LMFDB - Embedded newform 115.4.e.a.22.8

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			22.8
Character	$\chi$	$=$	115.22
Dual form			115.4.e.a.68.8

$q$-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} +(-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} + 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}+ \cdots - 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

Character values

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

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

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	0.0561697	−	0.998421i	$-0.482111\pi$
$2$	−2.66509	−	2.66509i	−0.942252	−	0.942252i	−0.998421	+	0.0561697i	$0.982111\pi$
$3$	−2.23283	+	2.23283i	−0.429708	+	0.429708i	−0.888529	−	0.458821i	$-0.848272\pi$
$3$	−2.23283	+	2.23283i	−0.429708	+	0.429708i	0.458821	+	0.888529i	$0.348272\pi$
$4$			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	−0.937307	−	0.348505i	$-0.886690\pi$
$7$	−10.9048	+	10.9048i	−0.588803	+	0.588803i	0.348505	+	0.937307i	$0.386690\pi$
$8$	−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	$0.0836001\pi$
$11$			18.9440i			0.519257i	−0.965709	+	0.259628i	$0.916400\pi$
$12$	−13.8556	−	13.8556i	−0.333314	−	0.333314i
$13$	43.9640	−	43.9640i	0.937955	−	0.937955i	−0.0602292	−	0.998185i	$-0.519183\pi$
$13$	43.9640	−	43.9640i	0.937955	−	0.937955i	0.998185	+	0.0602292i	$0.0191832\pi$
$14$	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	−0.927066	−	0.374899i	$-0.877677\pi$
$17$	−38.7029	+	38.7029i	−0.552166	+	0.552166i	0.374899	+	0.927066i	$0.377677\pi$
$18$	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	$0.0604955\pi$
$29$			59.0042i			0.377821i	−0.981994	+	0.188910i	$0.939504\pi$
$30$	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	−0.455839	+	0.890062i	$0.650661\pi$
$37$	−302.912	+	302.912i	−1.34590	+	1.34590i	−0.890062	+	0.455839i	$0.849339\pi$
$38$	−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	0.926763	−	0.375646i	$-0.122579\pi$
$43$	155.399	+	155.399i	0.551118	+	0.551118i	−0.375646	+	0.926763i	$0.622579\pi$
$44$	−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	0.970000	−	0.243106i	$-0.0781662\pi$
$47$	234.217	+	234.217i	0.726894	+	0.726894i	−0.243106	+	0.970000i	$0.578166\pi$
$48$	−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	0.107586	−	0.994196i	$-0.465688\pi$
$53$	−342.095	−	342.095i	−0.886610	−	0.886610i	−0.994196	+	0.107586i	$0.965688\pi$
$54$			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	$-0.969399\pi$
$59$		−	87.0009i		−	0.191975i	0.995383	−	0.0959877i	$-0.0306009\pi$
$60$	−218.672	+	13.2946i	−0.470508	+	0.0286053i
$61$			565.294i			1.18653i	0.805006	+	0.593267i	$0.202162\pi$
$61$			565.294i			1.18653i	−0.805006	+	0.593267i	$0.797838\pi$
$62$	−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	−0.710791	−	0.703403i	$-0.751663\pi$
$67$	−4.05177	+	4.05177i	−0.00738809	+	0.00738809i	0.703403	+	0.710791i	$0.251663\pi$
$68$	−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	−0.418398	−	0.908264i	$-0.637408\pi$
$73$	305.536	−	305.536i	0.489866	−	0.489866i	0.908264	+	0.418398i	$0.137408\pi$
$74$	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	0.997214	+	0.0745876i	$0.0237641\pi$
$83$	810.460	+	810.460i	1.07180	+	1.07180i	0.0745876	+	0.997214i	$0.476236\pi$
$84$	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	0.124820	−	0.992179i	$-0.460165\pi$
$97$	1067.11	−	1067.11i	1.11700	−	1.11700i	0.992179	−	0.124820i	$-0.0398353\pi$
$98$	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	0.945325	−	0.326129i	$-0.105745\pi$
$103$	647.268	+	647.268i	0.619196	+	0.619196i	−0.326129	+	0.945325i	$0.605745\pi$
$104$			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	−0.999904	−	0.0138547i	$-0.995590\pi$
$107$	−1091.38	+	1091.38i	−0.986049	+	0.986049i	0.0138547	+	0.999904i	$0.495590\pi$
$108$	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	0.677057	−	0.735931i	$-0.263255\pi$
$113$	−70.7193	−	70.7193i	−0.0588736	−	0.0588736i	−0.735931	+	0.677057i	$0.763255\pi$
$114$	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	0.874159	−	0.485640i	$-0.161414\pi$
$127$	556.054	+	556.054i	0.388518	+	0.388518i	−0.485640	+	0.874159i	$0.661414\pi$
$128$	−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	−0.474029	−	0.880509i	$-0.657201\pi$
$137$	651.809	−	651.809i	0.406480	−	0.406480i	0.880509	+	0.474029i	$0.157201\pi$
$138$	1306.51	+	128.019i	0.805926	+	0.0789688i
$139$		−	959.361i		−	0.585409i	−0.956203	−	0.292705i	$-0.905445\pi$
$139$		−	959.361i		−	0.585409i	0.956203	−	0.292705i	$-0.0945553\pi$
$140$	−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	0.133086	−	0.991105i	$-0.457511\pi$
$157$	2211.51	−	2211.51i	1.12419	−	1.12419i	0.991105	−	0.133086i	$-0.0424886\pi$
$158$	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	−0.709782	−	0.704422i	$-0.751206\pi$
$163$	−11.1549	+	11.1549i	−0.00536025	+	0.00536025i	0.704422	+	0.709782i	$0.251206\pi$
$164$			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	0.0606869	−	0.998157i	$-0.480671\pi$
$167$	−2023.17	−	2023.17i	−0.937470	−	0.937470i	−0.998157	+	0.0606869i	$0.980671\pi$
$168$	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	−0.636731	−	0.771086i	$-0.719714\pi$
$173$	305.721	−	305.721i	0.134356	−	0.134356i	0.771086	+	0.636731i	$0.219714\pi$
$174$			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	$-0.701104\pi$
$179$		−	3865.17i		−	1.61395i	0.590587	−	0.806974i	$-0.298896\pi$
$180$	−783.172	+	884.565i	−0.324301	+	0.366287i
$181$			667.154i			0.273973i	0.990573	+	0.136987i	$0.0437417\pi$
$181$			667.154i			0.273973i	−0.990573	+	0.136987i	$0.956258\pi$
$182$	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	$0.0648297\pi$
$191$			1067.82i			0.404527i	−0.979331	+	0.202263i	$0.935170\pi$
$192$	−585.686	−	585.686i	−0.220147	−	0.220147i
$193$	417.876	−	417.876i	0.155852	−	0.155852i	−0.624874	−	0.780726i	$-0.714850\pi$
$193$	417.876	−	417.876i	0.155852	−	0.155852i	0.780726	+	0.624874i	$0.214850\pi$
$194$	−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	0.802938	−	0.596063i	$-0.203269\pi$
$197$	572.015	+	572.015i	0.206875	+	0.206875i	−0.596063	+	0.802938i	$0.703269\pi$
$198$	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	−0.849329	−	0.527864i	$-0.822993\pi$
$223$	−1070.51	+	1070.51i	−0.321465	+	0.321465i	0.527864	+	0.849329i	$0.322993\pi$
$224$	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	−0.904853	−	0.425724i	$-0.860019\pi$
$227$	−1638.67	+	1638.67i	−0.479129	+	0.479129i	0.425724	+	0.904853i	$0.360019\pi$
$228$	−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	−0.618096	−	0.786103i	$-0.712096\pi$
$233$	597.533	−	597.533i	0.168007	−	0.168007i	0.786103	+	0.618096i	$0.212096\pi$
$234$		−	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	$0.00973933\pi$
$239$			226.067i			0.0611845i	−0.999532	+	0.0305922i	$0.990261\pi$
$240$	160.973	+	2647.73i	0.0432948	+	0.712125i
$241$		−	5848.33i		−	1.56317i	−0.623799	−	0.781585i	$-0.714412\pi$
$241$		−	5848.33i		−	1.56317i	0.623799	−	0.781585i	$-0.285588\pi$
$242$	−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	$-0.685083\pi$
$251$		−	6646.18i		−	1.67133i	0.549241	−	0.835664i	$-0.314917\pi$
$252$	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	0.848348	−	0.529438i	$-0.177597\pi$
$257$	1313.92	+	1313.92i	0.318910	+	0.318910i	−0.529438	+	0.848348i	$0.677597\pi$
$258$	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	0.995871	+	0.0907786i	$0.0289356\pi$
$263$	4634.72	+	4634.72i	1.08665	+	1.08665i	0.0907786	+	0.995871i	$0.471064\pi$
$264$	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	$-0.845396\pi$
$269$		−	4119.24i		−	0.933661i	0.884347	−	0.466830i	$-0.154604\pi$
$270$	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	−0.825229	−	0.564798i	$-0.808954\pi$
$277$	−6408.30	−	6408.30i	−1.39003	−	1.39003i	−0.564798	−	0.825229i	$-0.691046\pi$
$278$	−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	$-0.900608\pi$
$281$		−	2894.08i		−	0.614400i	0.951645	−	0.307200i	$-0.0993921\pi$
$282$	2787.50	+	2787.50i	0.588628	+	0.588628i
$283$	1464.96	+	1464.96i	0.307714	+	0.307714i	0.844022	−	0.536308i	$-0.180181\pi$
$283$	1464.96	+	1464.96i	0.307714	+	0.307714i	−0.536308	+	0.844022i	$0.680181\pi$
$284$		−	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	0.813611	−	0.581409i	$-0.197498\pi$
$293$	1164.58	+	1164.58i	0.232202	+	0.232202i	−0.581409	+	0.813611i	$0.697498\pi$
$294$			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	0.851371	−	0.524565i	$-0.175772\pi$
$307$	1757.91	+	1757.91i	0.326806	+	0.326806i	−0.524565	+	0.851371i	$0.675772\pi$
$308$	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	0.416708	−	0.909041i	$-0.363184\pi$
$313$	−2726.31	−	2726.31i	−0.492333	−	0.492333i	−0.909041	+	0.416708i	$0.863184\pi$
$314$	−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	0.440348	−	0.897827i	$-0.354855\pi$
$317$	−2582.03	−	2582.03i	−0.457480	−	0.457480i	−0.897827	+	0.440348i	$0.854855\pi$
$318$	−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	−0.892743	−	0.450567i	$-0.851222\pi$
$337$	−2735.52	+	2735.52i	−0.442176	+	0.442176i	0.450567	+	0.892743i	$0.351222\pi$
$338$	−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	0.999090	+	0.0426573i	$0.0135824\pi$
$347$	6733.74	+	6733.74i	1.04175	+	1.04175i	0.0426573	+	0.999090i	$0.486418\pi$
$348$	817.538	−	817.538i	0.125933	−	0.125933i
$349$			6515.26i			0.999295i	0.866229	+	0.499648i	$0.166537\pi$
$349$			6515.26i			0.999295i	−0.866229	+	0.499648i	$0.833463\pi$
$350$	−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	−0.753644	−	0.657283i	$-0.771706\pi$
$353$	−639.089	+	639.089i	−0.0963605	+	0.0963605i	0.657283	+	0.753644i	$0.271706\pi$
$354$		−	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	−0.705459	−	0.708750i	$-0.749259\pi$
$367$	23.1366	−	23.1366i	0.00329079	−	0.00329079i	0.708750	+	0.705459i	$0.249259\pi$
$368$	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	0.985609	−	0.169042i	$-0.0540672\pi$
$373$	5882.41	+	5882.41i	0.816567	+	0.816567i	−0.169042	+	0.985609i	$0.554067\pi$
$374$			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	0.256886	−	0.966442i	$-0.417304\pi$
$383$	−5318.45	−	5318.45i	−0.709556	−	0.709556i	−0.966442	+	0.256886i	$0.917304\pi$
$384$		−	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	0.999950	+	0.0100085i	$0.00318586\pi$
$397$	7988.94	+	7988.94i	1.00996	+	1.00996i	0.0100085	+	0.999950i	$0.496814\pi$
$398$	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	$0.216163\pi$
$401$			10087.1i			1.25618i	−0.778141	+	0.628090i	$0.783837\pi$
$402$	−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	$-0.992715\pi$
$409$		−	378.591i		−	0.0457705i	0.999738	−	0.0228853i	$-0.00728524\pi$
$410$	−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	$-0.831699\pi$
$421$		−	8714.92i		−	1.00888i	0.863446	−	0.504441i	$-0.168301\pi$
$422$	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	$0.208940\pi$
$431$			10921.2i			1.22054i	−0.792192	+	0.610272i	$0.791060\pi$
$432$	−7386.57	−	7386.57i	−0.822654	−	0.822654i
$433$	−4506.50	−	4506.50i	−0.500158	−	0.500158i	0.411329	−	0.911487i	$-0.365065\pi$
$433$	−4506.50	−	4506.50i	−0.500158	−	0.500158i	−0.911487	+	0.411329i	$0.865065\pi$
$434$	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	$0.0588461\pi$
$439$			3381.56i			0.367638i	−0.982960	+	0.183819i	$0.941154\pi$
$440$	−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	−0.239997	−	0.970774i	$-0.577147\pi$
$443$	6813.81	−	6813.81i	0.730776	−	0.730776i	0.970774	+	0.239997i	$0.0771466\pi$
$444$	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	$-0.862492\pi$
$449$		−	7966.78i		−	0.837363i	0.908133	−	0.418681i	$-0.137508\pi$
$450$	−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	−0.555253	−	0.831682i	$-0.687378\pi$
$457$	2700.58	−	2700.58i	0.276429	−	0.276429i	0.831682	+	0.555253i	$0.187378\pi$
$458$	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	−0.534419	−	0.845220i	$-0.679470\pi$
$463$	3096.37	−	3096.37i	0.310801	−	0.310801i	0.845220	+	0.534419i	$0.179470\pi$
$464$			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	−0.640389	−	0.768051i	$-0.721227\pi$
$467$	1288.36	−	1288.36i	0.127662	−	0.127662i	0.768051	+	0.640389i	$0.221227\pi$
$468$	−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	0.880424	−	0.474188i	$-0.157258\pi$
$487$	4365.88	+	4365.88i	0.406236	+	0.406236i	−0.474188	+	0.880424i	$0.657258\pi$
$488$	−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	$0.148915\pi$
$499$			10053.3i			0.901902i	−0.892549	+	0.450951i	$0.851085\pi$
$500$	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	0.891354	−	0.453308i	$-0.149756\pi$
$503$	4941.64	+	4941.64i	0.438046	+	0.438046i	−0.453308	+	0.891354i	$0.649756\pi$
$504$	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	$0.226731\pi$
$509$			15010.7i			1.30715i	−0.756864	+	0.653573i	$0.773269\pi$
$510$	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	$-0.578537\pi$
$521$		−	23063.8i		−	1.93943i	0.244236	−	0.969716i	$-0.421463\pi$
$522$	2677.83	+	2677.83i	0.224531	+	0.224531i
$523$	4272.34	+	4272.34i	0.357202	+	0.357202i	0.862781	−	0.505579i	$-0.168721\pi$
$523$	4272.34	+	4272.34i	0.357202	+	0.357202i	−0.505579	+	0.862781i	$0.668721\pi$
$524$			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	0.201243	−	0.979541i	$-0.435502\pi$
$547$	−9956.97	−	9956.97i	−0.778299	−	0.778299i	−0.979541	+	0.201243i	$0.935502\pi$
$548$	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	−0.963630	−	0.267239i	$-0.913889\pi$
$557$	−9154.53	+	9154.53i	−0.696391	+	0.696391i	0.267239	+	0.963630i	$0.413889\pi$
$558$	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	0.785503	−	0.618858i	$-0.212404\pi$
$563$	2226.16	+	2226.16i	0.166645	+	0.166645i	−0.618858	+	0.785503i	$0.712404\pi$
$564$		−	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	$-0.860452\pi$
$571$		−	11583.9i		−	0.848988i	0.905431	−	0.424494i	$-0.139548\pi$
$572$	−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	−0.944146	−	0.329527i	$-0.893111\pi$
$577$	−17653.1	−	17653.1i	−1.27367	−	1.27367i	−0.329527	−	0.944146i	$-0.606889\pi$
$578$	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	0.718143	−	0.695895i	$-0.244992\pi$
$587$	316.403	+	316.403i	0.0222476	+	0.0222476i	−0.695895	+	0.718143i	$0.744992\pi$
$588$	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	−0.0978059	+	0.995206i	$0.531182\pi$
$593$	−15783.6	+	15783.6i	−1.09301	+	1.09301i	−0.995206	+	0.0978059i	$0.968818\pi$
$594$	−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	$-0.958095\pi$
$599$		−	3848.82i		−	0.262535i	0.991347	−	0.131268i	$-0.0419047\pi$
$600$	−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	0.583482	−	0.812126i	$-0.301690\pi$
$607$	−3419.34	−	3419.34i	−0.228644	−	0.228644i	−0.812126	+	0.583482i	$0.801690\pi$
$608$	−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	−0.999394	−	0.0348041i	$-0.988919\pi$
$613$	−15696.2	−	15696.2i	−1.03420	−	1.03420i	−0.0348041	−	0.999394i	$-0.511081\pi$
$614$		−	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	−0.912811	−	0.408382i	$-0.866093\pi$
$617$	−7730.86	+	7730.86i	−0.504429	+	0.504429i	0.408382	+	0.912811i	$0.366093\pi$
$618$	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	$0.0533133\pi$
$631$			5284.78i			0.333414i	−0.986007	+	0.166707i	$0.946687\pi$
$632$	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	$0.155139\pi$
$641$			15200.5i			0.936633i	−0.883561	+	0.468316i	$0.844861\pi$
$642$	−12988.9	+	12988.9i	−0.798488	+	0.798488i
$643$	−7121.12	−	7121.12i	−0.436749	−	0.436749i	0.454168	−	0.890916i	$-0.349937\pi$
$643$	−7121.12	−	7121.12i	−0.436749	−	0.436749i	−0.890916	+	0.454168i	$0.849937\pi$
$644$	−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	0.412789	−	0.910827i	$-0.364555\pi$
$647$	−8196.32	−	8196.32i	−0.498038	−	0.498038i	−0.910827	+	0.412789i	$0.864555\pi$
$648$	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	0.0925400	−	0.995709i	$-0.470501\pi$
$653$	18159.3	−	18159.3i	1.08825	−	1.08825i	0.995709	−	0.0925400i	$-0.0294986\pi$
$654$	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	$-0.668788\pi$
$661$		−	29321.0i		−	1.72535i	0.505759	−	0.862675i	$-0.331212\pi$
$662$	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	−0.395777	−	0.918347i	$-0.629525\pi$
$673$	9123.62	−	9123.62i	0.522570	−	0.522570i	0.918347	+	0.395777i	$0.129525\pi$
$674$	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	0.137038	−	0.990566i	$-0.456242\pi$
$677$	19862.8	−	19862.8i	1.12760	−	1.12760i	0.990566	−	0.137038i	$-0.0437581\pi$
$678$	−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	−0.921217	−	0.389048i	$-0.872804\pi$
$683$	−9499.06	+	9499.06i	−0.532169	+	0.532169i	0.389048	+	0.921217i	$0.372804\pi$
$684$	−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	$0.162016\pi$
$701$			18088.4i			0.974591i	−0.873237	+	0.487295i	$0.837984\pi$
$702$	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	$-0.879423\pi$
$719$		−	14259.4i		−	0.739619i	0.929108	−	0.369810i	$-0.120577\pi$
$720$	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	−0.547240	−	0.836976i	$-0.684321\pi$
$727$	5679.43	−	5679.43i	0.289737	−	0.289737i	0.836976	+	0.547240i	$0.184321\pi$
$728$	−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	0.210338	−	0.977629i	$-0.432544\pi$
$733$	−15227.1	−	15227.1i	−0.767291	−	0.767291i	−0.977629	+	0.210338i	$0.932544\pi$
$734$	−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	$0.343781\pi$
$739$			35436.4i			1.76393i	−0.471311	+	0.881967i	$0.656219\pi$
$740$	−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	0.220226	−	0.975449i	$-0.429320\pi$
$743$	−15295.3	−	15295.3i	−0.755222	−	0.755222i	−0.975449	+	0.220226i	$0.929320\pi$
$744$		−	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	$-0.789497\pi$
$751$		−	25279.5i		−	1.22831i	0.789185	−	0.614155i	$-0.210503\pi$
$752$	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	−0.421065	−	0.907030i	$-0.638344\pi$
$757$	10121.6	−	10121.6i	0.485965	−	0.485965i	0.907030	+	0.421065i	$0.138344\pi$
$758$	−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	+	0.120890i
$773$	11098.1	+	11098.1i	0.516394	+	0.516394i	0.916478	−	0.400084i	$-0.131019\pi$
$773$	11098.1	+	11098.1i	0.516394	+	0.516394i	−0.400084	+	0.916478i	$0.631019\pi$
$774$	14105.1			0.655037
$775$	−5193.41	−	42553.4i	−0.240713	−	1.97234i
$776$			10207.5i			0.472200i
$777$	14750.9	+	14750.9i	0.681061	+	0.681061i
$778$	7042.64	+	7042.64i	0.324538	+	0.324538i
$779$	17042.5			0.783838
$780$	−9029.23	+	10198.2i	−0.414485	+	0.468146i
$781$		−	10542.4i		−	0.483016i
$782$	22646.5	+	2219.03i	1.03560	+	0.101473i
$783$	5800.64	−	5800.64i	0.264749	−	0.264749i
$784$			7902.20i			0.359976i
$785$	−2121.96	−	34902.6i	−0.0964792	−	1.58692i
$786$	5045.71			0.228975
$787$	1443.79	−	1443.79i	0.0653944	−	0.0653944i	−0.673653	−	0.739048i	$-0.735276\pi$
$787$	1443.79	−	1443.79i	0.0653944	−	0.0653944i	0.739048	+	0.673653i	$0.235276\pi$
$788$	−3549.59	+	3549.59i	−0.160468	+	0.160468i
$789$	−20697.0			−0.933883
$790$	13816.8	−	840.015i	0.622252	−	0.0378309i
$791$	1542.36			0.0693298
$792$	1542.90	−	1542.90i	0.0692229	−	0.0692229i
$793$	24852.6	+	24852.6i	1.11292	+	1.11292i
$794$		−	42582.5i		−	1.90327i
$795$	11322.2	−	12788.0i	0.505102	−	0.570495i
$796$		−	21136.0i		−	0.941138i
$797$	18915.6	−	18915.6i	0.840685	−	0.840685i	−0.148263	−	0.988948i	$-0.547368\pi$
$797$	18915.6	−	18915.6i	0.840685	−	0.840685i	0.988948	+	0.148263i	$0.0473681\pi$
$798$	−16046.2	+	16046.2i	−0.711818	+	0.711818i
$799$	−18129.7			−0.802733
$800$	−17645.8	+	22551.6i	−0.779840	+	0.996651i
$801$			3308.41i			0.145939i
$802$	26883.1	−	26883.1i	1.18364	−	1.18364i
$803$	5788.06	+	5788.06i	0.254366	+	0.254366i
$804$	112.279			0.00492510
$805$	−702.605	+	19005.6i	−0.0307622	+	0.832124i
$806$	−80366.3			−3.51214
$807$	9197.56	+	9197.56i	0.401201	+	0.401201i
$808$	5723.69	−	5723.69i	0.249206	−	0.249206i
$809$		−	10249.3i		−	0.445424i	−0.974884	−	0.222712i	$-0.928509\pi$
$809$		−	10249.3i		−	0.445424i	0.974884	−	0.222712i	$-0.0714909\pi$
$810$	873.531	−	53.1078i	0.0378923	−	0.00230373i
$811$	−3859.70			−0.167117			−0.0835587	−	0.996503i	$-0.526629\pi$
$811$	−3859.70			−0.167117			−0.0835587	+	0.996503i	$0.526629\pi$
$812$	3992.73	−	3992.73i	0.172558	−	0.172558i
$813$	−11683.1	+	11683.1i	−0.503989	+	0.503989i
$814$			30586.4i			1.31702i
$815$	10.7032	+	176.050i	0.000460022	+	0.00756657i
$816$		−	12986.1i		−	0.557112i
$817$	19213.5	+	19213.5i	0.822761	+	0.822761i
$818$	−1008.98	+	1008.98i	−0.0431273	+	0.0431273i
$819$	−16328.0			−0.696637
$820$	7160.02	+	6339.30i	0.304925	+	0.269973i
$821$	29254.9			1.24361			0.621804	−	0.783173i	$-0.286400\pi$
$821$	29254.9			1.24361			0.621804	+	0.783173i	$0.286400\pi$
$822$	7757.42	−	7757.42i	0.329162	−	0.329162i
$823$	−12146.6	+	12146.6i	−0.514463	+	0.514463i	−0.915891	−	0.401428i	$-0.868514\pi$
$823$	−12146.6	+	12146.6i	−0.514463	+	0.514463i	0.401428	+	0.915891i	$0.368514\pi$
$824$	−6191.44			−0.261758
$825$	−4607.85	+	5888.92i	−0.194454	+	0.248516i
$826$		−	5056.87i		−	0.213016i
$827$	5754.51	−	5754.51i	0.241963	−	0.241963i	−0.575699	−	0.817662i	$-0.695270\pi$
$827$	5754.51	−	5754.51i	0.241963	−	0.241963i	0.817662	+	0.575699i	$0.195270\pi$
$828$	−11600.5	−	1136.67i	−0.486889	−	0.0477079i
$829$		−	31276.9i		−	1.31036i	−0.755471	−	0.655182i	$-0.772592\pi$
$829$		−	31276.9i		−	1.31036i	0.755471	−	0.655182i	$-0.227408\pi$
$830$	−36161.3	−	32016.4i	−1.51226	−	1.33892i
$831$	28617.3			1.19461
$832$	11532.1	+	11532.1i	0.480532	+	0.480532i
$833$	−4070.45	−	4070.45i	−0.169307	−	0.169307i
$834$		−	11417.7i		−	0.474056i
$835$	−31930.1	+	1941.25i	−1.32334	+	0.0804546i
$836$	−14534.5			−0.601301
$837$	−33715.4	−	33715.4i	−1.39232	−	1.39232i
$838$	7635.60	+	7635.60i	0.314758	+	0.314758i
$839$	42594.8			1.75273			0.876363	−	0.481652i	$-0.159963\pi$
$839$	42594.8			1.75273			0.876363	+	0.481652i	$0.159963\pi$
$840$	3675.77	−	223.475i	0.150983	−	0.00917930i
$841$	20907.5			0.857252
$842$	−23226.1	+	23226.1i	−0.950621	+	0.950621i
$843$	6461.98	+	6461.98i	0.264012	+	0.264012i
$844$		−	15994.3i		−	0.652308i
$845$	−13968.2	−	12367.1i	−0.568664	−	0.503481i
$846$	21259.3			0.863958
$847$	−10600.8	+	10600.8i	−0.430045	+	0.430045i
$848$	−25703.7	−	25703.7i	−1.04088	−	1.04088i
$849$	−6542.02			−0.264454
$850$	−3123.94	−	25596.7i	−0.126059	−	1.03290i
$851$	−36511.5	+	29994.8i	−1.47074	+	1.20824i
$852$	7710.67	+	7710.67i	0.310051	+	0.310051i
$853$	−34306.5	+	34306.5i	−1.37706	+	1.37706i	−0.527513	+	0.849547i	$0.676876\pi$
$853$	−34306.5	+	34306.5i	−1.37706	+	1.37706i	−0.849547	+	0.527513i	$0.823124\pi$
$854$			32857.4i			1.31658i
$855$	17624.6	+	15604.4i	0.704969	+	0.624162i
$856$		−	10439.6i		−	0.416842i
$857$	30152.9	+	30152.9i	1.20187	+	1.20187i	0.973597	+	0.228272i	$0.0733075\pi$
$857$	30152.9	+	30152.9i	1.20187	+	1.20187i	0.228272	+	0.973597i	$0.426692\pi$
$858$	9912.09	+	9912.09i	0.394398	+	0.394398i
$859$			39680.0i			1.57609i	0.615615	+	0.788047i	$0.288908\pi$
$859$			39680.0i			1.57609i	−0.615615	+	0.788047i	$0.711092\pi$
$860$	925.265	+	15219.0i	0.0366875	+	0.603446i
$861$		−	6712.35i		−	0.265687i
$862$	29105.9	−	29105.9i	1.15006	−	1.15006i
$863$	−19509.0	+	19509.0i	−0.769517	+	0.769517i	−0.978021	−	0.208504i	$-0.933140\pi$
$863$	−19509.0	+	19509.0i	−0.769517	+	0.769517i	0.208504	+	0.978021i	$0.433140\pi$
$864$			31848.7i			1.25407i
$865$	−293.342	−	4824.97i	−0.0115306	−	0.189658i
$866$			24020.5i			0.942550i
$867$	−4280.72	−	4280.72i	−0.167683	−	0.167683i
$868$	−23207.2	−	23207.2i	−0.907492	−	0.907492i
$869$		−	6222.97i		−	0.242923i
$870$	5878.28	+	5204.49i	0.229072	+	0.202815i
$871$			356.264i			0.0138594i
$872$	−126.469	+	126.469i	−0.00491143	+	0.00491143i
$873$	18171.8	+	18171.8i	0.704494	+	0.704494i
$874$	−32628.9	−	39717.8i	−1.26280	−	1.53716i
$875$	21195.8	−	3904.44i	0.818915	−	0.150851i
$876$	−8466.76			−0.326558
$877$	−10899.2	−	10899.2i	−0.419658	−	0.419658i	0.465428	−	0.885086i	$-0.345901\pi$
$877$	−10899.2	−	10899.2i	−0.419658	−	0.419658i	−0.885086	+	0.465428i	$0.845901\pi$
$878$	9012.17	−	9012.17i	0.346408	−	0.346408i
$879$	−5200.59			−0.199558
$880$	11914.9	+	10549.2i	0.456423	+	0.404106i
$881$		−	10123.2i		−	0.387128i	−0.981088	−	0.193564i	$-0.937995\pi$
$881$		−	10123.2i		−	0.387128i	0.981088	−	0.193564i	$-0.0620046\pi$
$882$	4773.08	+	4773.08i	0.182220	+	0.182220i
$883$	22947.2	−	22947.2i	0.874559	−	0.874559i	−0.118406	−	0.992965i	$-0.537778\pi$
$883$	22947.2	−	22947.2i	0.874559	−	0.874559i	0.992965	+	0.118406i	$0.0377784\pi$
$884$	−21117.4			−0.803457
$885$	3065.82	−	186.392i	0.116448	−	0.00707966i
$886$	−36318.8			−1.37715
$887$	10590.2	+	10590.2i	0.400883	+	0.400883i	0.878544	−	0.477661i	$-0.158515\pi$
$887$	10590.2	+	10590.2i	0.400883	+	0.400883i	−0.477661	+	0.878544i	$0.658515\pi$
$888$	6469.62	+	6469.62i	0.244489	+	0.244489i
$889$	−12127.3			−0.457521
$890$	−8171.70	+	496.812i	−0.307771	+	0.0187114i
$891$		−	393.431i		−	0.0147929i
$892$	−6642.96	−	6642.96i	−0.249353	−	0.249353i
$893$	28958.6	+	28958.6i	1.08518	+	1.08518i
$894$	−26909.5			−1.00670
$895$	−32354.9	−	28646.2i	−1.20839	−	1.06988i
$896$		−	13015.7i		−	0.485295i
$897$	−2111.83	+	21552.6i	−0.0786087	+	0.802251i
$898$	−21232.2	+	21232.2i	−0.789006	+	0.789006i
$899$			20235.7i			0.750720i
$900$	1600.21	+	13111.7i	0.0592670	+	0.485618i
$901$	26480.1			0.979112
$902$	6959.14	−	6959.14i	0.256889	−	0.256889i
$903$	7567.44	−	7567.44i	0.278880	−	0.278880i
$904$	676.466			0.0248882
$905$	5584.66	+	4944.52i	0.205128	+	0.181615i
$906$	8051.94			0.295262
$907$	−25408.5	+	25408.5i	−0.930182	+	0.930182i	−0.997717	−	0.0675352i	$-0.978486\pi$
$907$	−25408.5	+	25408.5i	−0.930182	+	0.930182i	0.0675352	+	0.997717i	$0.478486\pi$
$908$	−10168.6	−	10168.6i	−0.371649	−	0.371649i
$909$		−	20379.2i		−	0.743603i
$910$	−2451.91	−	40329.7i	−0.0893187	−	1.46914i
$911$		−	20676.1i		−	0.751953i	−0.926629	−	0.375977i	$-0.877307\pi$
$911$		−	20676.1i		−	0.751953i	0.926629	−	0.375977i	$-0.122693\pi$
$912$	−20742.6	+	20742.6i	−0.753133	+	0.753133i
$913$	−15353.3	+	15353.3i	−0.556541	+	0.556541i
$914$	−14394.6			−0.520931
$915$	−19920.4	+	1211.10i	−0.719726	+	0.0437569i
$916$		−	14390.4i		−	0.519073i
$917$	−4623.19	+	4623.19i	−0.166490	+	0.166490i
$918$	−20280.5	−	20280.5i	−0.729146	−	0.729146i
$919$	−7362.30			−0.264265			−0.132133	−	0.991232i	$-0.542183\pi$
$919$	−7362.30			−0.264265			−0.132133	+	0.991232i	$0.542183\pi$
$920$	−308.157	+	8335.72i	−0.0110431	+	0.298718i
$921$	−7850.23			−0.280862
$922$	14625.1	+	14625.1i	0.522398	+	0.522398i
$923$	−24466.1	+	24466.1i	−0.872492	+	0.872492i
$924$			5724.57i			0.203815i
$925$	42172.1	+	32998.0i	1.49904	+	1.17294i
$926$	−16504.2			−0.585705
$927$	−11022.3	+	11022.3i	−0.390528	+	0.390528i
$928$	9557.65	−	9557.65i	0.338088	−	0.338088i
$929$		−	2698.64i		−	0.0953061i	−0.998864	−	0.0476531i	$-0.984826\pi$
$929$		−	2698.64i		−	0.0953061i	0.998864	−	0.0476531i	$-0.0151742\pi$
$930$	30250.3	−	34166.7i	1.06661	−	1.20470i
$931$			13003.5i			0.457756i
$932$	3707.94	+	3707.94i	0.130319	+	0.130319i
$933$	−4993.47	+	4993.47i	−0.175218	+	0.175218i
$934$	−6867.21			−0.240580
$935$	−11571.3	+	703.499i	−0.404731	+	0.0246063i
$936$	−7161.33			−0.250080
$937$	−21145.4	+	21145.4i	−0.737236	+	0.737236i	−0.972042	−	0.234806i	$-0.924554\pi$
$937$	−21145.4	+	21145.4i	−0.737236	+	0.737236i	0.234806	+	0.972042i	$0.424554\pi$
$938$	−235.507	+	235.507i	−0.00819783	+	0.00819783i
$939$	12174.8			0.423118
$940$	1394.56	+	22938.1i	0.0483888	+	0.795912i
$941$		−	29419.1i		−	1.01917i	−0.860421	−	0.509584i	$-0.829799\pi$
$941$		−	29419.1i		−	1.01917i	0.860421	−	0.509584i	$-0.170201\pi$
$942$	26320.0	−	26320.0i	0.910353	−	0.910353i
$943$	15131.8	+	1482.69i	0.522543	+	0.0512015i
$944$		−	6536.91i		−	0.225380i
$945$	15890.5	−	17947.8i	0.547005	−	0.617822i
$946$	15691.3			0.539291
$947$	−26514.1	−	26514.1i	−0.909813	−	0.909813i	0.0864433	−	0.996257i	$-0.472450\pi$
$947$	−26514.1	−	26514.1i	−0.909813	−	0.909813i	−0.996257	+	0.0864433i	$0.972450\pi$
$948$	4551.47	+	4551.47i	0.155933	+	0.155933i
$949$		−	26865.1i		−	0.918945i
$950$	−35895.8	+	45875.5i	−1.22591	+	1.56674i
$951$	11530.4			0.393165
$952$	4037.08	+	4037.08i	0.137440	+	0.137440i
$953$	22263.0	+	22263.0i	0.756737	+	0.756737i	0.975727	−	0.218990i	$-0.0702763\pi$
$953$	22263.0	+	22263.0i	0.756737	+	0.756737i	−0.218990	+	0.975727i	$0.570276\pi$
$954$	−31051.1			−1.05379
$955$	8938.58	+	7914.00i	0.302875	+	0.268158i
$956$	−1402.84			−0.0474593
$957$	2495.79	−	2495.79i	0.0843026	−	0.0843026i
$958$	33684.8	+	33684.8i	1.13602	+	1.13602i
$959$			14215.7i			0.478673i
$960$	−9243.45	+	561.971i	−0.310762	+	0.0188933i
$961$	87826.0			2.94807
$962$	70983.1	−	70983.1i	2.37899	−	2.37899i
$963$	−18585.0	−	18585.0i	−0.621904	−	0.621904i
$964$	36291.2			1.21251
$965$	−400.956	−	6595.02i	−0.0133754	−	0.220001i
$966$	−15643.2	+	12851.2i	−0.521028	+	0.428034i
$967$	29502.6	+	29502.6i	0.981115	+	0.981115i	0.999825	−	0.0187100i	$-0.00595592\pi$
$967$	29502.6	+	29502.6i	0.981115	+	0.981115i	−0.0187100	+	0.999825i	$0.505956\pi$
$968$	−4649.43	+	4649.43i	−0.154379	+	0.154379i
$969$		−	21369.2i		−	0.708439i
$970$	−42155.2	+	47612.8i	−1.39538	+	1.57603i
$971$		−	23515.6i		−	0.777189i	−0.921409	−	0.388595i	$-0.872961\pi$
$971$		−	23515.6i		−	0.777189i	0.921409	−	0.388595i	$-0.127039\pi$
$972$	16759.0	+	16759.0i	0.553031	+	0.553031i
$973$	10461.6	+	10461.6i	0.344691	+	0.344691i
$974$		−	23270.9i		−	0.765552i
$975$	24360.2	−	2973.03i	0.800156	−	0.0976546i
$976$			42474.1i			1.39299i
$977$	−273.011	+	273.011i	−0.00894001	+	0.00894001i	−0.711563	−	0.702623i	$-0.752012\pi$
$977$	−273.011	+	273.011i	−0.00894001	+	0.00894001i	0.702623	+	0.711563i	$0.252012\pi$
$978$	−132.759	+	132.759i	−0.00434065	+	0.00434065i
$979$			3680.47i			0.120151i
$980$	−4836.91	+	5463.11i	−0.157663	+	0.178074i
$981$			450.292i			0.0146551i
$982$	9428.55	+	9428.55i	0.306392	+	0.306392i
$983$	−19120.1	−	19120.1i	−0.620384	−	0.620384i	0.325246	−	0.945630i	$-0.394553\pi$
$983$	−19120.1	−	19120.1i	−0.620384	−	0.620384i	−0.945630	+	0.325246i	$0.894553\pi$
$984$		−	2943.98i		−	0.0953768i
$985$	9027.68	−	548.853i	0.292026	−	0.0177542i
$986$			12172.2i			0.393145i
$987$	11405.6	−	11405.6i	0.367827	−	0.367827i
$988$	33730.9	+	33730.9i	1.08616	+	1.08616i
$989$	15387.8	+	18731.0i	0.494747	+	0.602235i
$990$	13568.8	−	824.936i	0.435600	−	0.0264830i
$991$	13161.6			0.421890			0.210945	−	0.977498i	$-0.432346\pi$
$991$	13161.6			0.421890			0.210945	+	0.977498i	$0.432346\pi$
$992$	−55552.5	−	55552.5i	−1.77802	−	1.77802i
$993$	14513.1	−	14513.1i	0.463806	−	0.463806i
$994$	−32346.4			−1.03216
$995$	−25243.6	+	28511.7i	−0.804297	+	0.908425i
$996$		−	22458.8i		−	0.714493i
$997$	−441.130	−	441.130i	−0.0140128	−	0.0140128i	0.700066	−	0.714078i	$-0.253154\pi$
$997$	−441.130	−	441.130i	−0.0140128	−	0.0140128i	−0.714078	+	0.700066i	$0.753154\pi$
$998$	26793.1	−	26793.1i	0.849819	−	0.849819i
$999$	59557.9			1.88621

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.4.e.a.22.8	yes	68
5.3	odd	4	inner	115.4.e.a.68.7	yes	68
23.22	odd	2	inner	115.4.e.a.22.7	✓	68
115.68	even	4	inner	115.4.e.a.68.8	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.4.e.a.22.7	✓	68	23.22	odd	2	inner
115.4.e.a.22.8	yes	68	1.1	even	1	trivial
115.4.e.a.68.7	yes	68	5.3	odd	4	inner
115.4.e.a.68.8	yes	68	115.68	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
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} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 4 q^{2} + 4 q^{3} + 32 q^{6} + 28 q^{8} + 200 q^{12} - 100 q^{13} - 832 q^{16} - 112 q^{18} - 46 q^{23} - 372 q^{25} - 312 q^{26} - 704 q^{27} - 1056 q^{31} + 560 q^{32} - 348 q^{35} + 2424 q^{36}+ \cdots - 3612 q^{98}+O(q^{100}) \) 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

Modular forms

Varieties

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Representations

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Database

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