LMFDB - Embedded newform 115.4.e.a.68.8

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			68.8
Character	$\chi$	$=$	115.68
Dual form			115.4.e.a.22.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.66509 + 2.66509i) q^{2} +(-2.23283 - 2.23283i) q^{3} -6.20541i q^{4} +(7.41137 + 8.37088i) q^{5} +11.9014 q^{6} +(-10.9048 - 10.9048i) q^{7} +(-4.78275 - 4.78275i) q^{8} -17.0290i q^{9} +O(q^{10})$	\(q+(-2.66509 + 2.66509i) q^{2} +(-2.23283 - 2.23283i) q^{3} -6.20541i q^{4} +(7.41137 + 8.37088i) q^{5} +11.9014 q^{6} +(-10.9048 - 10.9048i) q^{7} +(-4.78275 - 4.78275i) q^{8} -17.0290i q^{9} +(-42.0611 - 2.55718i) q^{10} -18.9440i q^{11} +(-13.8556 + 13.8556i) q^{12} +(43.9640 + 43.9640i) q^{13} +58.1244 q^{14} +(2.14242 - 35.2390i) q^{15} +75.1362 q^{16} +(-38.7029 - 38.7029i) q^{17} +(45.3837 + 45.3837i) q^{18} +123.640 q^{19} +(51.9447 - 45.9906i) q^{20} +48.6969i q^{21} +(50.4874 + 50.4874i) q^{22} +(109.778 - 10.7567i) q^{23} +21.3581i q^{24} +(-15.1432 + 124.079i) q^{25} -234.336 q^{26} +(-98.3091 + 98.3091i) q^{27} +(-67.6686 + 67.6686i) q^{28} -59.0042i q^{29} +(88.2054 + 99.6249i) q^{30} +342.953 q^{31} +(-161.983 + 161.983i) q^{32} +(-42.2986 + 42.2986i) q^{33} +206.293 q^{34} +(10.4632 - 172.102i) q^{35} -105.672 q^{36} +(-302.912 - 302.912i) q^{37} +(-329.512 + 329.512i) q^{38} -196.328i q^{39} +(4.58909 - 75.4826i) q^{40} +137.839 q^{41} +(-129.782 - 129.782i) q^{42} +(155.399 - 155.399i) q^{43} -117.555 q^{44} +(142.547 - 126.208i) q^{45} +(-263.902 + 321.237i) q^{46} +(234.217 - 234.217i) q^{47} +(-167.766 - 167.766i) q^{48} -105.172i q^{49} +(-290.325 - 371.041i) q^{50} +172.834i q^{51} +(272.815 - 272.815i) q^{52} +(-342.095 + 342.095i) q^{53} -524.005i q^{54} +(158.578 - 140.401i) q^{55} +104.310i q^{56} +(-276.067 - 276.067i) q^{57} +(157.251 + 157.251i) q^{58} +87.0009i q^{59} +(-218.672 - 13.2946i) q^{60} -565.294i q^{61} +(-914.002 + 914.002i) q^{62} +(-185.697 + 185.697i) q^{63} -262.307i q^{64} +(-42.1838 + 693.851i) q^{65} -225.459i q^{66} +(-4.05177 - 4.05177i) q^{67} +(-240.167 + 240.167i) q^{68} +(-269.134 - 221.098i) q^{69} +(430.782 + 486.552i) q^{70} -556.502 q^{71} +(-81.4453 + 81.4453i) q^{72} +(305.536 + 305.536i) q^{73} +1614.57 q^{74} +(310.860 - 243.236i) q^{75} -767.238i q^{76} +(-206.580 + 206.580i) q^{77} +(523.232 + 523.232i) q^{78} -328.493 q^{79} +(556.862 + 628.956i) q^{80} -20.7681 q^{81} +(-367.354 + 367.354i) q^{82} +(810.460 - 810.460i) q^{83} +302.184 q^{84} +(37.1357 - 610.818i) q^{85} +828.302i q^{86} +(-131.746 + 131.746i) q^{87} +(-90.6043 + 90.6043i) q^{88} +194.282 q^{89} +(-43.5461 + 716.257i) q^{90} -958.835i q^{91} +(-66.7494 - 681.220i) q^{92} +(-765.755 - 765.755i) q^{93} +1248.42i q^{94} +(916.343 + 1034.98i) q^{95} +723.358 q^{96} +(1067.11 + 1067.11i) q^{97} +(280.292 + 280.292i) q^{98} -322.596 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 $

$2$	−2.66509	+	2.66509i	−0.942252	+	0.942252i	−0.998421	−	0.0561697i	$-0.982111\pi$
$2$	−2.66509	+	2.66509i	−0.942252	+	0.942252i	0.0561697	+	0.998421i	$0.482111\pi$
$3$	−2.23283	−	2.23283i	−0.429708	−	0.429708i	0.458821	−	0.888529i	$-0.348272\pi$
$3$	−2.23283	−	2.23283i	−0.429708	−	0.429708i	−0.888529	+	0.458821i	$0.848272\pi$
$4$		−	6.20541i		−	0.775676i
$5$	7.41137	+	8.37088i	0.662893	+	0.748714i
$5$	7.41137	+	8.37088i	0.662893	+	0.748714i
$6$	11.9014			0.809785
$7$	−10.9048	−	10.9048i	−0.588803	−	0.588803i	0.348505	−	0.937307i	$-0.386690\pi$
$7$	−10.9048	−	10.9048i	−0.588803	−	0.588803i	−0.937307	+	0.348505i	$0.886690\pi$
$8$	−4.78275	−	4.78275i	−0.211370	−	0.211370i
$9$		−	17.0290i		−	0.630703i
$10$	−42.0611	−	2.55718i	−1.33009	−	0.0808650i
$11$		−	18.9440i		−	0.519257i	−0.965709	−	0.259628i	$-0.916400\pi$
$11$		−	18.9440i		−	0.519257i	0.965709	−	0.259628i	$-0.0836001\pi$
$12$	−13.8556	+	13.8556i	−0.333314	+	0.333314i
$13$	43.9640	+	43.9640i	0.937955	+	0.937955i	0.998185	−	0.0602292i	$-0.0191832\pi$
$13$	43.9640	+	43.9640i	0.937955	+	0.937955i	−0.0602292	+	0.998185i	$0.519183\pi$
$14$	58.1244			1.10960
$15$	2.14242	−	35.2390i	0.0368780	−	0.606578i
$16$	75.1362			1.17400
$17$	−38.7029	−	38.7029i	−0.552166	−	0.552166i	0.374899	−	0.927066i	$-0.377677\pi$
$17$	−38.7029	−	38.7029i	−0.552166	−	0.552166i	−0.927066	+	0.374899i	$0.877677\pi$
$18$	45.3837	+	45.3837i	0.594281	+	0.594281i
$19$	123.640			1.49290			0.746448	−	0.665444i	$-0.231758\pi$
$19$	123.640			1.49290			0.746448	+	0.665444i	$0.231758\pi$
$20$	51.9447	−	45.9906i	0.580759	−	0.514190i
$21$			48.6969i			0.506026i
$22$	50.4874	+	50.4874i	0.489271	+	0.489271i
$23$	109.778	−	10.7567i	0.995234	−	0.0975182i
$23$	109.778	−	10.7567i	0.995234	−	0.0975182i
$24$			21.3581i			0.181654i
$25$	−15.1432	+	124.079i	−0.121146	+	0.992635i
$26$	−234.336			−1.76758
$27$	−98.3091	+	98.3091i	−0.700725	+	0.700725i
$28$	−67.6686	+	67.6686i	−0.456720	+	0.456720i
$29$		−	59.0042i		−	0.377821i	−0.981994	−	0.188910i	$-0.939504\pi$
$29$		−	59.0042i		−	0.377821i	0.981994	−	0.188910i	$-0.0604955\pi$
$30$	88.2054	+	99.6249i	0.536801	+	0.606298i
$31$	342.953			1.98698			0.993488	−	0.113938i	$-0.0363464\pi$
$31$	342.953			1.98698			0.993488	+	0.113938i	$0.0363464\pi$
$32$	−161.983	+	161.983i	−0.894836	+	0.894836i
$33$	−42.2986	+	42.2986i	−0.223129	+	0.223129i
$34$	206.293			1.04056
$35$	10.4632	−	172.102i	0.0505317	−	0.831158i
$36$	−105.672			−0.489221
$37$	−302.912	−	302.912i	−1.34590	−	1.34590i	−0.890062	−	0.455839i	$-0.849339\pi$
$37$	−302.912	−	302.912i	−1.34590	−	1.34590i	−0.455839	−	0.890062i	$-0.650661\pi$
$38$	−329.512	+	329.512i	−1.40668	+	1.40668i
$39$		−	196.328i		−	0.806093i
$40$	4.58909	−	75.4826i	0.0181400	−	0.298371i
$41$	137.839			0.525045			0.262523	−	0.964926i	$-0.415446\pi$
$41$	137.839			0.525045			0.262523	+	0.964926i	$0.415446\pi$
$42$	−129.782	−	129.782i	−0.476804	−	0.476804i
$43$	155.399	−	155.399i	0.551118	−	0.551118i	−0.375646	−	0.926763i	$-0.622579\pi$
$43$	155.399	−	155.399i	0.551118	−	0.551118i	0.926763	+	0.375646i	$0.122579\pi$
$44$	−117.555			−0.402775
$45$	142.547	−	126.208i	0.472216	−	0.418088i
$46$	−263.902	+	321.237i	−0.845874	+	1.02965i
$47$	234.217	−	234.217i	0.726894	−	0.726894i	−0.243106	−	0.970000i	$-0.578166\pi$
$47$	234.217	−	234.217i	0.726894	−	0.726894i	0.970000	+	0.243106i	$0.0781662\pi$
$48$	−167.766	−	167.766i	−0.504478	−	0.504478i
$49$		−	105.172i		−	0.306623i
$50$	−290.325	−	371.041i	−0.821162	−	1.04946i
$51$			172.834i			0.474540i
$52$	272.815	−	272.815i	0.727549	−	0.727549i
$53$	−342.095	+	342.095i	−0.886610	+	0.886610i	−0.994196	−	0.107586i	$-0.965688\pi$
$53$	−342.095	+	342.095i	−0.886610	+	0.886610i	0.107586	+	0.994196i	$0.465688\pi$
$54$		−	524.005i		−	1.32052i
$55$	158.578	−	140.401i	0.388775	−	0.344212i
$56$			104.310i			0.248910i
$57$	−276.067	−	276.067i	−0.641509	−	0.641509i
$58$	157.251	+	157.251i	0.356002	+	0.356002i
$59$			87.0009i			0.191975i	0.995383	+	0.0959877i	$0.0306009\pi$
$59$			87.0009i			0.191975i	−0.995383	+	0.0959877i	$0.969399\pi$
$60$	−218.672	−	13.2946i	−0.470508	−	0.0286053i
$61$		−	565.294i		−	1.18653i	−0.805006	−	0.593267i	$-0.797838\pi$
$61$		−	565.294i		−	1.18653i	0.805006	−	0.593267i	$-0.202162\pi$
$62$	−914.002	+	914.002i	−1.87223	+	1.87223i
$63$	−185.697	+	185.697i	−0.371359	+	0.371359i
$64$		−	262.307i		−	0.512319i
$65$	−42.1838	+	693.851i	−0.0804963	+	1.32402i
$66$		−	225.459i		−	0.420487i
$67$	−4.05177	−	4.05177i	−0.00738809	−	0.00738809i	0.703403	−	0.710791i	$-0.251663\pi$
$67$	−4.05177	−	4.05177i	−0.00738809	−	0.00738809i	−0.710791	+	0.703403i	$0.751663\pi$
$68$	−240.167	+	240.167i	−0.428302	+	0.428302i
$69$	−269.134	−	221.098i	−0.469564	−	0.385755i
$70$	430.782	+	486.552i	0.735546	+	0.830773i
$71$	−556.502			−0.930206			−0.465103	−	0.885257i	$-0.653983\pi$
$71$	−556.502			−0.930206			−0.465103	+	0.885257i	$0.653983\pi$
$72$	−81.4453	+	81.4453i	−0.133311	+	0.133311i
$73$	305.536	+	305.536i	0.489866	+	0.489866i	0.908264	−	0.418398i	$-0.137408\pi$
$73$	305.536	+	305.536i	0.489866	+	0.489866i	−0.418398	+	0.908264i	$0.637408\pi$
$74$	1614.57			2.53636
$75$	310.860	−	243.236i	0.478600	−	0.374486i
$76$		−	767.238i		−	1.15800i
$77$	−206.580	+	206.580i	−0.305740	+	0.305740i
$78$	523.232	+	523.232i	0.759543	+	0.759543i
$79$	−328.493			−0.467828			−0.233914	−	0.972257i	$-0.575153\pi$
$79$	−328.493			−0.467828			−0.233914	+	0.972257i	$0.575153\pi$
$80$	556.862	+	628.956i	0.778238	+	0.878992i
$81$	−20.7681			−0.0284885
$82$	−367.354	+	367.354i	−0.494725	+	0.494725i
$83$	810.460	−	810.460i	1.07180	−	1.07180i	0.0745876	−	0.997214i	$-0.476236\pi$
$83$	810.460	−	810.460i	1.07180	−	1.07180i	0.997214	−	0.0745876i	$-0.0237641\pi$
$84$	302.184			0.392512
$85$	37.1357	−	610.818i	0.0473875	−	0.779442i
$86$			828.302i			1.03858i
$87$	−131.746	+	131.746i	−0.162352	+	0.162352i
$88$	−90.6043	+	90.6043i	−0.109755	+	0.109755i
$89$	194.282			0.231391			0.115696	−	0.993285i	$-0.463090\pi$
$89$	194.282			0.231391			0.115696	+	0.993285i	$0.463090\pi$
$90$	−43.5461	+	716.257i	−0.0510018	+	0.838891i
$91$		−	958.835i		−	1.10454i
$92$	−66.7494	−	681.220i	−0.0756425	−	0.771979i
$93$	−765.755	−	765.755i	−0.853819	−	0.853819i
$94$			1248.42i			1.36983i
$95$	916.343	+	1034.98i	0.989630	+	1.11775i
$96$	723.358			0.769036
$97$	1067.11	+	1067.11i	1.11700	+	1.11700i	0.992179	+	0.124820i	$0.0398353\pi$
$97$	1067.11	+	1067.11i	1.11700	+	1.11700i	0.124820	+	0.992179i	$0.460165\pi$
$98$	280.292	+	280.292i	0.288916	+	0.288916i
$99$	−322.596			−0.327497
$100$	769.963	+	93.9697i	0.769963	+	0.0939697i
$101$	−1196.74			−1.17901			−0.589504	−	0.807766i	$-0.700677\pi$
$101$	−1196.74			−1.17901			−0.589504	+	0.807766i	$0.700677\pi$
$102$	−460.617	−	460.617i	−0.447136	−	0.447136i
$103$	647.268	−	647.268i	0.619196	−	0.619196i	−0.326129	−	0.945325i	$-0.605745\pi$
$103$	647.268	−	647.268i	0.619196	−	0.619196i	0.945325	+	0.326129i	$0.105745\pi$
$104$		−	420.538i		−	0.396511i
$105$	−407.636	+	360.911i	−0.378869	+	0.335441i
$106$		−	1823.43i		−	1.67082i
$107$	−1091.38	−	1091.38i	−0.986049	−	0.986049i	0.0138547	−	0.999904i	$-0.495590\pi$
$107$	−1091.38	−	1091.38i	−0.986049	−	0.986049i	−0.999904	+	0.0138547i	$0.995590\pi$
$108$	610.048	+	610.048i	0.543536	+	0.543536i
$109$	26.4427			0.0232362			0.0116181	−	0.999933i	$-0.496302\pi$
$109$	26.4427			0.0232362			0.0116181	+	0.999933i	$0.496302\pi$
$110$	−48.4431	+	796.805i	−0.0419897	+	0.690658i
$111$			1352.70i			1.15669i
$112$	−819.343	−	819.343i	−0.691256	−	0.691256i
$113$	−70.7193	+	70.7193i	−0.0588736	+	0.0588736i	−0.735931	−	0.677057i	$-0.763255\pi$
$113$	−70.7193	+	70.7193i	−0.0588736	+	0.0588736i	0.677057	+	0.735931i	$0.263255\pi$
$114$	1471.49			1.20892
$115$	903.651	+	839.220i	0.732747	+	0.680501i
$116$	−366.145			−0.293066
$117$	748.662	−	748.662i	0.591571	−	0.591571i
$118$	−231.865	−	231.865i	−0.180889	−	0.180889i
$119$			844.093i			0.650234i
$120$	−178.786	+	158.293i	−0.136007	+	0.120417i
$121$	972.126			0.730372
$122$	1506.56	+	1506.56i	1.11801	+	1.11801i
$123$	−307.771	−	307.771i	−0.225616	−	0.225616i
$124$		−	2128.17i		−	1.54125i
$125$	−1150.88	+	792.836i	−0.823506	+	0.567307i
$126$		−	989.799i		−	0.699828i
$127$	556.054	−	556.054i	0.388518	−	0.388518i	−0.485640	−	0.874159i	$-0.661414\pi$
$127$	556.054	−	556.054i	0.388518	−	0.388518i	0.874159	+	0.485640i	$0.161414\pi$
$128$	−596.789	−	596.789i	−0.412103	−	0.412103i
$129$	−693.956			−0.473639
$130$	−1736.75	−	1961.60i	−1.17172	−	1.32341i
$131$	423.960			0.282760			0.141380	−	0.989955i	$-0.454846\pi$
$131$	423.960			0.282760			0.141380	+	0.989955i	$0.454846\pi$
$132$	262.480	+	262.480i	0.173075	+	0.173075i
$133$	−1348.27	−	1348.27i	−0.879021	−	0.879021i
$134$	21.5966			0.0139229
$135$	−1551.54	−	94.3284i	−0.989149	−	0.0601370i
$136$			370.212i			0.233422i
$137$	651.809	+	651.809i	0.406480	+	0.406480i	0.880509	−	0.474029i	$-0.157201\pi$
$137$	651.809	+	651.809i	0.406480	+	0.406480i	−0.474029	+	0.880509i	$0.657201\pi$
$138$	1306.51	−	128.019i	0.805926	−	0.0789688i
$139$			959.361i			0.585409i	0.956203	+	0.292705i	$0.0945553\pi$
$139$			959.361i			0.585409i	−0.956203	+	0.292705i	$0.905445\pi$
$140$	−1067.96	−	64.9286i	−0.644709	−	0.0391962i
$141$	−1045.93			−0.624704
$142$	1483.13	−	1483.13i	0.876488	−	0.876488i
$143$	832.853	−	832.853i	0.487040	−	0.487040i
$144$		−	1279.49i		−	0.740447i
$145$	493.917	−	437.302i	0.282880	−	0.250455i
$146$	−1628.56			−0.923155
$147$	−234.830	+	234.830i	−0.131758	+	0.131758i
$148$	−1879.69	+	1879.69i	−1.04398	+	1.04398i
$149$	−2261.05			−1.24317			−0.621584	−	0.783347i	$-0.713511\pi$
$149$	−2261.05			−1.24317			−0.621584	+	0.783347i	$0.713511\pi$
$150$	−180.225	+	1476.71i	−0.0981019	+	0.803821i
$151$	676.556			0.364618			0.182309	−	0.983241i	$-0.441643\pi$
$151$	676.556			0.364618			0.182309	+	0.983241i	$0.441643\pi$
$152$	−591.340	−	591.340i	−0.315553	−	0.315553i
$153$	−659.070	+	659.070i	−0.348253	+	0.348253i
$154$		−	1101.11i		−	0.576167i
$155$	2541.75	+	2870.82i	1.31715	+	1.48768i
$156$	−1218.29			−0.625267
$157$	2211.51	+	2211.51i	1.12419	+	1.12419i	0.991105	+	0.133086i	$0.0424886\pi$
$157$	2211.51	+	2211.51i	1.12419	+	1.12419i	0.133086	+	0.991105i	$0.457511\pi$
$158$	875.464	−	875.464i	0.440811	−	0.440811i
$159$	1527.68			0.761966
$160$	−2556.45	−	155.424i	−1.26316	−	0.0767958i
$161$	−1314.41	−	1079.81i	−0.643415	−	0.528577i
$162$	55.3490	−	55.3490i	0.0268434	−	0.0268434i
$163$	−11.1549	−	11.1549i	−0.00536025	−	0.00536025i	0.704422	−	0.709782i	$-0.251206\pi$
$163$	−11.1549	−	11.1549i	−0.00536025	−	0.00536025i	−0.709782	+	0.704422i	$0.751206\pi$
$164$		−	855.348i		−	0.407265i
$165$	−667.567	−	40.5859i	−0.314970	−	0.0191491i
$166$			4319.90i			2.01981i
$167$	−2023.17	+	2023.17i	−0.937470	+	0.937470i	−0.998157	−	0.0606869i	$-0.980671\pi$
$167$	−2023.17	+	2023.17i	−0.937470	+	0.937470i	0.0606869	+	0.998157i	$0.480671\pi$
$168$	232.905	−	232.905i	0.106959	−	0.106959i
$169$			1668.67i			0.759521i
$170$	1528.92	+	1726.86i	0.689779	+	0.779081i
$171$		−	2105.47i		−	0.941573i
$172$	−964.312	−	964.312i	−0.427489	−	0.427489i
$173$	305.721	+	305.721i	0.134356	+	0.134356i	0.771086	−	0.636731i	$-0.219714\pi$
$173$	305.721	+	305.721i	0.134356	+	0.134356i	−0.636731	+	0.771086i	$0.719714\pi$
$174$		−	702.230i		−	0.305954i
$175$	1518.19	−	1187.92i	0.655797	−	0.513135i
$176$		−	1423.38i		−	0.609609i
$177$	194.258	−	194.258i	0.0824933	−	0.0824933i
$178$	−517.778	+	517.778i	−0.218029	+	0.218029i
$179$			3865.17i			1.61395i	0.590587	+	0.806974i	$0.298896\pi$
$179$			3865.17i			1.61395i	−0.590587	+	0.806974i	$0.701104\pi$
$180$	−783.172	−	884.565i	−0.324301	−	0.366287i
$181$		−	667.154i		−	0.273973i	−0.990573	−	0.136987i	$-0.956258\pi$
$181$		−	667.154i		−	0.273973i	0.990573	−	0.136987i	$-0.0437417\pi$
$182$	2555.38	+	2555.38i	1.04076	+	1.04076i
$183$	−1262.20	+	1262.20i	−0.509863	+	0.509863i
$184$	−576.489	−	473.596i	−0.230975	−	0.189750i
$185$	290.646	−	4780.62i	0.115507	−	1.89988i
$186$	4081.61			1.60902
$187$	−733.187	+	733.187i	−0.286716	+	0.286716i
$188$	−1453.41	−	1453.41i	−0.563834	−	0.563834i
$189$	2144.08			0.825178
$190$	−5200.45	−	316.170i	−1.98568	−	0.120723i
$191$		−	1067.82i		−	0.404527i	−0.979331	−	0.202263i	$-0.935170\pi$
$191$		−	1067.82i		−	0.404527i	0.979331	−	0.202263i	$-0.0648297\pi$
$192$	−585.686	+	585.686i	−0.220147	+	0.220147i
$193$	417.876	+	417.876i	0.155852	+	0.155852i	0.780726	−	0.624874i	$-0.214850\pi$
$193$	417.876	+	417.876i	0.155852	+	0.155852i	−0.624874	+	0.780726i	$0.714850\pi$
$194$	−5687.91			−2.10499
$195$	1643.44	−	1455.06i	0.603533	−	0.534354i
$196$	−652.633			−0.237840
$197$	572.015	−	572.015i	0.206875	−	0.206875i	−0.596063	−	0.802938i	$-0.703269\pi$
$197$	572.015	−	572.015i	0.206875	−	0.206875i	0.802938	+	0.596063i	$0.203269\pi$
$198$	859.749	−	859.749i	0.308584	−	0.308584i
$199$	−3406.06			−1.21331			−0.606657	−	0.794964i	$-0.707490\pi$
$199$	−3406.06			−1.21331			−0.606657	+	0.794964i	$0.707490\pi$
$200$	665.867	−	521.014i	0.235419	−	0.184206i
$201$			18.0938i			0.00634944i
$202$	3189.41	−	3189.41i	1.11092	−	1.11092i
$203$	−643.427	+	643.427i	−0.222462	+	0.222462i
$204$	1072.50			0.368089
$205$	1021.58	+	1153.83i	0.348049	+	0.393109i
$206$			3450.05i			1.16688i
$207$	−183.175	−	1869.41i	−0.0615050	−	0.627697i
$208$	3303.29	+	3303.29i	1.10116	+	1.10116i
$209$		−	2342.24i		−	0.775196i
$210$	124.527	−	2048.25i	0.0409198	−	0.673060i
$211$	−2577.48			−0.840954			−0.420477	−	0.907303i	$-0.638137\pi$
$211$	−2577.48			−0.840954			−0.420477	+	0.907303i	$0.638137\pi$
$212$	2122.84	+	2122.84i	0.687722	+	0.687722i
$213$	1242.57	+	1242.57i	0.399717	+	0.399717i
$214$	5817.23			1.85821
$215$	2452.54	+	149.106i	0.777962	+	0.0472975i
$216$	940.375			0.296224
$217$	−3739.83	−	3739.83i	−1.16994	−	1.16994i
$218$	−70.4721	+	70.4721i	−0.0218944	+	0.0218944i
$219$		−	1364.42i		−	0.420999i
$220$	−871.244	−	984.039i	−0.266997	−	0.301563i
$221$		−	3403.07i		−	1.03581i
$222$	−3605.06	−	3605.06i	−1.08989	−	1.08989i
$223$	−1070.51	−	1070.51i	−0.321465	−	0.321465i	0.527864	−	0.849329i	$-0.322993\pi$
$223$	−1070.51	−	1070.51i	−0.321465	−	0.321465i	−0.849329	+	0.527864i	$0.822993\pi$
$224$	3532.77			1.05376
$225$	2112.94	+	257.873i	0.626057	+	0.0764069i
$226$		−	376.947i		−	0.110947i
$227$	−1638.67	−	1638.67i	−0.479129	−	0.479129i	0.425724	−	0.904853i	$-0.360019\pi$
$227$	−1638.67	−	1638.67i	−0.479129	−	0.479129i	−0.904853	+	0.425724i	$0.860019\pi$
$228$	−1713.11	+	1713.11i	−0.497603	+	0.497603i
$229$	−2319.00			−0.669188			−0.334594	−	0.942362i	$-0.608599\pi$
$229$	−2319.00			−0.669188			−0.334594	+	0.942362i	$0.608599\pi$
$230$	−4644.91	+	171.714i	−1.33164	+	0.0492283i
$231$	922.514			0.262757
$232$	−282.202	+	282.202i	−0.0798598	+	0.0798598i
$233$	597.533	+	597.533i	0.168007	+	0.168007i	0.786103	−	0.618096i	$-0.212096\pi$
$233$	597.533	+	597.533i	0.168007	+	0.168007i	−0.618096	+	0.786103i	$0.712096\pi$
$234$			3990.50i			1.11482i
$235$	3696.47	+	224.733i	1.02609	+	0.0623828i
$236$	539.876			0.148911
$237$	733.468	+	733.468i	0.201029	+	0.201029i
$238$	−2249.58	−	2249.58i	−0.612684	−	0.612684i
$239$		−	226.067i		−	0.0611845i	−0.999532	−	0.0305922i	$-0.990261\pi$
$239$		−	226.067i		−	0.0611845i	0.999532	−	0.0305922i	$-0.00973933\pi$
$240$	160.973	−	2647.73i	0.0432948	−	0.712125i
$241$			5848.33i			1.56317i	0.623799	+	0.781585i	$0.285588\pi$
$241$			5848.33i			1.56317i	−0.623799	+	0.781585i	$0.714412\pi$
$242$	−2590.80	+	2590.80i	−0.688195	+	0.688195i
$243$	2700.72	+	2700.72i	0.712967	+	0.712967i
$244$	−3507.88			−0.920365
$245$	880.379	−	779.466i	0.229573	−	0.203258i
$246$	1640.47			0.425174
$247$	5435.72	+	5435.72i	1.40027	+	1.40027i
$248$	−1640.26	−	1640.26i	−0.419987	−	0.419987i
$249$	−3619.23			−0.921123
$250$	954.232	−	5180.19i	0.241404	−	1.31050i
$251$			6646.18i			1.67133i	0.549241	+	0.835664i	$0.314917\pi$
$251$			6646.18i			1.67133i	−0.549241	+	0.835664i	$0.685083\pi$
$252$	1152.33	+	1152.33i	0.288055	+	0.288055i
$253$	−203.774	−	2079.64i	−0.0506370	−	0.516782i
$254$			2963.87i			0.732164i
$255$	−1446.77	+	1280.93i	−0.355295	+	0.314569i
$256$	5279.45			1.28893
$257$	1313.92	−	1313.92i	0.318910	−	0.318910i	−0.529438	−	0.848348i	$-0.677597\pi$
$257$	1313.92	−	1313.92i	0.318910	−	0.318910i	0.848348	+	0.529438i	$0.177597\pi$
$258$	1849.46	−	1849.46i	0.446287	−	0.446287i
$259$			6606.37i			1.58494i
$260$	4305.63	+	261.768i	1.02701	+	0.0624390i
$261$	−1004.78			−0.238292
$262$	−1129.89	+	1129.89i	−0.266431	+	0.266431i
$263$	4634.72	−	4634.72i	1.08665	−	1.08665i	0.0907786	−	0.995871i	$-0.471064\pi$
$263$	4634.72	−	4634.72i	1.08665	−	1.08665i	0.995871	−	0.0907786i	$-0.0289356\pi$
$264$	404.608			0.0943253
$265$	−5399.02	−	328.243i	−1.25154	−	0.0760898i
$266$	7186.52			1.65652
$267$	−433.797	−	433.797i	−0.0994305	−	0.0994305i
$268$	−25.1429	+	25.1429i	−0.00573076	+	0.00573076i
$269$			4119.24i			0.933661i	0.884347	+	0.466830i	$0.154604\pi$
$269$			4119.24i			0.933661i	−0.884347	+	0.466830i	$0.845396\pi$
$270$	4386.38	−	3883.59i	0.988691	−	0.875363i
$271$	5232.41			1.17287			0.586433	−	0.809998i	$-0.300532\pi$
$271$	5232.41			1.17287			0.586433	+	0.809998i	$0.300532\pi$
$272$	−2907.99	−	2907.99i	−0.648245	−	0.648245i
$273$	−2140.91	+	2140.91i	−0.474630	+	0.474630i
$274$	−3474.26			−0.766014
$275$	2350.56	+	286.872i	0.515432	+	0.0629057i
$276$	−1372.01	+	1670.09i	−0.299221	+	0.364229i
$277$	−6408.30	+	6408.30i	−1.39003	+	1.39003i	−0.564798	+	0.825229i	$0.691046\pi$
$277$	−6408.30	+	6408.30i	−1.39003	+	1.39003i	−0.825229	+	0.564798i	$0.808954\pi$
$278$	−2556.78	−	2556.78i	−0.551603	−	0.551603i
$279$		−	5840.14i		−	1.25319i
$280$	−873.163	+	773.077i	−0.186362	+	0.165001i
$281$			2894.08i			0.614400i	0.951645	+	0.307200i	$0.0993921\pi$
$281$			2894.08i			0.614400i	−0.951645	+	0.307200i	$0.900608\pi$
$282$	2787.50	−	2787.50i	0.588628	−	0.588628i
$283$	1464.96	−	1464.96i	0.307714	−	0.307714i	−0.536308	−	0.844022i	$-0.680181\pi$
$283$	1464.96	−	1464.96i	0.307714	−	0.307714i	0.844022	+	0.536308i	$0.180181\pi$
$284$			3453.32i			0.721538i
$285$	264.889	−	4356.96i	0.0550549	−	0.905558i
$286$			4439.26i			0.917828i
$287$	−1503.11	−	1503.11i	−0.309148	−	0.309148i
$288$	2758.40	+	2758.40i	0.564376	+	0.564376i
$289$		−	1917.17i		−	0.390225i
$290$	−150.884	+	2481.78i	−0.0305525	+	0.502535i
$291$		−	4765.36i		−	0.959966i
$292$	1895.97	−	1895.97i	0.379977	−	0.379977i
$293$	1164.58	−	1164.58i	0.232202	−	0.232202i	−0.581409	−	0.813611i	$-0.697498\pi$
$293$	1164.58	−	1164.58i	0.232202	−	0.232202i	0.813611	+	0.581409i	$0.197498\pi$
$294$		−	1251.69i		−	0.248299i
$295$	−728.274	+	644.796i	−0.143735	+	0.127259i
$296$			2897.50i			0.568966i
$297$	1862.36	+	1862.36i	0.363856	+	0.363856i
$298$	6025.89	−	6025.89i	1.17138	−	1.17138i
$299$	5299.20	+	4353.39i	1.02495	+	0.842017i
$300$	−1509.38	−	1929.01i	−0.290479	−	0.371238i
$301$	−3389.17			−0.648999
$302$	−1803.08	+	1803.08i	−0.343562	+	0.343562i
$303$	2672.10	+	2672.10i	0.506628	+	0.506628i
$304$	9289.85			1.75266
$305$	4732.01	−	4189.61i	0.888374	−	0.786545i
$306$		−	3512.96i		−	0.656283i
$307$	1757.91	−	1757.91i	0.326806	−	0.326806i	−0.524565	−	0.851371i	$-0.675772\pi$
$307$	1757.91	−	1757.91i	0.326806	−	0.326806i	0.851371	+	0.524565i	$0.175772\pi$
$308$	1281.91	+	1281.91i	0.237155	+	0.237155i
$309$	−2890.47			−0.532146
$310$	−14425.0	−	876.992i	−2.64285	−	0.160677i
$311$	2236.39			0.407762			0.203881	−	0.978996i	$-0.434644\pi$
$311$	2236.39			0.407762			0.203881	+	0.978996i	$0.434644\pi$
$312$	−938.988	+	938.988i	−0.170384	+	0.170384i
$313$	−2726.31	+	2726.31i	−0.492333	+	0.492333i	−0.909041	−	0.416708i	$-0.863184\pi$
$313$	−2726.31	+	2726.31i	−0.492333	+	0.492333i	0.416708	+	0.909041i	$0.363184\pi$
$314$	−11787.8			−2.11854
$315$	−2930.72	−	178.178i	−0.524214	−	0.0318704i
$316$			2038.43i			0.362883i
$317$	−2582.03	+	2582.03i	−0.457480	+	0.457480i	−0.897827	−	0.440348i	$-0.854855\pi$
$317$	−2582.03	+	2582.03i	−0.457480	+	0.457480i	0.440348	+	0.897827i	$0.354855\pi$
$318$	−4071.39	+	4071.39i	−0.717964	+	0.717964i
$319$	−1117.77			−0.196186
$320$	2195.74	−	1944.06i	0.383580	−	0.339613i
$321$			4873.71i			0.847426i
$322$	6380.80	−	625.224i	1.10431	−	0.108206i
$323$	−4785.23	−	4785.23i	−0.824327	−	0.824327i
$324$			128.875i			0.0220979i
$325$	−6120.78	+	4789.27i	−1.04468	+	0.817418i
$326$	59.4577			0.0101014
$327$	−59.0419	−	59.0419i	−0.00998478	−	0.00998478i
$328$	−659.250	−	659.250i	−0.110979	−	0.110979i
$329$	−5108.16			−0.855994
$330$	1887.29	−	1670.96i	0.314824	−	0.278738i
$331$	−6499.87			−1.07935			−0.539676	−	0.841873i	$-0.681453\pi$
$331$	−6499.87			−1.07935			−0.539676	+	0.841873i	$0.681453\pi$
$332$	−5029.24	−	5029.24i	−0.831371	−	0.831371i
$333$	−5158.27	+	5158.27i	−0.848864	+	0.848864i
$334$		−	10783.9i		−	1.76666i
$335$	3.88770	−	63.9460i	0.000634053	−	0.0104291i
$336$			3658.90i			0.594076i
$337$	−2735.52	−	2735.52i	−0.442176	−	0.442176i	0.450567	−	0.892743i	$-0.351222\pi$
$337$	−2735.52	−	2735.52i	−0.442176	−	0.442176i	−0.892743	+	0.450567i	$0.851222\pi$
$338$	−4447.15	−	4447.15i	−0.715659	−	0.715659i
$339$	315.808			0.0505968
$340$	−3790.38	−	230.442i	−0.604594	−	0.0367573i
$341$		−	6496.90i		−	1.03175i
$342$	5611.26	+	5611.26i	0.887199	+	0.887199i
$343$	−4887.21	+	4887.21i	−0.769343	+	0.769343i
$344$	−1486.47			−0.232979
$345$	−143.863	−	3891.53i	−0.0224502	−	0.607284i
$346$	−1629.55			−0.253194
$347$	6733.74	−	6733.74i	1.04175	−	1.04175i	0.0426573	−	0.999090i	$-0.486418\pi$
$347$	6733.74	−	6733.74i	1.04175	−	1.04175i	0.999090	−	0.0426573i	$-0.0135824\pi$
$348$	817.538	+	817.538i	0.125933	+	0.125933i
$349$		−	6515.26i		−	0.999295i	−0.866229	−	0.499648i	$-0.833463\pi$
$349$		−	6515.26i		−	0.999295i	0.866229	−	0.499648i	$-0.166537\pi$
$350$	−880.190	+	7212.04i	−0.134423	+	1.10143i
$351$	−8644.12			−1.31450
$352$	3068.60	+	3068.60i	0.464650	+	0.464650i
$353$	−639.089	−	639.089i	−0.0963605	−	0.0963605i	0.657283	−	0.753644i	$-0.271706\pi$
$353$	−639.089	−	639.089i	−0.0963605	−	0.0963605i	−0.753644	+	0.657283i	$0.771706\pi$
$354$			1035.43i			0.155459i
$355$	−4124.44	−	4658.41i	−0.616627	−	0.696458i
$356$		−	1205.60i		−	0.179484i
$357$	1884.71	−	1884.71i	0.279410	−	0.279410i
$358$	−10301.0	−	10301.0i	−1.52075	−	1.52075i
$359$	827.280			0.121622			0.0608108	−	0.998149i	$-0.480631\pi$
$359$	827.280			0.121622			0.0608108	+	0.998149i	$0.480631\pi$
$360$	−1285.39	−	78.1475i	−0.188183	−	0.0114409i
$361$	8427.91			1.22874
$362$	1778.02	+	1778.02i	0.258152	+	0.258152i
$363$	−2170.59	−	2170.59i	−0.313847	−	0.313847i
$364$	−5949.96			−0.856766
$365$	−293.164	+	4822.04i	−0.0420408	+	0.691499i
$366$		−	6727.78i		−	0.960837i
$367$	23.1366	+	23.1366i	0.00329079	+	0.00329079i	0.708750	−	0.705459i	$-0.249259\pi$
$367$	23.1366	+	23.1366i	0.00329079	+	0.00329079i	−0.705459	+	0.708750i	$0.749259\pi$
$368$	8248.33	−	808.214i	1.16841	−	0.114487i
$369$		−	2347.26i		−	0.331148i
$370$	11966.2	+	13515.4i	1.68133	+	1.89900i
$371$	7460.93			1.04408
$372$	−4751.82	+	4751.82i	−0.662287	+	0.662287i
$373$	5882.41	−	5882.41i	0.816567	−	0.816567i	−0.169042	−	0.985609i	$-0.554067\pi$
$373$	5882.41	−	5882.41i	0.816567	−	0.816567i	0.985609	+	0.169042i	$0.0540672\pi$
$374$		−	3908.02i		−	0.540317i
$375$	4339.99	+	799.461i	0.597643	+	0.110091i
$376$	−2240.40			−0.307287
$377$	2594.06	−	2594.06i	0.354379	−	0.354379i
$378$	−5714.16	+	5714.16i	−0.777525	+	0.777525i
$379$	7914.92			1.07272			0.536362	−	0.843988i	$-0.319798\pi$
$379$	7914.92			1.07272			0.536362	+	0.843988i	$0.319798\pi$
$380$	6422.46	−	5686.28i	0.867013	−	0.767632i
$381$	−2483.14			−0.333899
$382$	2845.83	+	2845.83i	0.381166	+	0.381166i
$383$	−5318.45	+	5318.45i	−0.709556	+	0.709556i	−0.966442	−	0.256886i	$-0.917304\pi$
$383$	−5318.45	+	5318.45i	−0.709556	+	0.709556i	0.256886	+	0.966442i	$0.417304\pi$
$384$			2665.05i			0.354168i
$385$	−3260.29	−	198.215i	−0.431584	−	0.0262389i
$386$	−2227.35			−0.293703
$387$	−2646.28	−	2646.28i	−0.347591	−	0.347591i
$388$	6621.87	−	6621.87i	0.866429	−	0.866429i
$389$	−2642.55			−0.344428			−0.172214	−	0.985060i	$-0.555092\pi$
$389$	−2642.55			−0.344428			−0.172214	+	0.985060i	$0.555092\pi$
$390$	−502.045	+	8257.77i	−0.0651847	+	1.07218i
$391$	−4665.05	−	3832.43i	−0.603381	−	0.495688i
$392$	−503.010	+	503.010i	−0.0648108	+	0.0648108i
$393$	−946.630	−	946.630i	−0.121504	−	0.121504i
$394$			3048.94i			0.389857i
$395$	−2434.58	−	2749.78i	−0.310120	−	0.350269i
$396$			2001.84i			0.254031i
$397$	7988.94	−	7988.94i	1.00996	−	1.00996i	0.0100085	−	0.999950i	$-0.496814\pi$
$397$	7988.94	−	7988.94i	1.00996	−	1.00996i	0.999950	−	0.0100085i	$-0.00318586\pi$
$398$	9077.46	−	9077.46i	1.14325	−	1.14325i
$399$			6020.90i			0.755444i
$400$	−1137.80	+	9322.85i	−0.142225	+	1.16536i
$401$		−	10087.1i		−	1.25618i	−0.778141	−	0.628090i	$-0.783837\pi$
$401$		−	10087.1i		−	1.25618i	0.778141	−	0.628090i	$-0.216163\pi$
$402$	−48.2215	−	48.2215i	−0.00598277	−	0.00598277i
$403$	15077.6	+	15077.6i	1.86369	+	1.86369i
$404$			7426.24i			0.914527i
$405$	−153.920	−	173.848i	−0.0188849	−	0.0213298i
$406$		−	3429.58i		−	0.419230i
$407$	−5738.35	+	5738.35i	−0.698868	+	0.698868i
$408$	826.620	−	826.620i	0.100303	−	0.100303i
$409$			378.591i			0.0457705i	0.999738	+	0.0228853i	$0.00728524\pi$
$409$			378.591i			0.0457705i	−0.999738	+	0.0228853i	$0.992715\pi$
$410$	−5797.67	−	352.479i	−0.698357	−	0.0424578i
$411$		−	2910.75i		−	0.349335i
$412$	−4016.56	−	4016.56i	−0.480295	−	0.480295i
$413$	948.725	−	948.725i	0.113036	−	0.113036i
$414$	5470.33	+	4493.98i	0.649401	+	0.533495i
$415$	12790.9	+	777.643i	1.51296	+	0.0919832i
$416$	−14242.8			−1.67863
$417$	2142.09	−	2142.09i	0.251555	−	0.251555i
$418$	6242.27	+	6242.27i	0.730430	+	0.730430i
$419$	−2865.04			−0.334049			−0.167025	−	0.985953i	$-0.553416\pi$
$419$	−2865.04			−0.334049			−0.167025	+	0.985953i	$0.553416\pi$
$420$	2239.60	+	2529.55i	0.260194	+	0.293879i
$421$			8714.92i			1.00888i	0.863446	+	0.504441i	$0.168301\pi$
$421$			8714.92i			1.00888i	−0.863446	+	0.504441i	$0.831699\pi$
$422$	6869.23	−	6869.23i	0.792390	−	0.792390i
$423$	−3988.47	−	3988.47i	−0.458454	−	0.458454i
$424$	3272.31			0.374805
$425$	5388.31	−	4216.14i	0.614992	−	0.481207i
$426$	−6623.13			−0.753267
$427$	−6164.41	+	6164.41i	−0.698634	+	0.698634i
$428$	−6772.43	+	6772.43i	−0.764855	+	0.764855i
$429$	−3719.23			−0.418569
$430$	−6933.62	+	6138.86i	−0.777602	+	0.688470i
$431$		−	10921.2i		−	1.22054i	−0.792192	−	0.610272i	$-0.791060\pi$
$431$		−	10921.2i		−	1.22054i	0.792192	−	0.610272i	$-0.208940\pi$
$432$	−7386.57	+	7386.57i	−0.822654	+	0.822654i
$433$	−4506.50	+	4506.50i	−0.500158	+	0.500158i	−0.911487	−	0.411329i	$-0.865065\pi$
$433$	−4506.50	+	4506.50i	−0.500158	+	0.500158i	0.411329	+	0.911487i	$0.365065\pi$
$434$	19934.0			2.20475
$435$	−2079.25	−	126.411i	−0.229178	−	0.0139333i
$436$		−	164.088i		−	0.0180238i
$437$	13573.0	−	1329.96i	1.48578	−	0.145584i
$438$	3636.29	+	3636.29i	0.396687	+	0.396687i
$439$		−	3381.56i		−	0.367638i	−0.982960	−	0.183819i	$-0.941154\pi$
$439$		−	3381.56i		−	0.367638i	0.982960	−	0.183819i	$-0.0588461\pi$
$440$	−1429.94	−	86.9356i	−0.154931	−	0.00941930i
$441$	−1790.97			−0.193388
$442$	9069.48	+	9069.48i	0.975998	+	0.975998i
$443$	6813.81	+	6813.81i	0.730776	+	0.730776i	0.970774	−	0.239997i	$-0.0771466\pi$
$443$	6813.81	+	6813.81i	0.730776	+	0.730776i	−0.239997	+	0.970774i	$0.577147\pi$
$444$	8394.04			0.897215
$445$	1439.89	+	1626.31i	0.153387	+	0.173246i
$446$	5706.01			0.605802
$447$	5048.52	+	5048.52i	0.534199	+	0.534199i
$448$	−2860.40	+	2860.40i	−0.301655	+	0.301655i
$449$			7966.78i			0.837363i	0.908133	+	0.418681i	$0.137508\pi$
$449$			7966.78i			0.837363i	−0.908133	+	0.418681i	$0.862492\pi$
$450$	−6318.44	+	4943.93i	−0.661898	+	0.517909i
$451$		−	2611.22i		−	0.272633i
$452$	438.842	+	438.842i	0.0456668	+	0.0456668i
$453$	−1510.63	−	1510.63i	−0.156679	−	0.156679i
$454$	8734.39			0.902919
$455$	8026.29	−	7106.28i	0.826986	−	0.732193i
$456$			2640.72i			0.271191i
$457$	2700.58	+	2700.58i	0.276429	+	0.276429i	0.831682	−	0.555253i	$-0.187378\pi$
$457$	2700.58	+	2700.58i	0.276429	+	0.276429i	−0.555253	+	0.831682i	$0.687378\pi$
$458$	6180.35	−	6180.35i	0.630543	−	0.630543i
$459$	7609.69			0.773834
$460$	5207.70	−	5607.52i	0.527849	−	0.568374i
$461$	−5487.65			−0.554415			−0.277207	−	0.960810i	$-0.589409\pi$
$461$	−5487.65			−0.554415			−0.277207	+	0.960810i	$0.589409\pi$
$462$	−2458.58	+	2458.58i	−0.247584	+	0.247584i
$463$	3096.37	+	3096.37i	0.310801	+	0.310801i	0.845220	−	0.534419i	$-0.179470\pi$
$463$	3096.37	+	3096.37i	0.310801	+	0.310801i	−0.534419	+	0.845220i	$0.679470\pi$
$464$		−	4433.35i		−	0.443562i
$465$	734.749	−	12085.3i	0.0732756	−	1.20526i
$466$	−3184.96			−0.316610
$467$	1288.36	+	1288.36i	0.127662	+	0.127662i	0.768051	−	0.640389i	$-0.221227\pi$
$467$	1288.36	+	1288.36i	0.127662	+	0.127662i	−0.640389	+	0.768051i	$0.721227\pi$
$468$	−4645.75	−	4645.75i	−0.458867	−	0.458867i
$469$			88.3672i			0.00870025i
$470$	−10450.3	+	9252.48i	−1.02561	+	0.908053i
$471$		−	9875.85i		−	0.966146i
$472$	416.103	−	416.103i	0.0405778	−	0.0405778i
$473$	−2943.87	−	2943.87i	−0.286172	−	0.286172i
$474$	−3909.52			−0.378840
$475$	−1872.31	+	15341.2i	−0.180858	+	1.48190i
$476$	5237.94			0.504371
$477$	5825.52	+	5825.52i	0.559187	+	0.559187i
$478$	602.490	+	602.490i	0.0576511	+	0.0576511i
$479$	−12639.3			−1.20564			−0.602822	−	0.797876i	$-0.705957\pi$
$479$	−12639.3			−1.20564			−0.602822	+	0.797876i	$0.705957\pi$
$480$	5361.08	+	6055.14i	0.509789	+	0.575788i
$481$		−	26634.4i		−	2.52479i
$482$	−15586.3	−	15586.3i	−1.47290	−	1.47290i
$483$	523.816	+	5345.87i	0.0493467	+	0.503614i
$484$		−	6032.44i		−	0.566532i
$485$	−1023.90	+	16841.4i	−0.0958620	+	1.57676i
$486$	−14395.3			−1.34359
$487$	4365.88	−	4365.88i	0.406236	−	0.406236i	−0.474188	−	0.880424i	$-0.657258\pi$
$487$	4365.88	−	4365.88i	0.406236	−	0.406236i	0.880424	+	0.474188i	$0.157258\pi$
$488$	−2703.66	+	2703.66i	−0.250797	+	0.250797i
$489$			49.8140i			0.00460668i
$490$	−268.943	+	4423.64i	−0.0247951	+	0.407836i
$491$	−3537.80			−0.325170			−0.162585	−	0.986695i	$-0.551983\pi$
$491$	−3537.80			−0.325170			−0.162585	+	0.986695i	$0.551983\pi$
$492$	−1909.84	+	1909.84i	−0.175005	+	0.175005i
$493$	−2283.63	+	2283.63i	−0.208620	+	0.208620i
$494$	−28973.4			−2.63881
$495$	−2390.88	−	2700.42i	−0.217095	−	0.245201i
$496$	25768.2			2.33272
$497$	6068.53	+	6068.53i	0.547708	+	0.547708i
$498$	9645.58	−	9645.58i	0.867930	−	0.867930i
$499$		−	10053.3i		−	0.901902i	−0.892549	−	0.450951i	$-0.851085\pi$
$499$		−	10053.3i		−	0.901902i	0.892549	−	0.450951i	$-0.148915\pi$
$500$	4919.87	+	7141.71i	0.440047	+	0.638774i
$501$	9034.77			0.805676
$502$	−17712.7	−	17712.7i	−1.57481	−	1.57481i
$503$	4941.64	−	4941.64i	0.438046	−	0.438046i	−0.453308	−	0.891354i	$-0.649756\pi$
$503$	4941.64	−	4941.64i	0.438046	−	0.438046i	0.891354	+	0.453308i	$0.149756\pi$
$504$	1776.29			0.156988
$505$	−8869.45	−	10017.7i	−0.781556	−	0.882739i
$506$	6085.50	+	4999.35i	0.534651	+	0.439226i
$507$	3725.84	−	3725.84i	0.326372	−	0.326372i
$508$	−3450.54	−	3450.54i	−0.301364	−	0.301364i
$509$		−	15010.7i		−	1.30715i	−0.756864	−	0.653573i	$-0.773269\pi$
$509$		−	15010.7i		−	1.30715i	0.756864	−	0.653573i	$-0.226731\pi$
$510$	441.966	−	7269.57i	0.0383737	−	0.631181i
$511$		−	6663.60i		−	0.576869i
$512$	−9295.90	+	9295.90i	−0.802392	+	0.802392i
$513$	−12155.0	+	12155.0i	−1.04611	+	1.04611i
$514$			7003.41i			0.600987i
$515$	10215.3	+	621.059i	0.874061	+	0.0531400i
$516$			4306.28i			0.367390i
$517$	−4437.00	−	4437.00i	−0.377445	−	0.377445i
$518$	−17606.6	−	17606.6i	−1.49341	−	1.49341i
$519$		−	1365.25i		−	0.115467i
$520$	3520.27	−	3116.76i	0.296873	−	0.262844i
$521$			23063.8i			1.93943i	0.244236	+	0.969716i	$0.421463\pi$
$521$			23063.8i			1.93943i	−0.244236	+	0.969716i	$0.578537\pi$
$522$	2677.83	−	2677.83i	0.224531	−	0.224531i
$523$	4272.34	−	4272.34i	0.357202	−	0.357202i	−0.505579	−	0.862781i	$-0.668721\pi$
$523$	4272.34	−	4272.34i	0.357202	−	0.357202i	0.862781	+	0.505579i	$0.168721\pi$
$524$		−	2630.85i		−	0.219330i
$525$	−6042.29	−	737.428i	−0.502299	−	0.0613028i
$526$			24703.9i			2.04779i
$527$	−13273.3	−	13273.3i	−1.09714	−	1.09714i
$528$	−3178.16	+	3178.16i	−0.261954	+	0.261954i
$529$	11935.6	−	2361.70i	0.980980	−	0.194107i
$530$	15263.7	−	13514.1i	1.25097	−	1.10757i
$531$	1481.54			0.121079
$532$	−8366.56	+	8366.56i	−0.681835	+	0.681835i
$533$	6059.96	+	6059.96i	0.492469	+	0.492469i
$534$	2312.22			0.187377
$535$	1047.18	−	17224.4i	0.0846238	−	1.39191i
$536$			38.7572i			0.00312324i
$537$	8630.26	−	8630.26i	0.693526	−	0.693526i
$538$	−10978.2	−	10978.2i	−0.879743	−	0.879743i
$539$	−1992.37			−0.159216
$540$	−585.346	+	9627.92i	−0.0466468	+	0.767259i
$541$	−19660.0			−1.56238			−0.781192	−	0.624290i	$-0.785388\pi$
$541$	−19660.0			−1.56238			−0.781192	+	0.624290i	$0.785388\pi$
$542$	−13944.9	+	13944.9i	−1.10513	+	1.10513i
$543$	−1489.64	+	1489.64i	−0.117728	+	0.117728i
$544$	12538.4			0.988197
$545$	195.976	+	221.348i	0.0154031	+	0.0173973i
$546$		−	11411.4i		−	0.894441i
$547$	−9956.97	+	9956.97i	−0.778299	+	0.778299i	−0.979541	−	0.201243i	$-0.935502\pi$
$547$	−9956.97	+	9956.97i	−0.778299	+	0.778299i	0.201243	+	0.979541i	$0.435502\pi$
$548$	4044.74	−	4044.74i	0.315297	−	0.315297i
$549$	−9626.38			−0.748350
$550$	−7028.99	+	5499.90i	−0.544940	+	0.426394i
$551$		−	7295.29i		−	0.564047i
$552$	229.742	+	2344.66i	0.0177146	+	0.180789i
$553$	3582.15	+	3582.15i	0.275458	+	0.275458i
$554$		−	34157.4i		−	2.61951i
$555$	−11323.3	+	10025.3i	−0.866029	+	0.766761i
$556$	5953.22			0.454088
$557$	−9154.53	−	9154.53i	−0.696391	−	0.696391i	0.267239	−	0.963630i	$-0.413889\pi$
$557$	−9154.53	−	9154.53i	−0.696391	−	0.696391i	−0.963630	+	0.267239i	$0.913889\pi$
$558$	15564.5	+	15564.5i	1.18082	+	1.18082i
$559$	13663.9			1.03385
$560$	786.167	−	12931.1i	0.0593243	−	0.975782i
$561$	3274.16			0.246408
$562$	−7712.99	−	7712.99i	−0.578919	−	0.578919i
$563$	2226.16	−	2226.16i	0.166645	−	0.166645i	−0.618858	−	0.785503i	$-0.712404\pi$
$563$	2226.16	−	2226.16i	0.166645	−	0.166645i	0.785503	+	0.618858i	$0.212404\pi$
$564$			6490.42i			0.484568i
$565$	−1116.11	−	67.8558i	−0.0831063	−	0.00505259i
$566$			7808.52i			0.579888i
$567$	226.472	+	226.472i	0.0167741	+	0.0167741i
$568$	2661.61	+	2661.61i	0.196617	+	0.196617i
$569$	7597.95			0.559794			0.279897	−	0.960030i	$-0.409700\pi$
$569$	7597.95			0.559794			0.279897	+	0.960030i	$0.409700\pi$
$570$	10905.7	+	12317.6i	0.801388	+	0.905139i
$571$			11583.9i			0.848988i	0.905431	+	0.424494i	$0.139548\pi$
$571$			11583.9i			0.848988i	−0.905431	+	0.424494i	$0.860452\pi$
$572$	−5168.19	−	5168.19i	−0.377785	−	0.377785i
$573$	−2384.25	+	2384.25i	−0.173828	+	0.173828i
$574$	8011.82			0.582591
$575$	−327.717	+	13784.1i	−0.0237683	+	0.999717i
$576$	−4466.82			−0.323121
$577$	−17653.1	+	17653.1i	−1.27367	+	1.27367i	−0.329527	+	0.944146i	$0.606889\pi$
$577$	−17653.1	+	17653.1i	−1.27367	+	1.27367i	−0.944146	+	0.329527i	$0.893111\pi$
$578$	5109.44	+	5109.44i	0.367690	+	0.367690i
$579$		−	1866.09i		−	0.133941i
$580$	−2713.63	−	3064.95i	−0.194272	−	0.219423i
$581$	−17675.8			−1.26216
$582$	12700.1	+	12700.1i	0.904530	+	0.904530i
$583$	6480.64	+	6480.64i	0.460378	+	0.460378i
$584$		−	2922.60i		−	0.207086i
$585$	11815.6	+	718.347i	0.835066	+	0.0507692i
$586$			6207.40i			0.437586i
$587$	316.403	−	316.403i	0.0222476	−	0.0222476i	−0.695895	−	0.718143i	$-0.744992\pi$
$587$	316.403	−	316.403i	0.0222476	−	0.0222476i	0.718143	+	0.695895i	$0.244992\pi$
$588$	1457.22	+	1457.22i	0.102202	+	0.102202i
$589$	42402.8			2.96635
$590$	222.477	−	3659.35i	0.0155241	−	0.255344i
$591$	−2554.42			−0.177792
$592$	−22759.6	−	22759.6i	−1.58009	−	1.58009i
$593$	−15783.6	−	15783.6i	−1.09301	−	1.09301i	−0.995206	−	0.0978059i	$-0.968818\pi$
$593$	−15783.6	−	15783.6i	−1.09301	−	1.09301i	−0.0978059	−	0.995206i	$-0.531182\pi$
$594$	−9926.74			−0.685689
$595$	−7065.80	+	6255.88i	−0.486839	+	0.431036i
$596$			14030.7i			0.964296i
$597$	7605.14	+	7605.14i	0.521370	+	0.521370i
$598$	−25725.0	+	2520.67i	−1.75916	+	0.172371i
$599$			3848.82i			0.262535i	0.991347	+	0.131268i	$0.0419047\pi$
$599$			3848.82i			0.262535i	−0.991347	+	0.131268i	$0.958095\pi$
$600$	−2650.10	−	323.430i	−0.180316	−	0.0220066i
$601$	11585.6			0.786335			0.393168	−	0.919467i	$-0.371379\pi$
$601$	11585.6			0.786335			0.393168	+	0.919467i	$0.371379\pi$
$602$	9032.45	−	9032.45i	0.611520	−	0.611520i
$603$	−68.9974	+	68.9974i	−0.00465969	+	0.00465969i
$604$		−	4198.30i		−	0.282825i
$605$	7204.78	+	8137.55i	0.484159	+	0.546840i
$606$	−14242.8			−0.954743
$607$	−3419.34	+	3419.34i	−0.228644	+	0.228644i	−0.812126	−	0.583482i	$-0.801690\pi$
$607$	−3419.34	+	3419.34i	−0.228644	+	0.228644i	0.583482	+	0.812126i	$0.301690\pi$
$608$	−20027.6	+	20027.6i	−1.33590	+	1.33590i
$609$	2873.32			0.191187
$610$	−1445.56	+	23776.9i	−0.0959490	+	1.57820i
$611$	20594.2			1.36359
$612$	4089.80	+	4089.80i	0.270131	+	0.270131i
$613$	−15696.2	+	15696.2i	−1.03420	+	1.03420i	−0.0348041	+	0.999394i	$0.511081\pi$
$613$	−15696.2	+	15696.2i	−1.03420	+	1.03420i	−0.999394	+	0.0348041i	$0.988919\pi$
$614$			9370.00i			0.615867i
$615$	295.309	−	4857.32i	0.0193626	−	0.318481i
$616$	1976.04			0.129248
$617$	−7730.86	−	7730.86i	−0.504429	−	0.504429i	0.408382	−	0.912811i	$-0.366093\pi$
$617$	−7730.86	−	7730.86i	−0.504429	−	0.504429i	−0.912811	+	0.408382i	$0.866093\pi$
$618$	7703.37	−	7703.37i	0.501416	−	0.501416i
$619$	−18911.8			−1.22799			−0.613997	−	0.789308i	$-0.710439\pi$
$619$	−18911.8			−1.22799			−0.613997	+	0.789308i	$0.710439\pi$
$620$	17814.6	−	15772.6i	1.15396	−	1.02168i
$621$	−9734.73	+	11849.7i	−0.629052	+	0.765719i
$622$	−5960.18	+	5960.18i	−0.384214	+	0.384214i
$623$	−2118.60	−	2118.60i	−0.136244	−	0.136244i
$624$		−	14751.3i		−	0.946356i
$625$	−15166.4	−	3757.92i	−0.970647	−	0.240507i
$626$		−	14531.7i		−	0.927803i
$627$	−5229.81	+	5229.81i	−0.333108	+	0.333108i
$628$	13723.3	−	13723.3i	0.872007	−	0.872007i
$629$			23447.1i			1.48632i
$630$	8285.49	−	7335.77i	0.523971	−	0.463911i
$631$		−	5284.78i		−	0.333414i	−0.986007	−	0.166707i	$-0.946687\pi$
$631$		−	5284.78i		−	0.333414i	0.986007	−	0.166707i	$-0.0533133\pi$
$632$	1571.10	+	1571.10i	0.0988846	+	0.0988846i
$633$	5755.08	+	5755.08i	0.361364	+	0.361364i
$634$		−	13762.7i		−	0.862122i
$635$	8775.78	+	533.539i	0.548435	+	0.0333430i
$636$		−	9479.85i		−	0.591039i
$637$	4623.77	−	4623.77i	0.287599	−	0.287599i
$638$	2978.97	−	2978.97i	0.184856	−	0.184856i
$639$			9476.66i			0.586683i
$640$	572.624	−	9418.67i	0.0353671	−	0.581728i
$641$		−	15200.5i		−	0.936633i	−0.883561	−	0.468316i	$-0.844861\pi$
$641$		−	15200.5i		−	0.936633i	0.883561	−	0.468316i	$-0.155139\pi$
$642$	−12988.9	−	12988.9i	−0.798488	−	0.798488i
$643$	−7121.12	+	7121.12i	−0.436749	+	0.436749i	−0.890916	−	0.454168i	$-0.849937\pi$
$643$	−7121.12	+	7121.12i	−0.436749	+	0.436749i	0.454168	+	0.890916i	$0.349937\pi$
$644$	−6700.66	+	8156.44i	−0.410005	+	0.499082i
$645$	−5143.17	−	5809.02i	−0.313972	−	0.354620i
$646$	25506.2			1.55345
$647$	−8196.32	+	8196.32i	−0.498038	+	0.498038i	−0.910827	−	0.412789i	$-0.864555\pi$
$647$	−8196.32	+	8196.32i	−0.498038	+	0.498038i	0.412789	+	0.910827i	$0.364555\pi$
$648$	99.3288	+	99.3288i	0.00602161	+	0.00602161i
$649$	1648.14			0.0996845
$650$	3548.60	−	29076.3i	0.214135	−	1.75456i
$651$			16700.8i			1.00546i
$652$	−69.2208	+	69.2208i	−0.00415782	+	0.00415782i
$653$	18159.3	+	18159.3i	1.08825	+	1.08825i	0.995709	+	0.0925400i	$0.0294986\pi$
$653$	18159.3	+	18159.3i	1.08825	+	1.08825i	0.0925400	+	0.995709i	$0.470501\pi$
$654$	314.704			0.0188164
$655$	3142.13	+	3548.92i	0.187440	+	0.211707i
$656$	10356.7			0.616405
$657$	5202.96	−	5202.96i	0.308960	−	0.308960i
$658$	13613.7	−	13613.7i	0.806562	−	0.806562i
$659$	1528.01			0.0903230			0.0451615	−	0.998980i	$-0.485620\pi$
$659$	1528.01			0.0903230			0.0451615	+	0.998980i	$0.485620\pi$
$660$	−251.852	+	4142.53i	−0.0148535	+	0.244315i
$661$			29321.0i			1.72535i	0.505759	+	0.862675i	$0.331212\pi$
$661$			29321.0i			1.72535i	−0.505759	+	0.862675i	$0.668788\pi$
$662$	17322.7	−	17322.7i	1.01702	−	1.01702i
$663$	−7598.46	+	7598.46i	−0.445098	+	0.445098i
$664$	−7752.46			−0.453093
$665$	1293.68	−	21278.7i	0.0754385	−	1.24083i
$666$		−	27494.5i		−	1.59969i
$667$	−634.688	−	6477.38i	−0.0368444	−	0.376020i
$668$	12554.6	+	12554.6i	0.727173	+	0.727173i
$669$			4780.53i			0.276272i
$670$	160.061	+	180.783i	0.00922938	+	0.0104243i
$671$	−10708.9			−0.616116
$672$	−7888.06	−	7888.06i	−0.452810	−	0.452810i
$673$	9123.62	+	9123.62i	0.522570	+	0.522570i	0.918347	−	0.395777i	$-0.129525\pi$
$673$	9123.62	+	9123.62i	0.522570	+	0.522570i	−0.395777	+	0.918347i	$0.629525\pi$
$674$	14580.8			0.833282
$675$	−10709.4	−	13686.8i	−0.610675	−	0.780454i
$676$	10354.8			0.589142
$677$	19862.8	+	19862.8i	1.12760	+	1.12760i	0.990566	+	0.137038i	$0.0437581\pi$
$677$	19862.8	+	19862.8i	1.12760	+	1.12760i	0.137038	+	0.990566i	$0.456242\pi$
$678$	−841.656	+	841.656i	−0.0476749	+	0.0476749i
$679$		−	23273.3i		−	1.31538i
$680$	−3099.00	+	2743.78i	−0.174767	+	0.154734i
$681$			7317.72i			0.411771i
$682$	17314.8	+	17314.8i	0.972169	+	0.972169i
$683$	−9499.06	−	9499.06i	−0.532169	−	0.532169i	0.389048	−	0.921217i	$-0.372804\pi$
$683$	−9499.06	−	9499.06i	−0.532169	−	0.532169i	−0.921217	+	0.389048i	$0.872804\pi$
$684$	−13065.3			−0.730356
$685$	−625.416	+	10287.0i	−0.0348846	+	0.573791i
$686$		−	26049.7i		−	1.44983i
$687$	5177.93	+	5177.93i	0.287555	+	0.287555i
$688$	11676.1	−	11676.1i	0.647014	−	0.647014i
$689$	−30079.7			−1.66320
$690$	10754.7	+	9987.86i	0.593368	+	0.551060i
$691$	−13891.8			−0.764791			−0.382395	−	0.923999i	$-0.624901\pi$
$691$	−13891.8			−0.764791			−0.382395	+	0.923999i	$0.624901\pi$
$692$	1897.13	−	1897.13i	0.104217	−	0.104217i
$693$	3517.84	+	3517.84i	0.192831	+	0.192831i
$694$			35892.1i			1.96318i
$695$	−8030.69	+	7110.18i	−0.438304	+	0.388064i
$696$	1260.22			0.0686328
$697$	−5334.77	−	5334.77i	−0.289912	−	0.289912i
$698$	17363.8	+	17363.8i	0.941588	+	0.941588i
$699$		−	2668.38i		−	0.144388i
$700$	−7371.55	−	9420.99i	−0.398027	−	0.508686i
$701$		−	18088.4i		−	0.974591i	−0.873237	−	0.487295i	$-0.837984\pi$
$701$		−	18088.4i		−	0.974591i	0.873237	−	0.487295i	$-0.162016\pi$
$702$	23037.4	−	23037.4i	1.23859	−	1.23859i
$703$	−37452.1	−	37452.1i	−2.00929	−	2.00929i
$704$	−4969.14			−0.266025
$705$	−7751.78	−	8755.36i	−0.414112	−	0.467725i
$706$	3406.46			0.181592
$707$	13050.1	+	13050.1i	0.694202	+	0.694202i
$708$	−1205.45	−	1205.45i	−0.0639881	−	0.0639881i
$709$	11448.7			0.606441			0.303221	−	0.952920i	$-0.401938\pi$
$709$	11448.7			0.606441			0.303221	+	0.952920i	$0.401938\pi$
$710$	23407.1	+	1423.07i	1.23726	+	0.0752211i
$711$			5593.90i			0.295060i
$712$	−929.200	−	929.200i	−0.0489091	−	0.0489091i
$713$	37648.9	−	3689.03i	1.97751	−	0.193766i
$714$			10045.9i			0.526550i
$715$	13144.3	+	799.130i	0.687509	+	0.0417983i
$716$	23985.0			1.25190
$717$	−504.769	+	504.769i	−0.0262914	+	0.0262914i
$718$	−2204.78	+	2204.78i	−0.114598	+	0.114598i
$719$			14259.4i			0.739619i	0.929108	+	0.369810i	$0.120577\pi$
$719$			14259.4i			0.739619i	−0.929108	+	0.369810i	$0.879423\pi$
$720$	10710.5	−	9482.79i	0.554383	−	0.490837i
$721$	−14116.6			−0.729168
$722$	−22461.1	+	22461.1i	−1.15778	+	1.15778i
$723$	13058.3	−	13058.3i	0.671706	−	0.671706i
$724$	−4139.96			−0.212514
$725$	7321.20	+	893.512i	0.375038	+	0.0457713i
$726$	11569.6			0.591445
$727$	5679.43	+	5679.43i	0.289737	+	0.289737i	0.836976	−	0.547240i	$-0.184321\pi$
$727$	5679.43	+	5679.43i	0.289737	+	0.289737i	−0.547240	+	0.836976i	$0.684321\pi$
$728$	−4585.87	+	4585.87i	−0.233467	+	0.233467i
$729$		−	11499.7i		−	0.584246i
$730$	−12069.9	−	13632.5i	−0.611953	−	0.691179i
$731$	−12028.7			−0.608617
$732$	7832.49	+	7832.49i	0.395488	+	0.395488i
$733$	−15227.1	+	15227.1i	−0.767291	+	0.767291i	−0.977629	−	0.210338i	$-0.932544\pi$
$733$	−15227.1	+	15227.1i	−0.767291	+	0.767291i	0.210338	+	0.977629i	$0.432544\pi$
$734$	−123.322			−0.00620150
$735$	−3706.15	−	225.321i	−0.185991	−	0.0113076i
$736$	−16039.8	+	19524.6i	−0.803308	+	0.977834i
$737$	−76.7566	+	76.7566i	−0.00383632	+	0.00383632i
$738$	6255.66	+	6255.66i	0.312024	+	0.312024i
$739$		−	35436.4i		−	1.76393i	−0.471311	−	0.881967i	$-0.656219\pi$
$739$		−	35436.4i		−	1.76393i	0.471311	−	0.881967i	$-0.343781\pi$
$740$	−29665.7	−	1803.58i	−1.47369	−	0.0895957i
$741$		−	24274.0i		−	1.20341i
$742$	−19884.1	+	19884.1i	−0.983783	+	0.983783i
$743$	−15295.3	+	15295.3i	−0.755222	+	0.755222i	−0.975449	−	0.220226i	$-0.929320\pi$
$743$	−15295.3	+	15295.3i	−0.755222	+	0.755222i	0.220226	+	0.975449i	$0.429320\pi$
$744$			7324.84i			0.360943i
$745$	−16757.5	−	18926.9i	−0.824088	−	0.930778i
$746$			31354.3i			1.53882i
$747$	−13801.3	−	13801.3i	−0.675988	−	0.675988i
$748$	4549.72	+	4549.72i	0.222399	+	0.222399i
$749$			23802.4i			1.16118i
$750$	−13697.1	+	9435.83i	−0.666863	+	0.459397i
$751$			25279.5i			1.22831i	0.789185	+	0.614155i	$0.210503\pi$
$751$			25279.5i			1.22831i	−0.789185	+	0.614155i	$0.789497\pi$
$752$	17598.1	−	17598.1i	0.853376	−	0.853376i
$753$	14839.8	−	14839.8i	0.718183	−	0.718183i
$754$			13826.8i			0.667828i
$755$	5014.20	+	5663.36i	0.241703	+	0.272995i
$756$		−	13304.9i		−	0.640071i
$757$	10121.6	+	10121.6i	0.485965	+	0.485965i	0.907030	−	0.421065i	$-0.138344\pi$
$757$	10121.6	+	10121.6i	0.485965	+	0.485965i	−0.421065	+	0.907030i	$0.638344\pi$
$758$	−21094.0	+	21094.0i	−1.01078	+	1.01078i
$759$	−4188.48	+	5098.47i	−0.200306	+	0.243824i
$760$	567.396	−	9332.68i	0.0270811	−	0.445437i
$761$	33559.8			1.59861			0.799305	−	0.600926i	$-0.205201\pi$
$761$	33559.8			1.59861			0.799305	+	0.600926i	$0.205201\pi$
$762$	6617.80	−	6617.80i	0.314616	−	0.314616i
$763$	−288.351	−	288.351i	−0.0136815	−	0.0136815i
$764$	−6626.25			−0.313782
$765$	−10401.6	−	632.383i	−0.491596	−	0.0298874i
$766$		−	28348.3i		−	1.33716i
$767$	−3824.91	+	3824.91i	−0.180064	+	0.180064i
$768$	−11788.1	−	11788.1i	−0.553862	−	0.553862i
$769$	−21057.2			−0.987440			−0.493720	−	0.869621i	$-0.664363\pi$
$769$	−21057.2			−0.987440			−0.493720	+	0.869621i	$0.664363\pi$
$770$	9217.24	−	8160.72i	0.431385	−	0.381937i
$771$	−5867.50			−0.274076
$772$	2593.09	−	2593.09i	0.120890	−

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)

\(f(q)\)	\(=\)	\(q+(-2.66509 + 2.66509i) q^{2} +(-2.23283 - 2.23283i) q^{3} -6.20541i q^{4} +(7.41137 + 8.37088i) q^{5} +11.9014 q^{6} +(-10.9048 - 10.9048i) q^{7} +(-4.78275 - 4.78275i) q^{8} -17.0290i q^{9} +O(q^{10})\)	\(q+(-2.66509 + 2.66509i) q^{2} +(-2.23283 - 2.23283i) q^{3} -6.20541i q^{4} +(7.41137 + 8.37088i) q^{5} +11.9014 q^{6} +(-10.9048 - 10.9048i) q^{7} +(-4.78275 - 4.78275i) q^{8} -17.0290i q^{9} +(-42.0611 - 2.55718i) q^{10} -18.9440i q^{11} +(-13.8556 + 13.8556i) q^{12} +(43.9640 + 43.9640i) q^{13} +58.1244 q^{14} +(2.14242 - 35.2390i) q^{15} +75.1362 q^{16} +(-38.7029 - 38.7029i) q^{17} +(45.3837 + 45.3837i) q^{18} +123.640 q^{19} +(51.9447 - 45.9906i) q^{20} +48.6969i q^{21} +(50.4874 + 50.4874i) q^{22} +(109.778 - 10.7567i) q^{23} +21.3581i q^{24} +(-15.1432 + 124.079i) q^{25} -234.336 q^{26} +(-98.3091 + 98.3091i) q^{27} +(-67.6686 + 67.6686i) q^{28} -59.0042i q^{29} +(88.2054 + 99.6249i) q^{30} +342.953 q^{31} +(-161.983 + 161.983i) q^{32} +(-42.2986 + 42.2986i) q^{33} +206.293 q^{34} +(10.4632 - 172.102i) q^{35} -105.672 q^{36} +(-302.912 - 302.912i) q^{37} +(-329.512 + 329.512i) q^{38} -196.328i q^{39} +(4.58909 - 75.4826i) q^{40} +137.839 q^{41} +(-129.782 - 129.782i) q^{42} +(155.399 - 155.399i) q^{43} -117.555 q^{44} +(142.547 - 126.208i) q^{45} +(-263.902 + 321.237i) q^{46} +(234.217 - 234.217i) q^{47} +(-167.766 - 167.766i) q^{48} -105.172i q^{49} +(-290.325 - 371.041i) q^{50} +172.834i q^{51} +(272.815 - 272.815i) q^{52} +(-342.095 + 342.095i) q^{53} -524.005i q^{54} +(158.578 - 140.401i) q^{55} +104.310i q^{56} +(-276.067 - 276.067i) q^{57} +(157.251 + 157.251i) q^{58} +87.0009i q^{59} +(-218.672 - 13.2946i) q^{60} -565.294i q^{61} +(-914.002 + 914.002i) q^{62} +(-185.697 + 185.697i) q^{63} -262.307i q^{64} +(-42.1838 + 693.851i) q^{65} -225.459i q^{66} +(-4.05177 - 4.05177i) q^{67} +(-240.167 + 240.167i) q^{68} +(-269.134 - 221.098i) q^{69} +(430.782 + 486.552i) q^{70} -556.502 q^{71} +(-81.4453 + 81.4453i) q^{72} +(305.536 + 305.536i) q^{73} +1614.57 q^{74} +(310.860 - 243.236i) q^{75} -767.238i q^{76} +(-206.580 + 206.580i) q^{77} +(523.232 + 523.232i) q^{78} -328.493 q^{79} +(556.862 + 628.956i) q^{80} -20.7681 q^{81} +(-367.354 + 367.354i) q^{82} +(810.460 - 810.460i) q^{83} +302.184 q^{84} +(37.1357 - 610.818i) q^{85} +828.302i q^{86} +(-131.746 + 131.746i) q^{87} +(-90.6043 + 90.6043i) q^{88} +194.282 q^{89} +(-43.5461 + 716.257i) q^{90} -958.835i q^{91} +(-66.7494 - 681.220i) q^{92} +(-765.755 - 765.755i) q^{93} +1248.42i q^{94} +(916.343 + 1034.98i) q^{95} +723.358 q^{96} +(1067.11 + 1067.11i) q^{97} +(280.292 + 280.292i) q^{98} -322.596 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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