0.689830\pi$
$410$	3810.11	+	5019.84i	0.458946	+	0.604664i
$411$	−6971.46			−0.836683
$412$	1006.05	−	3602.70i	0.120302	−	0.430807i
$413$		−	6597.25i		−	0.786028i
$414$	12102.3	+	15944.9i	1.43671	+	1.89288i
$415$			12334.9i			1.45903i
$416$	−827.186	−	7877.87i	−0.0974907	−	0.928472i
$417$			9201.82i			1.08061i
$418$	2502.97	−	12394.2i	0.292881	−	1.45029i
$419$		−	8342.37i		−	0.972677i	−0.873770	−	0.486338i	$-0.838332\pi$
$419$		−	8342.37i		−	0.972677i	0.873770	−	0.486338i	$-0.161668\pi$
$420$	−5729.46	−	1599.95i	−0.665641	−	0.185879i
$421$		−	3217.13i		−	0.372430i	−0.982509	−	0.186215i	$-0.940378\pi$
$421$		−	3217.13i		−	0.372430i	0.982509	−	0.186215i	$-0.0596222\pi$
$422$	1392.93	−	1057.25i	0.160680	−	0.121958i
$423$			2558.90i			0.294133i
$424$	−13681.0	+	5415.71i	−1.56700	+	0.620307i
$425$	−703.950			−0.0803449
$426$	−1375.27	+	1043.84i	−0.156413	+	0.118719i
$427$		−	253.872i		−	0.0287722i
$428$	−865.076	+	3097.87i	−0.0976987	+	0.349862i
$429$	−19473.8			−2.19162
$430$	526.345	+	693.463i	0.0590293	+	0.0777715i
$431$	6540.79			0.730994			0.365497	−	0.930812i	$-0.380899\pi$
$431$	6540.79			0.730994			0.365497	+	0.930812i	$0.380899\pi$
$432$	6305.51	+	3819.45i	0.702254	+	0.425378i
$433$		−	2762.10i		−	0.306555i	−0.988183	−	0.153277i	$-0.951017\pi$
$433$		−	2762.10i		−	0.306555i	0.988183	−	0.153277i	$-0.0489828\pi$
$434$	1610.89	+	2122.36i	0.178169	+	0.234739i
$435$		−	279.267i		−	0.0307812i
$436$	−10863.8	−	3033.70i	−1.19330	−	0.333229i
$437$	10733.7	−	9457.69i	1.17497	−	1.03529i
$438$	20761.8	−	15758.4i	2.26492	−	1.71910i
$439$	8030.43			0.873055			0.436528	−	0.899691i	$-0.356208\pi$
$439$	8030.43			0.873055			0.436528	+	0.899691i	$0.356208\pi$
$440$	12301.0	−	4869.44i	1.33279	−	0.527594i
$441$	11212.5			1.21073
$442$	6862.18	+	9040.97i	0.738463	+	0.972930i
$443$			2090.03i			0.224154i	0.993700	+	0.112077i	$0.0357504\pi$
$443$			2090.03i			0.224154i	−0.993700	+	0.112077i	$0.964250\pi$
$444$	10118.0	+	2825.43i	1.08148	+	0.302002i
$445$			11226.1i			1.19589i
$446$	−5230.48	+	3969.98i	−0.555315	+	0.421489i
$447$	−16490.0			−1.74485
$448$	2918.02	+	3108.14i	0.307731	+	0.327781i
$449$			5954.95i			0.625905i	0.949769	+	0.312953i	$0.101318\pi$
$449$			5954.95i			0.625905i	−0.949769	+	0.312953i	$0.898682\pi$
$450$	708.569	−	537.810i	0.0742273	−	0.0563392i
$451$	−11103.7			−1.15931
$452$	16669.3	+	4654.88i	1.73464	+	0.484396i
$453$	−20881.3			−2.16576
$454$	5324.89	−	4041.64i	0.550461	−	0.417805i
$455$	3946.67			0.406643
$456$	7018.85	−	13763.7i	0.720806	−	1.41347i
$457$	−9073.80			−0.928785			−0.464392	−	0.885630i	$-0.653727\pi$
$457$	−9073.80			−0.928785			−0.464392	+	0.885630i	$0.653727\pi$
$458$	475.420	−	360.848i	0.0485042	−	0.0368151i
$459$	−10563.5			−1.07421
$460$	14416.6	+	4025.83i	1.46126	+	0.408055i
$461$	7334.64			0.741016			0.370508	−	0.928829i	$-0.379184\pi$
$461$	7334.64			0.741016			0.370508	+	0.928829i	$0.379184\pi$
$462$	8348.58	−	6336.65i	0.840717	−	0.638112i
$463$			14521.0i			1.45756i	0.684749	+	0.728779i	$0.259912\pi$
$463$			14521.0i			1.45756i	−0.684749	+	0.728779i	$0.740088\pi$
$464$	−103.694	+	171.187i	−0.0103747	+	0.0171275i
$465$	10103.0			1.00756
$466$	5796.05	−	4399.26i	0.576174	−	0.437321i
$467$		−	6164.98i		−	0.610881i	−0.952211	−	0.305441i	$-0.901196\pi$
$467$		−	6164.98i		−	0.610881i	0.952211	−	0.305441i	$-0.0988037\pi$
$468$	−13814.4	−	3857.66i	−1.36447	−	0.381027i
$469$			2318.97i			0.228316i
$470$	1156.82	+	1524.11i	0.113532	+	0.149579i
$471$	−19572.2			−1.91474
$472$	6598.63	+	16669.2i	0.643488	+	1.62556i
$473$	−1533.91			−0.149110
$474$	965.510	−	732.831i	0.0935597	−	0.0710127i
$475$	−420.286	−	476.989i	−0.0405980	−	0.0460752i
$476$	−5883.74	−	1643.03i	−0.566556	−	0.158210i
$477$			26642.6i			2.55740i
$478$	8186.41	+	10785.7i	0.783342	+	1.03206i
$479$		−	12691.5i		−	1.21062i	−0.795988	−	0.605312i	$-0.793048\pi$
$479$		−	12691.5i		−	1.21062i	0.795988	−	0.605312i	$-0.206952\pi$
$480$	16076.8	−	1688.09i	1.52876	−	0.160522i
$481$	−6969.63			−0.660681
$482$	−5850.00	−	7707.42i	−0.552822	−	0.728347i
$483$	11858.3			1.11712
$484$	−3405.47	+	12195.1i	−0.319822	+	1.14529i
$485$			1574.15i			0.147378i
$486$	−9914.97	+	7525.55i	−0.925416	+	0.702399i
$487$	11817.4			1.09958			0.549792	−	0.835301i	$-0.314707\pi$
$487$	11817.4			1.09958			0.549792	+	0.835301i	$0.314707\pi$
$488$	253.925	+	641.456i	0.0235546	+	0.0595027i
$489$		−	7080.05i		−	0.654746i
$490$	6678.34	−	5068.92i	0.615707	−	0.467327i
$491$		−	6262.42i		−	0.575599i	−0.957691	−	0.287800i	$-0.907076\pi$
$491$		−	6262.42i		−	0.575599i	0.957691	−	0.287800i	$-0.0929237\pi$
$492$	−13067.5	−	3649.08i	−1.19741	−	0.334376i
$493$		−	286.787i		−	0.0261992i
$494$	−2029.07	+	10047.6i	−0.184802	+	0.915103i
$495$		−	23955.2i		−	2.17516i
$496$	−6193.03	−	3751.32i	−0.560635	−	0.339595i
$497$			616.514i			0.0556427i
$498$	−16054.9	−	21152.4i	−1.44465	−	1.90334i
$499$			2958.80i			0.265439i	0.991154	+	0.132719i	$0.0423709\pi$
$499$			2958.80i			0.265439i	−0.991154	+	0.132719i	$0.957629\pi$
$500$	3092.16	−	11073.1i	0.276571	−	0.990412i
$501$	30598.4			2.72862
$502$	−52.4610	−	69.1177i	−0.00466424	−	0.00614517i
$503$			7221.67i			0.640156i	0.947391	+	0.320078i	$0.103709\pi$
$503$			7221.67i			0.640156i	−0.947391	+	0.320078i	$0.896291\pi$
$504$	7177.60	−	2841.31i	0.634357	−	0.251115i
$505$	1300.34			0.114583
$506$	−21006.9	+	15944.4i	−1.84560	+	1.40082i
$507$	−2326.35			−0.203781
$508$	2404.16	−	8609.38i	0.209975	−	0.751928i
$509$		−	16729.8i		−	1.45685i	−0.685125	−	0.728426i	$-0.740252\pi$
$509$		−	16729.8i		−	1.45685i	0.685125	−	0.728426i	$-0.259748\pi$
$510$	−18450.5	+	14004.1i	−1.60196	+	1.21590i
$511$		−	9307.21i		−	0.805728i
$512$	−10481.7	−	4934.68i	−0.904749	−	0.425945i
$513$	−6306.81	−	7157.69i	−0.542792	−	0.616023i
$514$	2356.68	+	3104.95i	0.202235	+	0.266446i
$515$	−5064.50			−0.433337
$516$	−1805.20	−	504.100i	−0.154011	−	0.0430073i
$517$	−3371.27			−0.286786
$518$	2987.93	−	2267.87i	0.253440	−	0.192364i
$519$			9392.04i			0.794345i
$520$	−9972.00	+	3947.49i	−0.840963	+	0.332902i
$521$			10904.0i			0.916914i	0.888717	+	0.458457i	$0.151598\pi$
$521$			10904.0i			0.916914i	−0.888717	+	0.458457i	$0.848402\pi$
$522$	219.102	+	288.668i	0.0183713	+	0.0242044i
$523$	2809.15			0.234867			0.117434	−	0.993081i	$-0.462533\pi$
$523$	2809.15			0.234867			0.117434	+	0.993081i	$0.462533\pi$
$524$	11557.2	+	3227.35i	0.963512	+	0.269060i
$525$		−	526.964i		−	0.0438069i
$526$	753.099	+	992.213i	0.0624271	+	0.0822482i
$527$	10375.0			0.857578
$528$	−14756.3	+	24361.1i	−1.21626	+	2.00792i
$529$	−17671.1			−1.45238
$530$	12044.4	+	15868.6i	0.987127	+	1.30055i
$531$	32461.9			2.65297
$532$	−2399.52	−	4967.71i	−0.195550	−	0.404845i
$533$	9001.36			0.731505
$534$	−14611.7	−	19251.1i	−1.18411	−	1.56007i
$535$	4354.83			0.351917
$536$	−2319.46	−	5859.32i	−0.186913	−	0.472172i
$537$	−3639.88			−0.292500
$538$	−5309.78	−	6995.68i	−0.425504	−	0.560604i
$539$			14772.2i			1.18049i
$540$	2684.60	−	9613.64i	0.213939	−	0.766121i
$541$	276.064			0.0219389			0.0109694	−	0.999940i	$-0.496508\pi$
$541$	276.064			0.0219389			0.0109694	+	0.999940i	$0.496508\pi$
$542$	1955.68	+	2576.62i	0.154988	+	0.204198i
$543$			27090.1i			2.14097i
$544$	16509.7	−	1733.54i	1.30119	−	0.136627i
$545$			15271.8i			1.20031i
$546$	−6767.91	+	5136.91i	−0.530476	+	0.402636i
$547$	−906.625			−0.0708674			−0.0354337	−	0.999372i	$-0.511281\pi$
$547$	−906.625			−0.0708674			−0.0354337	+	0.999372i	$0.511281\pi$
$548$	1819.43	−	6515.45i	0.141829	−	0.507895i
$549$	1249.18			0.0971107
$550$	708.548	+	933.517i	0.0549320	+	0.0723732i
$551$	194.323	−	171.223i	0.0150244	−	0.0132384i
$552$	−29962.2	+	11860.8i	−2.31028	+	0.914542i
$553$		−	432.824i		−	0.0332831i
$554$	15622.2	−	11857.4i	1.19805	−	0.909334i
$555$		−	14223.3i		−	1.08783i
$556$	−8599.92	−	2401.52i	−0.655967	−	0.183178i
$557$	14545.7			1.10650			0.553252	−	0.833014i	$-0.313387\pi$
$557$	14545.7			1.10650			0.553252	+	0.833014i	$0.313387\pi$
$558$	−10443.1	+	7926.42i	−0.792281	+	0.601348i
$559$	1243.49			0.0940857
$560$	2990.58	−	4937.13i	0.225670	−	0.372557i
$561$		−	40811.6i		−	3.07142i
$562$	10181.9	+	13414.8i	0.764234	+	1.00688i
$563$	−448.637			−0.0335840			−0.0167920	−	0.999859i	$-0.505345\pi$
$563$	−448.637			−0.0335840			−0.0167920	+	0.999859i	$0.505345\pi$
$564$	−3967.52	−	1107.93i	−0.296210	−	0.0827165i
$565$		−	23432.8i		−	1.74483i
$566$	−787.994	−	1038.19i	−0.0585192	−	0.0770995i
$567$			1303.63i			0.0965562i
$568$	−616.642	−	1557.74i	−0.0455524	−	0.115073i
$569$			11035.3i			0.813045i	0.913641	+	0.406523i	$0.133259\pi$
$569$			11035.3i			0.813045i	−0.913641	+	0.406523i	$0.866741\pi$
$570$	−20504.6	−	4140.85i	−1.50675	−	0.304283i
$571$			8153.77i			0.597592i	0.954317	+	0.298796i	$0.0965849\pi$
$571$			8153.77i			0.597592i	−0.954317	+	0.298796i	$0.903415\pi$
$572$	5082.35	−	18200.1i	0.371510	−	1.33039i
$573$		−	20365.3i		−	1.48477i
$574$	−3858.95	+	2928.98i	−0.280609	+	0.212985i
$575$			1325.96i			0.0961677i
$576$	−15293.7	+	14358.2i	−1.10631	+	1.03864i
$577$	−4525.76			−0.326534			−0.163267	−	0.986582i	$-0.552203\pi$
$577$	−4525.76			−0.326534			−0.163267	+	0.986582i	$0.552203\pi$
$578$	−7878.46	+	5979.83i	−0.566957	+	0.430325i
$579$		−	7794.11i		−	0.559434i
$580$	261.000	+	72.8839i	0.0186852	+	0.00521783i
$581$	−9482.32			−0.677096
$582$	−2048.88	−	2699.42i	−0.145926	−	0.192259i
$583$	−35100.7			−2.49352
$584$	9309.15	+	23516.4i	0.659615	+	1.66630i
$585$			19419.6i			1.37248i
$586$	−11546.3	−	15212.3i	−0.813946	−	1.07238i
$587$			7894.03i			0.555062i	0.960717	+	0.277531i	$0.0895161\pi$
$587$			7894.03i			0.555062i	−0.960717	+	0.277531i	$0.910484\pi$
$588$	−4854.69	+	17384.8i	−0.340483	+	1.21928i
$589$	6194.31	+	7030.01i	0.433331	+	0.491794i
$590$	19334.7	−	14675.2i	1.34915	−	1.02402i
$591$	35534.6			2.47326
$592$	−5281.23	+	8718.75i	−0.366651	+	0.605301i
$593$	6425.46			0.444961			0.222481	−	0.974937i	$-0.428585\pi$
$593$	6425.46			0.444961			0.222481	+	0.974937i	$0.428585\pi$
$594$	10632.5	+	14008.4i	0.734437	+	0.967626i
$595$			8271.07i			0.569884i
$596$	4303.61	−	15411.4i	0.295776	−	1.05918i
$597$		−	32437.7i		−	2.22377i
$598$	17029.6	−	12925.6i	1.16454	−	0.883893i
$599$	−12953.7			−0.883595			−0.441797	−	0.897115i	$-0.645659\pi$
$599$	−12953.7			−0.883595			−0.441797	+	0.897115i	$0.645659\pi$
$600$	527.074	+	1331.48i	0.0358629	+	0.0905954i
$601$		−	3637.72i		−	0.246898i	−0.992351	−	0.123449i	$-0.960605\pi$
$601$		−	3637.72i		−	0.246898i	0.992351	−	0.123449i	$-0.0393955\pi$
$602$	−533.092	+	404.622i	−0.0360917	+	0.0273940i
$603$	−11410.5			−0.770603
$604$	5449.67	−	19515.5i	0.367126	−	1.31469i
$605$	17143.3			1.15202
$606$	−2229.88	+	1692.50i	−0.149476	+	0.113454i
$607$	−23243.7			−1.55426			−0.777129	−	0.629342i	$-0.783325\pi$
$607$	−23243.7			−1.55426			−0.777129	+	0.629342i	$0.783325\pi$
$608$	11031.6	+	10151.8i	0.735839	+	0.677156i
$609$	214.683			0.0142847
$610$	744.029	−	564.725i	0.0493850	−	0.0374837i
$611$	2732.97			0.180956
$612$	8084.55	−	28951.0i	0.533984	−	1.91222i
$613$	4530.37			0.298499			0.149250	−	0.988800i	$-0.452314\pi$
$613$	4530.37			0.298499			0.149250	+	0.988800i	$0.452314\pi$
$614$	−8694.63	+	6599.30i	−0.571477	+	0.433756i
$615$			18369.6i			1.20445i
$616$	3743.33	+	9456.26i	0.244843	+	0.618512i
$617$	−27590.3			−1.80024			−0.900118	−	0.435647i	$-0.856520\pi$
$617$	−27590.3			−1.80024			−0.900118	+	0.435647i	$0.856520\pi$
$618$	8684.83	−	6591.87i	0.565299	−	0.429067i
$619$			1523.57i			0.0989300i	0.998776	+	0.0494650i	$0.0157516\pi$
$619$			1523.57i			0.0989300i	−0.998776	+	0.0494650i	$0.984248\pi$
$620$	−2636.71	+	9442.16i	−0.170795	+	0.611623i
$621$			19897.4i			1.28576i
$622$	−135.280	−	178.233i	−0.00872064	−	0.0114895i
$623$	−8629.98			−0.554980
$624$	11962.4	−	19748.7i	0.767437	−	1.26696i
$625$	−14606.6			−0.934819
$626$	−11948.0	+	9068.64i	−0.762841	+	0.579003i
$627$	27653.5	−	24366.1i	1.76136	−	1.55197i
$628$	5108.02	−	18292.0i	0.324574	−	1.16231i
$629$		−	14606.3i		−	0.925902i
$630$	−6319.01	−	8325.34i	−0.399612	−	0.526491i
$631$		−	2083.59i		−	0.131453i	−0.997838	−	0.0657263i	$-0.979064\pi$
$631$		−	2083.59i		−	0.131453i	0.997838	−	0.0657263i	$-0.0209364\pi$
$632$	432.914	+	1093.61i	0.0272475	+	0.0688315i
$633$	5097.30			0.320062
$634$	13595.8	+	17912.5i	0.851667	+	1.12208i
$635$	−12102.6			−0.756344
$636$	−41308.7	−	11535.4i	−2.57546	−	0.719196i
$637$		−	11975.3i		−	0.744864i
$638$	−380.311	+	288.660i	−0.0235998	+	0.0179125i
$639$	−3033.57			−0.187803
$640$	−2618.12	+	15465.8i	−0.161703	+	0.955219i
$641$			1554.43i			0.0957818i	0.998853	+	0.0478909i	$0.0152500\pi$
$641$			1554.43i			0.0957818i	−0.998853	+	0.0478909i	$0.984750\pi$
$642$	−7467.85	+	5668.17i	−0.459085	+	0.348450i
$643$		−	21731.9i		−	1.33285i	−0.745573	−	0.666424i	$-0.767824\pi$
$643$		−	21731.9i		−	1.33285i	0.745573	−	0.666424i	$-0.232176\pi$
$644$	−3094.81	+	11082.6i	−0.189367	+	0.678131i
$645$			2537.66i			0.154915i
$646$	−21056.8	−	4252.35i	−1.28246	−	0.258988i
$647$			7401.82i			0.449761i	0.974386	+	0.224881i	$0.0721992\pi$
$647$			7401.82i			0.449761i	−0.974386	+	0.224881i	$0.927801\pi$
$648$	−1303.90	−	3293.87i	−0.0790465	−	0.199684i
$649$			42767.5i			2.58671i
$650$	−574.396	−	756.770i	−0.0346610	−	0.0456661i
$651$			7766.57i			0.467582i
$652$	6616.94	+	1847.77i	0.397453	+	0.110988i
$653$	−10373.7			−0.621676			−0.310838	−	0.950463i	$-0.600610\pi$
$653$	−10373.7			−0.621676			−0.310838	+	0.950463i	$0.600610\pi$
$654$	−19877.5	−	26188.7i	−1.18849	−	1.56584i
$655$		−	16246.6i		−	0.969172i
$656$	6820.78	−	11260.4i	0.405955	−	0.670189i
$657$	45796.3			2.71946
$658$	−1171.65	+	889.291i	−0.0694157	+	0.0526872i
$659$	24282.1			1.43535			0.717676	−	0.696377i	$-0.245206\pi$
$659$	24282.1			1.43535			0.717676	+	0.696377i	$0.245206\pi$
$660$	37141.9	+	10371.8i	2.19053	+	0.611702i
$661$			1182.15i			0.0695618i	0.999395	+	0.0347809i	$0.0110733\pi$
$661$			1182.15i			0.0695618i	−0.999395	+	0.0347809i	$0.988927\pi$
$662$	4881.49	−	3705.10i	0.286593	−	0.217527i
$663$			33084.5i			1.93800i
$664$	23958.9	−	9484.30i	1.40028	−	0.554310i
$665$	−5604.39	+	4938.15i	−0.326810	+	0.287960i
$666$	11159.1	+	14702.2i	0.649258	+	0.855401i
$667$	−540.192			−0.0313588
$668$	−7985.68	+	28597.0i	−0.462537	+	1.65636i
$669$	−19140.4			−1.10615
$670$	−6796.27	+	5158.43i	−0.391885	+	0.297444i
$671$			1645.76i			0.0946852i
$672$	1297.70	+	12358.9i	0.0744938	+	0.709457i
$673$		−	11178.7i		−	0.640278i	−0.947371	−	0.320139i	$-0.896270\pi$
$673$		−	11178.7i		−	0.640278i	0.947371	−	0.320139i	$-0.103730\pi$
$674$	11205.3	+	14763.1i	0.640374	+	0.843697i
$675$	884.210			0.0504197
$676$	607.139	−	2174.19i	0.0345437	−	0.123702i
$677$			15827.8i			0.898538i	0.893397	+	0.449269i	$0.148315\pi$
$677$			15827.8i			0.898538i	−0.893397	+	0.449269i	$0.851685\pi$
$678$	30499.8	+	40183.7i	1.72764	+	2.27617i
$679$	−1210.11			−0.0683944
$680$	−8272.79	−	20898.4i	−0.466540	−	1.17856i
$681$	19485.9			1.09648
$682$	−10442.8	−	13758.5i	−0.586328	−	0.772491i
$683$	17273.7			0.967728			0.483864	−	0.875143i	$-0.339233\pi$
$683$	17273.7			0.967728			0.483864	+	0.875143i	$0.339233\pi$
$684$	24443.7	−	11806.9i	1.36642	−	0.660012i
$685$	−9159.11			−0.510878
$686$	8780.58	+	11568.5i	0.488694	+	0.643858i
$687$	1739.75			0.0966167
$688$	942.253	−	1555.56i	0.0522137	−	0.0861993i
$689$	28455.0			1.57336
$690$	26378.1	+	34753.3i	1.45536	+	1.91744i
$691$		−	21595.1i		−	1.18888i	−0.804141	−	0.594439i	$-0.797374\pi$
$691$		−	21595.1i		−	1.18888i	0.804141	−	0.594439i	$-0.202626\pi$
$692$	−8777.70	−	2451.16i	−0.482194	−	0.134652i
$693$	18415.3			1.00944
$694$	6437.31	+	8481.20i	0.352099	+	0.463893i
$695$			12089.3i			0.659820i
$696$	−542.438	+	214.728i	−0.0295418	+	0.0116943i
$697$			18864.3i			1.02516i
$698$	−9559.71	+	7255.91i	−0.518396	+	0.393467i
$699$	21210.1			1.14769
$700$	492.495	+	137.529i	0.0265923	+	0.00742586i
$701$	16705.4			0.900076			0.450038	−	0.893009i	$-0.351410\pi$
$701$	16705.4			0.900076			0.450038	+	0.893009i	$0.351410\pi$
$702$	−8619.38	−	11356.1i	−0.463415	−	0.610553i
$703$	9897.08	−	8720.55i	0.530975	−	0.467854i
$704$	−18916.5	−	20148.9i	−1.01270	−	1.07868i
$705$			5577.35i			0.297950i
$706$	−11527.5	+	8749.50i	−0.614510	+	0.466419i
$707$			999.622i			0.0531749i
$708$	−14055.0	+	50331.4i	−0.746073	+	2.67171i
$709$	−12352.1			−0.654293			−0.327146	−	0.944974i	$-0.606087\pi$
$709$	−12352.1			−0.654293			−0.327146	+	0.944974i	$0.606087\pi$
$710$	−1806.83	+	1371.40i	−0.0955059	+	0.0724898i
$711$	2129.72			0.112336
$712$	21805.3	−	8631.78i	1.14773	−	0.454339i
$713$		−	19542.5i		−	1.02647i
$714$	−10765.5	−	14183.6i	−0.564269	−	0.743428i
$715$	−25584.7			−1.33820
$716$	949.948	−	3401.79i	0.0495827	−	0.177557i
$717$			39469.0i			2.05578i
$718$	−15788.2	−	20801.1i	−0.820627	−	1.08118i
$719$		−	17034.4i		−	0.883553i	−0.897125	−	0.441776i	$-0.854348\pi$
$719$		−	17034.4i		−	0.883553i	0.897125	−	0.441776i	$-0.145652\pi$
$720$	24293.3	+	14715.2i	1.25744	+	0.761672i
$721$		−	3893.28i		−	0.201100i
$722$	−9690.37	−	16806.7i	−0.499499	−	0.866314i
$723$		−	28204.5i		−	1.45081i
$724$	−25318.1	−	7070.06i	−1.29964	−	0.362924i
$725$			24.0053i			0.00122970i
$726$	−29398.0	+	22313.4i	−1.50284	+	1.14067i
$727$			36743.0i			1.87445i	0.348731	+	0.937223i	$0.386613\pi$
$727$			36743.0i			1.87445i	−0.348731	+	0.937223i	$0.613387\pi$
$728$	−3034.59	−	7665.87i	−0.154491	−	0.390269i
$729$	−32055.7			−1.62860
$730$	27276.9	−	20703.4i	1.38296	−	1.04968i
$731$			2605.99i			0.131855i
$732$	−540.857	+	1936.83i	−0.0273096	+	0.0977968i
$733$	−14324.5			−0.721810			−0.360905	−	0.932603i	$-0.617532\pi$
$733$	−14324.5			−0.721810			−0.360905	+	0.932603i	$0.617532\pi$
$734$	660.322	+	869.979i	0.0332056	+	0.0437487i
$735$	24438.7			1.22644
$736$	−3265.31	−	31097.8i	−0.163534	−	1.55745i
$737$		−	15033.0i		−	0.751355i
$738$	−14412.1	−	18988.0i	−0.718857	−	0.947099i
$739$		−	22582.8i		−	1.12412i	−0.827098	−	0.562058i	$-0.810010\pi$
$739$		−	22582.8i		−	1.12412i	0.827098	−	0.562058i	$-0.189990\pi$
$740$	13293.0	+	3712.05i	0.660351	+	0.184402i
$741$	−22417.7	+	19752.8i	−1.11138	+	0.979266i
$742$	−12198.9	+	9259.04i	−0.603550	+	0.458100i
$743$	−10461.2			−0.516533			−0.258266	−	0.966074i	$-0.583151\pi$
$743$	−10461.2			−0.516533			−0.258266	+	0.966074i	$0.583151\pi$
$744$	−7768.19	−	19623.7i	−0.382790	−	0.966990i
$745$	−21664.5			−1.06541
$746$	−8968.37	−	11815.9i	−0.440155	−	0.579907i
$747$		−	46657.9i		−	2.28531i
$748$	38142.0	+	10651.1i	1.86445	+	0.520647i
$749$			3347.73i			0.163316i
$750$	26693.4	−	20260.5i	1.29961	−	0.986413i
$751$	−20249.7			−0.983919			−0.491959	−	0.870618i	$-0.663719\pi$
$751$	−20249.7			−0.983919			−0.491959	+	0.870618i	$0.663719\pi$
$752$	2070.91	−	3418.85i	0.100423	−	0.165788i
$753$		−	252.929i		−	0.0122407i
$754$	308.305	−	234.007i	0.0148910	−	0.0113024i
$755$	−27433.9			−1.32241
$756$	7390.39	+	2063.76i	0.355537	+	0.0992833i
$757$	13523.4			0.649293			0.324647	−	0.945835i	$-0.394755\pi$
$757$	13523.4			0.649293			0.324647	+	0.945835i	$0.394755\pi$
$758$	−15621.3	+	11856.7i	−0.748537	+	0.568147i
$759$	−76872.8			−3.67629
$760$	9221.36	−	18082.7i	0.440124	−	0.863065i
$761$	5278.02			0.251417			0.125708	−	0.992067i	$-0.459880\pi$
$761$	5278.02			0.251417			0.125708	+	0.992067i	$0.459880\pi$
$762$	20754.1	−	15752.6i	0.986671	−	0.748892i
$763$	−11740.0			−0.557034
$764$	19033.2	+	5314.99i	0.901303	+	0.251688i
$765$	−40697.9			−1.92345
$766$	32141.5	−	24395.7i	1.51608	−	1.15072i
$767$		−	34670.2i		−	1.63216i
$768$	−15640.4	−	29929.1i	−0.734861	−	1.40622i
$769$	−16532.4			−0.775260			−0.387630	−	0.921815i	$-0.626706\pi$
$769$	−16532.4			−0.775260			−0.387630	+	0.921815i	$0.626706\pi$
$770$	10968.4	−	8325.09i	0.513341	−	0.389631i
$771$			11362.2i			0.530741i
$772$	7284.30	+	2034.13i	0.339595	+	0.0948316i
$773$		−	16507.8i		−	0.768106i	−0.923311	−	0.384053i	$-0.874528\pi$
$773$		−	16507.8i		−	0.768106i	0.923311	−	0.384053i	$-0.125472\pi$
$774$	−1990.95	−	2623.09i	−0.0924590	−	0.121815i
$775$	−868.438			−0.0402519
$776$	3057.57	−	1210.36i	0.141444	−	0.0559916i
$777$	10934.0			0.504834
$778$	−8961.11	+	6801.56i	−0.412945	+	0.313429i
$779$	−12782.2	+	11262.7i	−0.587895	+	0.518008i
$780$	−30109.7	−	8408.10i	−1.38218	−	0.385972i
$781$		−	3996.63i		−	0.183112i
$782$	27088.4	+	35689.1i	1.23872	+	1.63202i
$783$			360.224i			0.0164411i
$784$	−14980.7	−	9074.28i	−0.682428	−	0.413369i
$785$	−25714.0			−1.16914
$786$	21146.3	+	27860.4i	0.959622	+	1.26431i
$787$	6081.09			0.275435			0.137718	−	0.990472i	$-0.456023\pi$
$787$	6081.09			0.275435			0.137718	+	0.990472i	$0.456023\pi$
$788$	−9273.93	+	33210.3i	−0.419251	+	1.50135i
$789$			3630.91i			0.163832i
$790$	1268.49	−	962.793i	0.0571275	−	0.0433603i
$791$	18013.8			0.809728
$792$	−46529.7	+	18419.1i	−2.08758	+	0.826382i
$793$		−	1334.16i		−	0.0597445i
$794$	−12057.8	+	9152.00i	−0.538937	+	0.409058i
$795$			58069.7i			2.59059i
$796$	30316.0	+	8465.70i	1.34990	+	0.376958i
$797$			9391.19i			0.417381i	0.977982	+	0.208691i	$0.0669202\pi$
$797$			9391.19i			0.417381i	−0.977982	+	0.208691i	$0.933080\pi$
$798$	3183.23	−	15762.7i	0.141210	−	0.699241i
$799$			5727.53i			0.253599i
$800$	−1381.94	+	145.105i	−0.0610737	+	0.00641281i
$801$		−	42464.0i		−	1.87315i
$802$	671.615	+	884.857i	0.0295705	+	0.0389593i
$803$			60335.1i			2.65153i
$804$	4940.41	−	17691.8i	0.216710	−	0.776047i
$805$	15579.4			0.682114
$806$	8465.63	+	11153.5i	0.369962	+	0.487427i
$807$		−	25600.0i		−	1.11668i
$808$	−999.830	−	2525.73i	−0.0435320	−	0.109969i
$809$	−4772.24			−0.207396			−0.103698	−	0.994609i	$-0.533067\pi$
$809$	−4772.24			−0.207396			−0.103698	+	0.994609i	$0.533067\pi$
$810$	−3820.58	+	2899.85i	−0.165730	+	0.125791i
$811$	−5522.21			−0.239101			−0.119551	−	0.992828i	$-0.538145\pi$
$811$	−5522.21			−0.239101			−0.119551	+	0.992828i	$0.538145\pi$
$812$	−56.0287	+	200.641i	−0.00242146	+	0.00867132i
$813$			9428.88i			0.406747i
$814$	−19369.6	+	14701.7i	−0.834036	+	0.633041i
$815$		−	9301.77i		−	0.399788i
$816$	41387.6	+	25069.8i	1.77556	+	1.07551i
$817$	−1765.79	+	1555.88i	−0.0756147	+	0.0666258i
$818$	−23405.7	−	30837.1i	−1.00044	−	1.31809i
$819$	−14928.6			−0.636934
$820$	−17168.1	−	4794.16i	−0.731139	−	0.204170i
$821$	9804.95			0.416803			0.208401	−	0.978043i	$-0.433174\pi$
$821$	9804.95			0.416803			0.208401	+	0.978043i	$0.433174\pi$
$822$	15706.4	−	11921.3i	0.666454	−	0.505844i
$823$			7930.93i			0.335911i	0.985795	+	0.167955i	$0.0537165\pi$
$823$			7930.93i			0.335911i	−0.985795	+	0.167955i	$0.946284\pi$
$824$	3894.09	+	9837.12i	0.164633	+	0.415889i
$825$			3416.11i			0.144162i
$826$	11281.4	+	14863.4i	0.475219	+	0.626105i
$827$	22575.7			0.949255			0.474627	−	0.880187i	$-0.342583\pi$
$827$	22575.7			0.949255			0.474627	+	0.880187i	$0.342583\pi$
$828$	−54532.2	−	15228.1i	−2.28880	−	0.639145i
$829$		−	24785.4i		−	1.03840i	−0.854654	−	0.519199i	$-0.826230\pi$
$829$		−	24785.4i		−	1.03840i	0.854654	−	0.519199i	$-0.173770\pi$
$830$	−21092.9	−	27790.1i	−0.882103	−	1.16218i
$831$	57167.8			2.38644
$832$	15334.9	+	16334.0i	0.638994	+	0.680626i
$833$	25096.8			1.04388
$834$	−15735.3	−	20731.3i	−0.653319	−	0.860752i
$835$	40200.2			1.66609
$836$	15555.2	+	32203.8i	0.643527	+	1.33229i
$837$	−13031.8			−0.538165
$838$	14265.6	+	18795.0i	0.588064	+	0.774778i
$839$	15875.5			0.653258			0.326629	−	0.945153i	$-0.394087\pi$
$839$	15875.5			0.653258			0.326629	+	0.945153i	$0.394087\pi$
$840$	15644.2	−	6192.87i	0.642590	−	0.254374i
$841$	24379.2			0.999599
$842$	5501.35	+	7248.06i	0.225165	+	0.296656i
$843$			49090.1i			2.00564i
$844$	−1330.31	+	4763.88i	−0.0542549	+	0.194289i
$845$	−3056.37			−0.124429
$846$	−4375.77	−	5765.11i	−0.177828	−	0.234289i
$847$			13178.7i			0.534623i
$848$	21561.7	−	35596.1i	0.873152	−	1.44148i
$849$		−	3799.15i		−	0.153576i
$850$	1585.97	−	1203.77i	0.0639981	−	0.0485751i
$851$	−27512.5			−1.10825
$852$	1313.44	−	4703.48i	0.0528143	−	0.189130i
$853$	−17536.1			−0.703897			−0.351948	−	0.936019i	$-0.614481\pi$
$853$	−17536.1			−0.703897			−0.351948	+	0.936019i	$0.614481\pi$
$854$	434.126	+	571.964i	0.0173952	+	0.0229183i
$855$	−24298.3	−	27576.5i	−0.971910	−	1.10304i
$856$	−3348.43	−	8458.67i	−0.133700	−	0.337747i
$857$		−	43551.9i		−	1.73594i	−0.496613	−	0.867972i	$-0.665423\pi$
$857$		−	43551.9i		−	1.73594i	0.496613	−	0.867972i	$-0.334577\pi$
$858$	43873.8	−	33300.6i	1.74572	−	1.32502i
$859$			8655.89i			0.343813i	0.985113	+	0.171906i	$0.0549927\pi$
$859$			8655.89i			0.343813i	−0.985113	+	0.171906i	$0.945007\pi$
$860$	−2371.67	−	662.286i	−0.0940387	−	0.0262602i
$861$	−14121.4			−0.558952
$862$	−14736.1	+	11184.9i	−0.582268	+	0.441947i
$863$	45399.0			1.79073			0.895364	−	0.445334i	$-0.146915\pi$
$863$	45399.0			1.79073			0.895364	+	0.445334i	$0.146915\pi$
$864$	−20737.4	+	2177.45i	−0.816552	+	0.0857389i
$865$			12339.3i			0.485026i
$866$	4723.25	+	6222.91i	0.185338	+	0.244184i
$867$	−28830.5			−1.12934
$868$	−7258.56	−	2026.94i	−0.283838	−	0.0792615i
$869$			2805.83i			0.109530i
$870$	477.551	+	629.177i	0.0186098	+	0.0245185i
$871$			12186.8i			0.474090i
$872$	29663.4	−	11742.5i	1.15198	−	0.456020i
$873$		−	5954.37i		−	0.230842i
$874$	−8009.74	+	39662.6i	−0.309993	+	1.53502i
$875$		−	11966.3i		−	0.462324i
$876$	−19828.4	+	71006.1i	−0.764771	+	2.73867i
$877$			28095.8i			1.08179i	0.841091	+	0.540894i	$0.181914\pi$
$877$			28095.8i			1.08179i	−0.841091	+	0.540894i	$0.818086\pi$
$878$	−18092.2	+	13732.2i	−0.695425	+	0.527834i
$879$		−	55667.9i		−	2.13610i
$880$	−19386.8	+	32005.6i	−0.742648	+	1.22603i
$881$	−36114.4			−1.38107			−0.690535	−	0.723299i	$-0.742625\pi$
$881$	−36114.4			−1.38107			−0.690535	+	0.723299i	$0.742625\pi$
$882$	−25261.4	+	19173.7i	−0.964396	+	0.731985i
$883$		−	44273.4i		−	1.68734i	−0.536865	−	0.843668i	$-0.680392\pi$
$883$		−	44273.4i		−	1.68734i	0.536865	−	0.843668i	$-0.319608\pi$
$884$	−30920.5	−	8634.51i	−1.17643	−	0.328518i
$885$	70753.5			2.68740
$886$	−3573.99	−	4708.76i	−0.135520	−	0.178548i
$887$	11620.8			0.439897			0.219949	−	0.975511i	$-0.429411\pi$
$887$	11620.8			0.439897			0.219949	+	0.975511i	$0.429411\pi$
$888$	−27626.9	+	10936.3i	−1.04403	+	0.413287i
$889$		−	9303.78i		−	0.351000i
$890$	−19196.9	−	25292.1i	−0.723014	−	0.952575i
$891$		−	8450.95i		−	0.317752i
$892$	4995.33	−	17888.4i	0.187507	−	0.671468i
$893$	−3880.91	+	3419.56i	−0.145431	+	0.128142i
$894$	37151.3	−	28198.2i	1.38985	−	1.05491i
$895$	−4782.08			−0.178600
$896$	−11889.2	−	2012.65i	−0.443292	−	0.0750423i
$897$	62318.1			2.31967
$898$	−10183.1	−	13416.3i	−0.378411	−	0.498560i
$899$		−	353.798i		−	0.0131255i
$900$	−676.713	+	2423.33i	−0.0250634	+	0.0897531i
$901$			59633.4i			2.20497i
$902$	25016.1	−	18987.5i	0.923443	−	0.700902i
$903$	−1950.80			−0.0718921
$904$	−45515.2	+	18017.5i	−1.67457	+	0.662891i
$905$			35591.0i			1.30728i
$906$	47044.8	−	35707.4i	1.72512	−	1.30938i
$907$	−10361.0			−0.379308			−0.189654	−	0.981851i	$-0.560737\pi$
$907$	−10361.0			−0.379308			−0.189654	+	0.981851i	$0.560737\pi$
$908$	−5085.49	+	18211.3i	−0.185868	+	0.665599i
$909$	−4918.66			−0.179474
$910$	−8891.69	+	6748.87i	−0.323908	+	0.245849i
$911$	23464.4			0.853357			0.426679	−	0.904403i	$-0.359684\pi$
$911$	23464.4			0.853357			0.426679	+	0.904403i	$0.359684\pi$
$912$	7722.97	+	43011.4i	0.280409	+	1.56168i
$913$	61470.3			2.22823
$914$	20442.9	−	15516.4i	0.739816	−	0.561527i
$915$	2722.70			0.0983712
$916$	−454.046	+	1625.95i	−0.0163778	+	0.0586496i
$917$	12489.4			0.449767
$918$	23799.1	−	18063.7i	0.855651	−	0.649447i
$919$		−	1012.80i		−	0.0363539i	−0.999835	−	0.0181769i	$-0.994214\pi$
$919$		−	1012.80i		−	0.0363539i	0.999835	−	0.0181769i	$-0.00578622\pi$
$920$	−39364.3	+	15582.7i	−1.41066	+	0.558418i
$921$	−31817.1			−1.13834
$922$	−16524.7	+	12542.4i	−0.590250	+	0.448005i
$923$			3239.93i			0.115540i
$924$	−7973.25	+	28552.5i	−0.283875	+	1.01657i
$925$			1222.62i			0.0434587i
$926$	−24831.2	−	32715.3i	−0.881215	−	1.16101i
$927$	19157.0			0.678746
$928$	−59.1154	−	562.997i	−0.00209112	−	0.0199152i
$929$	1877.93			0.0663217			0.0331608	−	0.999450i	$-0.489443\pi$
$929$	1877.93			0.0663217			0.0331608	+	0.999450i	$0.489443\pi$
$930$	−22761.7	+	17276.3i	−0.802564	+	0.609153i
$931$	14983.8	+	17005.3i	0.527468	+	0.598631i
$932$	−5535.47	+	19822.7i	−0.194550	+	0.696689i
$933$		−	652.224i		−	0.0228862i
$934$	10542.2	+	13889.5i	0.369328	+	0.486593i
$935$		−	53618.2i		−	1.87540i
$936$	37720.0	−	14931.8i	1.31722	−	0.521431i
$937$	54015.7			1.88326			0.941631	−	0.336648i	$-0.109293\pi$
$937$	54015.7			1.88326			0.941631	+	0.336648i	$0.109293\pi$
$938$	−3965.49	−	5224.56i	−0.138036	−	0.181863i
$939$	−43722.5			−1.51952
$940$	−5212.53	−	1455.59i	−0.180866	−	0.0505066i
$941$			41323.2i			1.43156i	0.698326	+	0.715780i	$0.253928\pi$
$941$			41323.2i			1.43156i	−0.698326	+	0.715780i	$0.746072\pi$
$942$	44095.5	−	33468.9i	1.52517	−	1.15762i
$943$	35532.8			1.22705
$944$	−43371.1	−	26271.3i	−1.49535	−	0.905782i
$945$		−	10389.0i		−	0.357625i
$946$	3455.84	−	2623.01i	0.118773	−	0.0901496i
$947$			55668.4i			1.91022i	0.296251	+	0.955110i	$0.404263\pi$
$947$			55668.4i			1.91022i	−0.296251	+	0.955110i	$0.595737\pi$
$948$	−922.102	+	3302.08i	−0.0315912	+	0.113129i
$949$		−	48911.7i		−	1.67307i
$950$	1762.55	+	355.941i	0.0601943	+	0.0121561i
$951$			65549.1i			2.23509i
$952$	16065.4	−	6359.62i	0.546937	−	0.216509i
$953$		−	40561.9i		−	1.37873i	−0.724415	−	0.689364i	$-0.757890\pi$
$953$		−	40561.9i		−	1.37873i	0.724415	−	0.689364i	$-0.242110\pi$
$954$	−45559.3	−	60024.7i	−1.54616	−	2.03708i
$955$		−	26755.9i		−	0.906597i
$956$	−36887.3	−	10300.7i	−1.24793	−	0.348483i
$957$	−1391.71			−0.0470090
$958$	21702.7	+	28593.5i	0.731923	+	0.964314i
$959$		−	7040.97i		−	0.237085i
$960$	−33333.9	+	31294.9i	−1.12067	+	1.05212i
$961$	−16991.7			−0.570363
$962$	15702.3	−	11918.2i	0.526260	−	0.399436i
$963$	−16472.6			−0.551216
$964$	26359.7	+	7360.91i	0.880692	+	0.245932i
$965$		−	10239.9i		−	0.341590i
$966$	−26716.3	+	20277.9i	−0.889836	+	0.675393i
$967$			19719.9i			0.655791i	0.944714	+	0.327895i	$0.106339\pi$
$967$			19719.9i			0.655791i	−0.944714	+	0.327895i	$0.893661\pi$
$968$	−13181.5	−	33298.5i	−0.437674	−	1.10563i
$969$	−41396.1	−	46981.1i	−1.37238	−	1.55753i
$970$	−2691.83	−	3546.50i	−0.0891024	−	0.117393i
$971$	−35347.2			−1.16822			−0.584112	−	0.811673i	$-0.698557\pi$
$971$	−35347.2			−1.16822			−0.584112	+	0.811673i	$0.698557\pi$
$972$	9469.21	−	33909.6i	0.312474	−	1.11898i
$973$	−9293.56			−0.306205
$974$	−26624.2	+	20208.0i	−0.875866	+	0.664790i
$975$		−	2769.33i		−	0.0909635i
$976$	−1668.98	−	1010.96i	−0.0547366	−	0.0331557i
$977$		−	12096.3i		−	0.396107i	−0.980191	−	0.198053i	$-0.936538\pi$
$977$		−	12096.3i		−	0.396107i	0.980191	−	0.198053i	$-0.0634619\pi$
$978$	12107.0	+	15951.1i	0.395848	+	0.521533i
$979$	55944.9			1.82636
$980$	−6378.09	+	22840.2i	−0.207899	+	0.744492i
$981$		−	57766.9i		−	1.88008i
$982$	10708.9	+	14109.0i	0.347997	+	0.458489i
$983$	37920.1			1.23038			0.615190	−	0.788379i	$-0.289079\pi$
$983$	37920.1			1.23038			0.615190	+	0.788379i	$0.289079\pi$
$984$	35680.5	−	14124.4i	1.15595	−	0.457591i
$985$	46685.4			1.51017
$986$	490.410	+	646.119i	0.0158396	+	0.0208688i
$987$	−4287.52			−0.138271
$988$	−12610.1	−	26106.5i	−0.406053	−	0.840646i
$989$	4908.65			0.157822
$990$	40963.8	+	53970.1i	1.31506	+	1.73261i
$991$	−44836.0			−1.43720			−0.718599	−	0.695425i	$-0.755216\pi$
$991$	−44836.0			−1.43720			−0.718599	+	0.695425i	$0.755216\pi$
$992$	20367.5	−	2138.61i	0.651883	−	0.0684485i
$993$	17863.3			0.570872
$994$	−1054.25	−	1388.98i	−0.0336406	−	0.0443218i
$995$		−	42616.7i		−	1.35783i
$996$	72342.1	+	20201.4i	2.30145	+	0.642678i
$997$	−41630.7			−1.32242			−0.661212	−	0.750199i	$-0.729958\pi$
$997$	−41630.7			−1.32242			−0.661212	+	0.750199i	$0.729958\pi$
$998$	−5059.60	−	6666.06i	−0.160480	−	0.211433i
$999$			18346.6i			0.581041i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.4.d.a.75.8	yes	28
4.3	odd	2	inner	76.4.d.a.75.22	yes	28
19.18	odd	2	inner	76.4.d.a.75.21	yes	28
76.75	even	2	inner	76.4.d.a.75.7	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.4.d.a.75.7	✓	28	76.75	even	2	inner
76.4.d.a.75.8	yes	28	1.1	even	1	trivial
76.4.d.a.75.21	yes	28	19.18	odd	2	inner
76.4.d.a.75.22	yes	28	4.3	odd	2	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	76.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.25296 + 1.71002i) q^{2} -8.24449 q^{3} +(2.15167 - 7.70521i) q^{4} -10.8316 q^{5} +(18.5745 - 14.0982i) q^{6} -8.32669i q^{7} +(8.32842 + 21.0389i) q^{8} +40.9716 q^{9} +O(q^{10})\)	\(q+(-2.25296 + 1.71002i) q^{2} -8.24449 q^{3} +(2.15167 - 7.70521i) q^{4} -10.8316 q^{5} +(18.5745 - 14.0982i) q^{6} -8.32669i q^{7} +(8.32842 + 21.0389i) q^{8} +40.9716 q^{9} +(24.4032 - 18.5223i) q^{10} +53.9788i q^{11} +(-17.7394 + 63.5255i) q^{12} -43.7588i q^{13} +(14.2388 + 18.7597i) q^{14} +89.3011 q^{15} +(-54.7406 - 33.1582i) q^{16} +91.7057 q^{17} +(-92.3075 + 70.0622i) q^{18} +(54.7519 + 62.1388i) q^{19} +(-23.3061 + 83.4599i) q^{20} +68.6493i q^{21} +(-92.3047 - 121.612i) q^{22} -172.737i q^{23} +(-68.6636 - 173.455i) q^{24} -7.67618 q^{25} +(74.8283 + 98.5868i) q^{26} -115.189 q^{27} +(-64.1589 - 17.9163i) q^{28} -3.12725i q^{29} +(-201.192 + 152.707i) q^{30} +113.134 q^{31} +(180.030 - 18.9033i) q^{32} -445.027i q^{33} +(-206.609 + 156.818i) q^{34} +90.1914i q^{35} +(88.1575 - 315.695i) q^{36} -159.274i q^{37} +(-229.612 - 46.3695i) q^{38} +360.769i q^{39} +(-90.2102 - 227.886i) q^{40} +205.704i q^{41} +(-117.392 - 154.664i) q^{42} +28.4169i q^{43} +(415.918 + 116.145i) q^{44} -443.789 q^{45} +(295.384 + 389.170i) q^{46} +62.4555i q^{47} +(451.308 + 273.372i) q^{48} +273.666 q^{49} +(17.2941 - 13.1264i) q^{50} -756.067 q^{51} +(-337.171 - 94.1545i) q^{52} +650.269i q^{53} +(259.516 - 196.975i) q^{54} -584.677i q^{55} +(175.185 - 69.3482i) q^{56} +(-451.402 - 512.303i) q^{57} +(5.34765 + 7.04557i) q^{58} +792.302 q^{59} +(192.147 - 688.084i) q^{60} +30.4890 q^{61} +(-254.887 + 193.461i) q^{62} -341.158i q^{63} +(-373.275 + 350.442i) q^{64} +473.978i q^{65} +(761.005 + 1002.63i) q^{66} -278.499 q^{67} +(197.321 - 706.612i) q^{68} +1424.13i q^{69} +(-154.229 - 203.198i) q^{70} -74.0407 q^{71} +(341.229 + 862.000i) q^{72} +1117.76 q^{73} +(272.361 + 358.838i) q^{74} +63.2862 q^{75} +(596.601 - 288.173i) q^{76} +449.464 q^{77} +(-616.921 - 812.798i) q^{78} +51.9803 q^{79} +(592.929 + 359.157i) q^{80} -156.561 q^{81} +(-351.758 - 463.444i) q^{82} -1138.79i q^{83} +(528.957 + 147.711i) q^{84} -993.321 q^{85} +(-48.5934 - 64.0222i) q^{86} +25.7826i q^{87} +(-1135.66 + 449.558i) q^{88} -1036.42i q^{89} +(999.839 - 758.887i) q^{90} -364.365 q^{91} +(-1330.98 - 371.674i) q^{92} -932.733 q^{93} +(-106.800 - 140.710i) q^{94} +(-593.051 - 673.063i) q^{95} +(-1484.25 + 155.848i) q^{96} -145.329i q^{97} +(-616.560 + 467.974i) q^{98} +2211.60i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 10 q^{4} - 4 q^{5} - 6 q^{6} + 192 q^{9}+O(q^{10}) \) 28 * q + 10 * q^4 - 4 * q^5 - 6 * q^6 + 192 * q^9	\( 28 q + 10 q^{4} - 4 q^{5} - 6 q^{6} + 192 q^{9} - 134 q^{16} - 80 q^{17} - 300 q^{20} - 26 q^{24} + 496 q^{25} - 90 q^{26} + 254 q^{28} - 16 q^{30} - 556 q^{36} - 626 q^{38} - 850 q^{42} + 976 q^{44} - 612 q^{45} + 188 q^{49} + 354 q^{54} - 580 q^{57} + 2534 q^{58} - 948 q^{61} - 1068 q^{62} - 1634 q^{64} + 1244 q^{66} + 1630 q^{68} - 184 q^{73} + 2276 q^{74} + 1688 q^{76} + 308 q^{77} + 3376 q^{80} - 2284 q^{81} - 740 q^{82} + 684 q^{85} + 1810 q^{92} + 824 q^{93} - 5222 q^{96}+O(q^{100}) \) 28 * q + 10 * q^4 - 4 * q^5 - 6 * q^6 + 192 * q^9 - 134 * q^16 - 80 * q^17 - 300 * q^20 - 26 * q^24 + 496 * q^25 - 90 * q^26 + 254 * q^28 - 16 * q^30 - 556 * q^36 - 626 * q^38 - 850 * q^42 + 976 * q^44 - 612 * q^45 + 188 * q^49 + 354 * q^54 - 580 * q^57 + 2534 * q^58 - 948 * q^61 - 1068 * q^62 - 1634 * q^64 + 1244 * q^66 + 1630 * q^68 - 184 * q^73 + 2276 * q^74 + 1688 * q^76 + 308 * q^77 + 3376 * q^80 - 2284 * q^81 - 740 * q^82 + 684 * q^85 + 1810 * q^92 + 824 * q^93 - 5222 * q^96

Introduction

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