LMFDB - Embedded newform 115.4.e.a.68.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,4,Mod(22,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("115.22");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	115.e (of order $4$, degree $2$, 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:	$6.78521965066$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			68.13
Character	$\chi$	$=$	115.68
Dual form			115.4.e.a.22.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32617 + 1.32617i) q^{2} +(2.49169 + 2.49169i) q^{3} +4.48253i q^{4} +(-3.09011 - 10.7448i) q^{5} -6.60883 q^{6} +(-19.9254 - 19.9254i) q^{7} +(-16.5540 - 16.5540i) q^{8} -14.5829i q^{9} +O(q^{10})$	\(q+(-1.32617 + 1.32617i) q^{2} +(2.49169 + 2.49169i) q^{3} +4.48253i q^{4} +(-3.09011 - 10.7448i) q^{5} -6.60883 q^{6} +(-19.9254 - 19.9254i) q^{7} +(-16.5540 - 16.5540i) q^{8} -14.5829i q^{9} +(18.3475 + 10.1515i) q^{10} +4.60762i q^{11} +(-11.1691 + 11.1691i) q^{12} +(8.15116 + 8.15116i) q^{13} +52.8491 q^{14} +(19.0732 - 34.4724i) q^{15} +8.04662 q^{16} +(-2.30353 - 2.30353i) q^{17} +(19.3395 + 19.3395i) q^{18} -21.1983 q^{19} +(48.1640 - 13.8515i) q^{20} -99.2960i q^{21} +(-6.11049 - 6.11049i) q^{22} +(-40.1668 - 102.731i) q^{23} -82.4949i q^{24} +(-105.902 + 66.4054i) q^{25} -21.6197 q^{26} +(103.612 - 103.612i) q^{27} +(89.3163 - 89.3163i) q^{28} +71.7600i q^{29} +(20.4220 + 71.0107i) q^{30} -80.9736 q^{31} +(121.761 - 121.761i) q^{32} +(-11.4808 + 11.4808i) q^{33} +6.10976 q^{34} +(-152.523 + 275.667i) q^{35} +65.3685 q^{36} +(-135.336 - 135.336i) q^{37} +(28.1125 - 28.1125i) q^{38} +40.6204i q^{39} +(-126.716 + 229.023i) q^{40} -72.5275 q^{41} +(131.684 + 131.684i) q^{42} +(-137.439 + 137.439i) q^{43} -20.6538 q^{44} +(-156.691 + 45.0629i) q^{45} +(189.507 + 82.9707i) q^{46} +(423.191 - 423.191i) q^{47} +(20.0497 + 20.0497i) q^{48} +451.044i q^{49} +(52.3799 - 228.510i) q^{50} -11.4794i q^{51} +(-36.5379 + 36.5379i) q^{52} +(-400.216 + 400.216i) q^{53} +274.814i q^{54} +(49.5080 - 14.2380i) q^{55} +659.690i q^{56} +(-52.8195 - 52.8195i) q^{57} +(-95.1662 - 95.1662i) q^{58} +553.316i q^{59} +(154.524 + 85.4962i) q^{60} -257.390i q^{61} +(107.385 - 107.385i) q^{62} +(-290.571 + 290.571i) q^{63} +387.324i q^{64} +(62.3948 - 112.771i) q^{65} -30.4509i q^{66} +(-408.295 - 408.295i) q^{67} +(10.3257 - 10.3257i) q^{68} +(155.890 - 356.057i) q^{69} +(-163.309 - 567.854i) q^{70} +494.756 q^{71} +(-241.406 + 241.406i) q^{72} +(-396.935 - 396.935i) q^{73} +358.958 q^{74} +(-429.338 - 98.4145i) q^{75} -95.0219i q^{76} +(91.8087 - 91.8087i) q^{77} +(-53.8696 - 53.8696i) q^{78} +100.503 q^{79} +(-24.8650 - 86.4595i) q^{80} +122.599 q^{81} +(96.1840 - 96.1840i) q^{82} +(461.939 - 461.939i) q^{83} +445.098 q^{84} +(-17.6329 + 31.8692i) q^{85} -364.534i q^{86} +(-178.804 + 178.804i) q^{87} +(76.2744 - 76.2744i) q^{88} +1017.99 q^{89} +(148.038 - 267.560i) q^{90} -324.831i q^{91} +(460.495 - 180.049i) q^{92} +(-201.761 - 201.761i) q^{93} +1122.45i q^{94} +(65.5049 + 227.771i) q^{95} +606.781 q^{96} +(-929.909 - 929.909i) q^{97} +(-598.163 - 598.163i) q^{98} +67.1926 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 4 q^{2} + 4 q^{3} + 32 q^{6} + 28 q^{8}+O(q^{10}) $ 68 * q - 4 * q^2 + 4 * q^3 + 32 * q^6 + 28 * q^8	$ 68 q - 4 q^{2} + 4 q^{3} + 32 q^{6} + 28 q^{8} + 200 q^{12} - 100 q^{13} - 832 q^{16} - 112 q^{18} - 46 q^{23} - 372 q^{25} - 312 q^{26} - 704 q^{27} - 1056 q^{31} + 560 q^{32} - 348 q^{35} + 2424 q^{36} + 2248 q^{41} - 96 q^{46} - 1412 q^{47} + 1532 q^{48} - 620 q^{50} + 112 q^{52} + 2688 q^{55} + 2044 q^{58} + 3948 q^{62} - 1836 q^{70} - 2272 q^{71} + 1128 q^{72} + 1100 q^{73} + 2828 q^{75} + 4216 q^{77} - 9180 q^{78} - 3580 q^{81} - 6516 q^{82} - 2684 q^{85} - 6304 q^{87} - 688 q^{92} - 1608 q^{93} - 8616 q^{95} - 544 q^{96} - 3612 q^{98}+O(q^{100}) $ 68 * q - 4 * q^2 + 4 * q^3 + 32 * q^6 + 28 * q^8 + 200 * q^12 - 100 * q^13 - 832 * q^16 - 112 * q^18 - 46 * q^23 - 372 * q^25 - 312 * q^26 - 704 * q^27 - 1056 * q^31 + 560 * q^32 - 348 * q^35 + 2424 * q^36 + 2248 * q^41 - 96 * q^46 - 1412 * q^47 + 1532 * q^48 - 620 * q^50 + 112 * q^52 + 2688 * q^55 + 2044 * q^58 + 3948 * q^62 - 1836 * q^70 - 2272 * q^71 + 1128 * q^72 + 1100 * q^73 + 2828 * q^75 + 4216 * q^77 - 9180 * q^78 - 3580 * q^81 - 6516 * q^82 - 2684 * q^85 - 6304 * q^87 - 688 * q^92 - 1608 * q^93 - 8616 * q^95 - 544 * q^96 - 3612 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−1.32617	+	1.32617i	−0.468873	+	0.468873i	−0.901549	−	0.432677i	$-0.857569\pi$
$2$	−1.32617	+	1.32617i	−0.468873	+	0.468873i	0.432677	+	0.901549i	$0.357569\pi$
$3$	2.49169	+	2.49169i	0.479527	+	0.479527i	0.904980	−	0.425454i	$-0.139885\pi$
$3$	2.49169	+	2.49169i	0.479527	+	0.479527i	−0.425454	+	0.904980i	$0.639885\pi$
$4$			4.48253i			0.560317i
$5$	−3.09011	−	10.7448i	−0.276388	−	0.961046i
$5$	−3.09011	−	10.7448i	−0.276388	−	0.961046i
$6$	−6.60883			−0.449674
$7$	−19.9254	−	19.9254i	−1.07587	−	1.07587i	−0.996875	−	0.0789964i	$-0.974828\pi$
$7$	−19.9254	−	19.9254i	−1.07587	−	1.07587i	−0.0789964	−	0.996875i	$-0.525172\pi$
$8$	−16.5540	−	16.5540i	−0.731590	−	0.731590i
$9$		−	14.5829i		−	0.540109i
$10$	18.3475	+	10.1515i	0.580199	+	0.321018i
$11$			4.60762i			0.126295i	0.998004	+	0.0631477i	$0.0201139\pi$
$11$			4.60762i			0.126295i	−0.998004	+	0.0631477i	$0.979886\pi$
$12$	−11.1691	+	11.1691i	−0.268687	+	0.268687i
$13$	8.15116	+	8.15116i	0.173902	+	0.173902i	0.788691	−	0.614789i	$-0.210759\pi$
$13$	8.15116	+	8.15116i	0.173902	+	0.173902i	−0.614789	+	0.788691i	$0.710759\pi$
$14$	52.8491			1.00889
$15$	19.0732	−	34.4724i	0.328312	−	0.593382i
$16$	8.04662			0.125728
$17$	−2.30353	−	2.30353i	−0.0328641	−	0.0328641i	0.690484	−	0.723348i	$-0.257398\pi$
$17$	−2.30353	−	2.30353i	−0.0328641	−	0.0328641i	−0.723348	+	0.690484i	$0.757398\pi$
$18$	19.3395	+	19.3395i	0.253242	+	0.253242i
$19$	−21.1983			−0.255959			−0.127979	−	0.991777i	$-0.540849\pi$
$19$	−21.1983			−0.255959			−0.127979	+	0.991777i	$0.540849\pi$
$20$	48.1640	−	13.8515i	0.538490	−	0.154865i
$21$		−	99.2960i		−	1.03182i
$22$	−6.11049	−	6.11049i	−0.0592164	−	0.0592164i
$23$	−40.1668	−	102.731i	−0.364146	−	0.931342i
$23$	−40.1668	−	102.731i	−0.364146	−	0.931342i
$24$		−	82.4949i		−	0.701634i
$25$	−105.902	+	66.4054i	−0.847219	+	0.531243i
$26$	−21.6197			−0.163076
$27$	103.612	−	103.612i	0.738523	−	0.738523i
$28$	89.3163	−	89.3163i	0.602829	−	0.602829i
$29$			71.7600i			0.459500i	0.973250	+	0.229750i	$0.0737909\pi$
$29$			71.7600i			0.459500i	−0.973250	+	0.229750i	$0.926209\pi$
$30$	20.4220	+	71.0107i	0.124284	+	0.432157i
$31$	−80.9736			−0.469138			−0.234569	−	0.972099i	$-0.575368\pi$
$31$	−80.9736			−0.469138			−0.234569	+	0.972099i	$0.575368\pi$
$32$	121.761	−	121.761i	0.672639	−	0.672639i
$33$	−11.4808	+	11.4808i	−0.0605620	+	0.0605620i
$34$	6.10976			0.0308181
$35$	−152.523	+	275.667i	−0.736604	+	1.33132i
$36$	65.3685			0.302632
$37$	−135.336	−	135.336i	−0.601328	−	0.601328i	0.339337	−	0.940665i	$-0.389797\pi$
$37$	−135.336	−	135.336i	−0.601328	−	0.601328i	−0.940665	+	0.339337i	$0.889797\pi$
$38$	28.1125	−	28.1125i	0.120012	−	0.120012i
$39$			40.6204i			0.166781i
$40$	−126.716	+	229.023i	−0.500889	+	0.905294i
$41$	−72.5275			−0.276266			−0.138133	−	0.990414i	$-0.544110\pi$
$41$	−72.5275			−0.276266			−0.138133	+	0.990414i	$0.544110\pi$
$42$	131.684	+	131.684i	0.483791	+	0.483791i
$43$	−137.439	+	137.439i	−0.487423	+	0.487423i	−0.907492	−	0.420069i	$-0.862006\pi$
$43$	−137.439	+	137.439i	−0.487423	+	0.487423i	0.420069	+	0.907492i	$0.362006\pi$
$44$	−20.6538			−0.0707654
$45$	−156.691	+	45.0629i	−0.519069	+	0.149279i
$46$	189.507	+	82.9707i	0.607419	+	0.265943i
$47$	423.191	−	423.191i	1.31338	−	1.31338i	0.394468	−	0.918910i	$-0.370929\pi$
$47$	423.191	−	423.191i	1.31338	−	1.31338i	0.918910	−	0.394468i	$-0.129071\pi$
$48$	20.0497	+	20.0497i	0.0602901	+	0.0602901i
$49$			451.044i			1.31500i
$50$	52.3799	−	228.510i	0.148153	−	0.646323i
$51$		−	11.4794i		−	0.0315184i
$52$	−36.5379	+	36.5379i	−0.0974402	+	0.0974402i
$53$	−400.216	+	400.216i	−1.03724	+	1.03724i	−0.0379650	+	0.999279i	$0.512088\pi$
$53$	−400.216	+	400.216i	−1.03724	+	1.03724i	−0.999279	+	0.0379650i	$0.987912\pi$
$54$			274.814i			0.692547i
$55$	49.5080	−	14.2380i	0.121376	−	0.0349065i
$56$			659.690i			1.57419i
$57$	−52.8195	−	52.8195i	−0.122739	−	0.122739i
$58$	−95.1662	−	95.1662i	−0.215447	−	0.215447i
$59$			553.316i			1.22094i	0.792039	+	0.610471i	$0.209020\pi$
$59$			553.316i			1.22094i	−0.792039	+	0.610471i	$0.790980\pi$
$60$	154.524	+	85.4962i	0.332482	+	0.183959i
$61$		−	257.390i		−	0.540252i	−0.962825	−	0.270126i	$-0.912935\pi$
$61$		−	257.390i		−	0.540252i	0.962825	−	0.270126i	$-0.0870654\pi$
$62$	107.385	−	107.385i	0.219966	−	0.219966i
$63$	−290.571	+	290.571i	−0.581087	+	0.581087i
$64$			387.324i			0.756493i
$65$	62.3948	−	112.771i	0.119063	−	0.215192i
$66$		−	30.4509i		−	0.0567917i
$67$	−408.295	−	408.295i	−0.744494	−	0.744494i	0.228945	−	0.973439i	$-0.426472\pi$
$67$	−408.295	−	408.295i	−0.744494	−	0.744494i	−0.973439	+	0.228945i	$0.926472\pi$
$68$	10.3257	−	10.3257i	0.0184143	−	0.0184143i
$69$	155.890	−	356.057i	0.271986	−	0.621221i
$70$	−163.309	−	567.854i	−0.278846	−	0.969593i
$71$	494.756			0.826996			0.413498	−	0.910505i	$-0.364307\pi$
$71$	494.756			0.826996			0.413498	+	0.910505i	$0.364307\pi$
$72$	−241.406	+	241.406i	−0.395138	+	0.395138i
$73$	−396.935	−	396.935i	−0.636408	−	0.636408i	0.313260	−	0.949667i	$-0.398579\pi$
$73$	−396.935	−	396.935i	−0.636408	−	0.636408i	−0.949667	+	0.313260i	$0.898579\pi$
$74$	358.958			0.563892
$75$	−429.338	−	98.4145i	−0.661009	−	0.151519i
$76$		−	95.0219i		−	0.143418i
$77$	91.8087	−	91.8087i	0.135878	−	0.135878i
$78$	−53.8696	−	53.8696i	−0.0781992	−	0.0781992i
$79$	100.503			0.143132			0.0715660	−	0.997436i	$-0.477200\pi$
$79$	100.503			0.143132			0.0715660	+	0.997436i	$0.477200\pi$
$80$	−24.8650	−	86.4595i	−0.0347498	−	0.120831i
$81$	122.599			0.168174
$82$	96.1840	−	96.1840i	0.129533	−	0.129533i
$83$	461.939	−	461.939i	0.610896	−	0.610896i	−0.332283	−	0.943180i	$-0.607819\pi$
$83$	461.939	−	461.939i	0.610896	−	0.610896i	0.943180	+	0.332283i	$0.107819\pi$
$84$	445.098			0.578145
$85$	−17.6329	+	31.8692i	−0.0225006	+	0.0406671i
$86$		−	364.534i		−	0.457078i
$87$	−178.804	+	178.804i	−0.220343	+	0.220343i
$88$	76.2744	−	76.2744i	0.0923964	−	0.0923964i
$89$	1017.99			1.21244			0.606219	−	0.795297i	$-0.292685\pi$
$89$	1017.99			1.21244			0.606219	+	0.795297i	$0.292685\pi$
$90$	148.038	−	267.560i	0.173384	−	0.313371i
$91$		−	324.831i		−	0.374192i
$92$	460.495	−	180.049i	0.521846	−	0.204037i
$93$	−201.761	−	201.761i	−0.224964	−	0.224964i
$94$			1122.45i			1.23161i
$95$	65.5049	+	227.771i	0.0707438	+	0.245988i
$96$	606.781			0.645097
$97$	−929.909	−	929.909i	−0.973381	−	0.973381i	0.0262735	−	0.999655i	$-0.491636\pi$
$97$	−929.909	−	929.909i	−0.973381	−	0.973381i	−0.999655	+	0.0262735i	$0.991636\pi$
$98$	−598.163	−	598.163i	−0.616567	−	0.616567i
$99$	67.1926			0.0682132
$100$	−297.664	−	474.711i	−0.297664	−	0.474711i
$101$	−34.5909			−0.0340784			−0.0170392	−	0.999855i	$-0.505424\pi$
$101$	−34.5909			−0.0340784			−0.0170392	+	0.999855i	$0.505424\pi$
$102$	15.2237	+	15.2237i	0.0147781	+	0.0147781i
$103$	1053.48	−	1053.48i	1.00779	−	1.00779i	0.00782110	−	0.999969i	$-0.497510\pi$
$103$	1053.48	−	1053.48i	1.00779	−	1.00779i	0.999969	−	0.00782110i	$-0.00248956\pi$
$104$		−	269.869i		−	0.254450i
$105$	−1066.92	+	306.836i	−0.991624	+	0.285182i
$106$		−	1061.51i		−	0.972671i
$107$	1331.60	+	1331.60i	1.20309	+	1.20309i	0.973220	+	0.229874i	$0.0738313\pi$
$107$	1331.60	+	1331.60i	1.20309	+	1.20309i	0.229874	+	0.973220i	$0.426169\pi$
$108$	464.444	+	464.444i	0.413807	+	0.413807i
$109$	−1753.37			−1.54076			−0.770380	−	0.637586i	$-0.779933\pi$
$109$	−1753.37			−1.54076			−0.770380	+	0.637586i	$0.779933\pi$
$110$	−46.7741	+	84.5383i	−0.0405430	+	0.0732764i
$111$		−	674.432i		−	0.576705i
$112$	−160.332	−	160.332i	−0.135268	−	0.135268i
$113$	−888.241	+	888.241i	−0.739458	+	0.739458i	−0.972473	−	0.233015i	$-0.925141\pi$
$113$	−888.241	+	888.241i	−0.739458	+	0.739458i	0.233015	+	0.972473i	$0.425141\pi$
$114$	140.096			0.115098
$115$	−979.705	+	749.035i	−0.794417	+	0.607373i
$116$	−321.667			−0.257466
$117$	118.868	−	118.868i	0.0939260	−	0.0939260i
$118$	−733.792	−	733.792i	−0.572466	−	0.572466i
$119$			91.7977i			0.0707150i
$120$	−886.393	+	254.918i	−0.674302	+	0.193923i
$121$	1309.77			0.984049
$122$	341.343	+	341.343i	0.253309	+	0.253309i
$123$	−180.716	−	180.716i	−0.132477	−	0.132477i
$124$		−	362.967i		−	0.262866i
$125$	1040.76	+	932.703i	0.744710	+	0.667388i
$126$		−	770.694i		−	0.544912i
$127$	544.813	−	544.813i	0.380664	−	0.380664i	−0.490678	−	0.871341i	$-0.663251\pi$
$127$	544.813	−	544.813i	0.380664	−	0.380664i	0.871341	+	0.490678i	$0.163251\pi$
$128$	460.427	+	460.427i	0.317940	+	0.317940i
$129$	−684.909			−0.467464
$130$	66.8073	+	232.300i	0.0450722	+	0.156723i
$131$	−768.525			−0.512568			−0.256284	−	0.966602i	$-0.582498\pi$
$131$	−768.525			−0.512568			−0.256284	+	0.966602i	$0.582498\pi$
$132$	−51.4629	−	51.4629i	−0.0339339	−	0.0339339i
$133$	422.384	+	422.384i	0.275378	+	0.275378i
$134$	1082.94			0.698146
$135$	−1433.46	−	793.119i	−0.913873	−	0.505636i
$136$			76.2653i			0.0480860i
$137$	−351.092	−	351.092i	−0.218948	−	0.218948i	0.589107	−	0.808055i	$-0.299480\pi$
$137$	−351.092	−	351.092i	−0.218948	−	0.218948i	−0.808055	+	0.589107i	$0.799480\pi$
$138$	265.455	+	678.931i	0.163747	+	0.418800i
$139$			2093.69i			1.27758i	0.769379	+	0.638792i	$0.220566\pi$
$139$			2093.69i			1.27758i	−0.769379	+	0.638792i	$0.779434\pi$
$140$	−1235.69	−	683.691i	−0.745961	−	0.412732i
$141$	2108.92			1.25960
$142$	−656.131	+	656.131i	−0.387756	+	0.387756i
$143$	−37.5574	+	37.5574i	−0.0219630	+	0.0219630i
$144$		−	117.343i		−	0.0679070i
$145$	771.049	−	221.746i	0.441601	−	0.127000i
$146$	1052.81			0.596788
$147$	−1123.86	+	1123.86i	−0.630576	+	0.630576i
$148$	606.649	−	606.649i	0.336934	−	0.336934i
$149$	1621.96			0.891787			0.445894	−	0.895086i	$-0.352886\pi$
$149$	1621.96			0.891787			0.445894	+	0.895086i	$0.352886\pi$
$150$	699.891	−	438.862i	0.380972	−	0.238886i
$151$	432.453			0.233063			0.116531	−	0.993187i	$-0.462822\pi$
$151$	432.453			0.233063			0.116531	+	0.993187i	$0.462822\pi$
$152$	350.916	+	350.916i	0.187257	+	0.187257i
$153$	−33.5923	+	33.5923i	−0.0177502	+	0.0177502i
$154$			243.508i			0.127419i
$155$	250.217	+	870.047i	0.129664	+	0.450863i
$156$	−182.082			−0.0934503
$157$	−264.445	−	264.445i	−0.134427	−	0.134427i	0.636692	−	0.771119i	$-0.280302\pi$
$157$	−264.445	−	264.445i	−0.134427	−	0.134427i	−0.771119	+	0.636692i	$0.780302\pi$
$158$	−133.284	+	133.284i	−0.0671107	+	0.0671107i
$159$	−1994.43			−0.994772
$160$	−1684.55	−	932.043i	−0.832347	−	0.460528i
$161$	−1246.61	+	2847.29i	−0.610230	+	1.39378i
$162$	−162.587	+	162.587i	−0.0788522	+	0.0788522i
$163$	−435.271	−	435.271i	−0.209160	−	0.209160i	0.594751	−	0.803910i	$-0.297251\pi$
$163$	−435.271	−	435.271i	−0.209160	−	0.209160i	−0.803910	+	0.594751i	$0.797251\pi$
$164$		−	325.107i		−	0.154796i
$165$	158.836	+	87.8819i	0.0749414	+	0.0414642i
$166$			1225.22i			0.572865i
$167$	1854.62	−	1854.62i	0.859369	−	0.859369i	−0.131895	−	0.991264i	$-0.542106\pi$
$167$	1854.62	−	1854.62i	0.859369	−	0.859369i	0.991264	+	0.131895i	$0.0421061\pi$
$168$	−1643.75	+	1643.75i	−0.754867	+	0.754867i
$169$		−	2064.12i		−	0.939516i
$170$	−18.8798	−	65.6483i	−0.00851775	−	0.0296176i
$171$			309.133i			0.138245i
$172$	−616.073	−	616.073i	−0.273111	−	0.273111i
$173$	374.012	+	374.012i	0.164368	+	0.164368i	0.784498	−	0.620131i	$-0.212920\pi$
$173$	374.012	+	374.012i	0.164368	+	0.164368i	−0.620131	+	0.784498i	$0.712920\pi$
$174$		−	474.250i		−	0.206625i
$175$	3433.30	+	786.995i	1.48305	+	0.339950i
$176$			37.0757i			0.0158789i
$177$	−1378.69	+	1378.69i	−0.585474	+	0.585474i
$178$	−1350.03	+	1350.03i	−0.568480	+	0.568480i
$179$		−	4574.50i		−	1.91013i	−0.296390	−	0.955067i	$-0.595783\pi$
$179$		−	4574.50i		−	1.91013i	0.296390	−	0.955067i	$-0.404217\pi$
$180$	−201.996	−	702.373i	−0.0836438	−	0.290843i
$181$			3352.54i			1.37675i	0.725353	+	0.688377i	$0.241677\pi$
$181$			3352.54i			1.37675i	−0.725353	+	0.688377i	$0.758323\pi$
$182$	430.781	+	430.781i	0.175449	+	0.175449i
$183$	641.336	−	641.336i	0.259065	−	0.259065i
$184$	−1035.68	+	2365.53i	−0.414955	+	0.947766i
$185$	−1035.96	+	1872.37i	−0.411704	+	0.744103i
$186$	535.141			0.210959
$187$	10.6138	−	10.6138i	0.00415058	−	0.00415058i
$188$	1896.97	+	1896.97i	0.735907	+	0.735907i
$189$	−4129.02			−1.58911
$190$	−388.935	−	215.193i	−0.148507	−	0.0821672i
$191$		−	2916.40i		−	1.10483i	−0.833568	−	0.552417i	$-0.813706\pi$
$191$		−	2916.40i		−	1.10483i	0.833568	−	0.552417i	$-0.186294\pi$
$192$	−965.093	+	965.093i	−0.362758	+	0.362758i
$193$	3016.99	+	3016.99i	1.12522	+	1.12522i	0.990944	+	0.134277i	$0.0428712\pi$
$193$	3016.99	+	3016.99i	1.12522	+	1.12522i	0.134277	+	0.990944i	$0.457129\pi$
$194$	2466.44			0.912784
$195$	436.459	−	125.522i	0.160284	−	0.0460963i
$196$	−2021.82			−0.736815
$197$	2033.77	−	2033.77i	0.735535	−	0.735535i	−0.236175	−	0.971710i	$-0.575894\pi$
$197$	2033.77	−	2033.77i	0.735535	−	0.735535i	0.971710	+	0.236175i	$0.0758940\pi$
$198$	−89.1089	+	89.1089i	−0.0319833	+	0.0319833i
$199$	4690.71			1.67093			0.835466	−	0.549542i	$-0.185198\pi$
$199$	4690.71			1.67093			0.835466	+	0.549542i	$0.185198\pi$
$200$	2852.38	+	653.834i	1.00847	+	0.231165i
$201$		−	2034.69i		−	0.714010i
$202$	45.8735	−	45.8735i	0.0159784	−	0.0159784i
$203$	1429.85	−	1429.85i	0.494363	−	0.494363i
$204$	51.4568			0.0176603
$205$	224.118	+	779.295i	0.0763565	+	0.265504i
$206$			2794.19i			0.945051i
$207$	−1498.12	+	585.750i	−0.503026	+	0.196678i
$208$	65.5893	+	65.5893i	0.0218644	+	0.0218644i
$209$		−	97.6734i		−	0.0323264i
$210$	1008.00	−	1821.83i	0.331232	−	0.598660i
$211$	−4249.66			−1.38653			−0.693267	−	0.720681i	$-0.743829\pi$
$211$	−4249.66			−1.38653			−0.693267	+	0.720681i	$0.743829\pi$
$212$	−1793.98	−	1793.98i	−0.581185	−	0.581185i
$213$	1232.78	+	1232.78i	0.396566	+	0.396566i
$214$	−3531.87			−1.12820
$215$	1901.45	+	1052.05i	0.603153	+	0.333718i
$216$	−3430.38			−1.08059
$217$	1613.43	+	1613.43i	0.504732	+	0.504732i
$218$	2325.28	−	2325.28i	0.722420	−	0.722420i
$219$		−	1978.08i		−	0.610349i
$220$	63.8225	+	221.921i	0.0195587	+	0.0680088i
$221$		−	37.5530i		−	0.0114302i
$222$	894.413	+	894.413i	0.270401	+	0.270401i
$223$	−3337.04	−	3337.04i	−1.00209	−	1.00209i	−0.999998	−	0.00208721i	$-0.999336\pi$
$223$	−3337.04	−	3337.04i	−1.00209	−	1.00209i	−0.00208721	−	0.999998i	$-0.500664\pi$
$224$	−4852.27			−1.44735
$225$	968.385	+	1544.37i	0.286929	+	0.457591i
$226$		−	2355.92i		−	0.693423i
$227$	768.521	+	768.521i	0.224707	+	0.224707i	0.810477	−	0.585770i	$-0.199208\pi$
$227$	768.521	+	768.521i	0.224707	+	0.224707i	−0.585770	+	0.810477i	$0.699208\pi$
$228$	236.765	−	236.765i	0.0687727	−	0.0687727i
$229$	982.207			0.283433			0.141716	−	0.989907i	$-0.454738\pi$
$229$	982.207			0.283433			0.141716	+	0.989907i	$0.454738\pi$
$230$	305.909	−	2292.61i	0.0877000	−	0.657261i
$231$	457.518			0.130314
$232$	1187.92	−	1187.92i	0.336166	−	0.336166i
$233$	−1134.09	−	1134.09i	−0.318871	−	0.318871i	0.529462	−	0.848334i	$-0.322394\pi$
$233$	−1134.09	−	1134.09i	−0.318871	−	0.318871i	−0.848334	+	0.529462i	$0.822394\pi$
$234$			315.279i			0.0880787i
$235$	−5854.82	−	3239.40i	−1.62522	−	0.899215i
$236$	−2480.26			−0.684114
$237$	250.422	+	250.422i	0.0686356	+	0.0686356i
$238$	−121.740	−	121.740i	−0.0331563	−	0.0331563i
$239$		−	4320.47i		−	1.16932i	−0.811278	−	0.584661i	$-0.801227\pi$
$239$		−	4320.47i		−	1.16932i	0.811278	−	0.584661i	$-0.198773\pi$
$240$	153.475	−	277.386i	0.0412781	−	0.0746051i
$241$			2223.34i			0.594265i	0.954836	+	0.297132i	$0.0960302\pi$
$241$			2223.34i			0.594265i	−0.954836	+	0.297132i	$0.903970\pi$
$242$	−1736.98	+	1736.98i	−0.461394	+	0.461394i
$243$	−2492.04	−	2492.04i	−0.657879	−	0.657879i
$244$	1153.76			0.302712
$245$	4846.39	−	1393.78i	1.26377	−	0.363450i
$246$	479.322			0.124229
$247$	−172.790	−	172.790i	−0.0445117	−	0.0445117i
$248$	1340.44	+	1340.44i	0.343217	+	0.343217i
$249$	2302.02			0.585882
$250$	−2617.16	+	143.308i	−0.662094	+	0.0362544i
$251$		−	6883.87i		−	1.73110i	−0.500823	−	0.865550i	$-0.666969\pi$
$251$		−	6883.87i		−	1.73110i	0.500823	−	0.865550i	$-0.333031\pi$
$252$	−1302.49	−	1302.49i	−0.325593	−	0.325593i
$253$	473.344	−	185.073i	0.117624	−	0.0459899i
$254$			1445.03i			0.356966i
$255$	−123.344	+	35.4726i	−0.0302906	+	0.00871130i
$256$	−4319.81			−1.05464
$257$	−3301.66	+	3301.66i	−0.801370	+	0.801370i	−0.983310	−	0.181940i	$-0.941762\pi$
$257$	−3301.66	+	3301.66i	−0.801370	+	0.801370i	0.181940	+	0.983310i	$0.441762\pi$
$258$	908.307	−	908.307i	0.219181	−	0.219181i
$259$			5393.26i			1.29390i
$260$	505.499	+	279.687i	0.120576	+	0.0667132i
$261$	1046.47			0.248180
$262$	1019.20	−	1019.20i	0.240329	−	0.240329i
$263$	4285.20	−	4285.20i	1.00470	−	1.00470i	0.00471301	−	0.999989i	$-0.498500\pi$
$263$	4285.20	−	4285.20i	1.00470	−	1.00470i	0.999989	−	0.00471301i	$-0.00150020\pi$
$264$	380.105			0.0886130
$265$	5536.97	+	3063.54i	1.28352	+	0.710158i
$266$	−1120.31			−0.258235
$267$	2536.53	+	2536.53i	0.581397	+	0.581397i
$268$	1830.19	−	1830.19i	0.417153	−	0.417153i
$269$		−	4595.54i		−	1.04162i	−0.853673	−	0.520809i	$-0.825630\pi$
$269$		−	4595.54i		−	1.04162i	0.853673	−	0.520809i	$-0.174370\pi$
$270$	2952.83	−	849.207i	0.665569	−	0.191411i
$271$	240.550			0.0539202			0.0269601	−	0.999637i	$-0.491417\pi$
$271$	240.550			0.0539202			0.0269601	+	0.999637i	$0.491417\pi$
$272$	−18.5357	−	18.5357i	−0.00413195	−	0.00413195i
$273$	809.378	−	809.378i	0.179435	−	0.179435i
$274$	931.217			0.205317
$275$	−305.971	−	487.958i	−0.0670935	−	0.107000i
$276$	1596.04	+	698.784i	0.348080	+	0.152398i
$277$	2328.38	−	2328.38i	0.505051	−	0.505051i	−0.407953	−	0.913003i	$-0.633757\pi$
$277$	2328.38	−	2328.38i	0.505051	−	0.505051i	0.913003	+	0.407953i	$0.133757\pi$
$278$	−2776.59	−	2776.59i	−0.599024	−	0.599024i
$279$			1180.83i			0.253386i
$280$	7088.26	−	2038.52i	1.51287	−	0.435088i
$281$			5657.00i			1.20096i	0.799641	+	0.600478i	$0.205023\pi$
$281$			5657.00i			1.20096i	−0.799641	+	0.600478i	$0.794977\pi$
$282$	−2796.80	+	2796.80i	−0.590591	+	0.590591i
$283$	−4363.26	+	4363.26i	−0.916498	+	0.916498i	−0.996773	−	0.0802745i	$-0.974420\pi$
$283$	−4363.26	+	4363.26i	−0.916498	+	0.916498i	0.0802745	+	0.996773i	$0.474420\pi$
$284$			2217.76i			0.463380i
$285$	−404.318	+	730.755i	−0.0840342	+	0.151881i
$286$		−	99.6153i		−	0.0205957i
$287$	1445.14	+	1445.14i	0.297226	+	0.297226i
$288$	−1775.63	−	1775.63i	−0.363298	−	0.363298i
$289$		−	4902.39i		−	0.997840i
$290$	−728.470	+	1316.62i	−0.147508	+	0.266602i
$291$		−	4634.10i		−	0.933524i
$292$	1779.28	−	1779.28i	0.356590	−	0.356590i
$293$	−6132.67	+	6132.67i	−1.22278	+	1.22278i	−0.256139	+	0.966640i	$0.582450\pi$
$293$	−6132.67	+	6132.67i	−1.22278	+	1.22278i	−0.966640	+	0.256139i	$0.917550\pi$
$294$		−	2980.87i		−	0.591320i
$295$	5945.28	−	1709.81i	1.17338	−	0.337453i
$296$			4480.71i			0.879850i
$297$	477.404	+	477.404i	0.0932720	+	0.0932720i
$298$	−2151.00	+	2151.00i	−0.418135	+	0.418135i
$299$	509.970	−	1164.78i	0.0986365	−	0.225288i
$300$	441.146	−	1924.52i	0.0848987	−	0.370375i
$301$	5477.04			1.04881
$302$	−573.507	+	573.507i	−0.109277	+	0.109277i
$303$	−86.1898	−	86.1898i	−0.0163415	−	0.0163415i
$304$	−170.574			−0.0321813
$305$	−2765.61	+	795.363i	−0.519207	+	0.149319i
$306$		−	89.0983i		−	0.0166451i
$307$	−3475.49	+	3475.49i	−0.646113	+	0.646113i	−0.952051	−	0.305938i	$-0.901030\pi$
$307$	−3475.49	+	3475.49i	−0.646113	+	0.646113i	0.305938	+	0.952051i	$0.401030\pi$
$308$	411.535	+	411.535i	0.0761344	+	0.0761344i
$309$	5249.89			0.966525
$310$	−1485.66	−	822.001i	−0.272194	−	0.150602i
$311$	−2417.38			−0.440762			−0.220381	−	0.975414i	$-0.570730\pi$
$311$	−2417.38			−0.440762			−0.220381	+	0.975414i	$0.570730\pi$
$312$	672.430	−	672.430i	0.122015	−	0.122015i
$313$	−4934.30	+	4934.30i	−0.891064	+	0.891064i	−0.994623	−	0.103559i	$-0.966977\pi$
$313$	−4934.30	+	4934.30i	−0.891064	+	0.891064i	0.103559	+	0.994623i	$0.466977\pi$
$314$	701.400			0.126058
$315$	4020.03	+	2224.24i	0.719057	+	0.397846i
$316$			450.506i			0.0801992i
$317$	−4601.84	+	4601.84i	−0.815348	+	0.815348i	−0.985430	−	0.170082i	$-0.945597\pi$
$317$	−4601.84	+	4601.84i	−0.815348	+	0.815348i	0.170082	+	0.985430i	$0.445597\pi$
$318$	2644.96	−	2644.96i	0.466421	−	0.466421i
$319$	−330.643			−0.0580327
$320$	4161.73	−	1196.88i	0.727025	−	0.209086i
$321$			6635.90i			1.15383i
$322$	−2122.78	−	5429.23i	−0.367384	−	0.939625i
$323$	48.8309	+	48.8309i	0.00841183	+	0.00841183i
$324$			549.553i			0.0942307i
$325$	−1404.51	−	321.947i	−0.239717	−	0.0549489i
$326$	1154.49			0.196139
$327$	−4368.87	−	4368.87i	−0.738835	−	0.738835i
$328$	1200.62	+	1200.62i	0.202113	+	0.202113i
$329$	−16864.5			−2.82605
$330$	−327.190	+	94.0968i	−0.0545794	+	0.0156965i
$331$	3823.59			0.634935			0.317468	−	0.948269i	$-0.397168\pi$
$331$	3823.59			0.634935			0.317468	+	0.948269i	$0.397168\pi$
$332$	2070.66	+	2070.66i	0.342295	+	0.342295i
$333$	−1973.60	+	1973.60i	−0.324782	+	0.324782i
$334$			4919.08i			0.805869i
$335$	−3125.38	+	5648.73i	−0.509724	+	0.921263i
$336$		−	798.998i		−	0.129729i
$337$	3852.91	+	3852.91i	0.622794	+	0.622794i	0.946245	−	0.323451i	$-0.104843\pi$
$337$	3852.91	+	3852.91i	0.622794	+	0.622794i	−0.323451	+	0.946245i	$0.604843\pi$
$338$	2737.38	+	2737.38i	0.440514	+	0.440514i
$339$	−4426.45			−0.709179
$340$	−142.855	−	79.0400i	−0.0227865	−	0.0126075i
$341$		−	373.095i		−	0.0592500i
$342$	−409.963	−	409.963i	−0.0648195	−	0.0648195i
$343$	2152.83	−	2152.83i	0.338897	−	0.338897i
$344$	4550.31			0.713187
$345$	−4307.49	−	574.759i	−0.672195	−	0.0896928i
$346$	−992.009			−0.154135
$347$	−2022.78	+	2022.78i	−0.312935	+	0.312935i	−0.846046	−	0.533111i	$-0.821023\pi$
$347$	−2022.78	+	2022.78i	−0.312935	+	0.312935i	0.533111	+	0.846046i	$0.321023\pi$
$348$	−801.495	−	801.495i	−0.123462	−	0.123462i
$349$		−	11306.6i		−	1.73418i	−0.498153	−	0.867089i	$-0.665988\pi$
$349$		−	11306.6i		−	1.73418i	0.498153	−	0.867089i	$-0.334012\pi$
$350$	−5596.85	+	3509.46i	−0.854754	+	0.535968i
$351$	1689.12			0.256861
$352$	561.027	+	561.027i	0.0849512	+	0.0849512i
$353$	5114.32	+	5114.32i	0.771128	+	0.771128i	0.978304	−	0.207176i	$-0.0664273\pi$
$353$	5114.32	+	5114.32i	0.771128	+	0.771128i	−0.207176	+	0.978304i	$0.566427\pi$
$354$		−	3656.77i		−	0.549025i
$355$	−1528.85	−	5316.06i	−0.228572	−	0.794781i
$356$			4563.19i			0.679350i
$357$	−228.732	+	228.732i	−0.0339097	+	0.0339097i
$358$	6066.57	+	6066.57i	0.895610	+	0.895610i
$359$	−8136.92			−1.19624			−0.598120	−	0.801406i	$-0.704085\pi$
$359$	−8136.92			−1.19624			−0.598120	+	0.801406i	$0.704085\pi$
$360$	3339.83	+	1847.89i	0.488957	+	0.270535i
$361$	−6409.63			−0.934485
$362$	−4446.05	−	4446.05i	−0.645522	−	0.645522i
$363$	3263.54	+	3263.54i	0.471878	+	0.471878i
$364$	1456.06			0.209666
$365$	−3038.42	+	5491.57i	−0.435722	+	0.787512i
$366$			1701.04i			0.242937i
$367$	401.662	+	401.662i	0.0571296	+	0.0571296i	0.735094	−	0.677965i	$-0.237138\pi$
$367$	401.662	+	401.662i	0.0571296	+	0.0571296i	−0.677965	+	0.735094i	$0.737138\pi$
$368$	−323.207	−	826.636i	−0.0457835	−	0.117096i
$369$			1057.66i			0.149214i
$370$	−1109.22	−	3856.94i	−0.155853	−	0.541926i
$371$	15949.0			2.23188
$372$	904.402	−	904.402i	0.126051	−	0.126051i
$373$	−6151.11	+	6151.11i	−0.853867	+	0.853867i	−0.990607	−	0.136740i	$-0.956338\pi$
$373$	−6151.11	+	6151.11i	−0.853867	+	0.853867i	0.136740	+	0.990607i	$0.456338\pi$
$374$			28.1515i			0.00389218i
$375$	269.256	+	4917.27i	0.0370782	+	0.677139i
$376$	−14011.0			−1.92171
$377$	−584.928	+	584.928i	−0.0799080	+	0.0799080i
$378$	5475.79	−	5475.79i	0.745091	−	0.745091i
$379$	9829.53			1.33221			0.666107	−	0.745857i	$-0.267960\pi$
$379$	9829.53			1.33221			0.666107	+	0.745857i	$0.267960\pi$
$380$	−1020.99	+	293.628i	−0.137831	+	0.0396390i
$381$	2715.01			0.365077
$382$	3867.65	+	3867.65i	0.518027	+	0.518027i
$383$	6163.24	−	6163.24i	0.822263	−	0.822263i	−0.164169	−	0.986432i	$-0.552494\pi$
$383$	6163.24	−	6163.24i	0.822263	−	0.822263i	0.986432	+	0.164169i	$0.0524943\pi$
$384$			2294.48i			0.304922i
$385$	−1270.17	−	702.769i	−0.168139	−	0.0930297i
$386$	−8002.10			−1.05517
$387$	2004.26	+	2004.26i	0.263261	+	0.263261i
$388$	4168.35	−	4168.35i	0.545402	−	0.545402i
$389$	−1817.57			−0.236901			−0.118450	−	0.992960i	$-0.537793\pi$
$389$	−1817.57			−0.236901			−0.118450	+	0.992960i	$0.537793\pi$
$390$	−412.357	+	745.283i	−0.0535397	+	0.0967663i
$391$	−144.118	+	329.169i	−0.0186404	+	0.0425750i
$392$	7466.58	−	7466.58i	0.962039	−	0.962039i
$393$	−1914.93	−	1914.93i	−0.245790	−	0.245790i
$394$			5394.27i			0.689745i
$395$	−310.564	−	1079.88i	−0.0395600	−	0.137556i
$396$			301.193i			0.0382210i
$397$	3671.19	−	3671.19i	0.464111	−	0.464111i	−0.435890	−	0.900000i	$-0.643566\pi$
$397$	3671.19	−	3671.19i	0.464111	−	0.464111i	0.900000	+	0.435890i	$0.143566\pi$
$398$	−6220.69	+	6220.69i	−0.783455	+	0.783455i
$399$			2104.90i			0.264103i
$400$	−852.157	+	534.339i	−0.106520	+	0.0667924i
$401$		−	10481.9i		−	1.30534i	−0.757644	−	0.652668i	$-0.773649\pi$
$401$		−	10481.9i		−	1.30534i	0.757644	−	0.652668i	$-0.226351\pi$
$402$	2698.35	+	2698.35i	0.334780	+	0.334780i
$403$	−660.029	−	660.029i	−0.0815841	−	0.0815841i
$404$		−	155.055i		−	0.0190947i
$405$	−378.844	−	1317.30i	−0.0464813	−	0.161623i
$406$			3792.45i			0.463587i
$407$	623.577	−	623.577i	0.0759449	−	0.0759449i
$408$	−190.030	+	190.030i	−0.0230585	+	0.0230585i
$409$		−	919.762i		−	0.111196i	−0.998453	−	0.0555982i	$-0.982293\pi$
$409$		−	919.762i		−	0.111196i	0.998453	−	0.0555982i	$-0.0177066\pi$
$410$	−1330.70	−	736.261i	−0.160289	−	0.0886862i
$411$		−	1749.63i		−	0.209982i
$412$	4722.26	+	4722.26i	0.564682	+	0.564682i
$413$	11025.0	−	11025.0i	1.31358	−	1.31358i
$414$	1209.96	−	2763.57i	0.143638	−	0.328072i
$415$	−6390.89	−	3536.01i	−0.755944	−	0.418255i
$416$	1984.98			0.233947
$417$	−5216.82	+	5216.82i	−0.612635	+	0.612635i
$418$	129.532	+	129.532i	0.0151570	+	0.0151570i
$419$	−1057.94			−0.123350			−0.0616751	−	0.998096i	$-0.519644\pi$
$419$	−1057.94			−0.123350			−0.0616751	+	0.998096i	$0.519644\pi$
$420$	−1375.40	−	4782.50i	−0.159792	−	0.555624i
$421$		−	5665.66i		−	0.655885i	−0.944698	−	0.327942i	$-0.893645\pi$
$421$		−	5665.66i		−	0.655885i	0.944698	−	0.327942i	$-0.106355\pi$
$422$	5635.78	−	5635.78i	0.650108	−	0.650108i
$423$	−6171.36	−	6171.36i	−0.709367	−	0.709367i
$424$	13250.4			1.51767
$425$	396.917	+	90.9828i	0.0453019	+	0.0103843i
$426$	−3269.76			−0.371878
$427$	−5128.60	+	5128.60i	−0.581242	+	0.581242i
$428$	−5968.96	+	5968.96i	−0.674114	+	0.674114i
$429$	−187.163			−0.0210637
$430$	−3916.86	+	1126.45i	−0.439273	+	0.126331i
$431$		−	11215.4i		−	1.25342i	−0.779251	−	0.626712i	$-0.784400\pi$
$431$		−	11215.4i		−	1.25342i	0.779251	−	0.626712i	$-0.215600\pi$
$432$	833.726	−	833.726i	0.0928534	−	0.0928534i
$433$	6882.83	−	6882.83i	0.763898	−	0.763898i	−0.213127	−	0.977025i	$-0.568365\pi$
$433$	6882.83	−	6882.83i	0.763898	−	0.763898i	0.977025	+	0.213127i	$0.0683647\pi$
$434$	−4279.38			−0.473310
$435$	2473.74	+	1368.69i	0.272659	+	0.150859i
$436$		−	7859.56i		−	0.863313i
$437$	851.466	+	2177.71i	0.0932062	+	0.238385i
$438$	2623.28	+	2623.28i	0.286176	+	0.286176i
$439$			8376.24i			0.910651i	0.890325	+	0.455326i	$0.150477\pi$
$439$			8376.24i			0.910651i	−0.890325	+	0.455326i	$0.849523\pi$
$440$	−1055.25	−	583.859i	−0.114334	−	0.0632600i
$441$	6577.55			0.710242
$442$	49.8017	+	49.8017i	0.00535933	+	0.00535933i
$443$	−2990.80	−	2990.80i	−0.320761	−	0.320761i	0.528298	−	0.849059i	$-0.322830\pi$
$443$	−2990.80	−	2990.80i	−0.320761	−	0.320761i	−0.849059	+	0.528298i	$0.822830\pi$
$444$	3023.16			0.323137
$445$	−3145.71	−	10938.2i	−0.335103	−	1.16521i
$446$	8850.99			0.939701
$447$	4041.43	+	4041.43i	0.427636	+	0.427636i
$448$	7717.60	−	7717.60i	0.813889	−	0.813889i
$449$			15.1435i			0.00159168i	1.00000		0.000795841i	$0.000253324\pi$
$449$			15.1435i			0.00159168i	−1.00000		0.000795841i	$0.999747\pi$
$450$	−3332.34	−	763.853i	−0.349085	−	0.0800186i
$451$		−	334.179i		−	0.0348911i
$452$	−3981.57	−	3981.57i	−0.414330	−	0.414330i
$453$	1077.54	+	1077.54i	0.111760	+	0.111760i
$454$	−2038.38			−0.210718
$455$	−3490.25	+	1003.76i	−0.359616	+	0.103422i
$456$			1748.75i			0.179589i
$457$	−12593.6	−	12593.6i	−1.28907	−	1.28907i	−0.935354	−	0.353714i	$-0.884919\pi$
$457$	−12593.6	−	12593.6i	−1.28907	−	1.28907i	−0.353714	−	0.935354i	$-0.615081\pi$
$458$	−1302.58	+	1302.58i	−0.132894	+	0.132894i
$459$	−477.347			−0.0485417
$460$	−3357.57	−	4391.56i	−0.340321	−	0.445125i
$461$	−7577.09			−0.765510			−0.382755	−	0.923850i	$-0.625025\pi$
$461$	−7577.09			−0.765510			−0.382755	+	0.923850i	$0.625025\pi$
$462$	−606.748	+	606.748i	−0.0611006	+	0.0611006i
$463$	−9385.37	−	9385.37i	−0.942063	−	0.942063i	0.0563483	−	0.998411i	$-0.482054\pi$
$463$	−9385.37	−	9385.37i	−0.942063	−	0.942063i	−0.998411	+	0.0563483i	$0.982054\pi$
$464$			577.426i			0.0577723i
$465$	−1544.42	+	2791.35i	−0.154024	+	0.278378i
$466$	3008.01			0.299020
$467$	−13304.3	−	13304.3i	−1.31830	−	1.31830i	−0.915117	−	0.403187i	$-0.867902\pi$
$467$	−13304.3	−	13304.3i	−1.31830	−	1.31830i	−0.403187	−	0.915117i	$-0.632098\pi$
$468$	532.829	+	532.829i	0.0526283	+	0.0526283i
$469$			16270.9i			1.60196i
$470$	12060.5	−	3468.49i	1.18364	−	0.340403i
$471$		−	1317.83i		−	0.128923i
$472$	9159.58	−	9159.58i	0.893229	−	0.893229i
$473$	−633.264	−	633.264i	−0.0615592	−	0.0615592i
$474$	−664.205			−0.0643627
$475$	2244.95	−	1407.68i	0.216853	−	0.135976i
$476$	−411.486			−0.0396228
$477$	5836.33	+	5836.33i	0.560224	+	0.560224i
$478$	5729.69	+	5729.69i	0.548263	+	0.548263i
$479$	15614.9			1.48948			0.744740	−	0.667355i	$-0.232573\pi$
$479$	15614.9			1.48948			0.744740	+	0.667355i	$0.232573\pi$
$480$	−1875.02	−	6519.75i	−0.178297	−	0.619968i
$481$		−	2206.29i		−	0.209144i
$482$	−2948.53	−	2948.53i	−0.278634	−	0.278634i
$483$	−10200.8	+	3988.40i	−0.960975	+	0.375732i
$484$			5871.09i			0.551379i
$485$	−7118.19	+	12865.2i	−0.666434	+	1.20450i
$486$	6609.76			0.616923
$487$	−10985.5	+	10985.5i	−1.02218	+	1.02218i	−0.0224287	+	0.999748i	$0.507140\pi$
$487$	−10985.5	+	10985.5i	−1.02218	+	1.02218i	−0.999748	+	0.0224287i	$0.992860\pi$
$488$	−4260.83	+	4260.83i	−0.395243	+	0.395243i
$489$		−	2169.12i		−	0.200595i
$490$	−4578.76	+	8275.54i	−0.422138	+	0.762961i
$491$	9973.79			0.916723			0.458362	−	0.888766i	$-0.348436\pi$
$491$	9973.79			0.916723			0.458362	+	0.888766i	$0.348436\pi$
$492$	810.067	−	810.067i	0.0742289	−	0.0742289i
$493$	165.302	−	165.302i	0.0151010	−	0.0151010i
$494$	458.300			0.0417406
$495$	−207.632	−	721.972i	−0.0188533	−	0.0655560i
$496$	−651.564			−0.0589840
$497$	−9858.21	−	9858.21i	−0.889741	−	0.889741i
$498$	−3052.87	+	3052.87i	−0.274704	+	0.274704i
$499$		−	1024.74i		−	0.0919313i	−0.998943	−	0.0459657i	$-0.985364\pi$
$499$		−	1024.74i		−	0.0919313i	0.998943	−	0.0459657i	$-0.0146365\pi$
$500$	−4180.87	+	4665.26i	−0.373949	+	0.417274i
$501$	9242.27			0.824180
$502$	9129.20	+	9129.20i	0.811665	+	0.811665i
$503$	−4651.86	+	4651.86i	−0.412358	+	0.412358i	−0.882559	−	0.470201i	$-0.844181\pi$
$503$	−4651.86	+	4651.86i	−0.412358	+	0.412358i	0.470201	+	0.882559i	$0.344181\pi$
$504$	9620.22			0.850235
$505$	106.890	+	371.673i	0.00941886	+	0.0327509i
$506$	−382.297	+	873.175i	−0.0335873	+	0.0767142i
$507$	5143.15	−	5143.15i	0.450523	−	0.450523i
$508$	2442.14	+	2442.14i	0.213292	+	0.213292i
$509$			4570.74i			0.398025i	0.979997	+	0.199012i	$0.0637734\pi$
$509$			4570.74i			0.398025i	−0.979997	+	0.199012i	$0.936227\pi$
$510$	116.533	−	210.618i	0.0101180	−	0.0182869i
$511$			15818.2i			1.36939i
$512$	2045.39	−	2045.39i	0.176552	−	0.176552i
$513$	−2196.39	+	2196.39i	−0.189031	+	0.189031i
$514$		−	8757.15i		−	0.751481i
$515$	−14574.8	−	8064.08i	−1.24707	−	0.689992i
$516$		−	3070.13i		−	0.261928i
$517$	1949.90	+	1949.90i	0.165873	+	0.165873i
$518$	−7152.39	−	7152.39i	−0.606675	−	0.606675i
$519$			1863.85i			0.157637i
$520$	−2899.69	+	833.924i	−0.244538	+	0.0703269i
$521$		−	2807.26i		−	0.236062i	−0.993010	−	0.118031i	$-0.962342\pi$
$521$		−	2807.26i		−	0.236062i	0.993010	−	0.118031i	$-0.0376582\pi$
$522$	−1387.80	+	1387.80i	−0.116365	+	0.116365i
$523$	−3525.14	+	3525.14i	−0.294730	+	0.294730i	−0.838945	−	0.544216i	$-0.816827\pi$
$523$	−3525.14	+	3525.14i	−0.294730	+	0.294730i	0.544216	+	0.838945i	$0.316827\pi$
$524$		−	3444.94i		−	0.287200i
$525$	6593.79	+	10515.7i	0.548146	+	0.874176i
$526$			11365.8i			0.942155i
$527$	186.525	+	186.525i	0.0154178	+	0.0154178i
$528$	−92.3814	+	92.3814i	−0.00761436	+	0.00761436i
$529$	−8940.26	+	8252.74i	−0.734796	+	0.678289i
$530$	−11405.8	+	3280.19i	−0.934782	+	0.268834i
$531$	8068.96			0.659441
$532$	−1893.35	+	1893.35i	−0.154299	+	0.154299i
$533$	−591.184	−	591.184i	−0.0480432	−	0.0480432i
$534$	−6727.74			−0.545202
$535$	10193.0	−	18422.7i	0.823708	−	1.48875i
$536$			13517.8i			1.08933i
$537$	11398.2	−	11398.2i	0.915960	−	0.915960i
$538$	6094.48	+	6094.48i	0.488386	+	0.488386i
$539$	−2078.24			−0.166078
$540$	3555.18	−	6425.55i	0.283316	−	0.512059i
$541$	9128.91			0.725476			0.362738	−	0.931891i	$-0.381842\pi$
$541$	9128.91			0.725476			0.362738	+	0.931891i	$0.381842\pi$
$542$	−319.011	+	319.011i	−0.0252817	+	0.0252817i
$543$	−8353.50	+	8353.50i	−0.660190	+	0.660190i
$544$	−560.960			−0.0442113
$545$	5418.12	+	18839.7i	0.425847	+	1.48074i
$546$			2146.75i			0.168264i
$547$	9547.42	−	9547.42i	0.746285	−	0.746285i	−0.227494	−	0.973779i	$-0.573053\pi$
$547$	9547.42	−	9547.42i	0.746285	−	0.746285i	0.973779	+	0.227494i	$0.0730533\pi$
$548$	1573.78	−	1573.78i	0.122680	−	0.122680i
$549$	−3753.50			−0.291795
$550$	1052.89	+	241.346i	0.0816276	+	0.0187110i
$551$		−	1521.19i		−	0.117613i
$552$	−8474.77	+	3313.56i	−0.653461	+	0.255497i
$553$	−2002.56	−	2002.56i	−0.153992	−	0.153992i
$554$			6175.68i			0.473609i
$555$	−7246.65	+	2084.07i	−0.554240	+	0.159394i
$556$	−9385.02			−0.715852
$557$	8292.37	+	8292.37i	0.630806	+	0.630806i	0.948270	−	0.317464i	$-0.102831\pi$
$557$	8292.37	+	8292.37i	0.630806	+	0.630806i	−0.317464	+	0.948270i	$0.602831\pi$
$558$	−1565.99	−	1565.99i	−0.118806	−	0.118806i
$559$	−2240.57			−0.169528
$560$	−1227.30	+	2218.19i	−0.0926121	+	0.167385i
$561$	52.8926			0.00398062
$562$	−7502.16	−	7502.16i	−0.563095	−	0.563095i
$563$	−8231.39	+	8231.39i	−0.616184	+	0.616184i	−0.944550	−	0.328366i	$-0.893502\pi$
$563$	−8231.39	+	8231.39i	−0.616184	+	0.616184i	0.328366	+	0.944550i	$0.393502\pi$
$564$			9453.32i			0.705774i
$565$	12288.8	+	6799.23i	0.915030	+	0.506276i
$566$		−	11572.9i		−	0.859442i
$567$	−2442.83	−	2442.83i	−0.180934	−	0.180934i
$568$	−8190.18	−	8190.18i	−0.605022	−	0.605022i
$569$	5417.98			0.399180			0.199590	−	0.979879i	$-0.436039\pi$
$569$	5417.98			0.399180			0.199590	+	0.979879i	$0.436039\pi$
$570$	−432.911	−	1505.30i	−0.0318117	−	0.110614i
$571$		−	1022.01i		−	0.0749032i	−0.999298	−	0.0374516i	$-0.988076\pi$
$571$		−	1022.01i		−	0.0749032i	0.999298	−	0.0374516i	$-0.0119240\pi$
$572$	−168.352	−	168.352i	−0.0123062	−	0.0123062i
$573$	7266.77	−	7266.77i	0.529797	−	0.529797i
$574$	−3833.01			−0.278723
$575$	11075.6	+	8212.16i	0.803280	+	0.595601i
$576$	5648.33			0.408588
$577$	7207.93	−	7207.93i	0.520052	−	0.520052i	−0.397535	−	0.917587i	$-0.630134\pi$
$577$	7207.93	−	7207.93i	0.520052	−	0.520052i	0.917587	+	0.397535i	$0.130134\pi$
$578$	6501.41	+	6501.41i	0.467860	+	0.467860i
$579$			15034.8i			1.07915i
$580$	993.986	+	3456.25i	0.0711604	+	0.247436i
$581$	−18408.6			−1.31449
$582$	6145.61	+	6145.61i	0.437704	+	0.437704i
$583$	−1844.04	−	1844.04i	−0.130999	−	0.130999i
$584$			13141.7i			0.931179i
$585$	−1644.53	−	909.899i	−0.116227	−	0.0643072i
$586$		−	16265.9i		−	1.14666i
$587$	7673.92	−	7673.92i	0.539585	−	0.539585i	−0.383822	−	0.923407i	$-0.625392\pi$
$587$	7673.92	−	7673.92i	0.539585	−	0.539585i	0.923407	+	0.383822i	$0.125392\pi$
$588$	−5037.76	−	5037.76i	−0.353323	−	0.353323i
$589$	1716.50			0.120080
$590$	−5616.97	+	10152.0i	−0.391944	+	0.708389i
$591$	10135.1			0.705417
$592$	−1089.00	−	1089.00i	−0.0756040	−	0.0756040i
$593$	−3832.73	−	3832.73i	−0.265415	−	0.265415i	0.561834	−	0.827250i	$-0.310096\pi$
$593$	−3832.73	−	3832.73i	−0.265415	−	0.265415i	−0.827250	+	0.561834i	$0.810096\pi$
$594$	−1266.24			−0.0874654
$595$	986.350	−	283.665i	0.0679604	−	0.0195448i
$596$			7270.50i			0.499683i
$597$	11687.8	+	11687.8i	0.801256	+	0.801256i
$598$	868.394	+	2221.01i	0.0593834	+	0.151879i
$599$			5384.67i			0.367298i	0.982992	+	0.183649i	$0.0587910\pi$
$599$			5384.67i			0.367298i	−0.982992	+	0.183649i	$0.941209\pi$
$600$	5478.11	+	8736.41i	0.372738	+	0.594438i
$601$	−2031.10			−0.137854			−0.0689270	−	0.997622i	$-0.521958\pi$
$601$	−2031.10			−0.137854			−0.0689270	+	0.997622i	$0.521958\pi$
$602$	−7263.50	+	7263.50i	−0.491758	+	0.491758i
$603$	−5954.13	+	5954.13i	−0.402108	+	0.402108i
$604$			1938.48i			0.130589i
$605$	−4047.33	−	14073.2i	−0.271979	−	0.945717i
$606$	228.605			0.0153242
$607$	1437.36	−	1437.36i	0.0961130	−	0.0961130i	−0.657415	−	0.753528i	$-0.728350\pi$
$607$	1437.36	−	1437.36i	0.0961130	−	0.0961130i	0.753528	+	0.657415i	$0.228350\pi$
$608$	−2581.11	+	2581.11i	−0.172168	+	0.172168i
$609$	7125.49			0.474120
$610$	2612.88	−	4722.46i	0.173430	−	0.313454i
$611$	6899.00			0.456798
$612$	−150.578	−	150.578i	−0.00994571	−	0.00994571i
$613$	12486.0	−	12486.0i	0.822683	−	0.822683i	−0.163809	−	0.986492i	$-0.552378\pi$
$613$	12486.0	−	12486.0i	0.822683	−	0.822683i	0.986492	+	0.163809i	$0.0523780\pi$
$614$		−	9218.20i		−	0.605889i
$615$	−1383.33	+	2500.20i	−0.0907013	+	0.163931i
$616$	−3039.60			−0.198813
$617$	6660.66	+	6660.66i	0.434599	+	0.434599i	0.890190	−	0.455590i	$-0.150572\pi$
$617$	6660.66	+	6660.66i	0.434599	+	0.434599i	−0.455590	+	0.890190i	$0.650572\pi$
$618$	−6962.27	+	6962.27i	−0.453177	+	0.453177i
$619$	19059.4			1.23758			0.618789	−	0.785557i	$-0.287624\pi$
$619$	19059.4			1.23758			0.618789	+	0.785557i	$0.287624\pi$
$620$	−3900.01	+	1121.61i	−0.252626	+	0.0726530i
$621$	−14805.9	−	6482.38i	−0.956747	−	0.418887i
$622$	3205.86	−	3205.86i	0.206661	−	0.206661i
$623$	−20283.9	−	20283.9i	−1.30443	−	1.30443i
$624$			326.857i			0.0209692i
$625$	6805.65	−	14065.0i	0.435562	−	0.900159i
$626$		−	13087.5i		−	0.835591i
$627$	243.372	−	243.372i	0.0155013	−	0.0155013i
$628$	1185.38	−	1185.38i	0.0753216	−	0.0753216i
$629$			623.502i			0.0395241i
$630$	−8280.98	+	2381.53i	−0.523686	+	0.150607i
$631$			22728.9i			1.43395i	0.697099	+	0.716975i	$0.254474\pi$
$631$			22728.9i			1.43395i	−0.697099	+	0.716975i	$0.745526\pi$
$632$	−1663.72	−	1663.72i	−0.104714	−	0.104714i
$633$	−10588.9	−	10588.9i	−0.664880	−	0.664880i
$634$		−	12205.7i		−	0.764588i
$635$	−7537.45	−	4170.38i	−0.471046	−	0.260625i
$636$		−	8940.11i		−	0.557387i
$637$	−3676.54	+	3676.54i	−0.228681	+	0.228681i
$638$	438.489	−	438.489i	0.0272100	−	0.0272100i
$639$		−	7214.99i		−	0.446668i
$640$	3524.44	−	6369.97i	0.217681	−	0.393430i
$641$		−	21074.7i		−	1.29860i	−0.760533	−	0.649299i	$-0.775062\pi$
$641$		−	21074.7i		−	1.29860i	0.760533	−	0.649299i	$-0.224938\pi$
$642$	−8800.35	−	8800.35i	−0.541000	−	0.541000i
$643$	−5345.61	+	5345.61i	−0.327854	+	0.327854i	−0.851770	−	0.523916i	$-0.824471\pi$
$643$	−5345.61	+	5345.61i	−0.327854	+	0.327854i	0.523916	+	0.851770i	$0.324471\pi$
$644$	−12763.1	−	5587.99i	−0.780957	−	0.341922i
$645$	2116.44	+	7359.23i	0.129201	+	0.449255i
$646$	−129.516			−0.00788816
$647$	937.636	−	937.636i	0.0569741	−	0.0569741i	−0.678046	−	0.735020i	$-0.737173\pi$
$647$	937.636	−	937.636i	0.0569741	−	0.0569741i	0.735020	+	0.678046i	$0.237173\pi$
$648$	−2029.50	−	2029.50i	−0.123034	−	0.123034i
$649$	−2549.47			−0.154199
$650$	2289.58	−	1435.66i	0.138161	−	0.0866329i
$651$			8040.36i			0.484065i
$652$	1951.12	−	1951.12i	0.117196	−	0.117196i
$653$	−4374.28	−	4374.28i	−0.262142	−	0.262142i	0.563782	−	0.825924i	$-0.309346\pi$
$653$	−4374.28	−	4374.28i	−0.262142	−	0.262142i	−0.825924	+	0.563782i	$0.809346\pi$
$654$	11587.7			0.692839
$655$	2374.83	+	8257.67i	0.141668	+	0.492601i
$656$	−583.602			−0.0347345
$657$	−5788.48	+	5788.48i	−0.343729	+	0.343729i
$658$	22365.2	−	22365.2i	1.32506	−	1.32506i
$659$	12314.7			0.727938			0.363969	−	0.931411i	$-0.381421\pi$
$659$	12314.7			0.727938			0.363969	+	0.931411i	$0.381421\pi$
$660$	−393.934	+	711.986i	−0.0232331	+	0.0419909i
$661$			23116.7i			1.36026i	0.733090	+	0.680132i	$0.238078\pi$
$661$			23116.7i			1.36026i	−0.733090	+	0.680132i	$0.761922\pi$
$662$	−5070.74	+	5070.74i	−0.297704	+	0.297704i
$663$	93.5704	−	93.5704i	0.00548111	−	0.00548111i
$664$	−15293.9			−0.893851
$665$	3233.23	−	5843.65i	0.188540	−	0.340763i
$666$		−	5234.66i		−	0.304563i
$667$	7371.97	−	2882.37i	0.427952	−	0.167325i
$668$	8313.38	+	8313.38i	0.481519	+	0.481519i
$669$		−	16629.8i		−	0.961053i
$670$	−3346.40	−	11636.0i	−0.192959	−	0.670951i
$671$	1185.95			0.0682313
$672$	−12090.4	−	12090.4i	−0.694041	−	0.694041i
$673$	22623.2	+	22623.2i	1.29578	+	1.29578i	0.931153	+	0.364629i	$0.118804\pi$
$673$	22623.2	+	22623.2i	1.29578	+	1.29578i	0.364629	+	0.931153i	$0.381196\pi$
$674$	−10219.3			−0.584022
$675$	−4092.36	+	17853.1i	−0.233356	+	1.01803i
$676$	9252.47			0.526427
$677$	2565.70	+	2565.70i	0.145654	+	0.145654i	0.776174	−	0.630519i	$-0.217158\pi$
$677$	2565.70	+	2565.70i	0.145654	+	0.145654i	−0.630519	+	0.776174i	$0.717158\pi$
$678$	5870.23	−	5870.23i	0.332515	−	0.332515i
$679$			37057.7i			2.09447i
$680$	819.458	−	235.668i	0.0462129	−	0.0132904i
$681$			3829.84i			0.215506i
$682$	494.789	+	494.789i	0.0277807	+	0.0277807i
$683$	3974.66	+	3974.66i	0.222673	+	0.222673i	0.809623	−	0.586950i	$-0.199671\pi$
$683$	3974.66	+	3974.66i	0.222673	+	0.222673i	−0.586950	+	0.809623i	$0.699671\pi$
$684$	−1385.70			−0.0774612
$685$	−2687.51	+	4857.33i	−0.149904	+	0.270933i
$686$			5710.04i			0.317799i
$687$	2447.36	+	2447.36i	0.135913	+	0.135913i
$688$	−1105.92	+	1105.92i	−0.0612829	+	0.0612829i
$689$	−6524.46			−0.360758
$690$	6474.70	−	4950.24i	0.357229	−	0.273120i
$691$	−12054.9			−0.663661			−0.331831	−	0.943339i	$-0.607666\pi$
$691$	−12054.9			−0.663661			−0.331831	+	0.943339i	$0.607666\pi$
$692$	−1676.52	+	1676.52i	−0.0920980	+	0.0920980i
$693$	−1338.84	−	1338.84i	−0.0733886	−	0.0733886i
$694$		−	5365.10i		−	0.293453i
$695$	22496.3	−	6469.72i	1.22782	−	0.353109i
$696$	5919.84			0.322401
$697$	167.070	+	167.070i	0.00907921	+	0.00907921i
$698$	14994.5	+	14994.5i	0.813109	+	0.813109i
$699$		−	5651.63i		−	0.305814i
$700$	−3527.73	+	15389.9i	−0.190480	+	0.830977i
$701$			4207.04i			0.226673i	0.993557	+	0.113336i	$0.0361538\pi$
$701$			4207.04i			0.226673i	−0.993557	+	0.113336i	$0.963846\pi$
$702$	−2240.06	+	2240.06i	−0.120435	+	0.120435i
$703$	2868.89	+	2868.89i	0.153915	+	0.153915i
$704$	−1784.64			−0.0955415
$705$	−6516.81	−	22660.0i	−0.348138	−	1.21053i
$706$	−13565.0			−0.723121
$707$	689.237	+	689.237i	0.0366640	+	0.0366640i
$708$	−6180.04	−	6180.04i	−0.328051	−	0.328051i
$709$	30617.4			1.62181			0.810904	−	0.585179i	$-0.198976\pi$
$709$	30617.4			1.62181			0.810904	+	0.585179i	$0.198976\pi$
$710$	9077.53	+	5022.50i	0.479822	+	0.265480i
$711$		−	1465.62i		−	0.0773068i
$712$	−16851.9	−	16851.9i	−0.887008	−	0.887008i
$713$	3252.45	+	8318.49i	0.170835	+	0.436928i
$714$		−	606.675i		−	0.0317987i
$715$	519.605	+	287.491i	0.0271778	+	0.0150372i
$716$	20505.3			1.07028
$717$	10765.3	−	10765.3i	0.560721	−	0.560721i
$718$	10791.0	−	10791.0i	0.560884	−	0.560884i
$719$			8132.52i			0.421825i	0.977505	+	0.210912i	$0.0676435\pi$
$719$			8132.52i			0.421825i	−0.977505	+	0.210912i	$0.932357\pi$
$720$	−1260.83	+	362.604i	−0.0652618	+	0.0187687i
$721$	−41982.0			−2.16851
$722$	8500.28	−	8500.28i	0.438155	−	0.438155i
$723$	−5539.87	+	5539.87i	−0.284966	+	0.284966i
$724$	−15027.9			−0.771418
$725$	−4765.25	−	7599.56i	−0.244106	−	0.389297i
$726$	−8656.04			−0.442501
$727$	−15804.0	−	15804.0i	−0.806240	−	0.806240i	0.177823	−	0.984063i	$-0.443095\pi$
$727$	−15804.0	−	15804.0i	−0.806240	−	0.806240i	−0.984063	+	0.177823i	$0.943095\pi$
$728$	−5377.24	+	5377.24i	−0.273755	+	0.273755i
$729$		−	15729.0i		−	0.799115i
$730$	−3253.30	−	11312.2i	−0.164945	−	0.573541i
$731$	633.188			0.0320374
$732$	2874.81	+	2874.81i	0.145159	+	0.145159i
$733$	−14509.7	+	14509.7i	−0.731142	+	0.731142i	−0.970846	−	0.239704i	$-0.922950\pi$
$733$	−14509.7	+	14509.7i	−0.731142	+	0.731142i	0.239704	+	0.970846i	$0.422950\pi$
$734$	−1065.35			−0.0535730
$735$	15548.6	+	8602.85i	0.780297	+	0.431729i
$736$	−17399.3	−	7617.85i	−0.871396	−	0.381518i
$737$	1881.27	−	1881.27i	0.0940262	−	0.0940262i
$738$	−1402.64	−	1402.64i	−0.0699621	−	0.0699621i
$739$		−	29009.7i		−	1.44403i	−0.691878	−	0.722015i	$-0.743216\pi$
$739$		−	29009.7i		−	1.44403i	0.691878	−	0.722015i	$-0.256784\pi$
$740$	−8392.94	−	4643.72i	−0.416933	−	0.230685i
$741$		−	861.081i		−	0.0426891i
$742$	−21151.1	+	21151.1i	−1.04647	+	1.04647i
$743$	8443.61	−	8443.61i	0.416912	−	0.416912i	−0.467226	−	0.884138i	$-0.654746\pi$
$743$	8443.61	−	8443.61i	0.416912	−	0.416912i	0.884138	+	0.467226i	$0.154746\pi$
$744$			6679.91i			0.329163i
$745$	−5012.04	−	17427.7i	−0.246479	−	0.857049i
$746$		−	16314.9i		−	0.800710i
$747$	−6736.42	−	6736.42i	−0.329950	−	0.329950i
$748$	47.5767	+	47.5767i	0.00232564	+	0.00232564i
$749$		−	53065.5i		−	2.58875i
$750$	−6878.23	−	6164.07i	−0.334877	−	0.300107i
$751$		−	3782.28i		−	0.183778i	−0.995769	−	0.0918891i	$-0.970709\pi$
$751$		−	3782.28i		−	0.183778i	0.995769	−	0.0918891i	$-0.0292905\pi$
$752$	3405.26	−	3405.26i	0.165129	−	0.165129i
$753$	17152.5	−	17152.5i	0.830108	−	0.830108i
$754$		−	1551.43i		−	0.0749334i
$755$	−1336.33	−	4646.63i	−0.0644158	−	0.223984i
$756$		−	18508.5i		−	0.890406i
$757$	6899.64	+	6899.64i	0.331270	+	0.331270i	0.853069	−	0.521799i	$-0.174739\pi$
$757$	6899.64	+	6899.64i	0.331270	+	0.331270i	−0.521799	+	0.853069i	$0.674739\pi$
$758$	−13035.6	+	13035.6i	−0.624639	+	0.624639i
$759$	1640.57	+	718.283i	0.0784573	+	0.0343505i
$760$	2686.16	−	4854.89i	0.128207	−	0.231718i
$761$	−6530.74			−0.311090			−0.155545	−	0.987829i	$-0.549713\pi$
$761$	−6530.74			−0.311090			−0.155545	+	0.987829i	$0.549713\pi$
$762$	−3600.57	+	3600.57i	−0.171175	+	0.171175i
$763$	34936.7	+	34936.7i	1.65766	+	1.65766i
$764$	13072.9			0.619057
$765$	464.747	+	257.139i	0.0219647	+	0.0121528i
$766$			16347.0i			0.771073i
$767$	−4510.17	+	4510.17i	−0.212324	+	0.212324i
$768$	−10763.6	−	10763.6i	−0.505728	−	0.505728i
$769$	−41859.0			−1.96290			−0.981452	−	0.191706i	$-0.938598\pi$
$769$	−41859.0			−1.96290			−0.981452	+	0.191706i	$0.938598\pi$
$770$	2616.45	−	752.467i	0.122455	−	0.0352169i
$771$	−16453.5			−0.768556
$772$	−13523.8	+

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	115.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32617 + 1.32617i) q^{2} +(2.49169 + 2.49169i) q^{3} +4.48253i q^{4} +(-3.09011 - 10.7448i) q^{5} -6.60883 q^{6} +(-19.9254 - 19.9254i) q^{7} +(-16.5540 - 16.5540i) q^{8} -14.5829i q^{9} +O(q^{10})\)	\(q+(-1.32617 + 1.32617i) q^{2} +(2.49169 + 2.49169i) q^{3} +4.48253i q^{4} +(-3.09011 - 10.7448i) q^{5} -6.60883 q^{6} +(-19.9254 - 19.9254i) q^{7} +(-16.5540 - 16.5540i) q^{8} -14.5829i q^{9} +(18.3475 + 10.1515i) q^{10} +4.60762i q^{11} +(-11.1691 + 11.1691i) q^{12} +(8.15116 + 8.15116i) q^{13} +52.8491 q^{14} +(19.0732 - 34.4724i) q^{15} +8.04662 q^{16} +(-2.30353 - 2.30353i) q^{17} +(19.3395 + 19.3395i) q^{18} -21.1983 q^{19} +(48.1640 - 13.8515i) q^{20} -99.2960i q^{21} +(-6.11049 - 6.11049i) q^{22} +(-40.1668 - 102.731i) q^{23} -82.4949i q^{24} +(-105.902 + 66.4054i) q^{25} -21.6197 q^{26} +(103.612 - 103.612i) q^{27} +(89.3163 - 89.3163i) q^{28} +71.7600i q^{29} +(20.4220 + 71.0107i) q^{30} -80.9736 q^{31} +(121.761 - 121.761i) q^{32} +(-11.4808 + 11.4808i) q^{33} +6.10976 q^{34} +(-152.523 + 275.667i) q^{35} +65.3685 q^{36} +(-135.336 - 135.336i) q^{37} +(28.1125 - 28.1125i) q^{38} +40.6204i q^{39} +(-126.716 + 229.023i) q^{40} -72.5275 q^{41} +(131.684 + 131.684i) q^{42} +(-137.439 + 137.439i) q^{43} -20.6538 q^{44} +(-156.691 + 45.0629i) q^{45} +(189.507 + 82.9707i) q^{46} +(423.191 - 423.191i) q^{47} +(20.0497 + 20.0497i) q^{48} +451.044i q^{49} +(52.3799 - 228.510i) q^{50} -11.4794i q^{51} +(-36.5379 + 36.5379i) q^{52} +(-400.216 + 400.216i) q^{53} +274.814i q^{54} +(49.5080 - 14.2380i) q^{55} +659.690i q^{56} +(-52.8195 - 52.8195i) q^{57} +(-95.1662 - 95.1662i) q^{58} +553.316i q^{59} +(154.524 + 85.4962i) q^{60} -257.390i q^{61} +(107.385 - 107.385i) q^{62} +(-290.571 + 290.571i) q^{63} +387.324i q^{64} +(62.3948 - 112.771i) q^{65} -30.4509i q^{66} +(-408.295 - 408.295i) q^{67} +(10.3257 - 10.3257i) q^{68} +(155.890 - 356.057i) q^{69} +(-163.309 - 567.854i) q^{70} +494.756 q^{71} +(-241.406 + 241.406i) q^{72} +(-396.935 - 396.935i) q^{73} +358.958 q^{74} +(-429.338 - 98.4145i) q^{75} -95.0219i q^{76} +(91.8087 - 91.8087i) q^{77} +(-53.8696 - 53.8696i) q^{78} +100.503 q^{79} +(-24.8650 - 86.4595i) q^{80} +122.599 q^{81} +(96.1840 - 96.1840i) q^{82} +(461.939 - 461.939i) q^{83} +445.098 q^{84} +(-17.6329 + 31.8692i) q^{85} -364.534i q^{86} +(-178.804 + 178.804i) q^{87} +(76.2744 - 76.2744i) q^{88} +1017.99 q^{89} +(148.038 - 267.560i) q^{90} -324.831i q^{91} +(460.495 - 180.049i) q^{92} +(-201.761 - 201.761i) q^{93} +1122.45i q^{94} +(65.5049 + 227.771i) q^{95} +606.781 q^{96} +(-929.909 - 929.909i) q^{97} +(-598.163 - 598.163i) q^{98} +67.1926 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 4 q^{2} + 4 q^{3} + 32 q^{6} + 28 q^{8}+O(q^{10}) \) 68 * q - 4 * q^2 + 4 * q^3 + 32 * q^6 + 28 * q^8	\( 68 q - 4 q^{2} + 4 q^{3} + 32 q^{6} + 28 q^{8} + 200 q^{12} - 100 q^{13} - 832 q^{16} - 112 q^{18} - 46 q^{23} - 372 q^{25} - 312 q^{26} - 704 q^{27} - 1056 q^{31} + 560 q^{32} - 348 q^{35} + 2424 q^{36} + 2248 q^{41} - 96 q^{46} - 1412 q^{47} + 1532 q^{48} - 620 q^{50} + 112 q^{52} + 2688 q^{55} + 2044 q^{58} + 3948 q^{62} - 1836 q^{70} - 2272 q^{71} + 1128 q^{72} + 1100 q^{73} + 2828 q^{75} + 4216 q^{77} - 9180 q^{78} - 3580 q^{81} - 6516 q^{82} - 2684 q^{85} - 6304 q^{87} - 688 q^{92} - 1608 q^{93} - 8616 q^{95} - 544 q^{96} - 3612 q^{98}+O(q^{100}) \) 68 * q - 4 * q^2 + 4 * q^3 + 32 * q^6 + 28 * q^8 + 200 * q^12 - 100 * q^13 - 832 * q^16 - 112 * q^18 - 46 * q^23 - 372 * q^25 - 312 * q^26 - 704 * q^27 - 1056 * q^31 + 560 * q^32 - 348 * q^35 + 2424 * q^36 + 2248 * q^41 - 96 * q^46 - 1412 * q^47 + 1532 * q^48 - 620 * q^50 + 112 * q^52 + 2688 * q^55 + 2044 * q^58 + 3948 * q^62 - 1836 * q^70 - 2272 * q^71 + 1128 * q^72 + 1100 * q^73 + 2828 * q^75 + 4216 * q^77 - 9180 * q^78 - 3580 * q^81 - 6516 * q^82 - 2684 * q^85 - 6304 * q^87 - 688 * q^92 - 1608 * q^93 - 8616 * q^95 - 544 * q^96 - 3612 * q^98

Introduction

L-functions

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