LMFDB - Embedded newform 750.2.l.c.107.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(107,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("750.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.l (of order $20$, degree $8$, not 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			107.10
Character	$\chi$	$=$	750.107
Dual form			750.2.l.c.743.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.891007 + 0.453990i) q^{2} +(1.65131 - 0.522656i) q^{3} +(0.587785 + 0.809017i) q^{4} +(1.70861 + 0.283990i) q^{6} +(0.712495 + 0.712495i) q^{7} +(0.156434 + 0.987688i) q^{8} +(2.45366 - 1.72614i) q^{9} +O(q^{10})$	\(q+(0.891007 + 0.453990i) q^{2} +(1.65131 - 0.522656i) q^{3} +(0.587785 + 0.809017i) q^{4} +(1.70861 + 0.283990i) q^{6} +(0.712495 + 0.712495i) q^{7} +(0.156434 + 0.987688i) q^{8} +(2.45366 - 1.72614i) q^{9} +(0.348148 - 0.113120i) q^{11} +(1.39345 + 1.02873i) q^{12} +(-1.19006 - 2.33563i) q^{13} +(0.311372 + 0.958303i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(5.80242 - 0.919013i) q^{17} +(2.96988 - 0.424059i) q^{18} +(-0.341785 + 0.470426i) q^{19} +(1.54894 + 0.804162i) q^{21} +(0.361558 + 0.0572652i) q^{22} +(-3.08387 + 6.05243i) q^{23} +(0.774543 + 1.54922i) q^{24} -2.62134i q^{26} +(3.14959 - 4.13281i) q^{27} +(-0.157626 + 0.995214i) q^{28} +(0.368253 - 0.267552i) q^{29} +(-2.36811 - 1.72054i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.515779 - 0.368759i) q^{33} +(5.58722 + 1.81540i) q^{34} +(2.83870 + 0.970457i) q^{36} +(-8.53839 + 4.35053i) q^{37} +(-0.518102 + 0.263986i) q^{38} +(-3.18589 - 3.23486i) q^{39} +(10.0917 + 3.27898i) q^{41} +(1.01503 + 1.41972i) q^{42} +(-7.18512 + 7.18512i) q^{43} +(0.296153 + 0.215168i) q^{44} +(-5.49549 + 3.99271i) q^{46} +(1.29277 - 8.16222i) q^{47} +(-0.0132082 + 1.73200i) q^{48} -5.98470i q^{49} +(9.10128 - 4.55025i) q^{51} +(1.19006 - 2.33563i) q^{52} +(-8.72670 - 1.38217i) q^{53} +(4.68256 - 2.25248i) q^{54} +(-0.592264 + 0.815182i) q^{56} +(-0.318522 + 0.955457i) q^{57} +(0.449582 - 0.0712068i) q^{58} +(2.91096 - 8.95903i) q^{59} +(-0.335312 - 1.03198i) q^{61} +(-1.32890 - 2.60811i) q^{62} +(2.97808 + 0.518359i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(0.626975 - 0.0944078i) q^{66} +(2.07319 + 13.0896i) q^{67} +(4.15407 + 4.15407i) q^{68} +(-1.92909 + 11.6062i) q^{69} +(-0.755873 - 1.04037i) q^{71} +(2.08872 + 2.15343i) q^{72} +(-8.50497 - 4.33350i) q^{73} -9.58285 q^{74} -0.581479 q^{76} +(0.328652 + 0.167456i) q^{77} +(-1.37006 - 4.32864i) q^{78} +(-7.17322 - 9.87309i) q^{79} +(3.04091 - 8.47071i) q^{81} +(7.50310 + 7.50310i) q^{82} +(-0.148436 - 0.937190i) q^{83} +(0.259864 + 1.72579i) q^{84} +(-9.66396 + 3.14001i) q^{86} +(0.468264 - 0.634281i) q^{87} +(0.166190 + 0.326166i) q^{88} +(0.626378 + 1.92779i) q^{89} +(0.816210 - 2.51204i) q^{91} +(-6.70917 + 1.06263i) q^{92} +(-4.80974 - 1.60343i) q^{93} +(4.85743 - 6.68568i) q^{94} +(-0.798080 + 1.53723i) q^{96} +(-17.7876 - 2.81727i) q^{97} +(2.71700 - 5.33241i) q^{98} +(0.658978 - 0.878510i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q + 4 * q^3 + 4 * q^7	$ 80 q + 4 q^{3} + 4 q^{7} + 16 q^{12} + 20 q^{16} - 8 q^{18} + 40 q^{19} + 4 q^{22} - 56 q^{27} + 4 q^{28} - 96 q^{33} + 40 q^{34} - 64 q^{37} + 40 q^{39} - 4 q^{42} - 24 q^{43} + 16 q^{48} - 64 q^{57} + 20 q^{58} + 4 q^{63} - 104 q^{67} - 140 q^{69} + 8 q^{72} - 60 q^{73} - 60 q^{78} - 80 q^{79} - 40 q^{81} + 96 q^{82} - 60 q^{84} + 80 q^{87} + 24 q^{88} + 12 q^{93} - 12 q^{97}+O(q^{100}) $ 80 * q + 4 * q^3 + 4 * q^7 + 16 * q^12 + 20 * q^16 - 8 * q^18 + 40 * q^19 + 4 * q^22 - 56 * q^27 + 4 * q^28 - 96 * q^33 + 40 * q^34 - 64 * q^37 + 40 * q^39 - 4 * q^42 - 24 * q^43 + 16 * q^48 - 64 * q^57 + 20 * q^58 + 4 * q^63 - 104 * q^67 - 140 * q^69 + 8 * q^72 - 60 * q^73 - 60 * q^78 - 80 * q^79 - 40 * q^81 + 96 * q^82 - 60 * q^84 + 80 * q^87 + 24 * q^88 + 12 * q^93 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{13}{20}\right)$	$-1$

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 $

$2$	0.891007	+	0.453990i	0.630037	+	0.321020i
$2$	0.891007	+	0.453990i	0.630037	+	0.321020i
$3$	1.65131	−	0.522656i	0.953385	−	0.301755i
$3$	1.65131	−	0.522656i	0.953385	−	0.301755i
$4$	0.587785	+	0.809017i	0.293893	+	0.404508i
$5$		0			0
$5$		0			0
$6$	1.70861	+	0.283990i	0.697537	+	0.115939i
$7$	0.712495	+	0.712495i	0.269298	+	0.269298i	0.828817	−	0.559519i	$-0.189014\pi$
$7$	0.712495	+	0.712495i	0.269298	+	0.269298i	−0.559519	+	0.828817i	$0.689014\pi$
$8$	0.156434	+	0.987688i	0.0553079	+	0.349201i
$9$	2.45366	−	1.72614i	0.817887	−	0.575378i
$10$		0			0
$11$	0.348148	−	0.113120i	0.104971	−	0.0341070i	−0.256061	−	0.966661i	$-0.582425\pi$
$11$	0.348148	−	0.113120i	0.104971	−	0.0341070i	0.361031	+	0.932554i	$0.382425\pi$
$12$	1.39345	+	1.02873i	0.402256	+	0.296969i
$13$	−1.19006	−	2.33563i	−0.330064	−	0.647787i	0.665020	−	0.746826i	$-0.268423\pi$
$13$	−1.19006	−	2.33563i	−0.330064	−	0.647787i	−0.995084	+	0.0990392i	$0.968423\pi$
$14$	0.311372	+	0.958303i	0.0832176	+	0.256117i
$15$		0			0
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	5.80242	−	0.919013i	1.40729	−	0.222893i	0.593868	−	0.804562i	$-0.297600\pi$
$17$	5.80242	−	0.919013i	1.40729	−	0.222893i	0.813426	+	0.581669i	$0.197600\pi$
$18$	2.96988	−	0.424059i	0.700007	−	0.0999516i
$19$	−0.341785	+	0.470426i	−0.0784108	+	0.107923i	−0.846421	−	0.532515i	$-0.821247\pi$
$19$	−0.341785	+	0.470426i	−0.0784108	+	0.107923i	0.768010	+	0.640438i	$0.221247\pi$
$20$		0			0
$21$	1.54894	+	0.804162i	0.338007	+	0.175482i
$22$	0.361558	+	0.0572652i	0.0770844	+	0.0122090i
$23$	−3.08387	+	6.05243i	−0.643031	+	1.26202i	0.307548	+	0.951533i	$0.400492\pi$
$23$	−3.08387	+	6.05243i	−0.643031	+	1.26202i	−0.950578	+	0.310486i	$0.899508\pi$
$24$	0.774543	+	1.54922i	0.158103	+	0.316233i
$25$		0			0
$26$		−	2.62134i		−	0.514086i
$27$	3.14959	−	4.13281i	0.606138	−	0.795359i
$28$	−0.157626	+	0.995214i	−0.0297886	+	0.188078i
$29$	0.368253	−	0.267552i	0.0683830	−	0.0496831i	−0.553069	−	0.833136i	$-0.686543\pi$
$29$	0.368253	−	0.267552i	0.0683830	−	0.0496831i	0.621452	+	0.783453i	$0.286543\pi$
$30$		0			0
$31$	−2.36811	−	1.72054i	−0.425326	−	0.309017i	0.354451	−	0.935074i	$-0.384668\pi$
$31$	−2.36811	−	1.72054i	−0.425326	−	0.309017i	−0.779777	+	0.626057i	$0.784668\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	0.515779	−	0.368759i	0.0897855	−	0.0641926i
$34$	5.58722	+	1.81540i	0.958200	+	0.311338i
$35$		0			0
$36$	2.83870	+	0.970457i	0.473117	+	0.161743i
$37$	−8.53839	+	4.35053i	−1.40370	+	0.715222i	−0.981533	−	0.191295i	$-0.938731\pi$
$37$	−8.53839	+	4.35053i	−1.40370	+	0.715222i	−0.422169	+	0.906517i	$0.638731\pi$
$38$	−0.518102	+	0.263986i	−0.0840472	+	0.0428242i
$39$	−3.18589	−	3.23486i	−0.510151	−	0.517992i
$40$		0			0
$41$	10.0917	+	3.27898i	1.57605	+	0.512090i	0.961036	−	0.276425i	$-0.0891497\pi$
$41$	10.0917	+	3.27898i	1.57605	+	0.512090i	0.615016	+	0.788515i	$0.289150\pi$
$42$	1.01503	+	1.41972i	0.156623	+	0.219067i
$43$	−7.18512	+	7.18512i	−1.09572	+	1.09572i	−0.100815	+	0.994905i	$0.532145\pi$
$43$	−7.18512	+	7.18512i	−1.09572	+	1.09572i	−0.994905	+	0.100815i	$0.967855\pi$
$44$	0.296153	+	0.215168i	0.0446467	+	0.0324377i
$45$		0			0
$46$	−5.49549	+	3.99271i	−0.810266	+	0.588693i
$47$	1.29277	−	8.16222i	0.188570	−	1.19058i	−0.693850	−	0.720119i	$-0.744087\pi$
$47$	1.29277	−	8.16222i	0.188570	−	1.19058i	0.882420	−	0.470463i	$-0.155913\pi$
$48$	−0.0132082	+	1.73200i	−0.00190644	+	0.249993i
$49$		−	5.98470i		−	0.854957i
$50$		0			0
$51$	9.10128	−	4.55025i	1.27443	−	0.637162i
$52$	1.19006	−	2.33563i	0.165032	−	0.323893i
$53$	−8.72670	−	1.38217i	−1.19870	−	0.189856i	−0.475012	−	0.879979i	$-0.657556\pi$
$53$	−8.72670	−	1.38217i	−1.19870	−	0.189856i	−0.723692	+	0.690123i	$0.757556\pi$
$54$	4.68256	−	2.25248i	0.637215	−	0.306523i
$55$		0			0
$56$	−0.592264	+	0.815182i	−0.0791446	+	0.108933i
$57$	−0.318522	+	0.955457i	−0.0421893	+	0.126553i
$58$	0.449582	−	0.0712068i	0.0590330	−	0.00934992i
$59$	2.91096	−	8.95903i	0.378975	−	1.16637i	−0.561782	−	0.827285i	$-0.689884\pi$
$59$	2.91096	−	8.95903i	0.378975	−	1.16637i	0.940757	−	0.339081i	$-0.110116\pi$
$60$		0			0
$61$	−0.335312	−	1.03198i	−0.0429323	−	0.132132i	0.927293	−	0.374337i	$-0.122130\pi$
$61$	−0.335312	−	1.03198i	−0.0429323	−	0.132132i	−0.970225	+	0.242205i	$0.922130\pi$
$62$	−1.32890	−	2.60811i	−0.168770	−	0.331230i
$63$	2.97808	+	0.518359i	0.375203	+	0.0653071i
$64$	−0.951057	+	0.309017i	−0.118882	+	0.0386271i
$65$		0			0
$66$	0.626975	−	0.0944078i	0.0771753	−	0.0116208i
$67$	2.07319	+	13.0896i	0.253280	+	1.59915i	0.706476	+	0.707737i	$0.250284\pi$
$67$	2.07319	+	13.0896i	0.253280	+	1.59915i	−0.453196	+	0.891411i	$0.649716\pi$
$68$	4.15407	+	4.15407i	0.503756	+	0.503756i
$69$	−1.92909	+	11.6062i	−0.232235	+	1.39723i
$70$		0			0
$71$	−0.755873	−	1.04037i	−0.0897056	−	0.123469i	0.761805	−	0.647806i	$-0.224313\pi$
$71$	−0.755873	−	1.04037i	−0.0897056	−	0.123469i	−0.851511	+	0.524337i	$0.824313\pi$
$72$	2.08872	+	2.15343i	0.246158	+	0.253784i
$73$	−8.50497	−	4.33350i	−0.995432	−	0.507198i	−0.121159	−	0.992633i	$-0.538661\pi$
$73$	−8.50497	−	4.33350i	−0.995432	−	0.507198i	−0.874273	+	0.485435i	$0.838661\pi$
$74$	−9.58285			−1.11398
$75$		0			0
$76$	−0.581479			−0.0667002
$77$	0.328652	+	0.167456i	0.0374533	+	0.0190834i
$78$	−1.37006	−	4.32864i	−0.155128	−	0.490122i
$79$	−7.17322	−	9.87309i	−0.807050	−	1.11081i	−0.991772	−	0.128018i	$-0.959138\pi$
$79$	−7.17322	−	9.87309i	−0.807050	−	1.11081i	0.184722	−	0.982791i	$-0.440862\pi$
$80$		0			0
$81$	3.04091	−	8.47071i	0.337879	−	0.941189i
$82$	7.50310	+	7.50310i	0.828579	+	0.828579i
$83$	−0.148436	−	0.937190i	−0.0162930	−	0.102870i	0.978202	−	0.207657i	$-0.0665838\pi$
$83$	−0.148436	−	0.937190i	−0.0162930	−	0.102870i	−0.994495	+	0.104787i	$0.966584\pi$
$84$	0.259864	+	1.72579i	0.0283535	+	0.188300i
$85$		0			0
$86$	−9.66396	+	3.14001i	−1.04209	+	0.338596i
$87$	0.468264	−	0.634281i	0.0502032	−	0.0680021i
$88$	0.166190	+	0.326166i	0.0177159	+	0.0347694i
$89$	0.626378	+	1.92779i	0.0663960	+	0.204346i	0.978750	−	0.205056i	$-0.0657375\pi$
$89$	0.626378	+	1.92779i	0.0663960	+	0.204346i	−0.912354	+	0.409401i	$0.865738\pi$
$90$		0			0
$91$	0.816210	−	2.51204i	0.0855620	−	0.263333i
$92$	−6.70917	+	1.06263i	−0.699479	+	0.110787i
$93$	−4.80974	−	1.60343i	−0.498747	−	0.166268i
$94$	4.85743	−	6.68568i	0.501006	−	0.689576i
$95$		0			0
$96$	−0.798080	+	1.53723i	−0.0814537	+	0.156893i
$97$	−17.7876	−	2.81727i	−1.80605	−	0.286051i	−0.839658	−	0.543115i	$-0.817245\pi$
$97$	−17.7876	−	2.81727i	−1.80605	−	0.286051i	−0.966394	+	0.257065i	$0.917245\pi$
$98$	2.71700	−	5.33241i	0.274458	−	0.538655i
$99$	0.658978	−	0.878510i	0.0662297	−	0.0882936i
$100$		0			0
$101$			0.362340i			0.0360542i	0.999837	+	0.0180271i	$0.00573851\pi$
$101$			0.362340i			0.0360542i	−0.999837	+	0.0180271i	$0.994261\pi$
$102$	10.1751	+	0.0775950i	1.00748	+	0.00768305i
$103$	−1.24118	+	7.83651i	−0.122297	+	0.772154i	0.847957	+	0.530065i	$0.177833\pi$
$103$	−1.24118	+	7.83651i	−0.122297	+	0.772154i	−0.970254	+	0.242089i	$0.922167\pi$
$104$	2.12071	−	1.54078i	0.207952	−	0.151086i
$105$		0			0
$106$	−7.14805	−	5.19336i	−0.694280	−	0.504424i
$107$	−9.06892	+	9.06892i	−0.876725	+	0.876725i	−0.993194	−	0.116469i	$-0.962842\pi$
$107$	−9.06892	+	9.06892i	−0.876725	+	0.876725i	0.116469	+	0.993194i	$0.462842\pi$
$108$	5.19479	+	0.118865i	0.499869	+	0.0114378i
$109$	4.33696	+	1.40916i	0.415405	+	0.134973i	0.509260	−	0.860613i	$-0.329919\pi$
$109$	4.33696	+	1.40916i	0.415405	+	0.134973i	−0.0938551	+	0.995586i	$0.529919\pi$
$110$		0			0
$111$	−11.8257	+	11.6467i	−1.12245	+	1.10546i
$112$	−0.897796	+	0.457450i	−0.0848337	+	0.0432249i
$113$	12.1221	−	6.17652i	1.14035	−	0.581038i	0.221311	−	0.975203i	$-0.428966\pi$
$113$	12.1221	−	6.17652i	1.14035	−	0.581038i	0.919039	+	0.394166i	$0.128966\pi$
$114$	−0.717574	+	0.706712i	−0.0672069	+	0.0661896i
$115$		0			0
$116$	0.432908	+	0.140660i	0.0401945	+	0.0130600i
$117$	−6.95162	−	3.67663i	−0.642677	−	0.339905i
$118$	6.66100	−	6.66100i	0.613195	−	0.613195i
$119$	4.78899	+	3.47940i	0.439006	+	0.318956i
$120$		0			0
$121$	−8.79078	+	6.38687i	−0.799161	+	0.580625i
$122$	0.169746	−	1.07173i	0.0153681	−	0.0970301i
$123$	18.3782	+	0.140152i	1.65711	+	0.0126371i
$124$		−	2.92715i		−	0.262866i
$125$		0			0
$126$	2.41816	+	1.81388i	0.215427	+	0.161594i
$127$	8.95420	−	17.5736i	0.794557	−	1.55941i	−0.0339477	−	0.999424i	$-0.510808\pi$
$127$	8.95420	−	17.5736i	0.794557	−	1.55941i	0.828505	−	0.559982i	$-0.189192\pi$
$128$	−0.987688	−	0.156434i	−0.0873001	−	0.0138270i
$129$	−8.10953	+	15.6202i	−0.714004	+	1.37528i
$130$		0			0
$131$	−6.37019	+	8.76782i	−0.556566	+	0.766048i	−0.990885	−	0.134711i	$-0.956989\pi$
$131$	−6.37019	+	8.76782i	−0.556566	+	0.766048i	0.434318	+	0.900759i	$0.356989\pi$
$132$	0.601499	+	0.200523i	0.0523538	+	0.0174533i
$133$	−0.578696	+	0.0916565i	−0.0501793	+	0.00794763i
$134$	−4.09532	+	12.6041i	−0.353782	+	1.08883i
$135$		0			0
$136$	1.81540	+	5.58722i	0.155669	+	0.479100i
$137$	3.95032	+	7.75294i	0.337498	+	0.662378i	0.995917	−	0.0902740i	$-0.0287743\pi$
$137$	3.95032	+	7.75294i	0.337498	+	0.662378i	−0.658419	+	0.752652i	$0.728774\pi$
$138$	−6.98796	+	9.46545i	−0.594854	+	0.805753i
$139$	2.91069	−	0.945741i	0.246882	−	0.0802167i	−0.182962	−	0.983120i	$-0.558569\pi$
$139$	2.91069	−	0.945741i	0.246882	−	0.0802167i	0.429844	+	0.902903i	$0.358569\pi$
$140$		0			0
$141$	−2.13127	−	14.1540i	−0.179485	−	1.19199i
$142$	−0.201170	−	1.27013i	−0.0168818	−	0.106587i
$143$	−0.678525	−	0.678525i	−0.0567411	−	0.0567411i
$144$	0.883429	+	2.86698i	0.0736191	+	0.238915i
$145$		0			0
$146$	−5.61062	−	7.72236i	−0.464338	−	0.639107i
$147$	−3.12794	−	9.88261i	−0.257988	−	0.815104i
$148$	−8.53839	−	4.35053i	−0.701851	−	0.357611i
$149$	5.85789			0.479897			0.239948	−	0.970786i	$-0.422869\pi$
$149$	5.85789			0.479897			0.239948	+	0.970786i	$0.422869\pi$
$150$		0			0
$151$	3.64976			0.297013			0.148507	−	0.988911i	$-0.452553\pi$
$151$	3.64976			0.297013			0.148507	+	0.988911i	$0.452553\pi$
$152$	−0.518102	−	0.263986i	−0.0420236	−	0.0214121i
$153$	12.6508	−	12.2707i	1.02276	−	0.992028i
$154$	0.216807	+	0.298409i	0.0174708	+	0.0240465i
$155$		0			0
$156$	0.744434	−	4.47884i	0.0596024	−	0.358594i
$157$	2.27502	+	2.27502i	0.181567	+	0.181567i	0.792038	−	0.610472i	$-0.209020\pi$
$157$	2.27502	+	2.27502i	0.181567	+	0.181567i	−0.610472	+	0.792038i	$0.709020\pi$
$158$	−1.90910	−	12.0536i	−0.151880	−	0.958930i
$159$	−15.1329	+	2.27866i	−1.20012	+	0.180709i
$160$		0			0
$161$	−6.50956	+	2.11508i	−0.513025	+	0.166692i
$162$	6.55509	−	6.16691i	0.515017	−	0.484518i
$163$	1.67923	+	3.29567i	0.131527	+	0.258137i	0.947372	−	0.320134i	$-0.103728\pi$
$163$	1.67923	+	3.29567i	0.131527	+	0.258137i	−0.815845	+	0.578270i	$0.803728\pi$
$164$	3.27898	+	10.0917i	0.256045	+	0.788026i
$165$		0			0
$166$	0.293218	−	0.902431i	0.0227581	−	0.0700422i
$167$	−9.02439	+	1.42932i	−0.698328	+	0.110604i	−0.495497	−	0.868610i	$-0.665014\pi$
$167$	−9.02439	+	1.42932i	−0.698328	+	0.110604i	−0.202831	+	0.979214i	$0.565014\pi$
$168$	−0.551953	+	1.65567i	−0.0425841	+	0.127738i
$169$	3.60230	−	4.95814i	0.277100	−	0.381395i
$170$		0			0
$171$	−0.0266046	+	1.74423i	−0.00203450	+	0.133385i
$172$	−10.0362	−	1.58958i	−0.765252	−	0.121204i
$173$	−4.18400	+	8.21156i	−0.318104	+	0.624313i	−0.993588	−	0.113061i	$-0.963935\pi$
$173$	−4.18400	+	8.21156i	−0.318104	+	0.624313i	0.675485	+	0.737374i	$0.263935\pi$
$174$	0.705184	−	0.352561i	0.0534598	−	0.0267276i
$175$		0			0
$176$			0.366065i			0.0275932i
$177$	0.124423	−	16.3156i	0.00935217	−	1.22635i
$178$	−0.317093	+	2.00205i	−0.0237671	+	0.150060i
$179$	−10.9316	+	7.94230i	−0.817069	+	0.593635i	−0.915871	−	0.401472i	$-0.868499\pi$
$179$	−10.9316	+	7.94230i	−0.817069	+	0.593635i	0.0988026	+	0.995107i	$0.468499\pi$
$180$		0			0
$181$	−13.0973	−	9.51573i	−0.973514	−	0.707299i	−0.0172639	−	0.999851i	$-0.505496\pi$
$181$	−13.0973	−	9.51573i	−0.973514	−	0.707299i	−0.956250	+	0.292552i	$0.905496\pi$
$182$	1.86769	−	1.86769i	0.138442	−	0.138442i
$183$	−1.09308	−	1.52887i	−0.0808026	−	0.113018i
$184$	−6.46034	−	2.09909i	−0.476262	−	0.154747i
$185$		0			0
$186$	−3.55757	−	3.61225i	−0.260854	−	0.264863i
$187$	1.91614	−	0.976324i	0.140122	−	0.0713959i
$188$	7.36324	−	3.75176i	0.537020	−	0.273625i
$189$	5.18867	−	0.700541i	0.377420	−	0.0509568i
$190$		0			0
$191$	14.6868	+	4.77202i	1.06270	+	0.345291i	0.787639	−	0.616136i	$-0.211303\pi$
$191$	14.6868	+	4.77202i	1.06270	+	0.345291i	0.275058	+	0.961428i	$0.411303\pi$
$192$	−1.40898	+	1.00736i	−0.101684	+	0.0726998i
$193$	6.05387	−	6.05387i	0.435767	−	0.435767i	−0.454817	−	0.890585i	$-0.650296\pi$
$193$	6.05387	−	6.05387i	0.435767	−	0.435767i	0.890585	+	0.454817i	$0.150296\pi$
$194$	−14.5698	−	10.5856i	−1.04605	−	0.760001i
$195$		0			0
$196$	4.84173	−	3.51772i	0.345838	−	0.251266i
$197$	0.990925	−	6.25646i	0.0706005	−	0.445754i	−0.926913	−	0.375277i	$-0.877548\pi$
$197$	0.990925	−	6.25646i	0.0706005	−	0.445754i	0.997513	−	0.0704774i	$-0.0224523\pi$
$198$	0.985989	−	0.483589i	0.0700712	−	0.0343672i
$199$			10.3976i			0.737069i	0.929614	+	0.368535i	$0.120140\pi$
$199$			10.3976i			0.737069i	−0.929614	+	0.368535i	$0.879860\pi$
$200$		0			0
$201$	10.2648	+	20.5314i	0.724025	+	1.44817i
$202$	−0.164499	+	0.322847i	−0.0115741	+	0.0227155i
$203$	0.453008	+	0.0717494i	0.0317949	+	0.00503582i
$204$	9.03082	+	4.68852i	0.632284	+	0.328262i
$205$		0			0
$206$	−4.66360	+	6.41889i	−0.324928	+	0.447225i
$207$	2.88055	+	20.1738i	0.200212	+	1.40217i
$208$	2.58906	−	0.410067i	0.179519	−	0.0284331i
$209$	−0.0657771	+	0.202441i	−0.00454990	+	0.0140031i
$210$		0			0
$211$	1.12958	+	3.47648i	0.0777632	+	0.239331i	0.982380	−	0.186896i	$-0.0598427\pi$
$211$	1.12958	+	3.47648i	0.0777632	+	0.239331i	−0.904617	+	0.426226i	$0.859843\pi$
$212$	−4.01122	−	7.87247i	−0.275492	−	0.540683i
$213$	−1.79194	−	1.32291i	−0.122781	−	0.0906445i
$214$	−12.1977	+	3.96326i	−0.833815	+	0.270923i
$215$		0			0
$216$	4.57463	+	2.46430i	0.311264	+	0.167674i
$217$	−0.461396	−	2.91314i	−0.0313216	−	0.197757i
$218$	3.22451	+	3.22451i	0.218391	+	0.218391i
$219$	−16.3093	−	2.71079i	−1.10208	−	0.183178i
$220$		0			0
$221$	−9.05171	−	12.4586i	−0.608884	−	0.838057i
$222$	−15.8243	+	5.00853i	−1.06206	+	0.336151i
$223$	1.88406	+	0.959975i	0.126166	+	0.0642847i	0.515934	−	0.856628i	$-0.327445\pi$
$223$	1.88406	+	0.959975i	0.126166	+	0.0642847i	−0.389768	+	0.920913i	$0.627445\pi$
$224$	−1.00762			−0.0673244
$225$		0			0
$226$	13.6049			0.904987
$227$	13.7998	+	7.03137i	0.915928	+	0.466689i	0.847397	−	0.530960i	$-0.178169\pi$
$227$	13.7998	+	7.03137i	0.915928	+	0.466689i	0.0685314	+	0.997649i	$0.478169\pi$
$228$	−0.960203	+	0.303913i	−0.0635910	+	0.0201272i
$229$	0.971347	+	1.33694i	0.0641884	+	0.0883477i	0.839904	−	0.542735i	$-0.182611\pi$
$229$	0.971347	+	1.33694i	0.0641884	+	0.0883477i	−0.775716	+	0.631082i	$0.782611\pi$
$230$		0			0
$231$	0.630228	+	0.104751i	0.0414660	+	0.00689211i
$232$	0.321865	+	0.321865i	0.0211315	+	0.0211315i
$233$	−2.73209	−	17.2497i	−0.178985	−	1.13007i	−0.899594	−	0.436726i	$-0.856138\pi$
$233$	−2.73209	−	17.2497i	−0.178985	−	1.13007i	0.720609	−	0.693342i	$-0.243862\pi$
$234$	−4.52478	−	6.43187i	−0.295794	−	0.420465i
$235$		0			0
$236$	8.95903	−	2.91096i	0.583183	−	0.189488i
$237$	−17.0054	−	12.5544i	−1.10462	−	0.815497i
$238$	2.68740	+	5.27432i	0.174198	+	0.341884i
$239$	−1.97435	−	6.07643i	−0.127710	−	0.393052i	0.866675	−	0.498873i	$-0.166253\pi$
$239$	−1.97435	−	6.07643i	−0.127710	−	0.393052i	−0.994385	+	0.105822i	$0.966253\pi$
$240$		0			0
$241$	5.94510	−	18.2971i	0.382958	−	1.17862i	−0.554993	−	0.831855i	$-0.687279\pi$
$241$	5.94510	−	18.2971i	0.382958	−	1.17862i	0.937951	−	0.346768i	$-0.112721\pi$
$242$	−10.7322	+	1.69982i	−0.689893	+	0.109268i
$243$	0.594232	−	15.5771i	0.0381200	−	0.999273i
$244$	0.637801	−	0.877858i	0.0408310	−	0.0561991i
$245$		0			0
$246$	16.3115	+	8.46842i	1.03998	+	0.539927i
$247$	1.50549	+	0.238446i	0.0957918	+	0.0151719i
$248$	1.32890	−	2.60811i	0.0843851	−	0.165615i
$249$	−0.734942	−	1.47001i	−0.0465751	−	0.0931582i
$250$		0			0
$251$		−	10.1849i		−	0.642864i	−0.946933	−	0.321432i	$-0.895836\pi$
$251$		−	10.1849i		−	0.642864i	0.946933	−	0.321432i	$-0.104164\pi$
$252$	1.33111	+	2.71400i	0.0838522	+	0.170966i
$253$	−0.388991	+	2.45599i	−0.0244556	+	0.154407i
$254$	15.9565	−	11.5931i	1.00120	−	0.727414i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−1.62811	+	1.62811i	−0.101558	+	0.101558i	−0.756060	−	0.654502i	$-0.772878\pi$
$257$	−1.62811	+	1.62811i	−0.101558	+	0.101558i	0.654502	+	0.756060i	$0.272878\pi$
$258$	−14.3171	+	10.2361i	−0.891342	+	0.637270i
$259$	−9.18328	−	2.98383i	−0.570621	−	0.185406i
$260$		0			0
$261$	0.441739	−	1.29214i	0.0273429	−	0.0799813i
$262$	−9.65639	+	4.92018i	−0.596574	+	0.303970i
$263$	−14.9902	+	7.63791i	−0.924338	+	0.470973i	−0.850310	−	0.526283i	$-0.823585\pi$
$263$	−14.9902	+	7.63791i	−0.924338	+	0.470973i	−0.0740278	+	0.997256i	$0.523585\pi$
$264$	0.444904	+	0.451742i	0.0273820	+	0.0278028i
$265$		0			0
$266$	−0.557233	−	0.181056i	−0.0341662	−	0.0111013i
$267$	2.04192	+	2.85601i	0.124963	+	0.174785i
$268$	−9.37111	+	9.37111i	−0.572432	+	0.572432i
$269$	4.85348	+	3.52626i	0.295922	+	0.215000i	0.725832	−	0.687872i	$-0.241455\pi$
$269$	4.85348	+	3.52626i	0.295922	+	0.215000i	−0.429910	+	0.902872i	$0.641455\pi$
$270$		0			0
$271$	−10.0235	+	7.28250i	−0.608885	+	0.442380i	−0.849021	−	0.528359i	$-0.822808\pi$
$271$	−10.0235	+	7.28250i	−0.608885	+	0.442380i	0.240137	+	0.970739i	$0.422808\pi$
$272$	−0.919013	+	5.80242i	−0.0557234	+	0.351823i
$273$	0.0348870	−	4.57475i	0.00211146	−	0.276876i
$274$			8.70132i			0.525666i
$275$		0			0
$276$	−10.5235	+	5.26132i	−0.633443	+	0.316694i
$277$	−2.80135	+	5.49796i	−0.168317	+	0.330340i	−0.959722	−	0.280952i	$-0.909350\pi$
$277$	−2.80135	+	5.49796i	−0.168317	+	0.330340i	0.791405	+	0.611292i	$0.209350\pi$
$278$	3.02280	+	0.478765i	0.181296	+	0.0287144i
$279$	−8.78043	−	0.133927i	−0.525671	−	0.00801799i
$280$		0			0
$281$	5.28744	−	7.27753i	0.315422	−	0.434141i	−0.621640	−	0.783303i	$-0.713533\pi$
$281$	5.28744	−	7.27753i	0.315422	−	0.434141i	0.937063	+	0.349161i	$0.113533\pi$
$282$	4.52683	−	13.5789i	0.269569	−	0.808613i
$283$	12.9466	−	2.05054i	0.769594	−	0.121892i	0.240723	−	0.970594i	$-0.422615\pi$
$283$	12.9466	−	2.05054i	0.769594	−	0.121892i	0.528871	+	0.848702i	$0.322615\pi$
$284$	0.397386	−	1.22303i	0.0235805	−	0.0725733i
$285$		0			0
$286$	−0.296526	−	0.912614i	−0.0175340	−	0.0539640i
$287$	4.85400	+	9.52650i	0.286522	+	0.562332i
$288$	−0.514439	+	2.95556i	−0.0303136	+	0.174158i
$289$	16.6555	−	5.41171i	0.979737	−	0.318336i
$290$		0			0
$291$	−30.8453	+	4.64457i	−1.80818	+	0.272270i
$292$	−1.49322	−	9.42784i	−0.0873842	−	0.551722i
$293$	9.52977	+	9.52977i	0.556735	+	0.556735i	0.928376	−	0.371641i	$-0.121205\pi$
$293$	9.52977	+	9.52977i	0.556735	+	0.556735i	−0.371641	+	0.928376i	$0.621205\pi$
$294$	1.69960	−	10.2255i	0.0991225	−	0.596365i
$295$		0			0
$296$	−5.63266	−	7.75269i	−0.327392	−	0.450616i
$297$	0.629019	−	1.79511i	0.0364994	−	0.104163i
$298$	5.21941	+	2.65942i	0.302353	+	0.154056i
$299$	17.8062			1.02976
$300$		0			0
$301$	−10.2387			−0.590150
$302$	3.25196	+	1.65696i	0.187129	+	0.0953472i
$303$	0.189379	+	0.598336i	0.0108795	+	0.0343735i
$304$	−0.341785	−	0.470426i	−0.0196027	−	0.0269808i
$305$		0			0
$306$	16.8428	−	5.18992i	0.962837	−	0.296688i
$307$	13.4223	+	13.4223i	0.766053	+	0.766053i	0.977409	−	0.211356i	$-0.0677880\pi$
$307$	13.4223	+	13.4223i	0.766053	+	0.766053i	−0.211356	+	0.977409i	$0.567788\pi$
$308$	0.0577015	+	0.364313i	0.00328785	+	0.0207587i
$309$	2.04622	+	13.5892i	0.116405	+	0.773064i
$310$		0			0
$311$	20.3576	−	6.61457i	1.15437	−	0.375078i	0.331583	−	0.943426i	$-0.392417\pi$
$311$	20.3576	−	6.61457i	1.15437	−	0.375078i	0.822788	+	0.568348i	$0.192417\pi$
$312$	2.69665	−	3.65271i	0.152668	−	0.206794i
$313$	−5.79816	−	11.3795i	−0.327732	−	0.643210i	0.667075	−	0.744990i	$-0.267546\pi$
$313$	−5.79816	−	11.3795i	−0.327732	−	0.643210i	−0.994807	+	0.101781i	$0.967546\pi$
$314$	0.994222	+	3.05990i	0.0561072	+	0.172680i
$315$		0			0
$316$	3.77118	−	11.6065i	0.212146	−	0.652917i
$317$	27.3883	−	4.33787i	1.53828	−	0.243639i	0.670997	−	0.741460i	$-0.265866\pi$
$317$	27.3883	−	4.33787i	1.53828	−	0.243639i	0.867280	+	0.497821i	$0.165866\pi$
$318$	−14.5180	−	4.83989i	−0.814129	−	0.271408i
$319$	0.0979413	−	0.134805i	0.00548366	−	0.00754761i
$320$		0			0
$321$	−10.2357	+	19.7155i	−0.571300	+	1.10041i
$322$	−6.76029	−	1.07072i	−0.376736	−	0.0596692i
$323$	−1.55085	+	3.04372i	−0.0862917	+	0.169357i
$324$	8.64035	−	2.51881i	0.480019	−	0.139934i
$325$		0			0
$326$			3.69881i			0.204858i
$327$	7.89818	+	0.0602315i	0.436770	+	0.00333081i
$328$	−1.65992	+	10.4804i	−0.0916540	+	0.578681i
$329$	6.73663	−	4.89445i	0.371402	−	0.269840i
$330$		0			0
$331$	15.0534	+	10.9369i	0.827410	+	0.601149i	0.918826	−	0.394664i	$-0.129139\pi$
$331$	15.0534	+	10.9369i	0.827410	+	0.601149i	−0.0914151	+	0.995813i	$0.529139\pi$
$332$	0.670954	−	0.670954i	0.0368234	−	0.0368234i
$333$	−13.4407	+	25.4131i	−0.736547	+	1.39263i
$334$	−8.68968	−	2.82345i	−0.475478	−	0.154492i
$335$		0			0
$336$	−1.24345	+	1.22463i	−0.0678359	+	0.0668091i
$337$	18.4916	−	9.42193i	1.00730	−	0.513245i	0.129148	−	0.991625i	$-0.458776\pi$
$337$	18.4916	−	9.42193i	1.00730	−	0.513245i	0.878153	+	0.478380i	$0.158776\pi$
$338$	5.46062	−	2.78232i	0.297019	−	0.151339i
$339$	16.7892	−	16.5350i	0.911862	−	0.898060i
$340$		0			0
$341$	−1.01908	−	0.331120i	−0.0551864	−	0.0179312i
$342$	−0.815571	+	1.54205i	−0.0441010	+	0.0833843i
$343$	9.25153	−	9.25153i	0.499536	−	0.499536i
$344$	−8.22066	−	5.97266i	−0.443228	−	0.322024i
$345$		0			0
$346$	−7.45594	+	5.41706i	−0.400834	+	0.291223i
$347$	−1.16592	+	7.36133i	−0.0625898	+	0.395177i	0.936428	+	0.350861i	$0.114111\pi$
$347$	−1.16592	+	7.36133i	−0.0625898	+	0.395177i	−0.999018	+	0.0443161i	$0.985889\pi$
$348$	0.788383	+	0.00601220i	0.0422618	+	0.000322288i
$349$			16.1042i			0.862040i	0.902342	+	0.431020i	$0.141846\pi$
$349$			16.1042i			0.862040i	−0.902342	+	0.431020i	$0.858154\pi$
$350$		0			0
$351$	−13.4009	−	2.43796i	−0.715287	−	0.130129i
$352$	−0.166190	+	0.326166i	−0.00885796	+	0.0173847i
$353$	0.427472	+	0.0677049i	0.0227520	+	0.00360357i	0.167800	−	0.985821i	$-0.446334\pi$
$353$	0.427472	+	0.0677049i	0.0227520	+	0.00360357i	−0.145048	+	0.989425i	$0.546334\pi$
$354$	7.51798	−	14.4808i	0.399576	−	0.769646i
$355$		0			0
$356$	−1.19144	+	1.63988i	−0.0631463	+	0.0869135i
$357$	9.72664	+	3.24259i	0.514788	+	0.171616i
$358$	−13.3459	+	2.11378i	−0.705352	+	0.111717i
$359$	0.0683480	−	0.210354i	0.00360727	−	0.0111020i	−0.949237	−	0.314563i	$-0.898142\pi$
$359$	0.0683480	−	0.210354i	0.00360727	−	0.0111020i	0.952844	+	0.303461i	$0.0981421\pi$
$360$		0			0
$361$	5.76684	+	17.7485i	0.303518	+	0.934132i
$362$	−7.34971	−	14.4246i	−0.386292	−	0.758141i
$363$	−11.1782	+	15.1413i	−0.586702	+	0.794710i
$364$	2.51204	−	0.816210i	0.131666	−	0.0427810i
$365$		0			0
$366$	−0.279844	−	1.85848i	−0.0146277	−	0.0971445i
$367$	2.61239	+	16.4940i	0.136366	+	0.860980i	0.957119	+	0.289697i	$0.0935544\pi$
$367$	2.61239	+	16.4940i	0.136366	+	0.860980i	−0.820753	+	0.571284i	$0.806446\pi$
$368$	−4.80323	−	4.80323i	−0.250386	−	0.250386i
$369$	30.4215	−	9.37406i	1.58368	−	0.487994i
$370$		0			0
$371$	−5.23293	−	7.20252i	−0.271680	−	0.373936i
$372$	−1.52989	−	4.83364i	−0.0793212	−	0.250612i
$373$	−0.0941389	−	0.0479661i	−0.00487433	−	0.00248359i	0.451552	−	0.892245i	$-0.350871\pi$
$373$	−0.0941389	−	0.0479661i	−0.00487433	−	0.00248359i	−0.456426	+	0.889761i	$0.650871\pi$
$374$	2.15054			0.111202
$375$		0			0
$376$	8.26396			0.426181
$377$	−1.06315	−	0.541700i	−0.0547548	−	0.0278990i
$378$	4.94118	+	1.73142i	0.254147	+	0.0890546i
$379$	5.78536	+	7.96287i	0.297174	+	0.409025i	0.931328	−	0.364182i	$-0.118651\pi$
$379$	5.78536	+	7.96287i	0.297174	+	0.409025i	−0.634154	+	0.773207i	$0.718651\pi$
$380$		0			0
$381$	5.60123	−	33.6995i	0.286960	−	1.72648i
$382$	10.9196	+	10.9196i	0.558693	+	0.558693i
$383$	5.20561	+	32.8669i	0.265994	+	1.67942i	0.653010	+	0.757349i	$0.273506\pi$
$383$	5.20561	+	32.8669i	0.265994	+	1.67942i	−0.387016	+	0.922073i	$0.626494\pi$
$384$	−1.71274	+	0.257899i	−0.0874030	+	0.0131609i
$385$		0			0
$386$	8.14244	−	2.64564i	0.414439	−	0.134659i
$387$	−5.22736	+	30.0323i	−0.265722	+	1.52663i
$388$	−8.17604	−	16.0464i	−0.415076	−	0.814632i
$389$	−10.3312	−	31.7962i	−0.523814	−	1.61213i	−0.766650	−	0.642066i	$-0.778078\pi$
$389$	−10.3312	−	31.7962i	−0.523814	−	1.61213i	0.242836	−	0.970067i	$-0.421922\pi$
$390$		0			0
$391$	−12.3316	+	37.9528i	−0.623637	+	1.91936i
$392$	5.91102	−	0.936214i	0.298552	−	0.0472859i
$393$	−5.93662	+	17.8078i	−0.299463	+	0.898286i
$394$	3.72329	−	5.12467i	0.187577	−	0.258177i
$395$		0			0
$396$	1.09807	+	0.0167487i	0.0551799	+	0.000841653i
$397$	13.5583	+	2.14742i	0.680471	+	0.107776i	0.487096	−	0.873349i	$-0.338056\pi$
$397$	13.5583	+	2.14742i	0.680471	+	0.107776i	0.193376	+	0.981125i	$0.438056\pi$
$398$	−4.72043	+	9.26436i	−0.236614	+	0.464381i
$399$	−0.907703	+	0.453812i	−0.0454420	+	0.0227190i
$400$		0			0
$401$			8.63025i			0.430974i	0.976507	+	0.215487i	$0.0691339\pi$
$401$			8.63025i			0.430974i	−0.976507	+	0.215487i	$0.930866\pi$
$402$	−0.175045	+	22.9538i	−0.00873046	+	1.14483i
$403$	−1.20033	+	7.57858i	−0.0597926	+	0.377516i
$404$	−0.293139	+	0.212978i	−0.0145842	+	0.0105961i
$405$		0			0
$406$	0.371060	+	0.269591i	0.0184154	+	0.0133796i
$407$	−2.48049	+	2.48049i	−0.122953	+	0.122953i
$408$	5.91798	+	8.27741i	0.292984	+	0.409793i
$409$	25.9908	+	8.44492i	1.28516	+	0.417574i	0.870395	−	0.492353i	$-0.163863\pi$
$409$	25.9908	+	8.44492i	1.28516	+	0.417574i	0.414767	+	0.909928i	$0.363863\pi$
$410$		0			0
$411$	10.5753	+	10.7379i	0.521642	+	0.529660i
$412$	−7.06941	+	3.60205i	−0.348285	+	0.177460i
$413$	8.45731	−	4.30921i	0.416157	−	0.212043i
$414$	−6.59212	+	19.2827i	−0.323985	+	0.947694i
$415$		0			0
$416$	2.49304	+	0.810037i	0.122231	+	0.0397154i
$417$	4.31216	−	3.08300i	0.211167	−	0.150975i
$418$	−0.150514	+	0.150514i	−0.00736189	+	0.00736189i
$419$	20.8362	+	15.1384i	1.01791	+	0.739557i	0.965854	−	0.259087i	$-0.0834215\pi$
$419$	20.8362	+	15.1384i	1.01791	+	0.739557i	0.0520594	+	0.998644i	$0.483421\pi$
$420$		0			0
$421$	28.5994	−	20.7787i	1.39385	−	1.01269i	0.398419	−	0.917203i	$-0.369559\pi$
$421$	28.5994	−	20.7787i	1.39385	−	1.01269i	0.995431	−	0.0954876i	$-0.0304410\pi$
$422$	−0.571828	+	3.61038i	−0.0278362	+	0.175751i
$423$	−10.9171	−	22.2588i	−0.530806	−	1.08226i
$424$		−	8.83548i		−	0.429089i
$425$		0			0
$426$	−0.996037	−	1.99225i	−0.0482582	−	0.0965246i
$427$	0.496375	−	0.974191i	0.0240213	−	0.0471444i
$428$	−12.6675	−	2.00633i	−0.612306	−	0.0969797i
$429$	−1.47509	−	0.765821i	−0.0712181	−	0.0369742i
$430$		0			0
$431$	−19.9752	+	27.4935i	−0.962171	+	1.32432i	−0.0162678	+	0.999868i	$0.505178\pi$
$431$	−19.9752	+	27.4935i	−0.962171	+	1.32432i	−0.945904	+	0.324448i	$0.894822\pi$
$432$	2.95726	+	4.27254i	0.142281	+	0.205563i
$433$	18.8393	−	2.98384i	0.905357	−	0.143394i	0.313641	−	0.949541i	$-0.398451\pi$
$433$	18.8393	−	2.98384i	0.905357	−	0.143394i	0.591715	+	0.806147i	$0.298451\pi$
$434$	0.911432	−	2.80510i	0.0437501	−	0.134649i
$435$		0			0
$436$	1.40916	+	4.33696i	0.0674867	+	0.207703i
$437$	−1.79320	−	3.51936i	−0.0857806	−	0.168354i
$438$	−13.3010	−	9.81959i	−0.635547	−	0.469198i
$439$	−33.6517	+	10.9341i	−1.60611	+	0.521856i	−0.968607	−	0.248596i	$-0.920031\pi$
$439$	−33.6517	+	10.9341i	−1.60611	+	0.521856i	−0.637499	+	0.770451i	$0.720031\pi$
$440$		0			0
$441$	−10.3304	−	14.6844i	−0.491924	−	0.699259i
$442$	−2.40904	−	15.2101i	−0.114586	−	0.723470i
$443$	10.2497	+	10.2497i	0.486977	+	0.486977i	0.907351	−	0.420374i	$-0.138101\pi$
$443$	10.2497	+	10.2497i	0.486977	+	0.486977i	−0.420374	+	0.907351i	$0.638101\pi$
$444$	−16.3734	−	2.72144i	−0.777046	−	0.129154i
$445$		0			0
$446$	1.24289	+	1.71069i	0.0588524	+	0.0810034i
$447$	9.67320	−	3.06166i	0.457526	−	0.144811i
$448$	−0.897796	−	0.457450i	−0.0424169	−	0.0216125i
$449$	−9.47944			−0.447362			−0.223681	−	0.974662i	$-0.571807\pi$
$449$	−9.47944			−0.447362			−0.223681	+	0.974662i	$0.571807\pi$
$450$		0			0
$451$	3.88431			0.182905
$452$	12.1221	+	6.17652i	0.570175	+	0.290519i
$453$	6.02689	−	1.90757i	0.283168	−	0.0896254i
$454$	9.10358	+	12.5300i	0.427252	+	0.588062i
$455$		0			0
$456$	−0.993521	−	0.165134i	−0.0465259	−	0.00773312i
$457$	−25.4852	−	25.4852i	−1.19215	−	1.19215i	−0.976464	−	0.215682i	$-0.930803\pi$
$457$	−25.4852	−	25.4852i	−1.19215	−	1.19215i	−0.215682	−	0.976464i	$-0.569197\pi$
$458$	0.258516	+	1.63221i	0.0120797	+	0.0762681i
$459$	14.4771	−	26.8748i	0.675734	−	1.25441i
$460$		0			0
$461$	21.4340	−	6.96431i	0.998279	−	0.324360i	0.236101	−	0.971728i	$-0.424130\pi$
$461$	21.4340	−	6.96431i	0.998279	−	0.324360i	0.762178	+	0.647368i	$0.224130\pi$
$462$	0.513982	+	0.379451i	0.0239126	+	0.0176537i
$463$	−2.57463	−	5.05300i	−0.119653	−	0.234833i	0.823409	−	0.567448i	$-0.192069\pi$
$463$	−2.57463	−	5.05300i	−0.119653	−	0.234833i	−0.943063	+	0.332615i	$0.892069\pi$
$464$	0.140660	+	0.432908i	0.00652999	+	0.0200972i
$465$		0			0
$466$	5.39691	−	16.6100i	0.250007	−	0.769442i
$467$	−11.4802	+	1.81829i	−0.531242	+	0.0841404i	−0.416292	−	0.909231i	$-0.636671\pi$
$467$	−11.4802	+	1.81829i	−0.531242	+	0.0841404i	−0.114950	+	0.993371i	$0.536671\pi$
$468$	−1.11160	−	7.78505i	−0.0513838	−	0.359864i
$469$	−7.84913	+	10.8034i	−0.362439	+	0.498854i
$470$		0			0
$471$	4.94583	+	2.56772i	0.227892	+	0.118314i
$472$	9.30410	+	1.47363i	0.428256	+	0.0678291i
$473$	−1.68871	+	3.31427i	−0.0776467	+	0.152390i
$474$	−9.45238	−	18.9064i	−0.434162	−	0.868399i
$475$		0			0
$476$			5.91951i			0.271320i
$477$	−23.7982	+	11.6721i	−1.08964	+	0.534428i
$478$	0.999482	−	6.31048i	0.0457152	−	0.288635i
$479$	2.20406	−	1.60135i	0.100706	−	0.0731673i	−0.536293	−	0.844032i	$-0.680176\pi$
$479$	2.20406	−	1.60135i	0.100706	−	0.0731673i	0.636999	+	0.770865i	$0.280176\pi$
$480$		0			0
$481$	20.3224	+	14.7651i	0.926622	+	0.673230i
$482$	13.6039	−	13.6039i	0.619639	−	0.619639i
$483$	−9.64386	+	6.89493i	−0.438811	+	0.313730i
$484$	−10.3342	−	3.35778i	−0.469735	−	0.152626i
$485$		0			0
$486$	7.60133	−	13.6095i	0.344803	−	0.617342i
$487$	24.1563	−	12.3082i	1.09462	−	0.557739i	0.189068	−	0.981964i	$-0.439453\pi$
$487$	24.1563	−	12.3082i	1.09462	−	0.557739i	0.905557	+	0.424225i	$0.139453\pi$
$488$	0.966824	−	0.492622i	0.0437661	−	0.0222999i
$489$	4.49543	+	4.56452i	0.203290	+	0.206415i
$490$		0			0
$491$	37.5268	+	12.1932i	1.69356	+	0.550271i	0.987464	−	0.157846i	$-0.0504550\pi$
$491$	37.5268	+	12.1932i	1.69356	+	0.550271i	0.706095	+	0.708117i	$0.250455\pi$
$492$	10.6891	+	14.9507i	0.481901	+	0.674029i
$493$	1.89088	−	1.89088i	0.0851609	−	0.0851609i
$494$	1.23315	+	0.895933i	0.0554819	+	0.0403099i
$495$		0			0
$496$	2.36811	−	1.72054i	0.106331	−	0.0772543i
$497$	0.202702	−	1.27981i	0.00909245	−	0.0574075i
$498$	0.0125329	−	1.64345i	0.000561613	−	0.0736446i
$499$			11.3155i			0.506552i	0.967394	+	0.253276i	$0.0815081\pi$
$499$			11.3155i			0.506552i	−0.967394	+	0.253276i	$0.918492\pi$
$500$		0			0
$501$	−14.1550	+	7.07690i	−0.632400	+	0.316173i
$502$	4.62384	−	9.07480i	0.206372	−	0.405028i
$503$	−8.50269	−	1.34669i	−0.379116	−	0.0600461i	−0.0360317	−	0.999351i	$-0.511472\pi$
$503$	−8.50269	−	1.34669i	−0.379116	−	0.0600461i	−0.343084	+	0.939305i	$0.611472\pi$
$504$	−0.0461019	+	3.02251i	−0.00205354	+	0.134633i
$505$		0			0
$506$	−1.46159	+	2.01171i	−0.0649756	+	0.0894312i
$507$	3.35712	−	10.0702i	0.149095	−	0.447233i
$508$	19.4805	−	3.08541i	0.864307	−	0.136893i
$509$	0.697725	−	2.14738i	0.0309261	−	0.0951808i	−0.934402	−	0.356220i	$-0.884065\pi$
$509$	0.697725	−	2.14738i	0.0309261	−	0.0951808i	0.965328	+	0.261039i	$0.0840653\pi$
$510$		0			0
$511$	−2.97215	−	9.14735i	−0.131480	−	0.404655i
$512$	−0.453990	−	0.891007i	−0.0200637	−	0.0393773i
$513$	0.867702	+	2.89418i	0.0383100	+	0.127781i
$514$	−2.18980	+	0.711508i	−0.0965878	+	0.0313833i
$515$		0			0
$516$	−17.4037	+	2.62059i	−0.766154	+	0.115365i
$517$	−0.473237	−	2.98790i	−0.0208129	−	0.131408i
$518$	−6.82773	−	6.82773i	−0.299993	−	0.299993i
$519$	−2.61727	+	15.7466i	−0.114885	+	0.691201i
$520$		0			0
$521$	−13.0319	−	17.9369i	−0.570938	−	0.785829i	0.421727	−	0.906723i	$-0.361424\pi$
$521$	−13.0319	−	17.9369i	−0.570938	−	0.785829i	−0.992665	+	0.120894i	$0.961424\pi$
$522$	0.980210	−	0.950757i	0.0429026	−	0.0416135i
$523$	9.99457	+	5.09249i	0.437032	+	0.222679i	0.658642	−	0.752456i	$-0.271131\pi$
$523$	9.99457	+	5.09249i	0.437032	+	0.222679i	−0.221610	+	0.975135i	$0.571131\pi$
$524$	−10.8376			−0.473444
$525$		0			0
$526$	−16.8239			−0.733558
$527$	−15.3220	−	7.80694i	−0.667436	−	0.340076i
$528$	0.191326	+	0.604487i	0.00832639	+	0.0263069i
$529$	−13.6026	−	18.7224i	−0.591417	−	0.814016i
$530$		0			0
$531$	−8.32197	−	27.0071i	−0.361143	−	1.17201i
$532$	−0.414301	−	0.414301i	−0.0179622	−	0.0179622i
$533$	−4.35122	−	27.4725i	−0.188472	−	1.18997i
$534$	0.522762	+	3.47174i	0.0226221	+	0.150237i
$535$		0			0
$536$	−12.6041	+	4.09532i	−0.544415	+	0.176891i
$537$	−13.9005	+	18.8287i	−0.599849	+	0.812518i
$538$	2.72359	+	5.34536i	0.117423	+	0.230455i
$539$	−0.676991	−	2.08356i	−0.0291601	−	0.0897455i
$540$		0			0
$541$	3.02125	−	9.29846i	0.129894	−	0.399772i	−0.864867	−	0.502001i	$-0.832597\pi$
$541$	3.02125	−	9.29846i	0.129894	−	0.399772i	0.994761	+	0.102229i	$0.0325974\pi$
$542$	−12.2372	+	1.93818i	−0.525632	+	0.0832520i
$543$	−26.6012	−	8.86807i	−1.14156	−	0.380565i
$544$	−3.45309	+	4.75277i	−0.148050	+	0.203773i
$545$		0			0
$546$	2.10798	−	4.06029i	0.0902131	−	0.173765i
$547$	−10.4482	−	1.65483i	−0.446732	−	0.0707555i	−0.0709846	−	0.997477i	$-0.522614\pi$
$547$	−10.4482	−	1.65483i	−0.446732	−	0.0707555i	−0.375748	+	0.926722i	$0.622614\pi$
$548$	−3.95032	+	7.75294i	−0.168749	+	0.331189i
$549$	−2.60409	−	1.95335i	−0.111140	−	0.0833668i
$550$		0			0
$551$			0.264681i			0.0112758i
$552$	−11.7651	−	0.0897208i	−0.500757	−	0.00381877i
$553$	1.92364	−	12.1454i	0.0818016	−	0.516475i
$554$	−4.99204	+	3.62693i	−0.212092	+	0.154094i
$555$		0			0
$556$	2.47598	+	1.79891i	0.105005	+	0.0762906i
$557$	2.23937	−	2.23937i	0.0948850	−	0.0948850i	−0.658071	−	0.752956i	$-0.728627\pi$
$557$	2.23937	−	2.23937i	0.0948850	−	0.0948850i	0.752956	+	0.658071i	$0.228627\pi$
$558$	−7.76262	−	4.10556i	−0.328618	−	0.173802i
$559$	25.3325	+	8.23103i	1.07145	+	0.348135i
$560$		0			0
$561$	2.65387	−	2.61370i	0.112047	−	0.110351i
$562$	8.01507	−	4.08388i	0.338095	−	0.172268i
$563$	−9.06485	+	4.61877i	−0.382038	+	0.194658i	−0.634454	−	0.772961i	$-0.718775\pi$
$563$	−9.06485	+	4.61877i	−0.382038	+	0.194658i	0.252416	+	0.967619i	$0.418775\pi$
$564$	10.1981	−	10.0438i	0.429419	−	0.422919i
$565$		0			0
$566$	12.4664	+	4.05058i	0.524002	+	0.170259i
$567$	8.20197	−	3.86870i	0.344450	−	0.162470i
$568$	0.909316	−	0.909316i	0.0381541	−	0.0381541i
$569$	−10.0063	−	7.26997i	−0.419484	−	0.304773i	0.357946	−	0.933742i	$-0.383477\pi$
$569$	−10.0063	−	7.26997i	−0.419484	−	0.304773i	−0.777430	+	0.628969i	$0.783477\pi$
$570$		0			0
$571$	22.7821	−	16.5522i	0.953402	−	0.692687i	0.00179324	−	0.999998i	$-0.499429\pi$
$571$	22.7821	−	16.5522i	0.953402	−	0.692687i	0.951609	+	0.307311i	$0.0994292\pi$
$572$	0.150111	−	0.947765i	0.00627647	−	0.0396281i
$573$	26.7466	+	0.203969i	1.11735	+	0.00852093i
$574$			10.6918i			0.446269i
$575$		0			0
$576$	−1.80017	+	2.39988i	−0.0750069	+	0.0999948i
$577$	5.07813	−	9.96640i	0.211405	−	0.414907i	−0.760817	−	0.648967i	$-0.775201\pi$
$577$	5.07813	−	9.96640i	0.211405	−	0.414907i	0.972222	+	0.234060i	$0.0752013\pi$
$578$	17.2971	+	2.73958i	0.719463	+	0.113952i
$579$	6.83274	−	13.1609i	0.283959	−	0.546949i
$580$		0			0
$581$	0.561983	−	0.773503i	0.0233150	−	0.0320903i
$582$	−29.5919	−	9.86511i	−1.22662	−	0.408922i
$583$	−3.19454	+	0.505965i	−0.132304	+	0.0209549i
$584$	2.94968	−	9.07817i	0.122059	−	0.375657i
$585$		0			0
$586$	4.16466	+	12.8175i	0.172041	+	0.529487i
$587$	0.272317	+	0.534451i	0.0112397	+	0.0220592i	0.896558	−	0.442926i	$-0.146060\pi$
$587$	0.272317	+	0.534451i	0.0112397	+	0.0220592i	−0.885318	+	0.464985i	$0.846060\pi$
$588$	6.15664	−	8.33941i	0.253896	−	0.343911i
$589$	1.61877	−	0.525971i	0.0667003	−	0.0216722i
$590$		0			0
$591$	−1.63365	−	10.8493i	−0.0671992	−	0.446279i
$592$	−1.49909	−	9.46487i	−0.0616122	−	0.389004i
$593$	1.69633	+	1.69633i	0.0696598	+	0.0696598i	0.741078	−	0.671419i	$-0.234315\pi$
$593$	1.69633	+	1.69633i	0.0696598	+	0.0696598i	−0.671419	+	0.741078i	$0.734315\pi$
$594$	1.37542	−	1.31389i	0.0564343	−	0.0539095i
$595$		0			0
$596$	3.44318	+	4.73913i	0.141038	+	0.194122i
$597$	5.43439	+	17.1697i	0.222415	+	0.702711i
$598$	15.8654	+	8.08385i	0.648786	+	0.330573i
$599$	−12.0681			−0.493088			−0.246544	−	0.969132i	$-0.579295\pi$
$599$	−12.0681			−0.493088			−0.246544	+	0.969132i	$0.579295\pi$
$600$		0			0
$601$	8.03062			0.327576			0.163788	−	0.986496i	$-0.447629\pi$
$601$	8.03062			0.327576			0.163788	+	0.986496i	$0.447629\pi$
$602$	−9.12277	−	4.64828i	−0.371816	−	0.189450i
$603$	27.6813	+	28.5388i	1.12727	+	1.16219i
$604$	2.14528	+	2.95272i	0.0872900	+	0.120144i
$605$		0			0
$606$	−0.102901	+	0.619098i	−0.00418007	+	0.0251491i
$607$	−27.1756	−	27.1756i	−1.10302	−	1.10302i	−0.994044	−	0.108980i	$-0.965242\pi$
$607$	−27.1756	−	27.1756i	−1.10302	−	1.10302i	−0.108980	−	0.994044i	$-0.534758\pi$
$608$	−0.0909634	−	0.574320i	−0.00368905	−	0.0232918i
$609$	0.785558	−	0.118287i	0.0318324	−	0.00479321i
$610$		0			0
$611$	−20.6024	+	6.69412i	−0.833483	+	0.270815i
$612$	17.3632	+	3.02220i	0.701865	+	0.122165i
$613$	13.2287	+	25.9627i	0.534300	+	1.04862i	0.987560	+	0.157245i	$0.0502612\pi$
$613$	13.2287	+	25.9627i	0.534300	+	1.04862i	−0.453259	+	0.891379i	$0.649739\pi$
$614$	5.86577	+	18.0530i	0.236723	+	0.728560i
$615$		0			0
$616$	−0.113982	+	0.350801i	−0.00459248	+	0.0141342i
$617$	18.9443	−	3.00048i	0.762667	−	0.120795i	0.237029	−	0.971503i	$-0.423826\pi$
$617$	18.9443	−	3.00048i	0.762667	−	0.120795i	0.525639	+	0.850708i	$0.323826\pi$
$618$	−4.34618	+	13.0371i	−0.174829	+	0.524427i
$619$	−11.4117	+	15.7069i	−0.458676	+	0.631314i	−0.974234	−	0.225541i	$-0.927585\pi$
$619$	−11.4117	+	15.7069i	−0.458676	+	0.631314i	0.515557	+	0.856855i	$0.327585\pi$
$620$		0			0
$621$	15.3006	+	31.8077i	0.613993	+	1.27640i
$622$	21.1417	+	3.34851i	0.847704	+	0.134263i
$623$	−0.927252	+	1.81984i	−0.0371496	+	0.0729102i
$624$	4.06103	−	2.03034i	0.162571	−	0.0812786i
$625$		0			0
$626$		−	12.7716i		−	0.510454i
$627$	−0.00281149	+	0.368672i	−0.000112280	+	0.0147233i
$628$	−0.503308	+	3.17776i	−0.0200842	+	0.126806i
$629$	−45.5451	+	33.0905i	−1.81600	+	1.31940i
$630$		0			0
$631$	8.91070	+	6.47400i	0.354729	+	0.257726i	0.750850	−	0.660472i	$-0.229644\pi$
$631$	8.91070	+	6.47400i	0.354729	+	0.257726i	−0.396121	+	0.918198i	$0.629644\pi$
$632$	8.62939	−	8.62939i	0.343259	−	0.343259i
$633$	3.68228	+	5.15037i	0.146358	+	0.204709i
$634$	26.3725	+	8.56893i	1.04738	+	0.340316i
$635$		0			0
$636$	−10.7384	−	10.9034i	−0.425804	−	0.432348i
$637$	−13.9780	+	7.12216i	−0.553830	+	0.282190i
$638$	0.148466	−	0.0756474i	0.00587784	−	0.00299491i
$639$	−3.65047	−	1.24798i	−0.144411	−	0.0493692i
$640$		0			0
$641$	−41.8679	−	13.6037i	−1.65368	−	0.537314i	−0.674148	−	0.738596i	$-0.735489\pi$
$641$	−41.8679	−	13.6037i	−1.65368	−	0.537314i	−0.979533	+	0.201283i	$0.935489\pi$
$642$	−18.0707	+	12.9198i	−0.713195	+	0.509902i
$643$	21.0709	−	21.0709i	0.830957	−	0.830957i	−0.156691	−	0.987648i	$-0.550083\pi$
$643$	21.0709	−	21.0709i	0.830957	−	0.830957i	0.987648	+	0.156691i	$0.0500826\pi$
$644$	−5.53736	−	4.02313i	−0.218203	−	0.158534i
$645$		0			0
$646$	−2.76364	+	2.00790i	−0.108734	+	0.0789998i
$647$	5.07470	−	32.0404i	0.199507	−	1.25964i	−0.661073	−	0.750322i	$-0.729899\pi$
$647$	5.07470	−	32.0404i	0.199507	−	1.25964i	0.860580	−	0.509316i	$-0.170101\pi$
$648$	8.84212	+	1.67836i	0.347351	+	0.0659324i
$649$		−	3.44836i		−	0.135360i
$650$		0			0
$651$	−2.28448	−	4.56935i	−0.0895358	−	0.179087i
$652$	−1.67923	+	3.29567i	−0.0657636	+	0.129068i
$653$	−30.5859	−	4.84433i	−1.19692	−	0.189573i	−0.474012	−	0.880518i	$-0.657195\pi$
$653$	−30.5859	−	4.84433i	−1.19692	−	0.189573i	−0.722907	+	0.690945i	$0.757195\pi$
$654$	7.00998	+	3.63936i	0.274112	+	0.142310i
$655$		0			0
$656$	−6.23698	+	8.58447i	−0.243513	+	0.335167i
$657$	−28.3485	+	4.04779i	−1.10598	+	0.157919i
$658$	8.22441	−	1.30262i	0.320621	−	0.0507814i
$659$	−6.85074	+	21.0844i	−0.266867	+	0.821332i	0.724390	+	0.689390i	$0.242121\pi$
$659$	−6.85074	+	21.0844i	−0.266867	+	0.821332i	−0.991257	+	0.131942i	$0.957879\pi$
$660$		0			0
$661$	−9.91334	−	30.5101i	−0.385584	−	1.18671i	−0.936056	−	0.351852i	$-0.885552\pi$
$661$	−9.91334	−	30.5101i	−0.385584	−	1.18671i	0.550471	−	0.834854i	$-0.314448\pi$
$662$	8.44742	+	16.5790i	0.328318	+	0.644361i
$663$	−21.4588	−	15.8421i	−0.833389	−	0.615257i
$664$	0.902431	−	0.293218i	0.0350211	−	0.0113790i
$665$		0			0
$666$	−23.5131	+	16.5413i	−0.911114	+	0.640963i
$667$	0.483694	+	3.05392i	0.0187287	+	0.118248i
$668$	−6.46075	−	6.46075i	−0.249974	−	0.249974i
$669$	3.61290	+	0.600505i	0.139683	+	0.0232169i
$670$		0			0
$671$	−0.233477	−	0.321353i	−0.00901327	−	0.0124057i
$672$	−1.66389	+	0.526638i	−0.0641861	+	0.0203155i
$673$	−33.4118	−	17.0242i	−1.28793	−	0.656234i	−0.330204	−	0.943910i	$-0.607117\pi$
$673$	−33.4118	−	17.0242i	−1.28793	−	0.656234i	−0.957728	+	0.287676i	$0.907117\pi$
$674$	20.7536			0.799398
$675$		0			0
$676$	6.12860			0.235715
$677$	−26.7784	−	13.6443i	−1.02918	−	0.524391i	−0.143966	−	0.989583i	$-0.545985\pi$
$677$	−26.7784	−	13.6443i	−1.02918	−	0.524391i	−0.885210	+	0.465192i	$0.845985\pi$
$678$	22.4660	−	7.11070i	0.862802	−	0.273085i
$679$	−10.6662	−	14.6808i	−0.409333	−	0.563399i
$680$		0			0
$681$	26.4628	+	4.39842i	1.01406	+	0.168548i
$682$	−0.757684	−	0.757684i	−0.0290132	−	0.0290132i
$683$	−5.21701	−	32.9389i	−0.199623	−	1.26037i	−0.860334	−	0.509731i	$-0.829745\pi$
$683$	−5.21701	−	32.9389i	−0.199623	−	1.26037i	0.660711	−	0.750640i	$-0.270255\pi$
$684$	−1.42675	+	1.00371i	−0.0545533	+	0.0383779i
$685$		0			0
$686$	12.4433	−	4.04307i	0.475087	−	0.154365i
$687$	2.30276	+	1.70003i	0.0878557	+	0.0648602i
$688$	−4.61313	−	9.05378i	−0.175874	−	0.345172i
$689$	7.15707	+	22.0272i	0.272663	+	0.839169i
$690$		0			0
$691$	0.495555	−	1.52516i	0.0188518	−	0.0580199i	−0.941188	−	0.337883i	$-0.890289\pi$
$691$	0.495555	−	1.52516i	0.0188518	−	0.0580199i	0.960040	+	0.279863i	$0.0902891\pi$
$692$	−9.10259	+	1.44171i	−0.346028	+	0.0548055i
$693$	1.09545	−	0.156416i	0.0416128	−	0.00594175i
$694$	−4.38081	+	6.02967i	−0.166293	+	0.228883i
$695$		0			0
$696$	0.699725	+	0.363275i	0.0265230	+	0.0137699i
$697$	61.5694	+	9.75164i	2.33211	+	0.369370i
$698$	−7.31117	+	14.3490i	−0.276732	+	0.543117i
$699$	−13.5272	−	27.0568i	−0.511646	−	1.02338i
$700$		0			0
$701$			17.1529i			0.647855i	0.946082	+	0.323928i	$0.105003\pi$
$701$			17.1529i			0.647855i	−0.946082	+	0.323928i	$0.894997\pi$
$702$	−10.8335	−	8.25612i	−0.408883	−	0.311607i
$703$	0.871689	−	5.50363i	0.0328764	−	0.207573i
$704$	−0.296153	+	0.215168i	−0.0111617	+	0.00810943i
$705$		0			0
$706$	0.350143	+	0.254394i	0.0131778	+	0.00957423i
$707$	−0.258165	+	0.258165i	−0.00970931	+	0.00970931i
$708$	13.2727	−	9.48940i	0.498819	−	0.356633i
$709$	−43.3999	−	14.1015i	−1.62992	−	0.529592i	−0.655664	−	0.755052i	$-0.727611\pi$
$709$	−43.3999	−	14.1015i	−1.62992	−	0.529592i	−0.974252	+	0.225460i	$0.927611\pi$
$710$		0			0
$711$	−34.6429	−	11.8433i	−1.29921	−	0.444157i
$712$	−1.80607	+	0.920240i	−0.0676855	+	0.0344875i
$713$	17.7164	−	9.02694i	0.663483	−	0.338062i
$714$	7.19440	+	7.30497i	0.269244	+	0.273382i
$715$		0			0
$716$	−12.8509	−	4.17551i	−0.480261	−	0.156046i
$717$	−6.43616	−	9.00218i	−0.240363	−	0.336193i
$718$	0.156397	−	0.156397i	0.00583669	−	0.00583669i
$719$	18.8277	+	13.6791i	0.702155	+	0.510145i	0.880633	−	0.473798i	$-0.157117\pi$
$719$	18.8277	+	13.6791i	0.702155	+	0.510145i	−0.178478	+	0.983944i	$0.557117\pi$
$720$		0			0
$721$	−6.46780	+	4.69913i	−0.240874	+	0.175005i
$722$	−2.91936	+	18.4321i	−0.108647	+	0.685973i
$723$	0.254110	−	33.3215i	0.00945044	−	1.23924i
$724$		−	16.1891i		−	0.601664i
$725$		0			0
$726$	−16.8338	+	8.41618i	−0.624762	+	0.312354i
$727$	−12.3793	+	24.2957i	−0.459122	+	0.901077i	0.539144	+	0.842213i	$0.318748\pi$
$727$	−12.3793	+	24.2957i	−0.459122	+	0.901077i	−0.998266	+	0.0588635i	$0.981252\pi$
$728$	2.60879	+	0.413192i	0.0966882	+	0.0153139i
$729$	−7.16021	−	26.0333i	−0.265193	−	0.964195i
$730$		0			0
$731$	−35.0879	+	48.2943i	−1.29777	+	1.78623i
$732$	0.594391	−	1.78297i	0.0219693	−	0.0659004i
$733$	−5.78324	+	0.915975i	−0.213609	+	0.0338323i	−0.262322	−	0.964981i	$-0.584488\pi$
$733$	−5.78324	+	0.915975i	−0.213609	+	0.0338323i	0.0487128	+	0.998813i	$0.484488\pi$
$734$	−5.16046	+	15.8823i	−0.190476	+	0.586225i
$735$		0			0
$736$	−2.09909	−	6.46034i	−0.0773735	−	0.238131i
$737$	2.20247	+	4.32260i	0.0811292	+	0.159225i
$738$	31.3615	+	5.45871i	1.15443	+	0.200938i
$739$	−10.9906	+	3.57105i	−0.404295	+	0.131363i	−0.504103	−	0.863643i	$-0.668177\pi$
$739$	−10.9906	+	3.57105i	−0.404295	+	0.131363i	0.0998086	+	0.995007i	$0.468177\pi$
$740$		0			0
$741$	2.61065	−	0.393103i	0.0959047	−	0.0144410i
$742$	−1.39270	−	8.79319i	−0.0511278	−	0.322808i
$743$	5.09866	+	5.09866i	0.187052	+	0.187052i	0.794420	−	0.607369i	$-0.207775\pi$
$743$	5.09866	+	5.09866i	0.187052	+	0.187052i	−0.607369	+	0.794420i	$0.707775\pi$
$744$	0.831282	−	5.00136i	0.0304763	−	0.183359i
$745$		0			0
$746$	−0.0621022	−	0.0854763i	−0.00227372	−	0.00312951i
$747$	−1.98193	−	2.04333i	−0.0725150	−	0.0747614i
$748$	1.91614	+	0.976324i	0.0700612	+	0.0356980i
$749$	−12.9231			−0.472200
$750$		0			0
$751$	−19.8804			−0.725445			−0.362723	−	0.931897i	$-0.618153\pi$
$751$	−19.8804			−0.725445			−0.362723	+	0.931897i	$0.618153\pi$
$752$	7.36324	+	3.75176i	0.268510	+	0.136813i
$753$	−5.32319	−	16.8184i	−0.193988	−	0.612897i
$754$	−0.701343	−	0.965316i	−0.0255414	−	0.0351547i
$755$		0			0
$756$	3.61657	+	3.78595i	0.131533	+	0.137694i
$757$	−16.4335	−	16.4335i	−0.597285	−	0.597285i	0.342304	−	0.939589i	$-0.388793\pi$
$757$	−16.4335	−	16.4335i	−0.597285	−	0.597285i	−0.939589	+	0.342304i	$0.888793\pi$
$758$	1.53973	+	9.72147i	0.0559255	+	0.353100i
$759$	0.641293	+	4.25892i	0.0232775	+	0.154589i
$760$		0			0
$761$	−4.02479	+	1.30773i	−0.145898	+	0.0474052i	−0.381056	−	0.924552i	$-0.624439\pi$
$761$	−4.02479	+	1.30773i	−0.145898	+	0.0474052i	0.235157	+	0.971957i	$0.424439\pi$
$762$	20.2900	−	27.4835i	0.735028	−	0.995624i
$763$	2.08604	+	4.09408i	0.0755197	+	0.148216i
$764$	4.77202	+	14.6868i	0.172646	+	0.531349i
$765$		0			0
$766$	−10.2830	+	31.6480i	−0.371542	+	1.14349i
$767$	−24.3892	+	3.86287i	−0.880642	+	0.139480i
$768$	−1.64315	−	0.547779i	−0.0592920	−	0.0197663i
$769$	−4.46592	+	6.14681i	−0.161045	+	0.221660i	−0.881912	−	0.471414i	$-0.843744\pi$
$769$	−4.46592	+	6.14681i	−0.161045	+	0.221660i	0.720867	+	0.693073i	$0.243744\pi$
$770$		0			0
$771$	−1.83757	+	3.53945i	−0.0661785	+	0.127470i
$772$	8.45606	+	1.33931i	0.304340	+	0.0482028i
$773$	6.27822	−	12.3217i	0.225812	−	0.443181i	−0.750106	−	0.661317i	$-0.769998\pi$
$773$	6.27822	−	12.3217i	0.225812	−	0.443181i	0.975918	+	0.218136i	$0.0699977\pi$
$774$	−18.2920	+	24.3858i	−0.657493	+	0.876531i
$775$		0			0
$776$		−	18.0093i		−	0.646495i
$777$	−16.7240	−	0.127537i	−0.599969	−	0.00457536i
$778$	5.23000	−	33.0209i	0.187505	−	1.18386i
$779$	−4.99169	+	3.62668i	−0.178846	+	0.129939i
$780$		0			0
$781$	−0.380843	−	0.276698i	−0.0136276	−	0.00990105i
$782$	−28.2178	+	28.2178i	−1.00907	+	1.00907i
$783$	0.0541056	−	2.36460i	0.00193358	−	0.0845039i
$784$	5.69179	+	1.84937i	0.203278	+	0.0660491i
$785$		0			0
$786$	−13.3742	+	13.1717i	−0.477040	+	0.469820i
$787$	10.1065	−	5.14950i	0.360257	−	0.183560i	−0.264488	−	0.964389i	$-0.585203\pi$
$787$	10.1065	−	5.14950i	0.360257	−	0.183560i	0.624745	+	0.780829i	$0.285203\pi$
$788$	5.64403	−	2.87578i	0.201060	−	0.102445i
$789$	−20.7616	+	20.4473i	−0.739131	+	0.727943i
$790$		0			0
$791$	13.0377	+	4.23619i	0.463566	+	0.150622i
$792$	0.970781	+	0.513435i	0.0344952	+	0.0182441i
$793$	−2.01129	+	2.01129i	−0.0714229	+	0.0714229i
$794$	11.1056	+	8.06871i	0.394124	+	0.286348i
$795$		0			0
$796$	−8.41187	+	6.11158i	−0.298151	+	0.216619i
$797$	−6.91637	+	43.6682i	−0.244990	+	1.54681i	0.491813	+	0.870701i	$0.336334\pi$
$797$	−6.91637	+	43.6682i	−0.244990	+	1.54681i	−0.736804	+	0.676107i	$0.763666\pi$
$798$	−1.01480	−	0.00773883i	−0.0359234	−	0.000273952i
$799$		−	48.5487i		−	1.71753i
$800$		0			0
$801$	4.86456	+	3.64894i	0.171881	+	0.128929i
$802$	−3.91805	+	7.68961i	−0.138351	+	0.271529i
$803$	−3.45120	−	0.546616i	−0.121790	−	0.0192897i
$804$	−10.5768	+	20.3725i	−0.373013	+	0.718482i
$805$		0			0
$806$	−4.51010	+	6.20762i	−0.158862	+	0.218654i
$807$	9.85763	+	3.28626i	0.347005	+	0.115682i
$808$	−0.357879	+	0.0566825i	−0.0125901	+	0.00199408i
$809$	6.33598	−	19.5001i	0.222761	−	0.685589i	−0.775750	−	0.631040i	$-0.782628\pi$
$809$	6.33598	−	19.5001i	0.222761	−	0.685589i	0.998511	−	0.0545481i	$-0.0173718\pi$
$810$		0			0
$811$	−14.2198	−	43.7640i	−0.499324	−	1.53676i	−0.810108	−	0.586280i	$-0.800592\pi$
$811$	−14.2198	−	43.7640i	−0.499324	−	1.53676i	0.310785	−	0.950480i	$-0.399408\pi$
$812$	0.208225	+	0.408664i	0.00730726	+	0.0143413i
$813$	−12.7457	+	17.2645i	−0.447011	+	0.605493i
$814$	−3.33626	+	1.08402i	−0.116936	+	0.0379947i
$815$		0			0
$816$	1.51509	+	10.0619i	0.0530388	+	0.352238i
$817$	−0.924305	−	5.83584i	−0.0323374	−	0.204170i
$818$	19.3241	+	19.3241i	0.675650	+	0.675650i
$819$	−2.33341	−	7.57257i	−0.0815360	−	0.264607i
$820$		0			0
$821$	−5.32407	−	7.32795i	−0.185811	−	0.255747i	0.705942	−	0.708270i	$-0.250524\pi$
$821$	−5.32407	−	7.32795i	−0.185811	−	0.255747i	−0.891753	+	0.452523i	$0.850524\pi$
$822$	4.54780	+	14.3686i	0.158623	+	0.501162i
$823$	42.4061	+	21.6070i	1.47819	+	0.753173i	0.992647	−	0.121042i	$-0.0386237\pi$
$823$	42.4061	+	21.6070i	1.47819	+	0.753173i	0.485538	+	0.874216i	$0.338624\pi$
$824$	−7.93419			−0.276401
$825$		0			0
$826$	9.49186			0.330264
$827$	−42.6460	−	21.7292i	−1.48295	−	0.755599i	−0.489729	−	0.871875i	$-0.662904\pi$
$827$	−42.6460	−	21.7292i	−1.48295	−	0.755599i	−0.993217	+	0.116276i	$0.962904\pi$
$828$	−14.6278	+	14.1883i	−0.508351	+	0.493076i
$829$	8.53245	+	11.7439i	0.296344	+	0.407883i	0.931062	−	0.364861i	$-0.118884\pi$
$829$	8.53245	+	11.7439i	0.296344	+	0.407883i	−0.634718	+	0.772744i	$0.718884\pi$
$830$		0			0
$831$	−1.75236	+	10.5430i	−0.0607888	+	0.365732i
$832$	1.85356	+	1.85356i	0.0642608	+	0.0642608i
$833$	−5.50002	−	34.7258i	−0.190564	−	1.20318i
$834$	5.24182	−	0.789295i	0.181509	−	0.0273310i
$835$		0			0
$836$	−0.202441	+	0.0657771i	−0.00700157	+	0.00227495i
$837$	−14.5692	+	4.36799i	−0.503586	+	0.150980i
$838$	11.6925	+	22.9478i	0.403910	+	0.792719i
$839$	1.29678	+	3.99108i	0.0447698	+	0.137787i	0.970943	−	0.239311i	$-0.0769217\pi$
$839$	1.29678	+	3.99108i	0.0447698	+	0.137787i	−0.926173	+	0.377099i	$0.876922\pi$
$840$		0			0
$841$	−8.89747	+	27.3836i	−0.306809	+	0.944262i
$842$	34.9156	−	5.53008i	1.20327	−	0.190579i
$843$	4.92756	−	14.7810i	0.169714	−	0.509084i
$844$	−2.14858	+	2.95727i	−0.0739572	+	0.101793i
$845$		0			0
$846$	0.378103	−	24.7890i	0.0129995	−	0.852263i
$847$	−10.8140	−	1.71277i	−0.371573	−	0.0588514i
$848$	4.01122	−	7.87247i	0.137746	−	0.270342i
$849$	20.3071	−	10.1527i	0.696938	−	0.348439i
$850$		0			0
$851$		−	65.0944i		−	2.23141i
$852$	0.0169853	−	2.22730i	0.000581908	−	0.0763059i
$853$	−8.47229	+	53.4919i	−0.290086	+	1.83153i	0.224963	+	0.974367i	$0.427774\pi$
$853$	−8.47229	+	53.4919i	−0.290086	+	1.83153i	−0.515049	+	0.857161i	$0.672226\pi$
$854$	0.884547	−	0.642661i	0.0302686	−	0.0219914i
$855$		0			0
$856$	−10.3760	−	7.53857i	−0.354643	−	0.257663i
$857$	25.7274	−	25.7274i	0.878831	−	0.878831i	−0.114583	−	0.993414i	$-0.536553\pi$
$857$	25.7274	−	25.7274i	0.878831	−	0.878831i	0.993414	+	0.114583i	$0.0365532\pi$
$858$	−0.966640	−	1.35203i	−0.0330006	−	0.0461575i
$859$	6.06408	+	1.97034i	0.206904	+	0.0672271i	0.410635	−	0.911800i	$-0.365307\pi$
$859$	6.06408	+	1.97034i	0.206904	+	0.0672271i	−0.203731	+	0.979027i	$0.565307\pi$
$860$		0			0
$861$	12.9945	+	13.1943i	0.442853	+	0.449659i
$862$	−30.2798	+	15.4283i	−1.03133	+	0.525491i
$863$	41.2325	−	21.0090i	1.40357	−	0.715155i	0.422062	−	0.906567i	$-0.361307\pi$
$863$	41.2325	−	21.0090i	1.40357	−	0.715155i	0.981510	+	0.191412i	$0.0613066\pi$
$864$	0.695243	+	5.14943i	0.0236527	+	0.175187i
$865$		0			0
$866$	18.1405	+	5.89422i	0.616440	+	0.200294i
$867$	24.6750	−	17.6415i	0.838008	−	0.599138i
$868$	2.08558	−	2.08558i	0.0707892	−	0.0707892i
$869$	−3.61419	−	2.62586i	−0.122603	−	0.0890763i
$870$		0			0
$871$	28.1052	−	20.4196i	0.952308	−	0.691892i
$872$	−0.713364	+	4.50400i	−0.0241576	+	0.152525i
$873$	−48.5076	+	23.7911i	−1.64173	+	0.805207i
$874$		−	3.94987i		−	0.133606i
$875$		0			0
$876$	−7.39329	−	14.7879i	−0.249796	−	0.499635i
$877$	−26.4275	+	51.8670i	−0.892395	+	1.75142i	−0.281815	+	0.959469i	$0.590936\pi$
$877$	−26.4275	+	51.8670i	−0.892395	+	1.75142i	−0.610580	+	0.791955i	$0.709064\pi$
$878$	−34.9478	−	5.53519i	−1.17943	−	0.186804i
$879$	20.7174	+	10.7558i	0.698781	+	0.362785i
$880$		0			0
$881$	−13.4206	+	18.4718i	−0.452151	+	0.622332i	−0.972858	−	0.231403i	$-0.925668\pi$
$881$	−13.4206	+	18.4718i	−0.452151	+	0.622332i	0.520707	+	0.853735i	$0.325668\pi$
$882$	−2.53787	−	17.7738i	−0.0854544	−	0.598476i
$883$	−54.5928	+	8.64665i	−1.83719	+	0.290983i	−0.976077	−	0.217425i	$-0.930234\pi$
$883$	−54.5928	+	8.64665i	−1.83719	+	0.290983i	−0.861116	+	0.508408i	$0.830234\pi$
$884$	4.75877	−	14.6460i	0.160055	−	0.492597i
$885$		0			0
$886$	4.47927	+	13.7858i	0.150484	+	0.463142i
$887$	−10.4418	−	20.4932i	−0.350601	−	0.688093i	0.646603	−	0.762827i	$-0.276189\pi$
$887$	−10.4418	−	20.4932i	−0.350601	−	0.688093i	−0.997203	+	0.0747341i	$0.976189\pi$
$888$	−13.3533	−	9.85817i	−0.448106	−	0.330819i
$889$	18.9009	−	6.14128i	0.633917	−	0.205972i
$890$		0			0
$891$	0.100480	−	3.29305i	0.00336622	−	0.110321i
$892$	0.330785	+	2.08849i	0.0110755	+	0.0699279i
$893$	3.39787	+	3.39787i	0.113706	+	0.113706i
$894$	10.0088	+	1.66358i	0.334746	+	0.0556385i
$895$		0			0
$896$	−0.592264	−	0.815182i	−0.0197862	−	0.0272333i
$897$	29.4036	−	9.30652i	0.981758	−	0.310736i
$898$	−8.44624	−	4.30358i	−0.281855	−	0.143612i
$899$	−1.33240			−0.0444380
$900$		0			0
$901$	−51.9062			−1.72925
$902$	3.46095	+	1.76344i	0.115237	+	0.0587161i
$903$	−16.9073	+	5.35133i	−0.562640	+	0.178081i
$904$	7.99679	+	11.0066i	0.265969	+	0.366075i
$905$		0			0
$906$	6.23602	+	1.03650i	0.207178	+	0.0344353i
$907$	−26.0875	−	26.0875i	−0.866221	−	0.866221i	0.125831	−	0.992052i	$-0.459840\pi$
$907$	−26.0875	−	26.0875i	−0.866221	−	0.866221i	−0.992052	+	0.125831i	$0.959840\pi$
$908$	2.42285	+	15.2973i	0.0804050	+	0.507657i
$909$	0.625448	+	0.889060i	0.0207448	+	0.0294883i
$910$		0			0
$911$	20.1733	−	6.55470i	0.668371	−	0.217167i	0.0448740	−	0.998993i	$-0.485711\pi$
$911$	20.1733	−	6.55470i	0.668371	−	0.217167i	0.623497	+	0.781826i	$0.285711\pi$
$912$	−0.810265	−	0.598185i	−0.0268305	−	0.0198079i
$913$	−0.157693	−	0.309490i	−0.00521888	−	0.0102426i
$914$	−11.1374	−	34.2775i	−0.368393	−	1.13380i
$915$		0			0
$916$	−0.510667	+	1.57167i	−0.0168729	+	0.0519295i
$917$	−10.7858	+	1.70830i	−0.356177	+	0.0564129i
$918$	25.1001	−	17.3732i	0.828427	−	0.573399i
$919$	20.7352	−	28.5396i	0.683991	−	0.941433i	−0.315982	−	0.948765i	$-0.602334\pi$
$919$	20.7352	−	28.5396i	0.683991	−	0.941433i	0.999973	+	0.00733203i	$0.00233388\pi$
$920$		0			0
$921$	29.1797	+	15.1492i	0.961504	+	0.499183i
$922$	22.2595	+	3.52556i	0.733079	+	0.116108i
$923$	−1.53038	+	3.00354i	−0.0503731	+	0.0988627i
$924$	0.285694	+	0.571436i	0.00939863	+	0.0187989i
$925$		0			0
$926$		−	5.67112i		−	0.186364i
$927$	10.4814	+	21.3706i	0.344255	+	0.701902i
$928$	−0.0712068	+	0.449582i	−0.00233748	+	0.0147583i
$929$	34.9866	−	25.4192i	1.14787	−	0.833978i	0.159676	−	0.987169i	$-0.448955\pi$
$929$	34.9866	−	25.4192i	1.14787	−	0.833978i	0.988197	+	0.153191i	$0.0489551\pi$
$930$		0			0
$931$	2.81536	+	2.04548i	0.0922698	+	0.0670379i
$932$	12.3494	−	12.3494i	0.404520	−	0.404520i
$933$	30.1595	−	21.5627i	0.987379	−	0.705932i
$934$	−11.0544	−	3.59181i	−0.361713	−	0.117528i
$935$		0			0
$936$	2.54389	−	7.44118i	0.0831498	−	0.243223i
$937$	22.2086	−	11.3158i	0.725523	−	0.369672i	−0.0518988	−	0.998652i	$-0.516527\pi$
$937$	22.2086	−	11.3158i	0.725523	−	0.369672i	0.777421	+	0.628980i	$0.216527\pi$
$938$	−11.8983	+	6.06247i	−0.388492	+	0.197947i
$939$	−15.5222	−	15.7607i	−0.506547	−	0.514332i
$940$		0			0
$941$	0.769225	+	0.249936i	0.0250760	+	0.00814769i	0.321528	−	0.946900i	$-0.395804\pi$
$941$	0.769225	+	0.249936i	0.0250760	+	0.00814769i	−0.296452	+	0.955048i	$0.595804\pi$
$942$	3.24105	+	4.53322i	0.105599	+	0.147700i
$943$	−50.9671	+	50.9671i	−1.65972	+	1.65972i
$944$	7.62100	+	5.53698i	0.248043	+	0.180213i
$945$		0			0
$946$	−3.00929	+	2.18638i	−0.0978406	+	0.0710854i
$947$	−1.89535	+	11.9668i	−0.0615907	+	0.388868i	0.937566	+	0.347808i	$0.113074\pi$
$947$	−1.89535	+	11.9668i	−0.0615907	+	0.388868i	−0.999157	+	0.0410609i	$0.986926\pi$
$948$	0.161191	−	21.1370i	0.00523523	−	0.686498i
$949$			25.0216i			0.812235i
$950$		0			0
$951$	42.9593	−	21.4778i	1.39305	−	0.696466i
$952$	−2.68740	+	5.27432i	−0.0870992	+	0.170942i
$953$	−13.3423	−	2.11321i	−0.432199	−	0.0684536i	−0.0634554	−	0.997985i	$-0.520212\pi$
$953$	−13.3423	−	2.11321i	−0.432199	−	0.0684536i	−0.368744	+	0.929531i	$0.620212\pi$
$954$	−26.5033	−	0.404252i	−0.858077	−	0.0130881i
$955$		0			0
$956$	3.75544	−	5.16892i	0.121460	−	0.167175i
$957$	0.0912752	−	0.273794i	0.00295051	−	0.00885051i
$958$	2.69083	−	0.426186i	0.0869368	−	0.0137694i
$959$	−2.70935	+	8.33851i	−0.0874893	+	0.269264i
$960$		0			0
$961$	−6.93181	−	21.3339i	−0.223607	−	0.688190i
$962$	11.4042	+	22.3820i	0.367686	+	0.721624i
$963$	−6.59788	+	37.9062i	−0.212614	+	1.22151i
$964$	18.2971	−	5.94510i	0.589311	−	0.191479i
$965$		0			0
$966$	−11.7230	+	1.76520i	−0.377180	+	0.0567945i
$967$	−1.74919	−	11.0440i	−0.0562502	−	0.355150i	−0.999719	−	0.0236894i	$-0.992459\pi$
$967$	−1.74919	−	11.0440i	−0.0562502	−	0.355150i	0.943469	−	0.331460i	$-0.107541\pi$
$968$	−7.68342	−	7.68342i	−0.246954	−	0.246954i
$969$	−0.970123	+	5.83669i	−0.0311648	+	0.187501i
$970$		0			0
$971$	15.8802	+	21.8573i	0.509621	+	0.701434i	0.983855	−	0.178965i	$-0.0572749\pi$
$971$	15.8802	+	21.8573i	0.509621	+	0.701434i	−0.474234	+	0.880399i	$0.657275\pi$
$972$	12.9514	−	8.67526i	0.415418	−	0.278259i
$973$	2.74769	+	1.40002i	0.0880868	+	0.0448825i
$974$	27.1112			0.868699
$975$		0			0
$976$	1.08509			0.0347330
$977$	23.4774	+	11.9623i	0.751109	+	0.382709i	0.787247	−	0.616638i	$-0.211506\pi$
$977$	23.4774	+	11.9623i	0.751109	+	0.382709i	−0.0361382	+	0.999347i	$0.511506\pi$
$978$	1.93321	+	6.10789i	0.0618171	+	0.195309i
$979$	0.436145	+	0.600303i	0.0139393	+	0.0191858i
$980$		0			0
$981$	13.0738	−	4.02857i	0.417415	−	0.128622i
$982$	27.9010	+	27.9010i	0.890357	+	0.890357i
$983$	6.78356	+	42.8297i	0.216362	+	1.36606i	0.821624	+	0.570029i	$0.193068\pi$
$983$	6.78356	+	42.8297i	0.216362	+	1.36606i	−0.605263	+	0.796026i	$0.706932\pi$
$984$	2.73656	+	18.1739i	0.0872385	+	0.579363i
$985$		0			0
$986$	2.54323	−	0.826344i	0.0809928	−	0.0263162i
$987$	8.56616	−	11.6032i	0.272664	−	0.369334i
$988$	0.691996	+	1.35812i	0.0220153	+	0.0432075i
$989$	−21.3295	−	65.6454i	−0.678238	−	2.08740i
$990$		0			0
$991$	−10.2129	+	31.4322i	−0.324424	+	0.998476i	0.647275	+	0.762256i	$0.275908\pi$
$991$	−10.2129	+	31.4322i	−0.324424	+	0.998476i	−0.971700	+	0.236220i	$0.924092\pi$
$992$	2.89111	−	0.457907i	0.0917929	−	0.0145386i
$993$	30.5741	+	10.1926i	0.970241	+	0.323451i
$994$	0.761632	−	1.04830i	0.0241575	−	0.0332500i
$995$		0			0
$996$	0.757276	−	1.45863i	0.0239952	−	0.0462185i
$997$	−36.0123	−	5.70379i	−1.14052	−	0.180641i	−0.442534	−	0.896752i	$-0.645920\pi$
$997$	−36.0123	−	5.70379i	−1.14052	−	0.180641i	−0.697986	+	0.716111i	$0.745920\pi$
$998$	−5.13714	+	10.0822i	−0.162613	+	0.319147i
$999$	−8.91250	+	48.9899i	−0.281979	+	1.54997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.l.c.107.10		80
3.2	odd	2	inner	750.2.l.c.107.1		80
5.2	odd	4		750.2.l.b.143.3		80
5.3	odd	4		150.2.l.a.83.8	yes	80
5.4	even	2		750.2.l.a.107.1		80
15.2	even	4		750.2.l.b.143.8		80
15.8	even	4		150.2.l.a.83.3	yes	80
15.14	odd	2		750.2.l.a.107.10		80
25.3	odd	20	inner	750.2.l.c.743.1		80
25.4	even	10		750.2.l.b.257.8		80
25.21	even	5		150.2.l.a.47.3	✓	80
25.22	odd	20		750.2.l.a.743.10		80
75.29	odd	10		750.2.l.b.257.3		80
75.47	even	20		750.2.l.a.743.1		80
75.53	even	20	inner	750.2.l.c.743.10		80
75.71	odd	10		150.2.l.a.47.8	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.47.3	✓	80	25.21	even	5
150.2.l.a.47.8	yes	80	75.71	odd	10
150.2.l.a.83.3	yes	80	15.8	even	4
150.2.l.a.83.8	yes	80	5.3	odd	4
750.2.l.a.107.1		80	5.4	even	2
750.2.l.a.107.10		80	15.14	odd	2
750.2.l.a.743.1		80	75.47	even	20
750.2.l.a.743.10		80	25.22	odd	20
750.2.l.b.143.3		80	5.2	odd	4
750.2.l.b.143.8		80	15.2	even	4
750.2.l.b.257.3		80	75.29	odd	10
750.2.l.b.257.8		80	25.4	even	10
750.2.l.c.107.1		80	3.2	odd	2	inner
750.2.l.c.107.10		80	1.1	even	1	trivial
750.2.l.c.743.1		80	25.3	odd	20	inner
750.2.l.c.743.10		80	75.53	even	20	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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.l (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.891007 + 0.453990i) q^{2} +(1.65131 - 0.522656i) q^{3} +(0.587785 + 0.809017i) q^{4} +(1.70861 + 0.283990i) q^{6} +(0.712495 + 0.712495i) q^{7} +(0.156434 + 0.987688i) q^{8} +(2.45366 - 1.72614i) q^{9} +O(q^{10})\)	\(q+(0.891007 + 0.453990i) q^{2} +(1.65131 - 0.522656i) q^{3} +(0.587785 + 0.809017i) q^{4} +(1.70861 + 0.283990i) q^{6} +(0.712495 + 0.712495i) q^{7} +(0.156434 + 0.987688i) q^{8} +(2.45366 - 1.72614i) q^{9} +(0.348148 - 0.113120i) q^{11} +(1.39345 + 1.02873i) q^{12} +(-1.19006 - 2.33563i) q^{13} +(0.311372 + 0.958303i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(5.80242 - 0.919013i) q^{17} +(2.96988 - 0.424059i) q^{18} +(-0.341785 + 0.470426i) q^{19} +(1.54894 + 0.804162i) q^{21} +(0.361558 + 0.0572652i) q^{22} +(-3.08387 + 6.05243i) q^{23} +(0.774543 + 1.54922i) q^{24} -2.62134i q^{26} +(3.14959 - 4.13281i) q^{27} +(-0.157626 + 0.995214i) q^{28} +(0.368253 - 0.267552i) q^{29} +(-2.36811 - 1.72054i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.515779 - 0.368759i) q^{33} +(5.58722 + 1.81540i) q^{34} +(2.83870 + 0.970457i) q^{36} +(-8.53839 + 4.35053i) q^{37} +(-0.518102 + 0.263986i) q^{38} +(-3.18589 - 3.23486i) q^{39} +(10.0917 + 3.27898i) q^{41} +(1.01503 + 1.41972i) q^{42} +(-7.18512 + 7.18512i) q^{43} +(0.296153 + 0.215168i) q^{44} +(-5.49549 + 3.99271i) q^{46} +(1.29277 - 8.16222i) q^{47} +(-0.0132082 + 1.73200i) q^{48} -5.98470i q^{49} +(9.10128 - 4.55025i) q^{51} +(1.19006 - 2.33563i) q^{52} +(-8.72670 - 1.38217i) q^{53} +(4.68256 - 2.25248i) q^{54} +(-0.592264 + 0.815182i) q^{56} +(-0.318522 + 0.955457i) q^{57} +(0.449582 - 0.0712068i) q^{58} +(2.91096 - 8.95903i) q^{59} +(-0.335312 - 1.03198i) q^{61} +(-1.32890 - 2.60811i) q^{62} +(2.97808 + 0.518359i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(0.626975 - 0.0944078i) q^{66} +(2.07319 + 13.0896i) q^{67} +(4.15407 + 4.15407i) q^{68} +(-1.92909 + 11.6062i) q^{69} +(-0.755873 - 1.04037i) q^{71} +(2.08872 + 2.15343i) q^{72} +(-8.50497 - 4.33350i) q^{73} -9.58285 q^{74} -0.581479 q^{76} +(0.328652 + 0.167456i) q^{77} +(-1.37006 - 4.32864i) q^{78} +(-7.17322 - 9.87309i) q^{79} +(3.04091 - 8.47071i) q^{81} +(7.50310 + 7.50310i) q^{82} +(-0.148436 - 0.937190i) q^{83} +(0.259864 + 1.72579i) q^{84} +(-9.66396 + 3.14001i) q^{86} +(0.468264 - 0.634281i) q^{87} +(0.166190 + 0.326166i) q^{88} +(0.626378 + 1.92779i) q^{89} +(0.816210 - 2.51204i) q^{91} +(-6.70917 + 1.06263i) q^{92} +(-4.80974 - 1.60343i) q^{93} +(4.85743 - 6.68568i) q^{94} +(-0.798080 + 1.53723i) q^{96} +(-17.7876 - 2.81727i) q^{97} +(2.71700 - 5.33241i) q^{98} +(0.658978 - 0.878510i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q + 4 * q^3 + 4 * q^7	\( 80 q + 4 q^{3} + 4 q^{7} + 16 q^{12} + 20 q^{16} - 8 q^{18} + 40 q^{19} + 4 q^{22} - 56 q^{27} + 4 q^{28} - 96 q^{33} + 40 q^{34} - 64 q^{37} + 40 q^{39} - 4 q^{42} - 24 q^{43} + 16 q^{48} - 64 q^{57} + 20 q^{58} + 4 q^{63} - 104 q^{67} - 140 q^{69} + 8 q^{72} - 60 q^{73} - 60 q^{78} - 80 q^{79} - 40 q^{81} + 96 q^{82} - 60 q^{84} + 80 q^{87} + 24 q^{88} + 12 q^{93} - 12 q^{97}+O(q^{100}) \) 80 * q + 4 * q^3 + 4 * q^7 + 16 * q^12 + 20 * q^16 - 8 * q^18 + 40 * q^19 + 4 * q^22 - 56 * q^27 + 4 * q^28 - 96 * q^33 + 40 * q^34 - 64 * q^37 + 40 * q^39 - 4 * q^42 - 24 * q^43 + 16 * q^48 - 64 * q^57 + 20 * q^58 + 4 * q^63 - 104 * q^67 - 140 * q^69 + 8 * q^72 - 60 * q^73 - 60 * q^78 - 80 * q^79 - 40 * q^81 + 96 * q^82 - 60 * q^84 + 80 * q^87 + 24 * q^88 + 12 * q^93 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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