LMFDB - Embedded newform 380.2.d.b.379.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(379,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("380.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.25
Character	$\chi$	$=$	380.379
Dual form			380.2.d.b.379.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.584780 - 1.28765i) q^{2} +2.81267i q^{3} +(-1.31606 - 1.50598i) q^{4} +(0.390055 - 2.20178i) q^{5} +(3.62172 + 1.64479i) q^{6} +4.13073 q^{7} +(-2.70878 + 0.813956i) q^{8} -4.91111 q^{9} +O(q^{10})$	\(q+(0.584780 - 1.28765i) q^{2} +2.81267i q^{3} +(-1.31606 - 1.50598i) q^{4} +(0.390055 - 2.20178i) q^{5} +(3.62172 + 1.64479i) q^{6} +4.13073 q^{7} +(-2.70878 + 0.813956i) q^{8} -4.91111 q^{9} +(-2.60702 - 1.78981i) q^{10} -0.681732i q^{11} +(4.23583 - 3.70165i) q^{12} +3.19485 q^{13} +(2.41557 - 5.31892i) q^{14} +(6.19289 + 1.09710i) q^{15} +(-0.535953 + 3.96393i) q^{16} -2.93351i q^{17} +(-2.87192 + 6.32377i) q^{18} +(2.23259 + 3.74374i) q^{19} +(-3.82918 + 2.31027i) q^{20} +11.6184i q^{21} +(-0.877829 - 0.398663i) q^{22} +6.41181 q^{23} +(-2.28939 - 7.61890i) q^{24} +(-4.69571 - 1.71763i) q^{25} +(1.86829 - 4.11384i) q^{26} -5.37533i q^{27} +(-5.43630 - 6.22080i) q^{28} +0.928351i q^{29} +(5.03415 - 7.33269i) q^{30} -6.68773 q^{31} +(4.79072 + 3.00815i) q^{32} +1.91749 q^{33} +(-3.77732 - 1.71546i) q^{34} +(1.61121 - 9.09498i) q^{35} +(6.46334 + 7.39604i) q^{36} +6.63253 q^{37} +(6.12618 - 0.685517i) q^{38} +8.98606i q^{39} +(0.735583 + 6.28163i) q^{40} -4.89391i q^{41} +(14.9604 + 6.79420i) q^{42} -7.02309 q^{43} +(-1.02667 + 0.897202i) q^{44} +(-1.91560 + 10.8132i) q^{45} +(3.74950 - 8.25615i) q^{46} -6.74187 q^{47} +(-11.1492 - 1.50746i) q^{48} +10.0629 q^{49} +(-4.95767 + 5.04198i) q^{50} +8.25100 q^{51} +(-4.20463 - 4.81138i) q^{52} -7.60467 q^{53} +(-6.92152 - 3.14339i) q^{54} +(-1.50103 - 0.265913i) q^{55} +(-11.1892 + 3.36223i) q^{56} +(-10.5299 + 6.27953i) q^{57} +(1.19539 + 0.542882i) q^{58} -13.1971 q^{59} +(-6.49804 - 10.7702i) q^{60} -5.76313 q^{61} +(-3.91085 + 8.61143i) q^{62} -20.2865 q^{63} +(6.67495 - 4.40965i) q^{64} +(1.24617 - 7.03438i) q^{65} +(1.12131 - 2.46904i) q^{66} +5.12809i q^{67} +(-4.41781 + 3.86069i) q^{68} +18.0343i q^{69} +(-10.7689 - 7.39324i) q^{70} -7.43972 q^{71} +(13.3031 - 3.99743i) q^{72} +10.1531i q^{73} +(3.87857 - 8.54034i) q^{74} +(4.83114 - 13.2075i) q^{75} +(2.69977 - 8.28923i) q^{76} -2.81605i q^{77} +(11.5709 + 5.25487i) q^{78} +4.94607 q^{79} +(8.51867 + 2.72621i) q^{80} +0.385683 q^{81} +(-6.30163 - 2.86187i) q^{82} +9.74393 q^{83} +(17.4970 - 15.2905i) q^{84} +(-6.45896 - 1.14423i) q^{85} +(-4.10697 + 9.04326i) q^{86} -2.61115 q^{87} +(0.554899 + 1.84666i) q^{88} -7.65281i q^{89} +(12.8034 + 8.78997i) q^{90} +13.1971 q^{91} +(-8.43836 - 9.65607i) q^{92} -18.8104i q^{93} +(-3.94252 + 8.68115i) q^{94} +(9.11373 - 3.45541i) q^{95} +(-8.46093 + 13.4747i) q^{96} -15.0798 q^{97} +(5.88460 - 12.9575i) q^{98} +3.34806i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{5} + 8 q^{6} - 8 q^{9}+O(q^{10}) $ 40 * q - 4 * q^5 + 8 * q^6 - 8 * q^9	$ 40 q - 4 q^{5} + 8 q^{6} - 8 q^{9} - 8 q^{16} - 20 q^{20} - 40 q^{24} - 84 q^{25} - 24 q^{26} + 24 q^{30} + 24 q^{36} - 40 q^{44} - 12 q^{45} + 128 q^{49} - 120 q^{54} + 24 q^{61} + 72 q^{64} + 112 q^{66} + 32 q^{74} + 56 q^{76} + 96 q^{80} - 72 q^{81} + 44 q^{85} - 40 q^{96}+O(q^{100}) $ 40 * q - 4 * q^5 + 8 * q^6 - 8 * q^9 - 8 * q^16 - 20 * q^20 - 40 * q^24 - 84 * q^25 - 24 * q^26 + 24 * q^30 + 24 * q^36 - 40 * q^44 - 12 * q^45 + 128 * q^49 - 120 * q^54 + 24 * q^61 + 72 * q^64 + 112 * q^66 + 32 * q^74 + 56 * q^76 + 96 * q^80 - 72 * q^81 + 44 * q^85 - 40 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.584780	−	1.28765i	0.413502	−	0.910503i
$2$	0.584780	−	1.28765i	0.413502	−	0.910503i
$3$			2.81267i			1.62390i	0.583730	+	0.811948i	$0.301593\pi$
$3$			2.81267i			1.62390i	−0.583730	+	0.811948i	$0.698407\pi$
$4$	−1.31606	−	1.50598i	−0.658032	−	0.752990i
$5$	0.390055	−	2.20178i	0.174438	−	0.984668i
$5$	0.390055	−	2.20178i	0.174438	−	0.984668i
$6$	3.62172	+	1.64479i	1.47856	+	0.671485i
$7$	4.13073			1.56127			0.780634	−	0.624988i	$-0.214896\pi$
$7$	4.13073			1.56127			0.780634	+	0.624988i	$0.214896\pi$
$8$	−2.70878	+	0.813956i	−0.957697	+	0.287777i
$9$	−4.91111			−1.63704
$10$	−2.60702	−	1.78981i	−0.824413	−	0.565989i
$11$		−	0.681732i		−	0.205550i	−0.994705	−	0.102775i	$-0.967228\pi$
$11$		−	0.681732i		−	0.205550i	0.994705	−	0.102775i	$-0.0327721\pi$
$12$	4.23583	−	3.70165i	1.22278	−	1.06857i
$13$	3.19485			0.886092			0.443046	−	0.896499i	$-0.353898\pi$
$13$	3.19485			0.886092			0.443046	+	0.896499i	$0.353898\pi$
$14$	2.41557	−	5.31892i	0.645588	−	1.42154i
$15$	6.19289	+	1.09710i	1.59900	+	0.283269i
$16$	−0.535953	+	3.96393i	−0.133988	+	0.990983i
$17$		−	2.93351i		−	0.711481i	−0.934585	−	0.355741i	$-0.884229\pi$
$17$		−	2.93351i		−	0.711481i	0.934585	−	0.355741i	$-0.115771\pi$
$18$	−2.87192	+	6.32377i	−0.676919	+	1.49053i
$19$	2.23259	+	3.74374i	0.512190	+	0.858872i
$19$	2.23259	+	3.74374i	0.512190	+	0.858872i
$20$	−3.82918	+	2.31027i	−0.856231	+	0.516593i
$21$			11.6184i			2.53534i
$22$	−0.877829	−	0.398663i	−0.187154	−	0.0849953i
$23$	6.41181			1.33696			0.668478	−	0.743732i	$-0.266946\pi$
$23$	6.41181			1.33696			0.668478	+	0.743732i	$0.266946\pi$
$24$	−2.28939	−	7.61890i	−0.467320	−	1.55520i
$25$	−4.69571	−	1.71763i	−0.939143	−	0.343527i
$26$	1.86829	−	4.11384i	0.366401	−	0.806790i
$27$		−	5.37533i		−	1.03448i
$28$	−5.43630	−	6.22080i	−1.02736	−	1.17562i
$29$			0.928351i			0.172391i	0.996278	+	0.0861953i	$0.0274709\pi$
$29$			0.928351i			0.172391i	−0.996278	+	0.0861953i	$0.972529\pi$
$30$	5.03415	−	7.33269i	0.919107	−	1.33876i
$31$	−6.68773			−1.20115			−0.600576	−	0.799568i	$-0.705062\pi$
$31$	−6.68773			−1.20115			−0.600576	+	0.799568i	$0.705062\pi$
$32$	4.79072	+	3.00815i	0.846889	+	0.531770i
$33$	1.91749			0.333791
$34$	−3.77732	−	1.71546i	−0.647806	−	0.294199i
$35$	1.61121	−	9.09498i	0.272344	−	1.53733i
$36$	6.46334	+	7.39604i	1.07722	+	1.23267i
$37$	6.63253			1.09038			0.545190	−	0.838312i	$-0.316457\pi$
$37$	6.63253			1.09038			0.545190	+	0.838312i	$0.316457\pi$
$38$	6.12618	−	0.685517i	0.993797	−	0.111205i
$39$			8.98606i			1.43892i
$40$	0.735583	+	6.28163i	0.116306	+	0.993213i
$41$		−	4.89391i		−	0.764301i	−0.924100	−	0.382151i	$-0.875184\pi$
$41$		−	4.89391i		−	0.764301i	0.924100	−	0.382151i	$-0.124816\pi$
$42$	14.9604	+	6.79420i	2.30843	+	1.04837i
$43$	−7.02309			−1.07101			−0.535506	−	0.844532i	$-0.679879\pi$
$43$	−7.02309			−1.07101			−0.535506	+	0.844532i	$0.679879\pi$
$44$	−1.02667	+	0.897202i	−0.154777	+	0.135258i
$45$	−1.91560	+	10.8132i	−0.285561	+	1.61194i
$46$	3.74950	−	8.25615i	0.552834	−	1.21730i
$47$	−6.74187			−0.983404			−0.491702	−	0.870764i	$-0.663625\pi$
$47$	−6.74187			−0.983404			−0.491702	+	0.870764i	$0.663625\pi$
$48$	−11.1492	−	1.50746i	−1.60925	−	0.217583i
$49$	10.0629			1.43756
$50$	−4.95767	+	5.04198i	−0.701120	+	0.713043i
$51$	8.25100			1.15537
$52$	−4.20463	−	4.81138i	−0.583077	−	0.667219i
$53$	−7.60467			−1.04458			−0.522291	−	0.852767i	$-0.674923\pi$
$53$	−7.60467			−1.04458			−0.522291	+	0.852767i	$0.674923\pi$
$54$	−6.92152	−	3.14339i	−0.941899	−	0.427761i
$55$	−1.50103	−	0.265913i	−0.202398	−	0.0358557i
$56$	−11.1892	+	3.36223i	−1.49522	+	0.449297i
$57$	−10.5299	+	6.27953i	−1.39472	+	0.831744i
$58$	1.19539	+	0.542882i	0.156962	+	0.0712839i
$59$	−13.1971			−1.71811			−0.859056	−	0.511882i	$-0.828949\pi$
$59$	−13.1971			−1.71811			−0.859056	+	0.511882i	$0.828949\pi$
$60$	−6.49804	−	10.7702i	−0.838893	−	1.39043i
$61$	−5.76313			−0.737893			−0.368947	−	0.929451i	$-0.620281\pi$
$61$	−5.76313			−0.737893			−0.368947	+	0.929451i	$0.620281\pi$
$62$	−3.91085	+	8.61143i	−0.496679	+	1.09365i
$63$	−20.2865			−2.55586
$64$	6.67495	−	4.40965i	0.834369	−	0.551206i
$65$	1.24617	−	7.03438i	0.154568	−	0.872507i
$66$	1.12131	−	2.46904i	0.138024	−	0.303918i
$67$			5.12809i			0.626496i	0.949671	+	0.313248i	$0.101417\pi$
$67$			5.12809i			0.626496i	−0.949671	+	0.313248i	$0.898583\pi$
$68$	−4.41781	+	3.86069i	−0.535738	+	0.468177i
$69$			18.0343i			2.17108i
$70$	−10.7689	−	7.39324i	−1.28713	−	0.883661i
$71$	−7.43972			−0.882933			−0.441466	−	0.897278i	$-0.645542\pi$
$71$	−7.43972			−0.882933			−0.441466	+	0.897278i	$0.645542\pi$
$72$	13.3031	−	3.99743i	1.56779	−	0.471101i
$73$			10.1531i			1.18833i	0.804342	+	0.594167i	$0.202518\pi$
$73$			10.1531i			1.18833i	−0.804342	+	0.594167i	$0.797482\pi$
$74$	3.87857	−	8.54034i	0.450875	−	0.992795i
$75$	4.83114	−	13.2075i	0.557852	−	1.52507i
$76$	2.69977	−	8.28923i	0.309685	−	0.950839i
$77$		−	2.81605i		−	0.320919i
$78$	11.5709	+	5.25487i	1.31014	+	0.594997i
$79$	4.94607			0.556476			0.278238	−	0.960512i	$-0.410250\pi$
$79$	4.94607			0.556476			0.278238	+	0.960512i	$0.410250\pi$
$80$	8.51867	+	2.72621i	0.952417	+	0.304799i
$81$	0.385683			0.0428536
$82$	−6.30163	−	2.86187i	−0.695899	−	0.316040i
$83$	9.74393			1.06954			0.534768	−	0.844999i	$-0.320399\pi$
$83$	9.74393			1.06954			0.534768	+	0.844999i	$0.320399\pi$
$84$	17.4970	−	15.2905i	1.90908	−	1.66833i
$85$	−6.45896	−	1.14423i	−0.700573	−	0.124109i
$86$	−4.10697	+	9.04326i	−0.442866	+	0.975159i
$87$	−2.61115			−0.279944
$88$	0.554899	+	1.84666i	0.0591525	+	0.196855i
$89$		−	7.65281i		−	0.811197i	−0.914051	−	0.405598i	$-0.867063\pi$
$89$		−	7.65281i		−	0.811197i	0.914051	−	0.405598i	$-0.132937\pi$
$90$	12.8034	+	8.78997i	1.34959	+	0.926545i
$91$	13.1971			1.38343
$92$	−8.43836	−	9.65607i	−0.879759	−	1.00671i
$93$		−	18.8104i		−	1.95054i
$94$	−3.94252	+	8.68115i	−0.406640	+	0.895392i
$95$	9.11373	−	3.45541i	0.935049	−	0.354518i
$96$	−8.46093	+	13.4747i	−0.863540	+	1.37526i
$97$	−15.0798			−1.53113			−0.765563	−	0.643361i	$-0.777539\pi$
$97$	−15.0798			−1.53113			−0.765563	+	0.643361i	$0.777539\pi$
$98$	5.88460	−	12.9575i	0.594434	−	1.30890i
$99$			3.34806i			0.336493i
$100$	3.59313	+	9.33217i	0.359313	+	0.933217i
$101$	7.45052			0.741355			0.370677	−	0.928762i	$-0.379126\pi$
$101$	7.45052			0.741355			0.370677	+	0.928762i	$0.379126\pi$
$102$	4.82502	−	10.6244i	0.477749	−	1.05197i
$103$			0.817949i			0.0805950i	0.999188	+	0.0402975i	$0.0128306\pi$
$103$			0.817949i			0.0805950i	−0.999188	+	0.0402975i	$0.987169\pi$
$104$	−8.65414	+	2.60047i	−0.848609	+	0.254997i
$105$	25.5812	+	4.53181i	2.49647	+	0.442259i
$106$	−4.44707	+	9.79213i	−0.431937	+	0.951095i
$107$			11.1238i			1.07538i	0.843143	+	0.537689i	$0.180702\pi$
$107$			11.1238i			1.07538i	−0.843143	+	0.537689i	$0.819298\pi$
$108$	−8.09514	+	7.07427i	−0.778955	+	0.680722i
$109$			3.24135i			0.310465i	0.987878	+	0.155232i	$0.0496126\pi$
$109$			3.24135i			0.310465i	−0.987878	+	0.155232i	$0.950387\pi$
$110$	−1.22017	+	1.77729i	−0.116339	+	0.169458i
$111$			18.6551i			1.77066i
$112$	−2.21388	+	16.3739i	−0.209192	+	1.54719i
$113$	−1.55514			−0.146295			−0.0731476	−	0.997321i	$-0.523304\pi$
$113$	−1.55514			−0.146295			−0.0731476	+	0.997321i	$0.523304\pi$
$114$	1.92813	+	17.2309i	0.180586	+	1.61382i
$115$	2.50096	−	14.1174i	0.233216	−	1.31646i
$116$	1.39808	−	1.22177i	0.129808	−	0.113438i
$117$	−15.6903			−1.45057
$118$	−7.71739	+	16.9931i	−0.710443	+	1.56435i
$119$		−	12.1175i		−	1.11081i
$120$	−17.6682	+	2.06895i	−1.61288	+	0.188869i
$121$	10.5352			0.957749
$122$	−3.37017	+	7.42087i	−0.305120	+	0.671854i
$123$	13.7650			1.24115
$124$	8.80148	+	10.0716i	0.790396	+	0.904455i
$125$	−5.61345	+	9.66898i	−0.502082	+	0.864820i
$126$	−11.8631	+	26.1218i	−1.05685	+	2.32711i
$127$		−	16.2908i		−	1.44557i	−0.691071	−	0.722787i	$-0.742861\pi$
$127$		−	16.2908i		−	1.44557i	0.691071	−	0.722787i	$-0.257139\pi$
$128$	−1.77469	−	11.1737i	−0.156862	−	0.987621i
$129$		−	19.7536i		−	1.73921i
$130$	−8.32905	−	5.71819i	−0.730506	−	0.501518i
$131$			5.44773i			0.475970i	0.971269	+	0.237985i	$0.0764870\pi$
$131$			5.44773i			0.475970i	−0.971269	+	0.237985i	$0.923513\pi$
$132$	−2.52353	−	2.88770i	−0.219645	−	0.251342i
$133$	9.22221	+	15.4644i	0.799667	+	1.34093i
$134$	6.60316	+	2.99881i	0.570427	+	0.259058i
$135$	−11.8353	−	2.09667i	−1.01862	−	0.180453i
$136$	2.38775	+	7.94623i	0.204748	+	0.681384i
$137$		−	21.1247i		−	1.80480i	−0.430897	−	0.902401i	$-0.641803\pi$
$137$		−	21.1247i		−	1.80480i	0.430897	−	0.902401i	$-0.358197\pi$
$138$	23.2218	+	10.5461i	1.97677	+	0.897745i
$139$			9.05531i			0.768062i	0.923320	+	0.384031i	$0.125464\pi$
$139$			9.05531i			0.768062i	−0.923320	+	0.384031i	$0.874536\pi$
$140$	−15.8173	+	9.54311i	−1.33681	+	0.806540i
$141$		−	18.9627i		−	1.59694i
$142$	−4.35060	+	9.57973i	−0.365095	+	0.803913i
$143$		−	2.17803i		−	0.182136i
$144$	2.63213	−	19.4673i	0.219344	−	1.62228i
$145$	2.04403	+	0.362108i	0.169747	+	0.0300714i
$146$	13.0736	+	5.93735i	1.08198	+	0.491379i
$147$			28.3037i			2.33445i
$148$	−8.72883	−	9.98845i	−0.717505	−	0.821046i
$149$	−1.55447			−0.127348			−0.0636738	−	0.997971i	$-0.520282\pi$
$149$	−1.55447			−0.127348			−0.0636738	+	0.997971i	$0.520282\pi$
$150$	−14.1814	−	13.9443i	−1.15791	−	1.13855i
$151$	−4.46517			−0.363371			−0.181685	−	0.983357i	$-0.558155\pi$
$151$	−4.46517			−0.363371			−0.181685	+	0.983357i	$0.558155\pi$
$152$	−9.09482	−	8.32372i	−0.737687	−	0.675143i
$153$			14.4068i			1.16472i
$154$	−3.62607	−	1.64677i	−0.292197	−	0.132701i
$155$	−2.60858	+	14.7249i	−0.209526	+	1.18274i
$156$	13.5328	−	11.8262i	1.08349	−	0.946856i
$157$		−	0.527586i		−	0.0421060i	−0.999778	−	0.0210530i	$-0.993298\pi$
$157$		−	0.527586i		−	0.0421060i	0.999778	−	0.0210530i	$-0.00670187\pi$
$158$	2.89236	−	6.36878i	0.230104	−	0.506673i
$159$		−	21.3894i		−	1.69629i
$160$	8.49194	−	9.37480i	0.671347	−	0.741143i
$161$	26.4855			2.08735
$162$	0.225540	−	0.496623i	0.0177201	−	0.0390184i
$163$	23.5089			1.84136			0.920679	−	0.390320i	$-0.127636\pi$
$163$	23.5089			1.84136			0.920679	+	0.390320i	$0.127636\pi$
$164$	−7.37014	+	6.44070i	−0.575511	+	0.502934i
$165$	0.747925	−	4.22189i	0.0582259	−	0.328674i
$166$	5.69806	−	12.5467i	0.442255	−	0.973815i
$167$			14.4543i			1.11851i	0.828996	+	0.559254i	$0.188912\pi$
$167$			14.4543i			1.11851i	−0.828996	+	0.559254i	$0.811088\pi$
$168$	−9.45685	−	31.4716i	−0.729611	−	2.42809i
$169$	−2.79292			−0.214840
$170$	−5.25044	+	7.64773i	−0.402690	+	0.586554i
$171$	−10.9645	−	18.3859i	−0.838475	−	1.40601i
$172$	9.24284	+	10.5766i	0.704760	+	0.806461i
$173$	17.4795			1.32894			0.664469	−	0.747315i	$-0.268658\pi$
$173$	17.4795			1.32894			0.664469	+	0.747315i	$0.268658\pi$
$174$	−1.52695	+	3.36223i	−0.115758	+	0.254890i
$175$	−19.3967	−	7.09508i	−1.46625	−	0.536338i
$176$	2.70234	+	0.365376i	0.203696	+	0.0275413i
$177$		−	37.1190i		−	2.79003i
$178$	−9.85411	−	4.47522i	−0.738597	−	0.335432i
$179$	3.96422			0.296300			0.148150	−	0.988965i	$-0.452668\pi$
$179$	3.96422			0.296300			0.148150	+	0.988965i	$0.452668\pi$
$180$	18.8055	−	11.3460i	1.40168	−	0.845682i
$181$			16.7164i			1.24252i	0.783604	+	0.621261i	$0.213379\pi$
$181$			16.7164i			1.24252i	−0.783604	+	0.621261i	$0.786621\pi$
$182$	7.71739	−	16.9931i	0.572051	−	1.25962i
$183$		−	16.2098i		−	1.19826i
$184$	−17.3682	+	5.21893i	−1.28040	+	0.384745i
$185$	2.58705	−	14.6034i	0.190204	−	1.07366i
$186$	−24.2211	−	10.9999i	−1.77598	−	0.806555i
$187$	−1.99987			−0.146245
$188$	8.87274	+	10.1531i	0.647111	+	0.740493i
$189$		−	22.2040i		−	1.61510i
$190$	0.880187	−	13.7559i	0.0638555	−	0.997959i
$191$		−	2.74091i		−	0.198325i	−0.995071	−	0.0991625i	$-0.968384\pi$
$191$		−	2.74091i		−	0.198325i	0.995071	−	0.0991625i	$-0.0316164\pi$
$192$	12.4029	+	18.7744i	0.895102	+	1.35493i
$193$	4.92107			0.354226			0.177113	−	0.984191i	$-0.443324\pi$
$193$	4.92107			0.354226			0.177113	+	0.984191i	$0.443324\pi$
$194$	−8.81840	+	19.4175i	−0.633124	+	1.39409i
$195$	19.7854	+	3.50506i	1.41686	+	0.251003i
$196$	−13.2434	−	15.1546i	−0.945960	−	1.08247i
$197$			6.48624i			0.462126i	0.972939	+	0.231063i	$0.0742203\pi$
$197$			6.48624i			0.462126i	−0.972939	+	0.231063i	$0.925780\pi$
$198$	4.31112	+	1.95788i	0.306378	+	0.139141i
$199$			4.63007i			0.328217i	0.986442	+	0.164109i	$0.0524747\pi$
$199$			4.63007i			0.328217i	−0.986442	+	0.164109i	$0.947525\pi$
$200$	14.1177	+	0.830587i	0.998274	+	0.0587313i
$201$	−14.4236			−1.01736
$202$	4.35692	−	9.59363i	0.306552	−	0.675006i
$203$			3.83477i			0.269148i
$204$	−10.8588	−	12.4258i	−0.760271	−	0.869983i
$205$	−10.7753	−	1.90890i	−0.752583	−	0.133323i
$206$	1.05323	+	0.478321i	0.0733820	+	0.0333262i
$207$	−31.4891			−2.18865
$208$	−1.71229	+	12.6642i	−0.118726	+	0.878102i
$209$	2.55222	−	1.52202i	0.176541	−	0.105281i
$210$	20.7947	−	30.2894i	1.43497	−	2.09017i
$211$	−14.4300			−0.993399			−0.496699	−	0.867923i	$-0.665455\pi$
$211$	−14.4300			−0.993399			−0.496699	+	0.867923i	$0.665455\pi$
$212$	10.0082	+	11.4525i	0.687368	+	0.786560i
$213$		−	20.9255i		−	1.43379i
$214$	14.3235	+	6.50498i	0.979135	+	0.444671i
$215$	−2.73939	+	15.4633i	−0.186825	+	1.05459i
$216$	4.37528	+	14.5606i	0.297700	+	0.990721i
$217$	−27.6252			−1.87532
$218$	4.17371	+	1.89548i	0.282679	+	0.128378i
$219$	−28.5574			−1.92973
$220$	1.57499	+	2.61047i	0.106186	+	0.175998i
$221$		−	9.37214i		−	0.630438i
$222$	24.0212	+	10.9091i	1.61220	+	0.732174i
$223$		−	18.6603i		−	1.24959i	−0.780790	−	0.624794i	$-0.785183\pi$
$223$		−	18.6603i		−	1.24959i	0.780790	−	0.624794i	$-0.214817\pi$
$224$	19.7892	+	12.4258i	1.32222	+	0.830237i
$225$	23.0612	+	8.43550i	1.53741	+	0.562366i
$226$	−0.909415	+	2.00247i	−0.0604934	+	0.133202i
$227$			2.50907i			0.166533i	0.996527	+	0.0832663i	$0.0265352\pi$
$227$			2.50907i			0.166533i	−0.996527	+	0.0832663i	$0.973465\pi$
$228$	23.3149	+	7.59355i	1.54406	+	0.502895i
$229$	−14.8673			−0.982461			−0.491231	−	0.871030i	$-0.663453\pi$
$229$	−14.8673			−0.982461			−0.491231	+	0.871030i	$0.663453\pi$
$230$	−16.7157	−	11.4760i	−1.10220	−	0.756702i
$231$	7.92062			0.521138
$232$	−0.755637	−	2.51470i	−0.0496100	−	0.165098i
$233$		−	3.78435i		−	0.247921i	−0.992287	−	0.123960i	$-0.960440\pi$
$233$		−	3.78435i		−	0.247921i	0.992287	−	0.123960i	$-0.0395596\pi$
$234$	−9.17537	+	20.2035i	−0.599812	+	1.32075i
$235$	−2.62970	+	14.8442i	−0.171543	+	0.968326i
$236$	17.3682	+	19.8745i	1.13057	+	1.29372i
$237$			13.9117i			0.903659i
$238$	−15.6031	−	7.08610i	−1.01140	−	0.459324i
$239$		−	23.0185i		−	1.48894i	−0.667654	−	0.744472i	$-0.732701\pi$
$239$		−	23.0185i		−	1.48894i	0.667654	−	0.744472i	$-0.267299\pi$
$240$	−7.66792	+	23.9602i	−0.494962	+	1.54663i
$241$			2.24624i			0.144693i	0.997380	+	0.0723466i	$0.0230488\pi$
$241$			2.24624i			0.144693i	−0.997380	+	0.0723466i	$0.976951\pi$
$242$	6.16080	−	13.5657i	0.396031	−	0.872034i
$243$		−	15.0412i		−	0.964892i
$244$	7.58464	+	8.67916i	0.485557	+	0.555626i
$245$	3.92509	−	22.1564i	0.250765	−	1.41552i
$246$	8.04948	−	17.7244i	0.513216	−	1.13007i
$247$	7.13278	+	11.9607i	0.453848	+	0.761040i
$248$	18.1156	−	5.44352i	1.15034	−	0.345664i
$249$			27.4065i			1.73681i
$250$	9.16759	+	12.8824i	0.579809	+	0.814752i
$251$			8.81332i			0.556292i	0.960539	+	0.278146i	$0.0897199\pi$
$251$			8.81332i			0.556292i	−0.960539	+	0.278146i	$0.910280\pi$
$252$	26.6983	+	30.5510i	1.68183	+	1.92453i
$253$		−	4.37114i		−	0.274811i
$254$	−20.9768	−	9.52654i	−1.31620	−	0.597748i
$255$	3.21834	−	18.1669i	0.201541	−	1.13766i
$256$	−15.4255	−	4.24897i	−0.964094	−	0.265560i
$257$	−7.30009			−0.455367			−0.227684	−	0.973735i	$-0.573115\pi$
$257$	−7.30009			−0.455367			−0.227684	+	0.973735i	$0.573115\pi$
$258$	−25.4357	−	11.5515i	−1.58356	−	0.719168i
$259$	27.3972			1.70238
$260$	−12.2337	+	7.38098i	−0.758700	+	0.457749i
$261$		−	4.55924i		−	0.282210i
$262$	7.01474	+	3.18573i	0.433372	+	0.196815i
$263$	−19.0639			−1.17553			−0.587766	−	0.809031i	$-0.699992\pi$
$263$	−19.0639			−1.17553			−0.587766	+	0.809031i	$0.699992\pi$
$264$	−5.19404	+	1.56075i	−0.319671	+	0.0960575i
$265$	−2.96624	+	16.7439i	−0.182215	+	1.02857i
$266$	25.3056	−	2.83168i	1.55158	−	0.173622i
$267$	21.5248			1.31730
$268$	7.72280	−	6.74889i	0.471745	−	0.412254i
$269$		−	18.9627i		−	1.15617i	−0.815975	−	0.578087i	$-0.803799\pi$
$269$		−	18.9627i		−	1.15617i	0.815975	−	0.578087i	$-0.196201\pi$
$270$	−9.62083	+	14.0136i	−0.585505	+	0.852840i
$271$			25.7581i			1.56469i	0.622844	+	0.782346i	$0.285977\pi$
$271$			25.7581i			1.56469i	−0.622844	+	0.782346i	$0.714023\pi$
$272$	11.6282	+	1.57223i	0.705066	+	0.0953302i
$273$			37.1190i			2.24654i
$274$	−27.2011	−	12.3533i	−1.64328	−	0.746290i
$275$	−1.17097	+	3.20122i	−0.0706119	+	0.193041i
$276$	27.1593	−	23.7343i	1.63480	−	1.42864i
$277$			23.2139i			1.39479i	0.716687	+	0.697395i	$0.245658\pi$
$277$			23.2139i			1.39479i	−0.716687	+	0.697395i	$0.754342\pi$
$278$	11.6600	+	5.29537i	0.699323	+	0.317595i
$279$	32.8442			1.96633
$280$	3.03850	+	25.9477i	0.181585	+	1.55067i
$281$			9.45315i			0.563928i	0.959425	+	0.281964i	$0.0909858\pi$
$281$			9.45315i			0.563928i	−0.959425	+	0.281964i	$0.909014\pi$
$282$	−24.4172	−	11.0890i	−1.45402	−	0.660340i
$283$	−21.0074			−1.24876			−0.624381	−	0.781120i	$-0.714649\pi$
$283$	−21.0074			−1.24876			−0.624381	+	0.781120i	$0.714649\pi$
$284$	9.79115	+	11.2041i	0.580998	+	0.664840i
$285$	9.71893	+	25.6339i	0.575700	+	1.51842i
$286$	−2.80453	−	1.27367i	−0.165836	−	0.0753137i
$287$		−	20.2154i		−	1.19328i
$288$	−23.5278	−	14.7734i	−1.38639	−	0.870528i
$289$	8.39451			0.493795
$290$	1.66158	−	2.42023i	0.0975711	−	0.142121i
$291$		−	42.4146i		−	2.48639i
$292$	15.2904	−	13.3622i	0.894804	−	0.781962i
$293$	32.7375			1.91255			0.956274	−	0.292474i	$-0.0944783\pi$
$293$	32.7375			1.91255			0.956274	+	0.292474i	$0.0944783\pi$
$294$	36.4451	+	16.5514i	2.12552	+	0.965299i
$295$	−5.14758	+	29.0571i	−0.299704	+	1.69177i
$296$	−17.9660	+	5.39858i	−1.04425	+	0.313786i
$297$	−3.66453			−0.212638
$298$	−0.909026	+	2.00161i	−0.0526585	+	0.115950i
$299$	20.4848			1.18467
$300$	−26.2483	+	10.1063i	−1.51545	+	0.583487i
$301$	−29.0105			−1.67214
$302$	−2.61115	+	5.74956i	−0.150255	+	0.330850i
$303$			20.9559i			1.20388i
$304$	−16.0365	+	6.84335i	−0.919755	+	0.392493i
$305$	−2.24794	+	12.6892i	−0.128717	+	0.726580i
$306$	18.5509	+	8.42482i	1.06048	+	0.481615i
$307$		−	24.7134i		−	1.41047i	−0.708975	−	0.705233i	$-0.750842\pi$
$307$		−	24.7134i		−	1.41047i	0.708975	−	0.705233i	$-0.249158\pi$
$308$	−4.24091	+	3.70610i	−0.241649	+	0.211175i
$309$	−2.30062			−0.130878
$310$	17.4351	+	11.9698i	0.990245	+	0.679838i
$311$			18.3688i			1.04160i	0.853679	+	0.520800i	$0.174366\pi$
$311$			18.3688i			1.04160i	−0.853679	+	0.520800i	$0.825634\pi$
$312$	−7.31426	−	24.3412i	−0.414088	−	1.37805i
$313$		−	13.0608i		−	0.738241i	−0.929382	−	0.369120i	$-0.879659\pi$
$313$		−	13.0608i		−	0.738241i	0.929382	−	0.369120i	$-0.120341\pi$
$314$	−0.679345	−	0.308522i	−0.0383376	−	0.0174109i
$315$	−7.91284	+	44.6664i	−0.445838	+	2.51667i
$316$	−6.50934	−	7.44868i	−0.366179	−	0.419021i
$317$	−5.67220			−0.318583			−0.159291	−	0.987232i	$-0.550921\pi$
$317$	−5.67220			−0.318583			−0.159291	+	0.987232i	$0.550921\pi$
$318$	−27.5420	−	12.5081i	−1.54448	−	0.701421i
$319$	0.632887			0.0354348
$320$	−7.10550	−	16.4168i	−0.397210	−	0.917728i
$321$	−31.2876			−1.74630
$322$	15.4882	−	34.1039i	0.863123	−	1.90054i
$323$	10.9823	−	6.54932i	0.611071	−	0.364414i
$324$	−0.507583	−	0.580830i	−0.0281990	−	0.0322684i
$325$	−15.0021	−	5.48759i	−0.832167	−	0.304397i
$326$	13.7475	−	30.2711i	0.761406	−	1.67656i
$327$	−9.11684			−0.504162
$328$	3.98343	+	13.2565i	0.219948	+	0.731969i
$329$	−27.8489			−1.53536
$330$	−4.99893	−	3.43194i	−0.275182	−	0.188922i
$331$	−3.78583			−0.208088			−0.104044	−	0.994573i	$-0.533178\pi$
$331$	−3.78583			−0.208088			−0.104044	+	0.994573i	$0.533178\pi$
$332$	−12.8236	−	14.6742i	−0.703788	−	0.805349i
$333$	−32.5731			−1.78499
$334$	18.6120	+	8.45260i	1.01840	+	0.462505i
$335$	11.2910	+	2.00024i	0.616891	+	0.109285i
$336$	−46.0545	−	6.22691i	−2.51248	−	0.339706i
$337$	28.8626			1.57225			0.786123	−	0.618070i	$-0.212085\pi$
$337$	28.8626			1.57225			0.786123	+	0.618070i	$0.212085\pi$
$338$	−1.63325	+	3.59629i	−0.0888369	+	0.195613i
$339$		−	4.37410i		−	0.237568i
$340$	6.77722	+	11.2330i	0.367546	+	0.609192i
$341$			4.55924i			0.246897i
$342$	−30.0863	+	3.36665i	−1.62688	+	0.182048i
$343$	12.6521			0.683149
$344$	19.0240	−	5.71649i	1.02571	−	0.308212i
$345$	39.7077	+	7.03438i	2.13779	+	0.378718i
$346$	10.2216	−	22.5074i	0.549519	−	1.21000i
$347$	5.58017			0.299559			0.149780	−	0.988719i	$-0.452144\pi$
$347$	5.58017			0.299559			0.149780	+	0.988719i	$0.452144\pi$
$348$	3.43643	+	3.93233i	0.184212	+	0.210795i
$349$	12.5906			0.673959			0.336980	−	0.941512i	$-0.390595\pi$
$349$	12.5906			0.673959			0.336980	+	0.941512i	$0.390595\pi$
$350$	−20.4788	+	20.8270i	−1.09464	+	1.11325i
$351$		−	17.1734i		−	0.916647i
$352$	2.05075	−	3.26599i	0.109305	−	0.174078i
$353$		−	0.501758i		−	0.0267059i	−0.999911	−	0.0133529i	$-0.995750\pi$
$353$		−	0.501758i		−	0.0267059i	0.999911	−	0.0133529i	$-0.00425050\pi$
$354$	−47.7961	−	21.7065i	−2.54033	−	1.15369i
$355$	−2.90190	+	16.3807i	−0.154017	+	0.869396i
$356$	−11.5250	+	10.0716i	−0.610823	+	0.533793i
$357$	34.0826			1.80384
$358$	2.31820	−	5.10451i	0.122521	−	0.269782i
$359$		−	17.0054i		−	0.897509i	−0.893655	−	0.448754i	$-0.851868\pi$
$359$		−	17.0054i		−	0.897509i	0.893655	−	0.448754i	$-0.148132\pi$
$360$	−3.61253	−	30.8498i	−0.190397	−	1.62593i
$361$	−9.03112	+	16.7164i	−0.475322	+	0.879812i
$362$	21.5248	+	9.77544i	1.13132	+	0.513786i
$363$			29.6322i			1.55528i
$364$	−17.3682	−	19.8745i	−0.910340	−	1.04171i
$365$	22.3550	+	3.96028i	1.17011	+	0.207291i
$366$	−20.8725	−	9.47916i	−1.09102	−	0.495484i
$367$	−0.980882			−0.0512016			−0.0256008	−	0.999672i	$-0.508150\pi$
$367$	−0.980882			−0.0512016			−0.0256008	+	0.999672i	$0.508150\pi$
$368$	−3.43643	+	25.4160i	−0.179136	+	1.32490i
$369$			24.0346i			1.25119i
$370$	−17.2911	−	11.8710i	−0.898924	−	0.617143i
$371$	−31.4128			−1.63087
$372$	−28.3281	+	24.7556i	−1.46874	+	1.28352i
$373$	−2.73331			−0.141526			−0.0707628	−	0.997493i	$-0.522543\pi$
$373$	−2.73331			−0.141526			−0.0707628	+	0.997493i	$0.522543\pi$
$374$	−1.16948	+	2.57512i	−0.0604726	+	0.133156i
$375$	−27.1957	−	15.7888i	−1.40438	−	0.815329i
$376$	18.2622	−	5.48759i	0.941803	−	0.283001i
$377$			2.96594i			0.152754i
$378$	−28.5909	−	12.9845i	−1.47056	−	0.667849i
$379$	−4.89460			−0.251419			−0.125709	−	0.992067i	$-0.540121\pi$
$379$	−4.89460			−0.251419			−0.125709	+	0.992067i	$0.540121\pi$
$380$	−17.1980	−	9.17756i	−0.882241	−	0.470799i
$381$	45.8206			2.34746
$382$	−3.52932	−	1.60283i	−0.180576	−	0.0820079i
$383$		−	0.855884i		−	0.0437336i	−0.999761	−	0.0218668i	$-0.993039\pi$
$383$		−	0.855884i		−	0.0437336i	0.999761	−	0.0218668i	$-0.00696098\pi$
$384$	31.4278	−	4.99161i	1.60379	−	0.254727i
$385$	−6.20033	−	1.09841i	−0.315998	−	0.0559804i
$386$	2.87774	−	6.33659i	0.146473	−	0.322524i
$387$	34.4912			1.75329
$388$	19.8460	+	22.7099i	1.00753	+	1.15292i
$389$	1.53950			0.0780560			0.0390280	−	0.999238i	$-0.487574\pi$
$389$	1.53950			0.0780560			0.0390280	+	0.999238i	$0.487574\pi$
$390$	16.0834	−	23.4269i	0.814414	−	1.18627i
$391$		−	18.8091i		−	0.951219i
$392$	−27.2582	+	8.19077i	−1.37675	+	0.413697i
$393$	−15.3227			−0.772926
$394$	8.35199	+	3.79303i	0.420767	+	0.191090i
$395$	1.92924	−	10.8902i	0.0970705	−	0.547944i
$396$	5.04211	−	4.40626i	0.253376	−	0.221423i
$397$		−	34.3640i		−	1.72468i	−0.506330	−	0.862340i	$-0.668998\pi$
$397$		−	34.3640i		−	1.72468i	0.506330	−	0.862340i	$-0.331002\pi$
$398$	5.96189	+	2.70758i	0.298843	+	0.135718i
$399$	−43.4961	+	25.9390i	−2.17753	+	1.29858i
$400$	9.32527	−	17.6929i	0.466264	−	0.884646i
$401$		−	25.1483i		−	1.25585i	−0.778275	−	0.627924i	$-0.783905\pi$
$401$		−	25.1483i		−	1.25585i	0.778275	−	0.627924i	$-0.216095\pi$
$402$	−8.43466	+	18.5725i	−0.420682	+	0.926313i
$403$	−21.3663			−1.06433
$404$	−9.80536	−	11.2203i	−0.487835	−	0.558233i
$405$	0.150437	−	0.849190i	0.00747530	−	0.0421966i
$406$	4.93782	+	2.24250i	0.245060	+	0.111293i
$407$		−	4.52160i		−	0.224128i
$408$	−22.3501	+	6.71595i	−1.10650	+	0.332489i
$409$			7.36766i			0.364307i	0.983270	+	0.182154i	$0.0583069\pi$
$409$			7.36766i			0.364307i	−0.983270	+	0.182154i	$0.941693\pi$
$410$	−8.75920	+	12.7585i	−0.432586	+	0.630100i
$411$	59.4167			2.93081
$412$	1.23182	−	1.07647i	0.0606872	−	0.0530340i
$413$	−54.5135			−2.68243
$414$	−18.4142	+	40.5469i	−0.905010	+	1.99277i
$415$	3.80067	−	21.4540i	0.186567	−	1.05314i
$416$	15.3057	+	9.61059i	0.750422	+	0.471198i
$417$	−25.4696			−1.24725
$418$	−0.467338	−	4.17641i	−0.0228583	−	0.204275i
$419$			6.90117i			0.337144i	0.985689	+	0.168572i	$0.0539156\pi$
$419$			6.90117i			0.337144i	−0.985689	+	0.168572i	$0.946084\pi$
$420$	−26.8416	−	44.4889i	−1.30974	−	2.17084i
$421$		−	1.83055i		−	0.0892154i	−0.999005	−	0.0446077i	$-0.985796\pi$
$421$		−	1.83055i		−	0.0892154i	0.999005	−	0.0446077i	$-0.0142038\pi$
$422$	−8.43836	+	18.5807i	−0.410773	+	0.904493i
$423$	33.1101			1.60987
$424$	20.5994	−	6.18987i	1.00039	−	0.300607i
$425$	−5.03870	+	13.7749i	−0.244413	+	0.668182i
$426$	−26.9446	−	12.2368i	−1.30547	−	0.592876i
$427$	−23.8059			−1.15205
$428$	16.7522	−	14.6396i	0.809749	−	0.707633i
$429$	6.12608			0.295770
$430$	18.3094	+	12.5700i	0.882956	+	0.606180i
$431$	14.0996			0.679152			0.339576	−	0.940579i	$-0.389716\pi$
$431$	14.0996			0.679152			0.339576	+	0.940579i	$0.389716\pi$
$432$	21.3074	+	2.88092i	1.02515	+	0.138609i
$433$	16.9499			0.814561			0.407280	−	0.913303i	$-0.366477\pi$
$433$	16.9499			0.814561			0.407280	+	0.913303i	$0.366477\pi$
$434$	−16.1547	+	35.5715i	−0.775449	+	1.70749i
$435$	−1.01849	+	5.74918i	−0.0488329	+	0.275652i
$436$	4.88141	−	4.26582i	0.233777	−	0.204296i
$437$	14.3149	+	24.0041i	0.684776	+	1.14827i
$438$	−16.6998	+	36.7718i	−0.797948	+	1.75703i
$439$	24.5284			1.17067			0.585337	−	0.810790i	$-0.300962\pi$
$439$	24.5284			1.17067			0.585337	+	0.810790i	$0.300962\pi$
$440$	4.28239	−	0.501470i	0.204155	−	0.0239067i
$441$	−49.4201			−2.35334
$442$	−12.0680	−	5.48064i	−0.574016	−	0.260688i
$443$	6.36297			0.302314			0.151157	−	0.988510i	$-0.451700\pi$
$443$	6.36297			0.302314			0.151157	+	0.988510i	$0.451700\pi$
$444$	28.0942	−	24.5513i	1.33329	−	1.16515i
$445$	−16.8498	−	2.98502i	−0.798759	−	0.141503i
$446$	−24.0279	−	10.9122i	−1.13775	−	0.516707i
$447$		−	4.37222i		−	0.206799i
$448$	27.5724	−	18.2151i	1.30267	−	0.860581i
$449$		−	24.8083i		−	1.17078i	−0.810753	−	0.585388i	$-0.800942\pi$
$449$		−	24.8083i		−	1.17078i	0.810753	−	0.585388i	$-0.199058\pi$
$450$	24.3477	−	24.7617i	1.14776	−	1.16728i
$451$	−3.33634			−0.157102
$452$	2.04666	+	2.34201i	0.0962669	+	0.110159i
$453$		−	12.5591i		−	0.590076i
$454$	3.23079	+	1.46725i	0.151628	+	0.0688616i
$455$	5.14758	−	29.0571i	0.241322	−	1.36222i
$456$	23.4119	−	25.5807i	1.09636	−	1.19793i
$457$			6.10142i			0.285413i	0.989765	+	0.142706i	$0.0455804\pi$
$457$			6.10142i			0.285413i	−0.989765	+	0.142706i	$0.954420\pi$
$458$	−8.69413	+	19.1439i	−0.406250	+	0.894534i
$459$	−15.7686			−0.736014
$460$	−24.5520	+	14.8130i	−1.14474	+	0.690662i
$461$	4.88681			0.227601			0.113801	−	0.993504i	$-0.463697\pi$
$461$	4.88681			0.227601			0.113801	+	0.993504i	$0.463697\pi$
$462$	4.63182	−	10.1989i	0.215492	−	0.474498i
$463$	0.798615			0.0371148			0.0185574	−	0.999828i	$-0.494093\pi$
$463$	0.798615			0.0371148			0.0185574	+	0.999828i	$0.494093\pi$
$464$	−3.67992	−	0.497553i	−0.170836	−	0.0230983i
$465$	−41.4164	−	7.33708i	−1.92064	−	0.340249i
$466$	−4.87290	−	2.21301i	−0.225733	−	0.102516i
$467$	−8.83970			−0.409053			−0.204526	−	0.978861i	$-0.565565\pi$
$467$	−8.83970			−0.409053			−0.204526	+	0.978861i	$0.565565\pi$
$468$	20.6494	+	23.6292i	0.954519	+	1.09226i
$469$			21.1828i			0.978129i
$470$	17.5762	+	12.0667i	0.810731	+	0.556595i
$471$	1.48393			0.0683757
$472$	35.7479	−	10.7418i	1.64543	−	0.494433i
$473$			4.78786i			0.220146i
$474$	17.9133	+	8.13526i	0.822784	+	0.373665i
$475$	−4.05322	−	21.4143i	−0.185974	−	0.982555i
$476$	−18.2488	+	15.9475i	−0.836432	+	0.730950i
$477$	37.3474			1.71002
$478$	−29.6397	−	13.4608i	−1.35569	−	0.615681i
$479$		−	9.69477i		−	0.442966i	−0.975164	−	0.221483i	$-0.928910\pi$
$479$		−	9.69477i		−	0.442966i	0.975164	−	0.221483i	$-0.0710897\pi$
$480$	26.3682	+	23.8850i	1.20354	+	1.09020i
$481$	21.1899			0.966178
$482$	2.89236	+	1.31356i	0.131744	+	0.0598309i
$483$			74.4949i			3.38963i
$484$	−13.8650	−	15.8659i	−0.630229	−	0.721176i
$485$	−5.88197	+	33.2026i	−0.267086	+	1.50765i
$486$	−19.3677	−	8.79579i	−0.878537	−	0.398985i
$487$		−	12.6428i		−	0.572902i	−0.958095	−	0.286451i	$-0.907524\pi$
$487$		−	12.6428i		−	0.572902i	0.958095	−	0.286451i	$-0.0924755\pi$
$488$	15.6110	−	4.69093i	0.706678	−	0.212349i
$489$			66.1228i			2.99017i
$490$	−26.2343	−	18.0108i	−1.18514	−	0.813643i
$491$			3.36009i			0.151639i	0.997122	+	0.0758193i	$0.0241572\pi$
$491$			3.36009i			0.151639i	−0.997122	+	0.0758193i	$0.975843\pi$
$492$	−18.1156	−	20.7298i	−0.816713	−	0.934570i
$493$	2.72333			0.122653
$494$	19.5722	−	2.19012i	0.880596	−	0.0985383i
$495$	7.37171	+	1.30593i	0.331334	+	0.0586971i
$496$	3.58431	−	26.5097i	0.160940	−	1.19032i
$497$	−30.7315			−1.37850
$498$	35.2898	+	16.0268i	1.58137	+	0.718176i
$499$		−	2.61776i		−	0.117187i	−0.998282	−	0.0585935i	$-0.981338\pi$
$499$		−	2.61776i		−	0.117187i	0.998282	−	0.0585935i	$-0.0186616\pi$
$500$	21.9490	−	4.27125i	0.981587	−	0.191016i
$501$	−40.6552			−1.81634
$502$	11.3484	+	5.15386i	0.506505	+	0.230028i
$503$	−33.9417			−1.51339			−0.756694	−	0.653769i	$-0.773187\pi$
$503$	−33.9417			−1.51339			−0.756694	+	0.653769i	$0.773187\pi$
$504$	54.9515	−	16.5123i	2.44774	−	0.735516i
$505$	2.90611	−	16.4044i	0.129320	−	0.729988i
$506$	−5.62848	−	2.55616i	−0.250216	−	0.113635i
$507$		−	7.85557i		−	0.348878i
$508$	−24.5336	+	21.4397i	−1.08850	+	0.951234i
$509$			1.44843i			0.0642006i	0.999485	+	0.0321003i	$0.0102196\pi$
$509$			1.44843i			0.0642006i	−0.999485	+	0.0321003i	$0.989780\pi$
$510$	−21.5105	−	14.7678i	−0.952503	−	0.653927i
$511$			41.9398i			1.85531i
$512$	−14.4917	+	17.3779i	−0.640449	+	0.768001i
$513$	20.1238	−	12.0009i	0.888488	−	0.529852i
$514$	−4.26895	+	9.39993i	−0.188295	+	0.414613i
$515$	1.80095	+	0.319045i	0.0793593	+	0.0140588i
$516$	−29.7486	+	25.9970i	−1.30961	+	1.14446i
$517$			4.59615i			0.202138i
$518$	16.0213	−	35.2778i	0.703937	−	1.55002i
$519$			49.1640i			2.15806i
$520$	2.35008	+	20.0689i	0.103058	+	0.880079i
$521$			33.3661i			1.46180i	0.682487	+	0.730898i	$0.260898\pi$
$521$			33.3661i			1.46180i	−0.682487	+	0.730898i	$0.739102\pi$
$522$	−5.87068	−	2.66615i	−0.256953	−	0.116694i
$523$		−	37.3100i		−	1.63145i	−0.578437	−	0.815727i	$-0.696337\pi$
$523$		−	37.3100i		−	1.63145i	0.578437	−	0.815727i	$-0.303663\pi$
$524$	8.20417	−	7.16956i	0.358401	−	0.313204i
$525$	19.9561	−	54.5566i	0.870957	−	2.38104i
$526$	−11.1482	+	24.5476i	−0.486085	+	1.07032i
$527$			19.6185i			0.854597i
$528$	−1.02768	+	7.60078i	−0.0447242	+	0.330782i
$529$	18.1114			0.787451
$530$	19.8256	+	13.6109i	0.861167	+	0.591222i
$531$	64.8123			2.81261
$532$	11.1520	−	34.2405i	0.483501	−	1.48452i
$533$		−	15.6353i		−	0.677241i
$534$	12.5873	−	27.7164i	0.544706	−	1.19940i
$535$	24.4922	+	4.33889i	1.05889	+	0.187587i
$536$	−4.17404	−	13.8909i	−0.180291	−	0.599994i
$537$			11.1500i			0.481160i
$538$	−24.4172	−	11.0890i	−1.05270	−	0.478081i
$539$		−	6.86021i		−	0.295490i
$540$	12.4185	+	20.5831i	0.534406	+	0.885756i
$541$	0.420141			0.0180633			0.00903163	−	0.999959i	$-0.497125\pi$
$541$	0.420141			0.0180633			0.00903163	+	0.999959i	$0.497125\pi$
$542$	33.1673	+	15.0628i	1.42466	+	0.647004i
$543$	−47.0178			−2.01773
$544$	8.82444	−	14.0536i	0.378345	−	0.602545i
$545$	7.13675	+	1.26430i	0.305705	+	0.0541568i
$546$	47.7961	+	21.7065i	2.04548	+	0.928951i
$547$		−	1.24302i		−	0.0531479i	−0.999647	−	0.0265739i	$-0.991540\pi$
$547$		−	1.24302i		−	0.0531479i	0.999647	−	0.0265739i	$-0.00845974\pi$
$548$	−31.8133	+	27.8014i	−1.35900	+	1.18762i
$549$	28.3034			1.20796
$550$	3.43728	+	3.37980i	0.146566	+	0.144115i
$551$	−3.47550	+	2.07262i	−0.148061	+	0.0882968i
$552$	−14.6791	−	48.8510i	−0.624786	−	2.07923i
$553$	20.4309			0.868809
$554$	29.8913	+	13.5751i	1.26996	+	0.576749i
$555$	41.0745	+	7.27652i	1.74352	+	0.308871i
$556$	13.6371	−	11.9174i	0.578343	−	0.505409i
$557$			24.3255i			1.03071i	0.856978	+	0.515353i	$0.172339\pi$
$557$			24.3255i			1.03071i	−0.856978	+	0.515353i	$0.827661\pi$
$558$	19.2066	−	42.2917i	0.813082	−	1.79035i
$559$	−22.4377			−0.949015
$560$	35.1883	+	11.2612i	1.48698	+	0.475873i
$561$		−	5.62497i		−	0.237486i
$562$	12.1723	+	5.52802i	0.513458	+	0.233185i
$563$		−	17.4856i		−	0.736928i	−0.929642	−	0.368464i	$-0.879884\pi$
$563$		−	17.4856i		−	0.736928i	0.929642	−	0.368464i	$-0.120116\pi$
$564$	−28.5574	+	24.9561i	−1.20248	+	1.05084i
$565$	−0.606590	+	3.42408i	−0.0255194	+	0.144052i
$566$	−12.2847	+	27.0501i	−0.516366	+	1.13700i
$567$	1.59315			0.0669060
$568$	20.1526	−	6.05561i	0.845582	−	0.254088i
$569$		−	42.2662i		−	1.77189i	−0.463790	−	0.885945i	$-0.653511\pi$
$569$		−	42.2662i		−	1.77189i	0.463790	−	0.885945i	$-0.346489\pi$
$570$	38.6909	+	2.47567i	1.62058	+	0.103695i
$571$		−	20.7425i		−	0.868047i	−0.900902	−	0.434023i	$-0.857093\pi$
$571$		−	20.7425i		−	0.868047i	0.900902	−	0.434023i	$-0.142907\pi$
$572$	−3.28007	+	2.86643i	−0.137147	+	0.119851i
$573$	7.70927			0.322059
$574$	−26.0303	−	11.8216i	−1.08648	−	0.493424i
$575$	−30.1080	−	11.0132i	−1.25559	−	0.459280i
$576$	−32.7814	+	21.6563i	−1.36589	+	0.902345i
$577$		−	3.16844i		−	0.131904i	−0.997823	−	0.0659519i	$-0.978992\pi$
$577$		−	3.16844i		−	0.131904i	0.997823	−	0.0659519i	$-0.0210084\pi$
$578$	4.90894	−	10.8092i	0.204185	−	0.449601i
$579$			13.8413i			0.575226i
$580$	−2.14475	−	3.55483i	−0.0890557	−	0.147606i
$581$	40.2495			1.66983
$582$	−54.6150	−	24.8032i	−2.26386	−	1.02813i
$583$			5.18435i			0.214714i
$584$	−8.26420	−	27.5026i	−0.341975	−	1.13806i
$585$	−6.12007	+	34.5466i	−0.253034	+	1.42833i
$586$	19.1443	−	42.1544i	0.790843	−	1.74138i
$587$	23.4852			0.969336			0.484668	−	0.874698i	$-0.338940\pi$
$587$	23.4852			0.969336			0.484668	+	0.874698i	$0.338940\pi$
$588$	42.6248	−	37.2494i	1.75782	−	1.53614i
$589$	−14.9309	−	25.0371i	−0.615218	−	1.03164i
$590$	34.4051	+	23.6203i	1.41643	+	0.972432i
$591$	−18.2437			−0.750444
$592$	−3.55472	+	26.2909i	−0.146098	+	1.08055i
$593$			30.3518i			1.24640i	0.782062	+	0.623200i	$0.214168\pi$
$593$			30.3518i			1.24640i	−0.782062	+	0.623200i	$0.785832\pi$
$594$	−2.14295	+	4.71862i	−0.0879261	+	0.193607i
$595$	−26.6802	−	4.72651i	−1.09378	−	0.193768i
$596$	2.04579	+	2.34101i	0.0837987	+	0.0958914i
$597$	−13.0229			−0.532990
$598$	11.9791	−	26.3772i	0.489862	−	1.07864i
$599$	−22.8129			−0.932109			−0.466055	−	0.884756i	$-0.654325\pi$
$599$	−22.8129			−0.932109			−0.466055	+	0.884756i	$0.654325\pi$
$600$	−2.33617	+	39.7085i	−0.0953736	+	1.62109i
$601$		−	34.9549i		−	1.42584i	−0.701246	−	0.712920i	$-0.747372\pi$
$601$		−	34.9549i		−	1.42584i	0.701246	−	0.712920i	$-0.252628\pi$
$602$	−16.9648	+	37.3552i	−0.691432	+	1.52249i
$603$		−	25.1846i		−	1.02560i
$604$	5.87645	+	6.72446i	0.239109	+	0.273614i
$605$	4.10932	−	23.1963i	0.167068	−	0.943065i
$606$	26.9837	+	12.2546i	1.09614	+	0.497808i
$607$			39.4409i			1.60085i	0.599430	+	0.800427i	$0.295394\pi$
$607$			39.4409i			1.60085i	−0.599430	+	0.800427i	$0.704606\pi$
$608$	−0.566005	+	24.6512i	−0.0229545	+	0.999737i
$609$	−10.7859			−0.437068
$610$	15.0246	+	10.3149i	0.608329	+	0.417639i
$611$	−21.5393			−0.871386
$612$	21.6964	−	18.9603i	0.877024	−	0.766424i
$613$			26.3466i			1.06413i	0.846703	+	0.532065i	$0.178584\pi$
$613$			26.3466i			1.06413i	−0.846703	+	0.532065i	$0.821416\pi$
$614$	−31.8221	−	14.4519i	−1.28423	−	0.583231i
$615$	5.36910	−	30.3075i	0.216503	−	1.22212i
$616$	2.29214	+	7.62805i	0.0923529	+	0.307343i
$617$		−	13.0674i		−	0.526074i	−0.964786	−	0.263037i	$-0.915276\pi$
$617$		−	13.0674i		−	0.526074i	0.964786	−	0.263037i	$-0.0847242\pi$
$618$	−1.34536	+	2.96239i	−0.0541183	+	0.119165i
$619$			10.7709i			0.432917i	0.976292	+	0.216459i	$0.0694506\pi$
$619$			10.7709i			0.432917i	−0.976292	+	0.216459i	$0.930549\pi$
$620$	25.6085	−	15.4505i	1.02846	−	0.620506i
$621$		−	34.4656i		−	1.38306i
$622$	23.6525	+	10.7417i	0.948380	+	0.430704i
$623$		−	31.6117i		−	1.26650i
$624$	−35.6201	−	4.81611i	−1.42595	−	0.192799i
$625$	19.0995	+	16.1310i	0.763978	+	0.645242i
$626$	−16.8177	−	7.63771i	−0.672171	−	0.305264i
$627$	4.28095	+	7.17856i	0.170965	+	0.286684i
$628$	−0.794535	+	0.694337i	−0.0317054	+	0.0277071i
$629$		−	19.4566i		−	0.775785i
$630$	52.8873	+	36.3090i	2.10708	+	1.44659i
$631$		−	10.0679i		−	0.400795i	−0.979715	−	0.200397i	$-0.935777\pi$
$631$		−	10.0679i		−	0.400795i	0.979715	−	0.200397i	$-0.0642233\pi$
$632$	−13.3978	+	4.02588i	−0.532936	+	0.160141i
$633$		−	40.5867i		−	1.61318i
$634$	−3.31699	+	7.30379i	−0.131735	+	0.290071i
$635$	−35.8688	−	6.35431i	−1.42341	−	0.252163i
$636$	−32.2121	+	28.1499i	−1.27729	+	1.11621i
$637$	32.1495			1.27381
$638$	0.370100	−	0.814934i	0.0146524	−	0.0322635i
$639$	36.5373			1.44539
$640$	−25.2942	−	0.450861i	−0.999841	−	0.0178218i
$641$		−	13.1666i		−	0.520048i	−0.965602	−	0.260024i	$-0.916270\pi$
$641$		−	13.1666i		−	0.520048i	0.965602	−	0.260024i	$-0.0837304\pi$
$642$	−18.2964	+	40.2873i	−0.722099	+	1.59001i
$643$	31.8875			1.25752			0.628761	−	0.777599i	$-0.283562\pi$
$643$	31.8875			1.25752			0.628761	+	0.777599i	$0.283562\pi$
$644$	−34.8566	−	39.8866i	−1.37354	−	1.57175i
$645$	−43.4933	−	7.70501i	−1.71255	−	0.303384i
$646$	−2.01097	−	17.9712i	−0.0791206	−	0.707068i
$647$	−20.6536			−0.811979			−0.405989	−	0.913878i	$-0.633073\pi$
$647$	−20.6536			−0.811979			−0.405989	+	0.913878i	$0.633073\pi$
$648$	−1.04473	+	0.313929i	−0.0410408	+	0.0123323i
$649$			8.99686i			0.353158i
$650$	−15.8390	+	16.1084i	−0.621257	+	0.631822i
$651$		−	77.7006i		−	3.04533i
$652$	−30.9392	−	35.4039i	−1.21167	−	1.38653i
$653$		−	29.4300i		−	1.15169i	−0.817560	−	0.575843i	$-0.804674\pi$
$653$		−	29.4300i		−	1.15169i	0.817560	−	0.575843i	$-0.195326\pi$
$654$	−5.33135	+	11.7393i	−0.208472	+	0.459041i
$655$	11.9947	+	2.12491i	0.468673	+	0.0830273i
$656$	19.3991	+	2.62291i	0.757409	+	0.102407i
$657$		−	49.8632i		−	1.94535i
$658$	−16.2855	+	35.8595i	−0.634874	+	1.39795i
$659$	−11.5946			−0.451660			−0.225830	−	0.974167i	$-0.572509\pi$
$659$	−11.5946			−0.451660			−0.225830	+	0.974167i	$0.572509\pi$
$660$	−7.34240	+	4.42992i	−0.285803	+	0.172434i
$661$		−	29.8500i		−	1.16103i	−0.814250	−	0.580515i	$-0.802851\pi$
$661$		−	29.8500i		−	1.16103i	0.814250	−	0.580515i	$-0.197149\pi$
$662$	−2.21388	+	4.87481i	−0.0860448	+	0.189465i
$663$	26.3607			1.02377
$664$	−26.3941	+	7.93113i	−1.02429	+	0.307787i
$665$	37.6464	−	14.2734i	1.45986	−	0.553498i
$666$	−19.0481	+	41.9426i	−0.738099	+	1.62524i
$667$			5.95242i			0.230478i
$668$	21.7679	−	19.0228i	0.842225	−	0.736014i
$669$	52.4853			2.02920
$670$	9.17833	−	13.3690i	0.354590	−	0.516491i
$671$			3.92891i			0.151674i
$672$	−34.9498	+	55.6604i	−1.34822	+	2.14715i
$673$	41.0916			1.58396			0.791982	−	0.610545i	$-0.209050\pi$
$673$	41.0916			1.58396			0.791982	+	0.610545i	$0.209050\pi$
$674$	16.8783	−	37.1648i	0.650128	−	1.43154i
$675$	−9.23285	+	25.2410i	−0.355372	+	0.971526i
$676$	3.67566	+	4.20609i	0.141372	+	0.161773i
$677$	−32.6916			−1.25644			−0.628220	−	0.778036i	$-0.716216\pi$
$677$	−32.6916			−1.25644			−0.628220	+	0.778036i	$0.716216\pi$
$678$	−5.63229	−	2.55789i	−0.216307	−	0.0982350i
$679$	−62.2907			−2.39050
$680$	18.4272	−	2.15784i	0.706653	−	0.0827495i
$681$	−7.05718			−0.270432
$682$	5.87068	+	2.66615i	0.224800	+	0.102092i
$683$			7.06028i			0.270154i	0.990835	+	0.135077i	$0.0431282\pi$
$683$			7.06028i			0.270154i	−0.990835	+	0.135077i	$0.956872\pi$
$684$	−13.2589	+	40.7093i	−0.506965	+	1.55656i
$685$	−46.5120	−	8.23978i	−1.77713	−	0.314826i
$686$	7.39870	−	16.2914i	0.282484	−	0.622010i
$687$		−	41.8169i		−	1.59541i
$688$	3.76405	−	27.8391i	0.143503	−	1.06135i
$689$	−24.2958			−0.925597
$690$	32.2781	−	47.0159i	1.22880	−	1.78986i
$691$			11.1247i			0.423203i	0.977356	+	0.211602i	$0.0678679\pi$
$691$			11.1247i			0.423203i	−0.977356	+	0.211602i	$0.932132\pi$
$692$	−23.0041	−	26.3237i	−0.874484	−	1.00068i
$693$			13.8299i			0.525356i
$694$	3.26317	−	7.18528i	0.123868	−	0.272749i
$695$	19.9379	+	3.53207i	0.756286	+	0.133979i
$696$	7.07301	−	2.12536i	0.268102	−	0.0805615i
$697$	−14.3564			−0.543786
$698$	7.36274	−	16.2122i	0.278684	−	0.613642i
$699$	10.6441			0.402598
$700$	14.8423	+	38.5487i	0.560985	+	1.45700i
$701$	−0.945903			−0.0357263			−0.0178631	−	0.999840i	$-0.505686\pi$
$701$	−0.945903			−0.0357263			−0.0178631	+	0.999840i	$0.505686\pi$
$702$	−22.1132	−	10.0427i	−0.834610	−	0.379035i
$703$	14.8077	+	24.8304i	0.558482	+	0.936497i
$704$	−3.00620	−	4.55053i	−0.113300	−	0.171504i
$705$	−41.7517	−	7.39648i	−1.57246	−	0.278568i
$706$	−0.646086	−	0.293418i	−0.0243158	−	0.0110429i
$707$	30.7761			1.15745
$708$	−55.9005	+	48.8510i	−2.10087	+	1.83593i
$709$	−20.0593			−0.753342			−0.376671	−	0.926347i	$-0.622931\pi$
$709$	−20.0593			−0.753342			−0.376671	+	0.926347i	$0.622931\pi$
$710$	19.3955	+	13.3157i	0.727901	+	0.499730i
$711$	−24.2907			−0.910972
$712$	6.22905	+	20.7298i	0.233444	+	0.776881i
$713$	−42.8805			−1.60589
$714$	19.9309	−	43.8864i	0.745894	−	1.64241i
$715$	−4.79556	−	0.849552i	−0.179344	−	0.0317715i
$716$	−5.21717	−	5.97004i	−0.194975	−	0.223111i
$717$	64.7434			2.41789
$718$	−21.8969	−	9.94440i	−0.817184	−	0.371122i
$719$			31.0420i			1.15767i	0.815444	+	0.578836i	$0.196493\pi$
$719$			31.0420i			1.15767i	−0.815444	+	0.578836i	$0.803507\pi$
$720$	−41.8362	−	13.3887i	−1.55914	−	0.498967i
$721$			3.37873i			0.125830i
$722$	16.2436	+	21.4043i	0.604525	+	0.796586i
$723$	−6.31793			−0.234967
$724$	25.1746	−	21.9999i	0.935607	−	0.817619i
$725$	1.59457	−	4.35927i	0.0592208	−	0.161899i
$726$	38.1557	+	17.3283i	1.41609	+	0.643114i
$727$	10.7341			0.398106			0.199053	−	0.979989i	$-0.436213\pi$
$727$	10.7341			0.398106			0.199053	+	0.979989i	$0.436213\pi$
$728$	−35.7479	+	10.7418i	−1.32491	+	0.398119i
$729$	43.4629			1.60974
$730$	18.1722	−	26.4694i	0.672584	−	0.979678i
$731$			20.6023i			0.762004i
$732$	−24.4116	+	21.3331i	−0.902279	+	0.788494i
$733$			39.1519i			1.44611i	0.690792	+	0.723053i	$0.257262\pi$
$733$			39.1519i			1.44611i	−0.690792	+	0.723053i	$0.742738\pi$
$734$	−0.573601	+	1.26303i	−0.0211720	+	0.0466193i
$735$	62.3186	+	11.0400i	2.29866	+	0.407216i
$736$	30.7172	+	19.2877i	1.13225	+	0.710954i
$737$	3.49598			0.128776
$738$	30.9480	+	14.0549i	1.13921	+	0.517370i
$739$		−	10.7025i		−	0.393697i	−0.980434	−	0.196849i	$-0.936929\pi$
$739$		−	10.7025i		−	0.393697i	0.980434	−	0.196849i	$-0.0630707\pi$
$740$	−25.3971	+	15.3229i	−0.933618	+	0.563283i
$741$	−33.6414	+	20.0622i	−1.23585	+	0.737002i
$742$	−18.3696	+	40.4486i	−0.674370	+	1.48492i
$743$			30.9024i			1.13370i	0.823822	+	0.566849i	$0.191838\pi$
$743$			30.9024i			1.13370i	−0.823822	+	0.566849i	$0.808162\pi$
$744$	15.3108	+	50.9531i	0.561322	+	1.86803i
$745$	−0.606331	+	3.42262i	−0.0222142	+	0.125395i
$746$	−1.59839	+	3.51954i	−0.0585212	+	0.128860i
$747$	−47.8535			−1.75087
$748$	2.63195	+	3.01176i	0.0962338	+	0.110121i
$749$			45.9494i			1.67895i
$750$	−36.2338	+	25.7854i	−1.32307	+	0.941549i
$751$	−10.3152			−0.376408			−0.188204	−	0.982130i	$-0.560267\pi$
$751$	−10.3152			−0.376408			−0.188204	+	0.982130i	$0.560267\pi$
$752$	3.61333	−	26.7243i	0.131765	−	0.974536i
$753$	−24.7890			−0.903360
$754$	3.81909	+	1.73443i	0.139083	+	0.0631641i
$755$	−1.74166	+	9.83135i	−0.0633856	+	0.357799i
$756$	−33.4388	+	29.2219i	−1.21616	+	1.06279i
$757$		−	12.5915i		−	0.457645i	−0.973468	−	0.228823i	$-0.926512\pi$
$757$		−	12.5915i		−	0.457645i	0.973468	−	0.228823i	$-0.0734876\pi$
$758$	−2.86227	+	6.30252i	−0.103962	+	0.228918i
$759$	12.2946			0.446264
$760$	−21.8745	+	16.7781i	−0.793472	+	0.608606i
$761$	31.3117			1.13505			0.567523	−	0.823357i	$-0.307902\pi$
$761$	31.3117			1.13505			0.567523	+	0.823357i	$0.307902\pi$
$762$	26.7950	−	59.0008i	0.970681	−	2.13737i
$763$			13.3891i			0.484719i
$764$	−4.12775	+	3.60721i	−0.149337	+	0.130504i
$765$	31.7207	+	5.61945i	1.14686	+	0.203172i
$766$	−1.10208	−	0.500504i	−0.0398196	−	0.0180840i
$767$	−42.1627			−1.52241
$768$	11.9509	−	43.3869i	0.431242	−	1.56559i
$769$	0.105528			0.00380544			0.00190272	−	0.999998i	$-0.499394\pi$
$769$	0.105528			0.00380544			0.00190272	+	0.999998i	$0.499394\pi$
$770$	−5.04020	+	7.34150i	−0.181636	+	0.264569i
$771$		−	20.5327i		−	0.739469i
$772$	−6.47644	−	7.41103i	−0.233092	−	0.266729i
$773$	13.6012			0.489200			0.244600	−	0.969624i	$-0.421343\pi$
$773$	13.6012			0.489200			0.244600	+	0.969624i	$0.421343\pi$
$774$	20.1698	−	44.4124i	0.724988	−	1.59637i
$775$	31.4037	+	11.4871i	1.12805	+	0.412628i
$776$	40.8479	−	12.2743i	1.46636	−	0.440623i
$777$			77.0592i			2.76448i
$778$	0.900272	−	1.98234i	0.0322763	−	0.0710702i
$779$	18.3215	−	10.9261i	0.656437	−	0.391468i
$780$	−20.7603	−	34.4093i	−0.743337	−	1.23205i
$781$			5.07189i			0.181487i
$782$	−24.2195	−	10.9992i	−0.866088	−	0.393331i
$783$	4.99019			0.178335
$784$	−5.39326	+	39.8887i	−0.192616	+	1.42460i
$785$	−1.16163	−	0.205788i	−0.0414604	−	0.00734488i
$786$	−8.96039	+	19.7302i	−0.319607	+	0.703752i
$787$		−	38.3007i		−	1.36527i	−0.730758	−	0.682637i	$-0.760833\pi$
$787$		−	38.3007i		−	1.36527i	0.730758	−	0.682637i	$-0.239167\pi$
$788$	9.76816	−	8.53631i	0.347976	−	0.304093i
$789$		−	53.6205i		−	1.90894i
$790$	−12.8945	−	8.85254i	−0.458766	−	0.314959i
$791$	−6.42386			−0.228406
$792$	−2.72517	−	9.06915i	−0.0968348	−	0.322258i
$793$	−18.4123			−0.653841
$794$	−44.2486	−	20.0954i	−1.57033	−	0.713159i
$795$	−47.0949	−	8.34306i	−1.67029	−	0.295898i
$796$	6.97280	−	6.09347i	0.247144	−	0.215977i
$797$	35.6646			1.26330			0.631652	−	0.775252i	$-0.282377\pi$
$797$	35.6646			1.26330			0.631652	+	0.775252i	$0.282377\pi$
$798$	7.96459	+	71.1763i	0.281943	+	2.51961i
$799$			19.7774i			0.699673i
$800$	−17.3290	−	22.3541i	−0.612672	−	0.790337i
$801$			37.5838i			1.32796i
$802$	−32.3821	−	14.7062i	−1.14345	−	0.519296i
$803$	6.92171			0.244262
$804$	18.9824	+	21.7217i	0.669458	+	0.766065i
$805$	10.3308	−	58.3153i	0.364113	−	2.05534i
$806$	−12.4946	+	27.5122i	−0.440103	+	0.969077i
$807$	53.3357			1.87751
$808$	−20.1818	+	6.06440i	−0.709994	+	0.213345i
$809$	−6.99766			−0.246024			−0.123012	−	0.992405i	$-0.539255\pi$
$809$	−6.99766			−0.246024			−0.123012	+	0.992405i	$0.539255\pi$
$810$	−1.00548	−	0.690300i	−0.0353291	−	0.0242547i
$811$	−7.46612			−0.262171			−0.131085	−	0.991371i	$-0.541846\pi$
$811$	−7.46612			−0.262171			−0.131085	+	0.991371i	$0.541846\pi$
$812$	5.77508	−	5.04680i	0.202666	−	0.177108i
$813$	−72.4490			−2.54090
$814$	−5.82222	−	2.64415i	−0.204069	−	0.0926772i
$815$	9.16976	−	51.7615i	0.321203	−	1.81313i
$816$	−4.42215	+	32.7064i	−0.154806	+	1.14495i
$817$	−15.6797	−	26.2926i	−0.548562	−	0.919862i
$818$	9.48694	+	4.30847i	0.331703	+	0.150642i
$819$	−64.8123			−2.26472
$820$	11.3063	+	18.7397i	0.394833	+	0.654418i
$821$	−45.6471			−1.59310			−0.796548	−	0.604576i	$-0.793343\pi$
$821$	−45.6471			−1.59310			−0.796548	+	0.604576i	$0.793343\pi$
$822$	34.7457	−	76.5077i	1.21190	−	2.66851i
$823$	17.1790			0.598821			0.299410	−	0.954124i	$-0.403210\pi$
$823$	17.1790			0.598821			0.299410	+	0.954124i	$0.403210\pi$
$824$	−0.665775	−	2.21564i	−0.0231934	−	0.0771856i
$825$	−9.00397	−	3.29354i	−0.313478	−	0.114666i
$826$	−31.8784	+	70.1941i	−1.10919	+	2.44236i
$827$			15.8191i			0.550084i	0.961432	+	0.275042i	$0.0886917\pi$
$827$			15.8191i			0.550084i	−0.961432	+	0.275042i	$0.911308\pi$
$828$	41.4417	+	47.4220i	1.44020	+	1.64803i
$829$			37.5577i			1.30443i	0.758033	+	0.652216i	$0.226160\pi$
$829$			37.5577i			1.30443i	−0.758033	+	0.652216i	$0.773840\pi$
$830$	−25.4026	−	17.4398i	−0.881739	−	0.605345i
$831$	−65.2932			−2.26499
$832$	21.3255	−	14.0882i	0.739328	−	0.488420i
$833$		−	29.5197i		−	1.02280i
$834$	−14.8941	+	32.7958i	−0.515742	+	1.13563i
$835$	31.8253	+	5.63798i	1.10136	+	0.195110i
$836$	−5.65103	−	1.84052i	−0.195445	−	0.0636556i
$837$			35.9487i			1.24257i
$838$	8.88627	+	4.03567i	0.306971	+	0.139410i
$839$	26.3813			0.910784			0.455392	−	0.890291i	$-0.349499\pi$
$839$	26.3813			0.910784			0.455392	+	0.890291i	$0.349499\pi$
$840$	−72.9824	+	8.54628i	−2.51813	+	0.294875i
$841$	28.1382			0.970282
$842$	−2.35710	−	1.07047i	−0.0812309	−	0.0368908i
$843$	−26.5886			−0.915760
$844$	18.9907	+	21.7312i	0.653688	+	0.748020i
$845$	−1.08939	+	6.14941i	−0.0374763	+	0.211546i
$846$	19.3621	−	42.6341i	0.665684	−	1.46579i
$847$	43.5182			1.49530
$848$	4.07575	−	30.1444i	0.139962	−	1.03516i
$849$		−	59.0870i		−	2.02786i
$850$	14.7907	+	14.5434i	0.507317	+	0.498834i
$851$	42.5265			1.45779
$852$	−31.5134	+	27.5393i	−1.07963	+	0.943480i
$853$		−	3.94363i		−	0.135027i	−0.997718	−	0.0675137i	$-0.978493\pi$
$853$		−	3.94363i		−	0.135027i	0.997718	−	0.0675137i	$-0.0215066\pi$
$854$	−13.9212	+	30.6536i	−0.476375	+	1.04894i
$855$	−44.7586	+	16.9699i	−1.53071	+	0.580359i
$856$	−9.05428	−	30.1319i	−0.309469	−	1.02989i
$857$	51.9532			1.77469			0.887344	−	0.461109i	$-0.152548\pi$
$857$	51.9532			1.77469			0.887344	+	0.461109i	$0.152548\pi$
$858$	3.58241	−	7.88823i	0.122302	−	0.269300i
$859$		−	16.6922i		−	0.569532i	−0.958597	−	0.284766i	$-0.908084\pi$
$859$		−	16.6922i		−	0.569532i	0.958597	−	0.284766i	$-0.0919159\pi$
$860$	26.8927	−	16.2253i	0.917033	−	0.553277i
$861$	56.8593			1.93776
$862$	8.24515	−	18.1553i	0.280831	−	0.618370i
$863$			21.9125i			0.745910i	0.927849	+	0.372955i	$0.121655\pi$
$863$			21.9125i			0.745910i	−0.927849	+	0.372955i	$0.878345\pi$
$864$	16.1698	−	25.7517i	0.550107	−	0.876091i
$865$	6.81795	−	38.4860i	0.231817	−	1.30856i
$866$	9.91198	−	21.8255i	0.336823	−	0.741660i
$867$			23.6110i			0.801871i
$868$	36.3565	+	41.6030i	1.23402	+	1.41210i
$869$		−	3.37189i		−	0.114384i
$870$	6.80732	+	4.67346i	0.230790	+	0.158445i
$871$			16.3835i			0.555133i
$872$	−2.63831	−	8.78009i	−0.0893446	−	0.297331i
$873$	74.0588			2.50651
$874$	39.2799	−	4.39541i	1.32866	−	0.148677i
$875$	−23.1876	+	39.9399i	−0.783885	+	1.35022i
$876$	37.5834	+	43.0069i	1.26982	+	1.45307i
$877$	10.8819			0.367455			0.183728	−	0.982977i	$-0.441184\pi$
$877$	10.8819			0.367455			0.183728	+	0.982977i	$0.441184\pi$
$878$	14.3437	−	31.5838i	0.484077	−	1.06590i
$879$			92.0799i			3.10578i
$880$	1.85854	−	5.80745i	0.0626514	−	0.195769i
$881$	3.53485			0.119092			0.0595460	−	0.998226i	$-0.481035\pi$
$881$	3.53485			0.119092			0.0595460	+	0.998226i	$0.481035\pi$
$882$	−28.8999	+	63.6356i	−0.973111	+	2.14272i
$883$	−6.96126			−0.234265			−0.117132	−	0.993116i	$-0.537370\pi$
$883$	−6.96126			−0.234265			−0.117132	+	0.993116i	$0.537370\pi$
$884$	−14.1143	+	12.3343i	−0.474714	+	0.414848i
$885$	−81.7280	−	14.4785i	−2.74726	−	0.486688i
$886$	3.72094	−	8.19325i	0.125007	−	0.275258i
$887$		−	12.1852i		−	0.409138i	−0.978852	−	0.204569i	$-0.934421\pi$
$887$		−	12.1852i		−	0.409138i	0.978852	−	0.204569i	$-0.0655792\pi$
$888$	−15.1844	−	50.5325i	−0.509556	−	1.69576i
$889$		−	67.2929i		−	2.25693i
$890$	−13.6971	+	19.9511i	−0.459128	+	0.668761i
$891$		−	0.262932i		−	0.00880855i
$892$	−28.1021	+	24.5582i	−0.940927	+	0.822268i
$893$	−15.0518	−	25.2398i	−0.503690	−	0.844618i
$894$	−5.62988	−	2.55679i	−0.188291	−	0.0855119i
$895$	1.54626	−	8.72836i	0.0516859	−	0.291757i
$896$	−7.33075	−	46.1553i	−0.244903	−	1.54194i
$897$			57.6170i			1.92377i
$898$	−31.9443	−	14.5074i	−1.06600	−	0.484119i
$899$		−	6.20856i		−	0.207067i
$900$	−17.6463	−	45.8313i	−0.588209	−	1.52771i
$901$			22.3084i			0.743201i
$902$	−1.95102	+	4.29602i	−0.0649620	+	0.143042i
$903$		−	81.5969i		−	2.71538i
$904$	4.21253	−	1.26582i	0.140107	−	0.0421004i
$905$	36.8060	+	6.52033i	1.22347	+	0.216743i
$906$	−16.1716	−	7.34429i	−0.537266	−	0.243998i
$907$		−	31.9261i		−	1.06009i	−0.847970	−	0.530044i	$-0.822175\pi$
$907$		−	31.9261i		−	1.06009i	0.847970	−	0.530044i	$-0.177825\pi$
$908$	3.77861	−	3.30209i	0.125397	−	0.109584i
$909$	−36.5903			−1.21363
$910$	−34.4051	−	23.6203i	−1.14052	−	0.783005i
$911$	−35.0406			−1.16095			−0.580473	−	0.814280i	$-0.697132\pi$
$911$	−35.0406			−1.16095			−0.580473	+	0.814280i	$0.697132\pi$
$912$	−19.2481	−	45.1053i	−0.637368	−	1.49359i
$913$		−	6.64274i		−	0.219843i
$914$	7.85647	+	3.56799i	0.259869	+	0.118019i
$915$	−35.6904	−	6.32271i	−1.17989	−	0.209022i
$916$	19.5664	+	22.3899i	0.646491	+	0.739784i
$917$			22.5031i			0.743117i
$918$	−9.22116	+	20.3044i	−0.304344	+	0.670143i
$919$		−	31.1838i		−	1.02866i	−0.857592	−	0.514330i	$-0.828041\pi$
$919$		−	31.1838i		−	1.02866i	0.857592	−	0.514330i	$-0.171959\pi$
$920$	4.71642	+	40.2767i	0.155496	+	1.32788i
$921$	69.5105			2.29045
$922$	2.85771	−	6.29248i	0.0941137	−	0.207232i
$923$	−23.7688			−0.782360
$924$	−10.4240	−	11.9283i	−0.342926	−	0.392412i
$925$	−31.1444	−	11.3923i	−1.02402	−	0.374575i
$926$	0.467015	−	1.02833i	0.0153471	−	0.0337931i
$927$		−	4.01704i		−	0.131937i
$928$	−2.79262	+	4.44748i	−0.0916722	+	0.145996i
$929$	2.93575			0.0963188			0.0481594	−	0.998840i	$-0.484664\pi$
$929$	2.93575			0.0963188			0.0481594	+	0.998840i	$0.484664\pi$
$930$	−33.6671	+	49.0391i	−1.10399	+	1.60805i
$931$	22.4663	+	37.6729i	0.736305	+	1.23468i
$932$	−5.69916	+	4.98044i	−0.186682	+	0.163140i
$933$	−51.6654			−1.69145
$934$	−5.16929	+	11.3824i	−0.169144	+	0.372444i
$935$	−0.780059	+	4.40328i	−0.0255106	+	0.144003i
$936$	42.5015	−	12.7712i	1.38920	−	0.417439i
$937$			36.6167i			1.19622i	0.801416	+	0.598108i	$0.204081\pi$
$937$			36.6167i			1.19622i	−0.801416	+	0.598108i	$0.795919\pi$
$938$	27.2759	+	12.3873i	0.890589	+	0.404458i
$939$	36.7358			1.19883
$940$	25.8159	−	15.5756i	0.842021	−	0.508019i
$941$			34.9115i			1.13808i	0.822309	+	0.569041i	$0.192685\pi$
$941$			34.9115i			1.13808i	−0.822309	+	0.569041i	$0.807315\pi$
$942$	0.867771	−	1.91077i	0.0282735	−	0.0622563i
$943$		−	31.3789i		−	1.02184i
$944$	7.07301	−	52.3123i	0.230207	−	1.70262i
$945$	−48.8885	−	8.66079i	−1.59034	−	0.281735i
$946$	6.16507	+	2.79985i	0.200444	+	0.0910310i
$947$	−43.7796			−1.42264			−0.711322	−	0.702866i	$-0.751903\pi$
$947$	−43.7796			−1.42264			−0.711322	+	0.702866i	$0.751903\pi$
$948$	20.9507	−	18.3086i	0.680446	−	0.594636i
$949$			32.4377i			1.05297i
$950$	−29.9443	−	7.30355i	−0.971520	−	0.236958i
$951$		−	15.9540i		−	0.517345i
$952$	9.86314	+	32.8237i	0.319666	+	1.06382i
$953$	−34.1942			−1.10766			−0.553830	−	0.832630i	$-0.686834\pi$
$953$	−34.1942			−1.10766			−0.553830	+	0.832630i	$0.686834\pi$
$954$	21.8400	−	48.0902i	0.707097	−	1.55698i
$955$	−6.03489	−	1.06910i	−0.195284	−	0.0345954i
$956$	−34.6654	+	30.2938i	−1.12116	+	0.979772i
$957$			1.78010i			0.0575425i
$958$	−12.4834	−	5.66932i	−0.403322	−	0.183167i
$959$		−	87.2603i		−	2.81778i
$960$	46.1751	−	19.9854i	1.49029	−	0.645027i
$961$	13.7257			0.442765
$962$	12.3915	−	27.2851i	0.399517	−	0.879708i
$963$		−	54.6302i		−	1.76043i
$964$	3.38279	−	2.95620i	0.108952	−	0.0952127i
$965$	1.91949	−	10.8351i	0.0617905	−	0.348795i
$966$	95.9230	+	43.5631i	3.08627	+	1.40162i
$967$	17.9312			0.576627			0.288314	−	0.957536i	$-0.406905\pi$
$967$	17.9312			0.576627			0.288314	+	0.957536i	$0.406905\pi$
$968$	−28.5376	+	8.57522i	−0.917234	+	0.275618i
$969$	18.4211	+	30.8896i	0.591770	+	0.992316i
$970$	39.3135	+	26.9901i	1.26228	+	0.866600i
$971$	−33.5761			−1.07751			−0.538754	−	0.842463i	$-0.681105\pi$
$971$	−33.5761			−1.07751			−0.538754	+	0.842463i	$0.681105\pi$
$972$	−22.6517	+	19.7951i	−0.726554	+	0.634930i
$973$			37.4050i			1.19915i
$974$	−16.2795	−	7.39329i	−0.521629	−	0.236896i
$975$	15.4348	−	42.1960i	0.494308	−	1.35135i
$976$	3.08877	−	22.8446i	0.0988691	−	0.731239i
$977$	44.2614			1.41605			0.708024	−	0.706189i	$-0.249587\pi$
$977$	44.2614			1.41605			0.708024	+	0.706189i	$0.249587\pi$
$978$	85.1427	+	38.6673i	2.72256	+	1.23644i
$979$	−5.21717			−0.166741
$980$	−38.5328	+	23.2481i	−1.23088	+	0.742633i
$981$		−	15.9186i		−	0.508242i
$982$	4.32660	+	1.96491i	0.138067	+	0.0627029i
$983$			44.5179i			1.41990i	0.704252	+	0.709950i	$0.251282\pi$
$983$			44.5179i			1.41990i	−0.704252	+	0.709950i	$0.748718\pi$
$984$	−37.2862	+	11.2041i	−1.18864	+	0.357173i
$985$	14.2813	+	2.52999i	0.455041	+	0.0806123i
$986$	1.59255	−	3.50668i	0.0507171	−	0.111676i
$987$		−	78.3296i		−	2.49326i
$988$	8.62536	−	26.4828i	0.274409	−	0.842532i
$989$	−45.0308			−1.43189
$990$	5.99240	−	8.72847i	0.190451	−	0.277409i
$991$	35.8187			1.13782			0.568910	−	0.822400i	$-0.307365\pi$
$991$	35.8187			1.13782			0.568910	+	0.822400i	$0.307365\pi$
$992$	−32.0391	−	20.1177i	−1.01724	−	0.638737i
$993$		−	10.6483i		−	0.337913i
$994$	−17.9712	+	39.5713i	−0.570011	+	1.25512i
$995$	10.1944	+	1.80598i	0.323185	+	0.0572535i
$996$	41.2736	−	36.0686i	1.30780	−	1.14288i
$997$		−	34.3781i		−	1.08876i	−0.838837	−	0.544382i	$-0.816764\pi$
$997$		−	34.3781i		−	1.08876i	0.838837	−	0.544382i	$-0.183236\pi$
$998$	−3.37074	−	1.53081i	−0.106699	−	0.0484570i
$999$		−	35.6520i		−	1.12798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.d.b.379.25	yes	40
4.3	odd	2	inner	380.2.d.b.379.27	yes	40
5.4	even	2	inner	380.2.d.b.379.16	yes	40
19.18	odd	2	inner	380.2.d.b.379.15	yes	40
20.19	odd	2	inner	380.2.d.b.379.14	yes	40
76.75	even	2	inner	380.2.d.b.379.13	✓	40
95.94	odd	2	inner	380.2.d.b.379.26	yes	40
380.379	even	2	inner	380.2.d.b.379.28	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.d.b.379.13	✓	40	76.75	even	2	inner
380.2.d.b.379.14	yes	40	20.19	odd	2	inner
380.2.d.b.379.15	yes	40	19.18	odd	2	inner
380.2.d.b.379.16	yes	40	5.4	even	2	inner
380.2.d.b.379.25	yes	40	1.1	even	1	trivial
380.2.d.b.379.26	yes	40	95.94	odd	2	inner
380.2.d.b.379.27	yes	40	4.3	odd	2	inner
380.2.d.b.379.28	yes	40	380.379	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.584780 - 1.28765i) q^{2} +2.81267i q^{3} +(-1.31606 - 1.50598i) q^{4} +(0.390055 - 2.20178i) q^{5} +(3.62172 + 1.64479i) q^{6} +4.13073 q^{7} +(-2.70878 + 0.813956i) q^{8} -4.91111 q^{9} +O(q^{10})\)	\(q+(0.584780 - 1.28765i) q^{2} +2.81267i q^{3} +(-1.31606 - 1.50598i) q^{4} +(0.390055 - 2.20178i) q^{5} +(3.62172 + 1.64479i) q^{6} +4.13073 q^{7} +(-2.70878 + 0.813956i) q^{8} -4.91111 q^{9} +(-2.60702 - 1.78981i) q^{10} -0.681732i q^{11} +(4.23583 - 3.70165i) q^{12} +3.19485 q^{13} +(2.41557 - 5.31892i) q^{14} +(6.19289 + 1.09710i) q^{15} +(-0.535953 + 3.96393i) q^{16} -2.93351i q^{17} +(-2.87192 + 6.32377i) q^{18} +(2.23259 + 3.74374i) q^{19} +(-3.82918 + 2.31027i) q^{20} +11.6184i q^{21} +(-0.877829 - 0.398663i) q^{22} +6.41181 q^{23} +(-2.28939 - 7.61890i) q^{24} +(-4.69571 - 1.71763i) q^{25} +(1.86829 - 4.11384i) q^{26} -5.37533i q^{27} +(-5.43630 - 6.22080i) q^{28} +0.928351i q^{29} +(5.03415 - 7.33269i) q^{30} -6.68773 q^{31} +(4.79072 + 3.00815i) q^{32} +1.91749 q^{33} +(-3.77732 - 1.71546i) q^{34} +(1.61121 - 9.09498i) q^{35} +(6.46334 + 7.39604i) q^{36} +6.63253 q^{37} +(6.12618 - 0.685517i) q^{38} +8.98606i q^{39} +(0.735583 + 6.28163i) q^{40} -4.89391i q^{41} +(14.9604 + 6.79420i) q^{42} -7.02309 q^{43} +(-1.02667 + 0.897202i) q^{44} +(-1.91560 + 10.8132i) q^{45} +(3.74950 - 8.25615i) q^{46} -6.74187 q^{47} +(-11.1492 - 1.50746i) q^{48} +10.0629 q^{49} +(-4.95767 + 5.04198i) q^{50} +8.25100 q^{51} +(-4.20463 - 4.81138i) q^{52} -7.60467 q^{53} +(-6.92152 - 3.14339i) q^{54} +(-1.50103 - 0.265913i) q^{55} +(-11.1892 + 3.36223i) q^{56} +(-10.5299 + 6.27953i) q^{57} +(1.19539 + 0.542882i) q^{58} -13.1971 q^{59} +(-6.49804 - 10.7702i) q^{60} -5.76313 q^{61} +(-3.91085 + 8.61143i) q^{62} -20.2865 q^{63} +(6.67495 - 4.40965i) q^{64} +(1.24617 - 7.03438i) q^{65} +(1.12131 - 2.46904i) q^{66} +5.12809i q^{67} +(-4.41781 + 3.86069i) q^{68} +18.0343i q^{69} +(-10.7689 - 7.39324i) q^{70} -7.43972 q^{71} +(13.3031 - 3.99743i) q^{72} +10.1531i q^{73} +(3.87857 - 8.54034i) q^{74} +(4.83114 - 13.2075i) q^{75} +(2.69977 - 8.28923i) q^{76} -2.81605i q^{77} +(11.5709 + 5.25487i) q^{78} +4.94607 q^{79} +(8.51867 + 2.72621i) q^{80} +0.385683 q^{81} +(-6.30163 - 2.86187i) q^{82} +9.74393 q^{83} +(17.4970 - 15.2905i) q^{84} +(-6.45896 - 1.14423i) q^{85} +(-4.10697 + 9.04326i) q^{86} -2.61115 q^{87} +(0.554899 + 1.84666i) q^{88} -7.65281i q^{89} +(12.8034 + 8.78997i) q^{90} +13.1971 q^{91} +(-8.43836 - 9.65607i) q^{92} -18.8104i q^{93} +(-3.94252 + 8.68115i) q^{94} +(9.11373 - 3.45541i) q^{95} +(-8.46093 + 13.4747i) q^{96} -15.0798 q^{97} +(5.88460 - 12.9575i) q^{98} +3.34806i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{5} + 8 q^{6} - 8 q^{9}+O(q^{10}) \) 40 * q - 4 * q^5 + 8 * q^6 - 8 * q^9	\( 40 q - 4 q^{5} + 8 q^{6} - 8 q^{9} - 8 q^{16} - 20 q^{20} - 40 q^{24} - 84 q^{25} - 24 q^{26} + 24 q^{30} + 24 q^{36} - 40 q^{44} - 12 q^{45} + 128 q^{49} - 120 q^{54} + 24 q^{61} + 72 q^{64} + 112 q^{66} + 32 q^{74} + 56 q^{76} + 96 q^{80} - 72 q^{81} + 44 q^{85} - 40 q^{96}+O(q^{100}) \) 40 * q - 4 * q^5 + 8 * q^6 - 8 * q^9 - 8 * q^16 - 20 * q^20 - 40 * q^24 - 84 * q^25 - 24 * q^26 + 24 * q^30 + 24 * q^36 - 40 * q^44 - 12 * q^45 + 128 * q^49 - 120 * q^54 + 24 * q^61 + 72 * q^64 + 112 * q^66 + 32 * q^74 + 56 * q^76 + 96 * q^80 - 72 * q^81 + 44 * q^85 - 40 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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