LMFDB - Embedded newform 819.2.j.h.352.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(235,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("819.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.j (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 8x^{8} + 7x^{7} + 41x^{6} + 18x^{5} + 58x^{4} + 28x^{3} + 64x^{2} + 16x + 4 $ x^10 - x^9 + 8x^8 + 7x^7 + 41x^6 + 18x^5 + 58x^4 + 28x^3 + 64x^2 + 16x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			352.5
Root			$-0.862625 + 1.49411i$ of defining polynomial
Character	$\chi$	$=$	819.352
Dual form			819.2.j.h.235.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36263 - 2.36014i) q^{2} +(-2.71349 - 4.69991i) q^{4} +(1.09358 - 1.89414i) q^{5} +(-2.19729 + 1.47375i) q^{7} -9.33940 q^{8} +O(q^{10})$	\(q+(1.36263 - 2.36014i) q^{2} +(-2.71349 - 4.69991i) q^{4} +(1.09358 - 1.89414i) q^{5} +(-2.19729 + 1.47375i) q^{7} -9.33940 q^{8} +(-2.98028 - 5.16200i) q^{10} +(-0.524077 - 0.907729i) q^{11} +1.00000 q^{13} +(0.484172 + 7.19406i) q^{14} +(-7.29912 + 12.6424i) q^{16} +(-2.64562 - 4.58236i) q^{17} +(-0.378453 + 0.655500i) q^{19} -11.8697 q^{20} -2.85648 q^{22} +(0.326792 - 0.566020i) q^{23} +(0.108157 + 0.187333i) q^{25} +(1.36263 - 2.36014i) q^{26} +(12.8888 + 6.32803i) q^{28} +3.10408 q^{29} +(-0.513956 - 0.890198i) q^{31} +(10.5525 + 18.2775i) q^{32} -14.4200 q^{34} +(0.388575 + 5.77363i) q^{35} +(5.44661 - 9.43381i) q^{37} +(1.03138 + 1.78640i) q^{38} +(-10.2134 + 17.6901i) q^{40} -7.32040 q^{41} +0.887771 q^{43} +(-2.84416 + 4.92623i) q^{44} +(-0.890590 - 1.54255i) q^{46} +(1.16875 - 2.02434i) q^{47} +(2.65613 - 6.47650i) q^{49} +0.589510 q^{50} +(-2.71349 - 4.69991i) q^{52} +(2.44407 + 4.23325i) q^{53} -2.29249 q^{55} +(20.5213 - 13.7639i) q^{56} +(4.22970 - 7.32606i) q^{58} +(-0.524077 - 0.907729i) q^{59} +(6.24989 - 10.8251i) q^{61} -2.80132 q^{62} +28.3200 q^{64} +(1.09358 - 1.89414i) q^{65} +(-2.23944 - 3.87883i) q^{67} +(-14.3578 + 24.8684i) q^{68} +(14.1560 + 6.95021i) q^{70} +6.60274 q^{71} +(4.14174 + 7.17370i) q^{73} +(-14.8434 - 25.7095i) q^{74} +4.10772 q^{76} +(2.48931 + 1.22218i) q^{77} +(-1.07007 + 1.85342i) q^{79} +(15.9644 + 27.6511i) q^{80} +(-9.97496 + 17.2771i) q^{82} +6.66558 q^{83} -11.5728 q^{85} +(1.20970 - 2.09526i) q^{86} +(4.89457 + 8.47765i) q^{88} +(-2.88388 + 4.99503i) q^{89} +(-2.19729 + 1.47375i) q^{91} -3.54699 q^{92} +(-3.18515 - 5.51684i) q^{94} +(0.827739 + 1.43369i) q^{95} -2.88777 q^{97} +(-11.6661 - 15.0939i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} - 8 q^{4} + 2 q^{5} + q^{7} - 18 q^{8}+O(q^{10}) $ 10 * q + 4 * q^2 - 8 * q^4 + 2 * q^5 + q^7 - 18 * q^8	$ 10 q + 4 q^{2} - 8 q^{4} + 2 q^{5} + q^{7} - 18 q^{8} + 5 q^{10} + 11 q^{11} + 10 q^{13} - 10 q^{14} - 10 q^{16} - 5 q^{17} - 9 q^{19} - 2 q^{20} + 16 q^{22} + 10 q^{23} - 9 q^{25} + 4 q^{26} + 37 q^{28} + 6 q^{29} + 6 q^{31} + 22 q^{32} - 44 q^{34} + 4 q^{35} - 4 q^{37} - 10 q^{38} - 28 q^{40} - 28 q^{41} + 4 q^{43} - 3 q^{46} + q^{47} - 11 q^{49} - 18 q^{50} - 8 q^{52} + 17 q^{53} + 21 q^{56} + 27 q^{58} + 11 q^{59} + 11 q^{61} + 46 q^{62} + 18 q^{64} + 2 q^{65} - 13 q^{67} - 32 q^{68} + 49 q^{70} - 30 q^{71} - 33 q^{74} + 16 q^{76} + 46 q^{77} - 2 q^{79} + 55 q^{80} - 34 q^{82} - 12 q^{83} - 44 q^{85} + 28 q^{86} + 3 q^{88} - 4 q^{89} + q^{91} - 42 q^{92} - 20 q^{94} - 12 q^{95} - 24 q^{97} + 7 q^{98}+O(q^{100}) $ 10 * q + 4 * q^2 - 8 * q^4 + 2 * q^5 + q^7 - 18 * q^8 + 5 * q^10 + 11 * q^11 + 10 * q^13 - 10 * q^14 - 10 * q^16 - 5 * q^17 - 9 * q^19 - 2 * q^20 + 16 * q^22 + 10 * q^23 - 9 * q^25 + 4 * q^26 + 37 * q^28 + 6 * q^29 + 6 * q^31 + 22 * q^32 - 44 * q^34 + 4 * q^35 - 4 * q^37 - 10 * q^38 - 28 * q^40 - 28 * q^41 + 4 * q^43 - 3 * q^46 + q^47 - 11 * q^49 - 18 * q^50 - 8 * q^52 + 17 * q^53 + 21 * q^56 + 27 * q^58 + 11 * q^59 + 11 * q^61 + 46 * q^62 + 18 * q^64 + 2 * q^65 - 13 * q^67 - 32 * q^68 + 49 * q^70 - 30 * q^71 - 33 * q^74 + 16 * q^76 + 46 * q^77 - 2 * q^79 + 55 * q^80 - 34 * q^82 - 12 * q^83 - 44 * q^85 + 28 * q^86 + 3 * q^88 - 4 * q^89 + q^91 - 42 * q^92 - 20 * q^94 - 12 * q^95 - 24 * q^97 + 7 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.36263	−	2.36014i	0.963521	−	1.66887i	0.249986	−	0.968250i	$-0.419574\pi$
$2$	1.36263	−	2.36014i	0.963521	−	1.66887i	0.713536	−	0.700619i	$-0.247093\pi$
$3$		0			0
$3$		0			0
$4$	−2.71349	−	4.69991i	−1.35675	−	2.34996i
$5$	1.09358	−	1.89414i	0.489065	−	0.847085i	−0.510856	−	0.859666i	$-0.670672\pi$
$5$	1.09358	−	1.89414i	0.489065	−	0.847085i	0.999921	+	0.0125813i	$0.00400485\pi$
$6$		0			0
$7$	−2.19729	+	1.47375i	−0.830496	+	0.557025i
$7$	−2.19729	+	1.47375i	−0.830496	+	0.557025i
$8$	−9.33940			−3.30198
$9$		0			0
$10$	−2.98028	−	5.16200i	−0.942449	−	1.63237i
$11$	−0.524077	−	0.907729i	−0.158015	−	0.273691i	0.776138	−	0.630564i	$-0.217176\pi$
$11$	−0.524077	−	0.907729i	−0.158015	−	0.273691i	−0.934153	+	0.356873i	$0.883843\pi$
$12$		0			0
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	0.484172	+	7.19406i	0.129400	+	1.92269i
$15$		0			0
$16$	−7.29912	+	12.6424i	−1.82478	+	3.16061i
$17$	−2.64562	−	4.58236i	−0.641658	−	1.11138i	−0.985063	−	0.172197i	$-0.944913\pi$
$17$	−2.64562	−	4.58236i	−0.641658	−	1.11138i	0.343404	−	0.939188i	$-0.388420\pi$
$18$		0			0
$19$	−0.378453	+	0.655500i	−0.0868231	+	0.150382i	−0.906167	−	0.422921i	$-0.861005\pi$
$19$	−0.378453	+	0.655500i	−0.0868231	+	0.150382i	0.819344	+	0.573303i	$0.194338\pi$
$20$	−11.8697			−2.65415
$21$		0			0
$22$	−2.85648			−0.609005
$23$	0.326792	−	0.566020i	0.0681408	−	0.118023i	−0.829942	−	0.557850i	$-0.811627\pi$
$23$	0.326792	−	0.566020i	0.0681408	−	0.118023i	0.898083	+	0.439826i	$0.144960\pi$
$24$		0			0
$25$	0.108157	+	0.187333i	0.0216314	+	0.0374667i
$26$	1.36263	−	2.36014i	0.267233	−	0.462861i
$27$		0			0
$28$	12.8888	+	6.32803i	2.43576	+	1.19589i
$29$	3.10408			0.576414			0.288207	−	0.957568i	$-0.406941\pi$
$29$	3.10408			0.576414			0.288207	+	0.957568i	$0.406941\pi$
$30$		0			0
$31$	−0.513956	−	0.890198i	−0.0923092	−	0.159884i	0.816173	−	0.577807i	$-0.196091\pi$
$31$	−0.513956	−	0.890198i	−0.0923092	−	0.159884i	−0.908482	+	0.417923i	$0.862758\pi$
$32$	10.5525	+	18.2775i	1.86544	+	3.23104i
$33$		0			0
$34$	−14.4200			−2.47301
$35$	0.388575	+	5.77363i	0.0656811	+	0.975922i
$36$		0			0
$37$	5.44661	−	9.43381i	0.895418	−	1.55091i	0.0621309	−	0.998068i	$-0.480210\pi$
$37$	5.44661	−	9.43381i	0.895418	−	1.55091i	0.833287	−	0.552841i	$-0.186456\pi$
$38$	1.03138	+	1.78640i	0.167312	+	0.289793i
$39$		0			0
$40$	−10.2134	+	17.6901i	−1.61488	+	2.79706i
$41$	−7.32040			−1.14325			−0.571627	−	0.820514i	$-0.693688\pi$
$41$	−7.32040			−1.14325			−0.571627	+	0.820514i	$0.693688\pi$
$42$		0			0
$43$	0.887771			0.135384			0.0676919	−	0.997706i	$-0.478437\pi$
$43$	0.887771			0.135384			0.0676919	+	0.997706i	$0.478437\pi$
$44$	−2.84416	+	4.92623i	−0.428774	+	0.742658i
$45$		0			0
$46$	−0.890590	−	1.54255i	−0.131310	−	0.227436i
$47$	1.16875	−	2.02434i	0.170480	−	0.295281i	−0.768108	−	0.640321i	$-0.778801\pi$
$47$	1.16875	−	2.02434i	0.170480	−	0.295281i	0.938588	+	0.345040i	$0.112135\pi$
$48$		0			0
$49$	2.65613	−	6.47650i	0.379447	−	0.925214i
$50$	0.589510			0.0833692
$51$		0			0
$52$	−2.71349	−	4.69991i	−0.376294	−	0.651760i
$53$	2.44407	+	4.23325i	0.335719	+	0.581482i	0.983623	−	0.180240i	$-0.0576875\pi$
$53$	2.44407	+	4.23325i	0.335719	+	0.581482i	−0.647904	+	0.761722i	$0.724354\pi$
$54$		0			0
$55$	−2.29249			−0.309119
$56$	20.5213	−	13.7639i	2.74228	−	1.83928i
$57$		0			0
$58$	4.22970	−	7.32606i	0.555387	−	0.961959i
$59$	−0.524077	−	0.907729i	−0.0682291	−	0.118176i	0.829893	−	0.557923i	$-0.188402\pi$
$59$	−0.524077	−	0.907729i	−0.0682291	−	0.118176i	−0.898122	+	0.439747i	$0.855068\pi$
$60$		0			0
$61$	6.24989	−	10.8251i	0.800217	−	1.38602i	−0.119256	−	0.992864i	$-0.538051\pi$
$61$	6.24989	−	10.8251i	0.800217	−	1.38602i	0.919473	−	0.393153i	$-0.128616\pi$
$62$	−2.80132			−0.355768
$63$		0			0
$64$	28.3200			3.54000
$65$	1.09358	−	1.89414i	0.135642	−	0.234939i
$66$		0			0
$67$	−2.23944	−	3.87883i	−0.273592	−	0.473875i	0.696187	−	0.717860i	$-0.254878\pi$
$67$	−2.23944	−	3.87883i	−0.273592	−	0.473875i	−0.969779	+	0.243986i	$0.921545\pi$
$68$	−14.3578	+	24.8684i	−1.74114	+	3.01574i
$69$		0			0
$70$	14.1560	+	6.95021i	1.69197	+	0.830708i
$71$	6.60274			0.783601			0.391801	−	0.920050i	$-0.371852\pi$
$71$	6.60274			0.783601			0.391801	+	0.920050i	$0.371852\pi$
$72$		0			0
$73$	4.14174	+	7.17370i	0.484754	+	0.839618i	0.999847	−	0.0175164i	$-0.00557593\pi$
$73$	4.14174	+	7.17370i	0.484754	+	0.839618i	−0.515093	+	0.857134i	$0.672243\pi$
$74$	−14.8434	−	25.7095i	−1.72551	−	2.98867i
$75$		0			0
$76$	4.10772			0.471188
$77$	2.48931	+	1.22218i	0.283683	+	0.139280i
$78$		0			0
$79$	−1.07007	+	1.85342i	−0.120392	+	0.208526i	−0.919922	−	0.392100i	$-0.871749\pi$
$79$	−1.07007	+	1.85342i	−0.120392	+	0.208526i	0.799530	+	0.600626i	$0.205082\pi$
$80$	15.9644	+	27.6511i	1.78487	+	3.09149i
$81$		0			0
$82$	−9.97496	+	17.2771i	−1.10155	+	1.90794i
$83$	6.66558			0.731642			0.365821	−	0.930685i	$-0.380788\pi$
$83$	6.66558			0.731642			0.365821	+	0.930685i	$0.380788\pi$
$84$		0			0
$85$	−11.5728			−1.25525
$86$	1.20970	−	2.09526i	0.130445	−	0.225938i
$87$		0			0
$88$	4.89457	+	8.47765i	0.521763	+	0.903720i
$89$	−2.88388	+	4.99503i	−0.305691	+	0.529472i	−0.977415	−	0.211329i	$-0.932221\pi$
$89$	−2.88388	+	4.99503i	−0.305691	+	0.529472i	0.671724	+	0.740802i	$0.265554\pi$
$90$		0			0
$91$	−2.19729	+	1.47375i	−0.230338	+	0.154491i
$92$	−3.54699			−0.369800
$93$		0			0
$94$	−3.18515	−	5.51684i	−0.328523	−	0.569019i
$95$	0.827739	+	1.43369i	0.0849242	+	0.147093i
$96$		0			0
$97$	−2.88777			−0.293209			−0.146604	−	0.989195i	$-0.546834\pi$
$97$	−2.88777			−0.293209			−0.146604	+	0.989195i	$0.546834\pi$
$98$	−11.6661	−	15.0939i	−1.17845	−	1.52471i
$99$		0			0
$100$	0.586967	−	1.01666i	0.0586967	−	0.101666i
$101$	−5.62716	−	9.74653i	−0.559924	−	0.969816i	−0.997502	−	0.0706359i	$-0.977497\pi$
$101$	−5.62716	−	9.74653i	−0.559924	−	0.969816i	0.437579	−	0.899180i	$-0.355836\pi$
$102$		0			0
$103$	−10.1167	+	17.5226i	−0.996828	+	1.72656i	−0.429487	+	0.903073i	$0.641306\pi$
$103$	−10.1167	+	17.5226i	−0.996828	+	1.72656i	−0.567341	+	0.823483i	$0.692028\pi$
$104$	−9.33940			−0.915804
$105$		0			0
$106$	13.3214			1.29389
$107$	4.52758	−	7.84201i	0.437698	−	0.758115i	−0.559813	−	0.828619i	$-0.689127\pi$
$107$	4.52758	−	7.84201i	0.437698	−	0.758115i	0.997512	+	0.0705034i	$0.0224606\pi$
$108$		0			0
$109$	−7.55070	−	13.0782i	−0.723226	−	1.25266i	−0.959700	−	0.281026i	$-0.909325\pi$
$109$	−7.55070	−	13.0782i	−0.723226	−	1.25266i	0.236474	−	0.971638i	$-0.424008\pi$
$110$	−3.12380	+	5.41058i	−0.297843	+	0.515879i
$111$		0			0
$112$	−2.59354	−	38.5361i	−0.245067	−	3.64132i
$113$	−3.10408			−0.292008			−0.146004	−	0.989284i	$-0.546641\pi$
$113$	−3.10408			−0.292008			−0.146004	+	0.989284i	$0.546641\pi$
$114$		0			0
$115$	−0.714748	−	1.23798i	−0.0666506	−	0.115442i
$116$	−8.42292	−	14.5889i	−0.782048	−	1.35455i
$117$		0			0
$118$	−2.85648			−0.262961
$119$	12.5664	+	6.16976i	1.15196	+	0.565581i
$120$		0			0
$121$	4.95069	−	8.57484i	0.450062	−	0.779531i
$122$	−17.0325	−	29.5012i	−1.54205	−	2.67091i
$123$		0			0
$124$	−2.78923	+	4.83109i	−0.250481	+	0.433845i
$125$	11.4089			1.02045
$126$		0			0
$127$	8.78914			0.779910			0.389955	−	0.920834i	$-0.372491\pi$
$127$	8.78914			0.779910			0.389955	+	0.920834i	$0.372491\pi$
$128$	17.4846	−	30.2841i	1.54543	−	2.67676i
$129$		0			0
$130$	−2.98028	−	5.16200i	−0.261388	−	0.452738i
$131$	−5.25723	+	9.10580i	−0.459327	+	0.795577i	−0.998925	−	0.0463451i	$-0.985243\pi$
$131$	−5.25723	+	9.10580i	−0.459327	+	0.795577i	0.539599	+	0.841922i	$0.318576\pi$
$132$		0			0
$133$	−0.134473	−	1.99807i	−0.0116603	−	0.173254i
$134$	−12.2061			−1.05445
$135$		0			0
$136$	24.7086	+	42.7965i	2.11874	+	3.66977i
$137$	4.36583	+	7.56183i	0.372998	+	0.646051i	0.990025	−	0.140891i	$-0.0449966\pi$
$137$	4.36583	+	7.56183i	0.372998	+	0.646051i	−0.617028	+	0.786942i	$0.711663\pi$
$138$		0			0
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$	26.0812	−	17.4930i	2.20426	−	1.47843i
$141$		0			0
$142$	8.99706	−	15.5834i	0.755016	−	1.30773i
$143$	−0.524077	−	0.907729i	−0.0438256	−	0.0759081i
$144$		0			0
$145$	3.39457	−	5.87957i	0.281904	−	0.488272i
$146$	22.5745			1.86828
$147$		0			0
$148$	−59.1174			−4.85942
$149$	7.69632	−	13.3304i	0.630507	−	1.09207i	−0.356941	−	0.934127i	$-0.616180\pi$
$149$	7.69632	−	13.3304i	0.630507	−	1.09207i	0.987448	−	0.157944i	$-0.0504864\pi$
$150$		0			0
$151$	6.83786	+	11.8435i	0.556457	+	0.963812i	0.997789	+	0.0664680i	$0.0211730\pi$
$151$	6.83786	+	11.8435i	0.556457	+	0.963812i	−0.441331	+	0.897344i	$0.645494\pi$
$152$	3.53453	−	6.12198i	0.286688	−	0.496558i
$153$		0			0
$154$	6.27651	−	4.20974i	0.505776	−	0.339231i
$155$	−2.24821			−0.180581
$156$		0			0
$157$	−1.69378	−	2.93371i	−0.135178	−	0.234136i	0.790487	−	0.612478i	$-0.209827\pi$
$157$	−1.69378	−	2.93371i	−0.135178	−	0.234136i	−0.925666	+	0.378343i	$0.876494\pi$
$158$	2.91621	+	5.05102i	0.232001	+	0.401838i
$159$		0			0
$160$	46.1602			3.64928
$161$	0.116117	+	1.72532i	0.00915128	+	0.135974i
$162$		0			0
$163$	6.90502	−	11.9598i	0.540843	−	0.936767i	−0.458013	−	0.888946i	$-0.651439\pi$
$163$	6.90502	−	11.9598i	0.540843	−	0.936767i	0.998856	−	0.0478219i	$-0.0152280\pi$
$164$	19.8639	+	34.4052i	1.55111	+	2.68660i
$165$		0			0
$166$	9.08268	−	15.7317i	0.704953	−	1.22101i
$167$	−16.3783			−1.26739			−0.633695	−	0.773583i	$-0.718462\pi$
$167$	−16.3783			−1.26739			−0.633695	+	0.773583i	$0.718462\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	−15.7694	+	27.3134i	−1.20946	+	2.09485i
$171$		0			0
$172$	−2.40896	−	4.17244i	−0.183682	−	0.318146i
$173$	2.06273	−	3.57275i	0.156826	−	0.271631i	−0.776896	−	0.629629i	$-0.783207\pi$
$173$	2.06273	−	3.57275i	0.156826	−	0.271631i	0.933723	+	0.357997i	$0.116540\pi$
$174$		0			0
$175$	−0.513734	−	0.252229i	−0.0388346	−	0.0190667i
$176$	15.3012			1.15337
$177$		0			0
$178$	7.85930	+	13.6127i	0.589080	+	1.02032i
$179$	7.20679	+	12.4825i	0.538661	+	0.932988i	0.998976	+	0.0452324i	$0.0144028\pi$
$179$	7.20679	+	12.4825i	0.538661	+	0.932988i	−0.460316	+	0.887755i	$0.652264\pi$
$180$		0			0
$181$	18.1014			1.34547			0.672733	−	0.739885i	$-0.265120\pi$
$181$	18.1014			1.34547			0.672733	+	0.739885i	$0.265120\pi$
$182$	0.484172	+	7.19406i	0.0358892	+	0.533259i
$183$		0			0
$184$	−3.05204	+	5.28629i	−0.225000	+	0.389711i
$185$	−11.9126	−	20.6333i	−0.875834	−	1.51699i
$186$		0			0
$187$	−2.77302	+	4.80302i	−0.202784	+	0.351232i
$188$	−12.6856			−0.925195
$189$		0			0
$190$	4.51159			0.327305
$191$	2.77068	−	4.79895i	0.200479	−	0.347240i	−0.748204	−	0.663469i	$-0.769083\pi$
$191$	2.77068	−	4.79895i	0.200479	−	0.347240i	0.948683	+	0.316229i	$0.102417\pi$
$192$		0			0
$193$	4.37044	+	7.56983i	0.314591	+	0.544888i	0.979351	−	0.202170i	$-0.0647992\pi$
$193$	4.37044	+	7.56983i	0.314591	+	0.544888i	−0.664759	+	0.747058i	$0.731466\pi$
$194$	−3.93495	+	6.81553i	−0.282513	+	0.489327i
$195$		0			0
$196$	−37.6463	+	5.09038i	−2.68902	+	0.363598i
$197$	5.46874			0.389632			0.194816	−	0.980840i	$-0.437589\pi$
$197$	5.46874			0.389632			0.194816	+	0.980840i	$0.437589\pi$
$198$		0			0
$199$	−9.76839	−	16.9193i	−0.692463	−	1.19938i	−0.971029	−	0.238963i	$-0.923192\pi$
$199$	−9.76839	−	16.9193i	−0.692463	−	1.19938i	0.278566	−	0.960417i	$-0.410141\pi$
$200$	−1.01012	−	1.74958i	−0.0714264	−	0.123714i
$201$		0			0
$202$	−30.6708			−2.15799
$203$	−6.82056	+	4.57464i	−0.478709	+	0.321077i
$204$		0			0
$205$	−8.00546	+	13.8659i	−0.559125	+	0.968433i
$206$	27.5705	+	47.7536i	1.92093	+	3.32715i
$207$		0			0
$208$	−7.29912	+	12.6424i	−0.506103	+	0.876596i
$209$	0.793355			0.0548775
$210$		0			0
$211$	16.6905			1.14902			0.574511	−	0.818497i	$-0.305192\pi$
$211$	16.6905			1.14902			0.574511	+	0.818497i	$0.305192\pi$
$212$	13.2639	−	22.9738i	0.910971	−	1.57785i
$213$		0			0
$214$	−12.3388	−	21.3714i	−0.843463	−	1.46092i
$215$	0.970850	−	1.68156i	0.0662114	−	0.114682i
$216$		0			0
$217$	2.44124	+	1.19858i	0.165722	+	0.0813647i
$218$	−41.1551			−2.78737
$219$		0			0
$220$	6.22065	+	10.7745i	0.419396	+	0.726415i
$221$	−2.64562	−	4.58236i	−0.177964	−	0.308243i
$222$		0			0
$223$	−5.34217			−0.357738			−0.178869	−	0.983873i	$-0.557244\pi$
$223$	−5.34217			−0.357738			−0.178869	+	0.983873i	$0.557244\pi$
$224$	−50.1233	−	24.6091i	−3.34901	−	1.64427i
$225$		0			0
$226$	−4.22970	+	7.32606i	−0.281356	+	0.487322i
$227$	10.0608	+	17.4258i	0.667757	+	1.15659i	0.978530	+	0.206104i	$0.0660786\pi$
$227$	10.0608	+	17.4258i	0.667757	+	1.15659i	−0.310774	+	0.950484i	$0.600588\pi$
$228$		0			0
$229$	−12.6249	+	21.8669i	−0.834275	+	1.44501i	0.0603445	+	0.998178i	$0.480780\pi$
$229$	−12.6249	+	21.8669i	−0.834275	+	1.44501i	−0.894619	+	0.446829i	$0.852553\pi$
$230$	−3.89573			−0.256877
$231$		0			0
$232$	−28.9903			−1.90331
$233$	−0.396678	+	0.687066i	−0.0259872	+	0.0450112i	−0.878727	−	0.477326i	$-0.841606\pi$
$233$	−0.396678	+	0.687066i	−0.0259872	+	0.0450112i	0.852739	+	0.522337i	$0.174940\pi$
$234$		0			0
$235$	−2.55626	−	4.42757i	−0.166752	−	0.288823i
$236$	−2.84416	+	4.92623i	−0.185139	+	0.320671i
$237$		0			0
$238$	31.6848	−	21.2514i	2.05382	−	1.37753i
$239$	−20.0488			−1.29685			−0.648425	−	0.761279i	$-0.724572\pi$
$239$	−20.0488			−1.29685			−0.648425	+	0.761279i	$0.724572\pi$
$240$		0			0
$241$	−6.90602	−	11.9616i	−0.444856	−	0.770513i	0.553186	−	0.833058i	$-0.313412\pi$
$241$	−6.90602	−	11.9616i	−0.444856	−	0.770513i	−0.998042	+	0.0625446i	$0.980078\pi$
$242$	−13.4919	−	23.3686i	−0.867289	−	1.50219i
$243$		0			0
$244$	−67.8362			−4.34277
$245$	−9.36269	−	12.1137i	−0.598161	−	0.773913i
$246$		0			0
$247$	−0.378453	+	0.655500i	−0.0240804	+	0.0417085i
$248$	4.80004	+	8.31392i	0.304803	+	0.527934i
$249$		0			0
$250$	15.5461	−	26.9266i	0.983222	−	1.70299i
$251$	26.1095			1.64802			0.824010	−	0.566576i	$-0.191732\pi$
$251$	26.1095			1.64802			0.824010	+	0.566576i	$0.191732\pi$
$252$		0			0
$253$	−0.685057			−0.0430692
$254$	11.9763	−	20.7436i	0.751460	−	1.30157i
$255$		0			0
$256$	−19.3298	−	33.4801i	−1.20811	−	2.09251i
$257$	5.30990	−	9.19701i	0.331222	−	0.573694i	−0.651530	−	0.758623i	$-0.725872\pi$
$257$	5.30990	−	9.19701i	0.331222	−	0.573694i	0.982752	+	0.184930i	$0.0592057\pi$
$258$		0			0
$259$	1.93531	+	28.7557i	0.120254	+	1.78679i
$260$	−11.8697			−0.736128
$261$		0			0
$262$	14.3273	+	24.8156i	0.885142	+	1.53311i
$263$	5.17888	+	8.97008i	0.319343	+	0.553119i	0.980351	−	0.197260i	$-0.0632044\pi$
$263$	5.17888	+	8.97008i	0.319343	+	0.553119i	−0.661008	+	0.750379i	$0.729871\pi$
$264$		0			0
$265$	10.6912			0.656753
$266$	−4.89894	−	2.40524i	−0.300374	−	0.147475i
$267$		0			0
$268$	−12.1534	+	21.0504i	−0.742389	+	1.28586i
$269$	5.98503	+	10.3664i	0.364914	+	0.632049i	0.988762	−	0.149496i	$-0.0477652\pi$
$269$	5.98503	+	10.3664i	0.364914	+	0.632049i	−0.623849	+	0.781545i	$0.714432\pi$
$270$		0			0
$271$	1.37845	−	2.38755i	0.0837351	−	0.145033i	−0.821116	−	0.570761i	$-0.806648\pi$
$271$	1.37845	−	2.38755i	0.0837351	−	0.145033i	0.904852	+	0.425727i	$0.139982\pi$
$272$	77.2429			4.68354
$273$		0			0
$274$	23.7959			1.43757
$275$	0.113365	−	0.196354i	0.00683618	−	0.0118406i
$276$		0			0
$277$	11.9637	+	20.7218i	0.718831	+	1.24505i	0.961463	+	0.274933i	$0.0886558\pi$
$277$	11.9637	+	20.7218i	0.718831	+	1.24505i	−0.242632	+	0.970118i	$0.578011\pi$
$278$	−5.45050	+	9.44054i	−0.326899	+	0.566206i
$279$		0			0
$280$	−3.62906	−	53.9223i	−0.216878	−	3.22247i
$281$	3.87870			0.231384			0.115692	−	0.993285i	$-0.463091\pi$
$281$	3.87870			0.231384			0.115692	+	0.993285i	$0.463091\pi$
$282$		0			0
$283$	3.10499	+	5.37801i	0.184573	+	0.319689i	0.943432	−	0.331565i	$-0.107577\pi$
$283$	3.10499	+	5.37801i	0.184573	+	0.319689i	−0.758860	+	0.651254i	$0.774243\pi$
$284$	−17.9165	−	31.0323i	−1.06315	−	1.84143i
$285$		0			0
$286$	−2.85648			−0.168907
$287$	16.0850	−	10.7884i	0.949468	−	0.636821i
$288$		0			0
$289$	−5.49866	+	9.52395i	−0.323450	+	0.560232i
$290$	−9.25106	−	16.0233i	−0.543241	−	0.940920i
$291$		0			0
$292$	22.4772	−	38.9316i	1.31538	−	2.27830i
$293$	−16.5754			−0.968347			−0.484174	−	0.874972i	$-0.660880\pi$
$293$	−16.5754			−0.968347			−0.484174	+	0.874972i	$0.660880\pi$
$294$		0			0
$295$	−2.29249			−0.133474
$296$	−50.8681	+	88.1062i	−2.95665	+	5.12107i
$297$		0			0
$298$	−20.9744	−	36.3287i	−1.21501	−	2.10447i
$299$	0.326792	−	0.566020i	0.0188989	−	0.0327338i
$300$		0			0
$301$	−1.95069	+	1.30835i	−0.112436	+	0.0754121i
$302$	37.2698			2.14463
$303$		0			0
$304$	−5.52475	−	9.56914i	−0.316866	−	0.548828i
$305$	−13.6695	−	23.6763i	−0.782716	−	1.35570i
$306$		0			0
$307$	−7.05788			−0.402815			−0.201407	−	0.979508i	$-0.564551\pi$
$307$	−7.05788			−0.402815			−0.201407	+	0.979508i	$0.564551\pi$
$308$	−1.01060	−	15.0159i	−0.0575841	−	0.855612i
$309$		0			0
$310$	−3.06347	+	5.30609i	−0.173993	+	0.301365i
$311$	10.5551	+	18.2820i	0.598525	+	1.03668i	0.993039	+	0.117785i	$0.0375795\pi$
$311$	10.5551	+	18.2820i	0.598525	+	1.03668i	−0.394514	+	0.918890i	$0.629087\pi$
$312$		0			0
$313$	−0.990260	+	1.71518i	−0.0559728	+	0.0969477i	−0.892654	−	0.450742i	$-0.851159\pi$
$313$	−0.990260	+	1.71518i	−0.0559728	+	0.0969477i	0.836681	+	0.547690i	$0.184493\pi$
$314$	−9.23194			−0.520989
$315$		0			0
$316$	11.6145			0.653368
$317$	−9.02297	+	15.6282i	−0.506781	+	0.877770i	0.493189	+	0.869922i	$0.335831\pi$
$317$	−9.02297	+	15.6282i	−0.506781	+	0.877770i	−0.999969	+	0.00784727i	$0.997502\pi$
$318$		0			0
$319$	−1.62678	−	2.81767i	−0.0910822	−	0.157759i
$320$	30.9703	−	53.6421i	1.73129	−	2.99868i
$321$		0			0
$322$	4.23021	+	2.07691i	0.235740	+	0.115742i
$323$	4.00498			0.222843
$324$		0			0
$325$	0.108157	+	0.187333i	0.00599947	+	0.0103914i
$326$	−18.8179	−	32.5936i	−1.04223	−	1.80519i
$327$		0			0
$328$	68.3682			3.77500
$329$	0.415285	+	6.17051i	0.0228954	+	0.340191i
$330$		0			0
$331$	7.33689	−	12.7079i	0.403272	−	0.698488i	−0.590847	−	0.806784i	$-0.701206\pi$
$331$	7.33689	−	12.7079i	0.403272	−	0.698488i	0.994119	+	0.108296i	$0.0345395\pi$
$332$	−18.0870	−	31.3276i	−0.992653	−	1.71933i
$333$		0			0
$334$	−22.3175	+	38.6550i	−1.22116	+	2.11511i
$335$	−9.79606			−0.535216
$336$		0			0
$337$	12.8080			0.697698			0.348849	−	0.937179i	$-0.386573\pi$
$337$	12.8080			0.697698			0.348849	+	0.937179i	$0.386573\pi$
$338$	1.36263	−	2.36014i	0.0741170	−	0.128374i
$339$		0			0
$340$	31.4028	+	54.3913i	1.70306	+	2.94978i
$341$	−0.538705	+	0.933065i	−0.0291725	+	0.0505283i
$342$		0			0
$343$	3.70846	+	18.1452i	0.200238	+	0.979747i
$344$	−8.29125			−0.447034
$345$		0			0
$346$	−5.62146	−	9.73665i	−0.302211	−	0.523445i
$347$	10.1027	+	17.4984i	0.542342	+	0.939363i	0.998769	+	0.0496025i	$0.0157954\pi$
$347$	10.1027	+	17.4984i	0.542342	+	0.939363i	−0.456428	+	0.889761i	$0.650871\pi$
$348$		0			0
$349$	−18.4434			−0.987252			−0.493626	−	0.869674i	$-0.664329\pi$
$349$	−18.4434			−0.987252			−0.493626	+	0.869674i	$0.664329\pi$
$350$	−1.29532	+	0.868789i	−0.0692378	+	0.0464387i
$351$		0			0
$352$	11.0607	−	19.1576i	0.589536	−	1.02111i
$353$	−4.07218	−	7.05322i	−0.216740	−	0.375405i	0.737069	−	0.675817i	$-0.236209\pi$
$353$	−4.07218	−	7.05322i	−0.216740	−	0.375405i	−0.953810	+	0.300412i	$0.902876\pi$
$354$		0			0
$355$	7.22064	−	12.5065i	0.383232	−	0.663777i
$356$	31.3016			1.65898
$357$		0			0
$358$	39.2806			2.07604
$359$	−16.3050	+	28.2411i	−0.860545	+	1.49051i	0.0108595	+	0.999941i	$0.496543\pi$
$359$	−16.3050	+	28.2411i	−0.860545	+	1.49051i	−0.871404	+	0.490566i	$0.836790\pi$
$360$		0			0
$361$	9.21355	+	15.9583i	0.484923	+	0.839912i
$362$	24.6654	−	42.7218i	1.29639	−	2.24541i
$363$		0			0
$364$	12.8888	+	6.32803i	0.675557	+	0.331679i
$365$	18.1173			0.948304
$366$		0			0
$367$	1.58006	+	2.73675i	0.0824786	+	0.142857i	0.904314	−	0.426868i	$-0.140383\pi$
$367$	1.58006	+	2.73675i	0.0824786	+	0.142857i	−0.821835	+	0.569725i	$0.807050\pi$
$368$	4.77059	+	8.26290i	0.248684	+	0.430733i
$369$		0			0
$370$	−64.9298			−3.37554
$371$	−11.6091	−	5.69972i	−0.602713	−	0.295915i
$372$		0			0
$373$	0.738849	−	1.27972i	0.0382561	−	0.0662616i	−0.846263	−	0.532765i	$-0.821153\pi$
$373$	0.738849	−	1.27972i	0.0382561	−	0.0662616i	0.884520	+	0.466503i	$0.154486\pi$
$374$	7.55718	+	13.0894i	0.390773	+	0.676838i
$375$		0			0
$376$	−10.9155	+	18.9061i	−0.562922	+	0.975010i
$377$	3.10408			0.159868
$378$		0			0
$379$	10.7254			0.550927			0.275463	−	0.961312i	$-0.411169\pi$
$379$	10.7254			0.550927			0.275463	+	0.961312i	$0.411169\pi$
$380$	4.49213	−	7.78060i	0.230441	−	0.399136i
$381$		0			0
$382$	−7.55079	−	13.0784i	−0.386332	−	0.669147i
$383$	−10.7054	+	18.5424i	−0.547023	+	0.947471i	0.451454	+	0.892294i	$0.350906\pi$
$383$	−10.7054	+	18.5424i	−0.547023	+	0.947471i	−0.998477	+	0.0551766i	$0.982428\pi$
$384$		0			0
$385$	5.03725	−	3.37855i	0.256722	−	0.172187i
$386$	23.8211			1.21246
$387$		0			0
$388$	7.83595	+	13.5723i	0.397810	+	0.689027i
$389$	17.3909	+	30.1220i	0.881755	+	1.52725i	0.849388	+	0.527769i	$0.176971\pi$
$389$	17.3909	+	30.1220i	0.881755	+	1.52725i	0.0323675	+	0.999476i	$0.489695\pi$
$390$		0			0
$391$	−3.45828			−0.174893
$392$	−24.8066	+	60.4866i	−1.25292	+	3.05503i
$393$		0			0
$394$	7.45185	−	12.9070i	0.375419	−	0.650244i
$395$	2.34042	+	4.05373i	0.117759	+	0.203965i
$396$		0			0
$397$	−2.22605	+	3.85564i	−0.111722	+	0.193509i	−0.916465	−	0.400115i	$-0.868970\pi$
$397$	−2.22605	+	3.85564i	−0.111722	+	0.193509i	0.804742	+	0.593624i	$0.202303\pi$
$398$	−53.2426			−2.66881
$399$		0			0
$400$	−3.15780			−0.157890
$401$	−6.87687	+	11.9111i	−0.343415	+	0.594811i	−0.985064	−	0.172186i	$-0.944917\pi$
$401$	−6.87687	+	11.9111i	−0.343415	+	0.594811i	0.641650	+	0.766998i	$0.278250\pi$
$402$		0			0
$403$	−0.513956	−	0.890198i	−0.0256020	−	0.0443439i
$404$	−30.5385	+	52.8943i	−1.51935	+	2.63159i
$405$		0			0
$406$	1.50291	+	22.3310i	0.0745882	+	1.10827i
$407$	−11.4178			−0.565959
$408$		0			0
$409$	1.74603	+	3.02422i	0.0863358	+	0.149538i	0.905960	−	0.423364i	$-0.139151\pi$
$409$	1.74603	+	3.02422i	0.0863358	+	0.149538i	−0.819624	+	0.572902i	$0.805818\pi$
$410$	21.8169	+	37.7879i	1.07746	+	1.86621i
$411$		0			0
$412$	109.806			5.40977
$413$	2.48931	+	1.22218i	0.122491	+	0.0601396i
$414$		0			0
$415$	7.28935	−	12.6255i	0.357820	−	0.619763i
$416$	10.5525	+	18.2775i	0.517380	+	0.896128i
$417$		0			0
$418$	1.08105	−	1.87243i	0.0528757	−	0.0915834i
$419$	3.56737			0.174278			0.0871388	−	0.996196i	$-0.472228\pi$
$419$	3.56737			0.174278			0.0871388	+	0.996196i	$0.472228\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	22.7429	−	39.3919i	1.10711	−	1.91757i
$423$		0			0
$424$	−22.8262	−	39.5361i	−1.10854	−	1.92004i
$425$	0.572285	−	0.991227i	0.0277599	−	0.0480816i
$426$		0			0
$427$	2.22073	+	32.9967i	0.107469	+	1.59682i
$428$	−49.1423			−2.37538
$429$		0			0
$430$	−2.64581	−	4.58268i	−0.127592	−	0.220996i
$431$	−5.68211	−	9.84171i	−0.273698	−	0.474059i	0.696108	−	0.717937i	$-0.254913\pi$
$431$	−5.68211	−	9.84171i	−0.273698	−	0.474059i	−0.969806	+	0.243879i	$0.921580\pi$
$432$		0			0
$433$	−21.2136			−1.01946			−0.509731	−	0.860334i	$-0.670255\pi$
$433$	−21.2136			−1.01946			−0.509731	+	0.860334i	$0.670255\pi$
$434$	6.15529	−	4.12844i	0.295464	−	0.198171i
$435$		0			0
$436$	−40.9776	+	70.9752i	−1.96247	+	3.39910i
$437$	0.247351	+	0.428424i	0.0118324	+	0.0204943i
$438$		0			0
$439$	12.2503	−	21.2182i	0.584676	−	1.01269i	−0.410239	−	0.911978i	$-0.634555\pi$
$439$	12.2503	−	21.2182i	0.584676	−	1.01269i	0.994916	−	0.100711i	$-0.0321118\pi$
$440$	21.4105			1.02070
$441$		0			0
$442$	−14.4200			−0.685888
$443$	20.2344	−	35.0470i	0.961366	−	1.66513i	0.242288	−	0.970204i	$-0.422102\pi$
$443$	20.2344	−	35.0470i	0.961366	−	1.66513i	0.719077	−	0.694930i	$-0.244565\pi$
$444$		0			0
$445$	6.30753	+	10.9250i	0.299005	+	0.517893i
$446$	−7.27937	+	12.6082i	−0.344688	+	0.597017i
$447$		0			0
$448$	−62.2272	+	41.7366i	−2.93996	+	1.97187i
$449$	27.7638			1.31025			0.655127	−	0.755519i	$-0.272615\pi$
$449$	27.7638			1.31025			0.655127	+	0.755519i	$0.272615\pi$
$450$		0			0
$451$	3.83646	+	6.64494i	0.180652	+	0.312898i
$452$	8.42292	+	14.5889i	0.396181	+	0.686205i
$453$		0			0
$454$	54.8362			2.57359
$455$	0.388575	+	5.77363i	0.0182167	+	0.270672i
$456$		0			0
$457$	5.59696	−	9.69422i	0.261815	−	0.453476i	−0.704910	−	0.709297i	$-0.749012\pi$
$457$	5.59696	−	9.69422i	0.261815	−	0.453476i	0.966724	+	0.255821i	$0.0823457\pi$
$458$	34.4059	+	59.5928i	1.60768	+	2.78459i
$459$		0			0
$460$	−3.87893	+	6.71850i	−0.180856	+	0.313252i
$461$	9.29773			0.433038			0.216519	−	0.976278i	$-0.430530\pi$
$461$	9.29773			0.433038			0.216519	+	0.976278i	$0.430530\pi$
$462$		0			0
$463$	28.2439			1.31260			0.656302	−	0.754499i	$-0.272120\pi$
$463$	28.2439			1.31260			0.656302	+	0.754499i	$0.272120\pi$
$464$	−22.6571	+	39.2432i	−1.05183	+	1.82182i
$465$		0			0
$466$	1.08105	+	1.87243i	0.0500785	+	0.0867385i
$467$	11.1303	−	19.2783i	0.515050	−	0.892093i	−0.484797	−	0.874626i	$-0.661107\pi$
$467$	11.1303	−	19.2783i	0.515050	−	0.892093i	0.999847	−	0.0174663i	$-0.00555997\pi$
$468$		0			0
$469$	10.6371	+	5.22252i	0.491177	+	0.241154i
$470$	−13.9329			−0.642676
$471$		0			0
$472$	4.89457	+	8.47765i	0.225291	+	0.390215i
$473$	−0.465261	−	0.805855i	−0.0213927	−	0.0370533i
$474$		0			0
$475$	−0.163729			−0.00751242
$476$	−5.10165	−	75.8027i	−0.233834	−	3.47441i
$477$		0			0
$478$	−27.3190	+	47.3179i	−1.24954	+	2.16427i
$479$	−16.4382	−	28.4718i	−0.751081	−	1.30091i	−0.947299	−	0.320350i	$-0.896200\pi$
$479$	−16.4382	−	28.4718i	−0.751081	−	1.30091i	0.196219	−	0.980560i	$-0.437134\pi$
$480$		0			0
$481$	5.44661	−	9.43381i	0.248344	−	0.430145i
$482$	−37.6413			−1.71451
$483$		0			0
$484$	−53.7346			−2.44248
$485$	−3.15801	+	5.46984i	−0.143398	+	0.248373i
$486$		0			0
$487$	13.9462	+	24.1555i	0.631962	+	1.09459i	0.987150	+	0.159796i	$0.0510836\pi$
$487$	13.9462	+	24.1555i	0.631962	+	1.09459i	−0.355188	+	0.934795i	$0.615583\pi$
$488$	−58.3703	+	101.100i	−2.64230	+	4.57660i
$489$		0			0
$490$	−41.3477	+	5.59086i	−1.86790	+	0.252569i
$491$	−10.6571			−0.480948			−0.240474	−	0.970656i	$-0.577303\pi$
$491$	−10.6571			−0.480948			−0.240474	+	0.970656i	$0.577303\pi$
$492$		0			0
$493$	−8.21224	−	14.2240i	−0.369861	−	0.640618i
$494$	1.03138	+	1.78640i	0.0464040	+	0.0803740i
$495$		0			0
$496$	15.0057			0.673776
$497$	−14.5081	+	9.73078i	−0.650777	+	0.436485i
$498$		0			0
$499$	12.2557	−	21.2275i	0.548641	−	0.950274i	−0.449727	−	0.893166i	$-0.648479\pi$
$499$	12.2557	−	21.2275i	0.548641	−	0.950274i	0.998368	−	0.0571077i	$-0.0181878\pi$
$500$	−30.9581	−	53.6210i	−1.38449	−	2.39800i
$501$		0			0
$502$	35.5775	−	61.6221i	1.58790	−	2.75033i
$503$	38.0054			1.69458			0.847288	−	0.531134i	$-0.178234\pi$
$503$	38.0054			1.69458			0.847288	+	0.531134i	$0.178234\pi$
$504$		0			0
$505$	−24.6151			−1.09536
$506$	−0.933476	+	1.61683i	−0.0414981	+	0.0718768i
$507$		0			0
$508$	−23.8493	−	41.3082i	−1.05814	−	1.83275i
$509$	19.9250	−	34.5112i	0.883161	−	1.52968i	0.0353545	−	0.999375i	$-0.488744\pi$
$509$	19.9250	−	34.5112i	0.883161	−	1.52968i	0.847807	−	0.530305i	$-0.177923\pi$
$510$		0			0
$511$	−19.6728	−	9.65878i	−0.870274	−	0.427279i
$512$	−35.4186			−1.56530
$513$		0			0
$514$	−14.4708	−	25.0642i	−0.638279	−	1.10553i
$515$	22.1269	+	38.3249i	0.975027	+	1.68880i
$516$		0			0
$517$	−2.45007			−0.107754
$518$	70.5045	+	34.6157i	3.09779	+	1.52093i
$519$		0			0
$520$	−10.2134	+	17.6901i	−0.447887	+	0.775764i
$521$	−9.81670	−	17.0030i	−0.430077	−	0.744916i	0.566802	−	0.823854i	$-0.308180\pi$
$521$	−9.81670	−	17.0030i	−0.430077	−	0.744916i	−0.996880	+	0.0789382i	$0.974847\pi$
$522$		0			0
$523$	−11.4162	+	19.7734i	−0.499195	+	0.864632i	−1.00000		0.000928862i	$-0.999704\pi$
$523$	−11.4162	+	19.7734i	−0.499195	+	0.864632i	0.500804	+	0.865561i	$0.333038\pi$
$524$	57.0619			2.49276
$525$		0			0
$526$	28.2275			1.23078
$527$	−2.71947	+	4.71026i	−0.118462	+	0.205182i
$528$		0			0
$529$	11.2864	+	19.5486i	0.490714	+	0.849941i
$530$	14.5681	−	25.2326i	0.632796	−	1.09603i
$531$		0			0
$532$	−9.02584	+	6.05375i	−0.391320	+	0.262463i
$533$	−7.32040			−0.317082
$534$		0			0
$535$	−9.90257	−	17.1518i	−0.428125	−	0.741535i
$536$	20.9151	+	36.2260i	0.903394	+	1.56472i
$537$		0			0
$538$	32.6214			1.40641
$539$	−7.27092	+	0.983142i	−0.313181	+	0.0423469i
$540$		0			0
$541$	4.82334	−	8.35427i	0.207372	−	0.359178i	−0.743514	−	0.668720i	$-0.766842\pi$
$541$	4.82334	−	8.35427i	0.207372	−	0.359178i	0.950886	+	0.309542i	$0.100176\pi$
$542$	−3.75663	−	6.50667i	−0.161361	−	0.279486i
$543$		0			0
$544$	55.8360	−	96.7108i	2.39395	−	4.14644i
$545$	−33.0292			−1.41482
$546$		0			0
$547$	−43.8570			−1.87519			−0.937596	−	0.347728i	$-0.886953\pi$
$547$	−43.8570			−1.87519			−0.937596	+	0.347728i	$0.886953\pi$
$548$	23.6933	−	41.0380i	1.01213	−	1.75306i
$549$		0			0
$550$	−0.308949	−	0.535115i	−0.0131736	−	0.0228174i
$551$	−1.17475	+	2.03473i	−0.0500461	+	0.0866823i
$552$		0			0
$553$	−0.380221	−	5.64950i	−0.0161686	−	0.240241i
$554$	65.2083			2.77044
$555$		0			0
$556$	10.8540	+	18.7996i	0.460311	+	0.797282i
$557$	7.45977	+	12.9207i	0.316080	+	0.547467i	0.979667	−	0.200633i	$-0.0642997\pi$
$557$	7.45977	+	12.9207i	0.316080	+	0.547467i	−0.663586	+	0.748100i	$0.730966\pi$
$558$		0			0
$559$	0.887771			0.0375487
$560$	−75.8290	−	37.2299i	−3.20436	−	1.57325i
$561$		0			0
$562$	5.28521	−	9.15426i	0.222943	−	0.386149i
$563$	−8.63486	−	14.9560i	−0.363916	−	0.630321i	0.624686	−	0.780876i	$-0.285227\pi$
$563$	−8.63486	−	14.9560i	−0.363916	−	0.630321i	−0.988602	+	0.150555i	$0.951894\pi$
$564$		0			0
$565$	−3.39457	+	5.87957i	−0.142811	+	0.247355i
$566$	16.9238			0.711359
$567$		0			0
$568$	−61.6657			−2.58743
$569$	13.2662	−	22.9777i	0.556148	−	0.963277i	−0.441665	−	0.897180i	$-0.645612\pi$
$569$	13.2662	−	22.9777i	0.556148	−	0.963277i	0.997813	−	0.0660972i	$-0.0210547\pi$
$570$		0			0
$571$	0.992844	+	1.71966i	0.0415492	+	0.0719654i	0.886052	−	0.463586i	$-0.153437\pi$
$571$	0.992844	+	1.71966i	0.0415492	+	0.0719654i	−0.844503	+	0.535551i	$0.820104\pi$
$572$	−2.84416	+	4.92623i	−0.118920	+	0.205976i
$573$		0			0
$574$	−3.54433	−	52.6634i	−0.147938	−	2.19813i
$575$	0.141379			0.00589593
$576$		0			0
$577$	−5.94915	−	10.3042i	−0.247666	−	0.428971i	0.715212	−	0.698908i	$-0.246330\pi$
$577$	−5.94915	−	10.3042i	−0.247666	−	0.428971i	−0.962878	+	0.269937i	$0.912997\pi$
$578$	14.9852	+	25.9551i	0.623303	+	1.07959i
$579$		0			0
$580$	−36.8446			−1.52989
$581$	−14.6462	+	9.82339i	−0.607626	+	0.407543i
$582$		0			0
$583$	2.56176	−	4.43711i	0.106097	−	0.183766i
$584$	−38.6814	−	66.9981i	−1.60065	−	2.77240i
$585$		0			0
$586$	−22.5861	+	39.1203i	−0.933024	+	1.61604i
$587$	−33.5122			−1.38320			−0.691598	−	0.722283i	$-0.743093\pi$
$587$	−33.5122			−1.38320			−0.691598	+	0.722283i	$0.743093\pi$
$588$		0			0
$589$	0.778033			0.0320583
$590$	−3.12380	+	5.41058i	−0.128605	+	0.222750i
$591$		0			0
$592$	79.5109	+	137.717i	3.26788	+	5.66013i
$593$	17.6408	−	30.5547i	0.724419	−	1.25473i	−0.234793	−	0.972045i	$-0.575441\pi$
$593$	17.6408	−	30.5547i	0.724419	−	1.25473i	0.959213	−	0.282686i	$-0.0912253\pi$
$594$		0			0
$595$	25.4288	−	17.0554i	1.04248	−	0.699205i
$596$	−83.5357			−3.42176
$597$		0			0
$598$	−0.890590	−	1.54255i	−0.0364189	−	0.0630794i
$599$	−12.5034	−	21.6565i	−0.510876	−	0.884863i	−0.999921	−	0.0126040i	$-0.995988\pi$
$599$	−12.5034	−	21.6565i	−0.510876	−	0.884863i	0.489045	−	0.872259i	$-0.337345\pi$
$600$		0			0
$601$	−28.4688			−1.16127			−0.580634	−	0.814165i	$-0.697195\pi$
$601$	−28.4688			−1.16127			−0.580634	+	0.814165i	$0.697195\pi$
$602$	0.429834	+	6.38668i	0.0175187	+	0.260301i
$603$		0			0
$604$	37.1090	−	64.2747i	1.50994	−	2.61530i
$605$	−10.8280	−	18.7546i	−0.440219	−	0.762482i
$606$		0			0
$607$	−18.0234	+	31.2175i	−0.731549	+	1.26708i	0.224672	+	0.974434i	$0.427869\pi$
$607$	−18.0234	+	31.2175i	−0.731549	+	1.26708i	−0.956221	+	0.292646i	$0.905464\pi$
$608$	−15.9745			−0.647853
$609$		0			0
$610$	−74.5058			−3.01665
$611$	1.16875	−	2.02434i	0.0472827	−	0.0818961i
$612$		0			0
$613$	−9.16264	−	15.8702i	−0.370075	−	0.640989i	0.619501	−	0.784996i	$-0.287335\pi$
$613$	−9.16264	−	15.8702i	−0.370075	−	0.640989i	−0.989577	+	0.144006i	$0.954001\pi$
$614$	−9.61725	+	16.6576i	−0.388121	+	0.672245i
$615$		0			0
$616$	−23.2487	−	11.4144i	−0.936717	−	0.459901i
$617$	−44.3782			−1.78660			−0.893299	−	0.449463i	$-0.851615\pi$
$617$	−44.3782			−1.78660			−0.893299	+	0.449463i	$0.851615\pi$
$618$		0			0
$619$	12.5043	+	21.6580i	0.502588	+	0.870509i	0.999996	+	0.00299144i	$0.000952205\pi$
$619$	12.5043	+	21.6580i	0.502588	+	0.870509i	−0.497407	+	0.867517i	$0.665714\pi$
$620$	6.10051	+	10.5664i	0.245002	+	0.424357i
$621$		0			0
$622$	57.5306			2.30677
$623$	−1.02471	−	15.2256i	−0.0410541	−	0.610002i
$624$		0			0
$625$	11.9358	−	20.6734i	0.477433	−	0.826938i
$626$	2.69871	+	4.67429i	0.107862	+	0.186822i
$627$		0			0
$628$	−9.19212	+	15.9212i	−0.366806	+	0.635326i
$629$	−57.6388			−2.29821
$630$		0			0
$631$	−18.4638			−0.735032			−0.367516	−	0.930017i	$-0.619792\pi$
$631$	−18.4638			−0.735032			−0.367516	+	0.930017i	$0.619792\pi$
$632$	9.99382	−	17.3098i	0.397533	−	0.688547i
$633$		0			0
$634$	24.5899	+	42.5909i	0.976588	+	1.69150i
$635$	9.61165	−	16.6479i	0.381427	−	0.660650i
$636$		0			0
$637$	2.65613	−	6.47650i	0.105240	−	0.256608i
$638$	−8.86677			−0.351039
$639$		0			0
$640$	−38.2416	−	66.2364i	−1.51163	−	2.61822i
$641$	−10.6284	−	18.4088i	−0.419795	−	0.727106i	0.576124	−	0.817362i	$-0.304565\pi$
$641$	−10.6284	−	18.4088i	−0.419795	−	0.727106i	−0.995919	+	0.0902567i	$0.971231\pi$
$642$		0			0
$643$	−36.0554			−1.42188			−0.710942	−	0.703251i	$-0.751731\pi$
$643$	−36.0554			−1.42188			−0.710942	+	0.703251i	$0.751731\pi$
$644$	7.79376	−	5.22738i	0.307117	−	0.205988i
$645$		0			0
$646$	5.45729	−	9.45230i	0.214714	−	0.371896i
$647$	19.9117	+	34.4881i	0.782809	+	1.35587i	0.930299	+	0.366802i	$0.119547\pi$
$647$	19.9117	+	34.4881i	0.782809	+	1.35587i	−0.147490	+	0.989064i	$0.547119\pi$
$648$		0			0
$649$	−0.549314	+	0.951440i	−0.0215625	+	0.0373473i
$650$	0.589510			0.0231225
$651$		0			0
$652$	−74.9469			−2.93515
$653$	−16.2335	+	28.1172i	−0.635265	+	1.10031i	0.351195	+	0.936303i	$0.385776\pi$
$653$	−16.2335	+	28.1172i	−0.635265	+	1.10031i	−0.986459	+	0.164008i	$0.947558\pi$
$654$		0			0
$655$	11.4984	+	19.9159i	0.449281	+	0.778177i
$656$	53.4324	−	92.5477i	2.08619	−	3.61338i
$657$		0			0
$658$	15.1291	+	7.42796i	0.589794	+	0.289572i
$659$	−23.5230			−0.916327			−0.458164	−	0.888868i	$-0.651493\pi$
$659$	−23.5230			−0.916327			−0.458164	+	0.888868i	$0.651493\pi$
$660$		0			0
$661$	−7.01944	−	12.1580i	−0.273025	−	0.472893i	0.696610	−	0.717450i	$-0.254691\pi$
$661$	−7.01944	−	12.1580i	−0.273025	−	0.472893i	−0.969635	+	0.244557i	$0.921357\pi$
$662$	−19.9949	−	34.6321i	−0.777122	−	1.34602i
$663$		0			0
$664$	−62.2525			−2.41587
$665$	−3.93167	−	1.93034i	−0.152464	−	0.0748553i
$666$		0			0
$667$	1.01439	−	1.75698i	0.0392773	−	0.0680303i
$668$	44.4424	+	76.9765i	1.71953	+	2.97831i
$669$		0			0
$670$	−13.3484	+	23.1200i	−0.515692	+	0.893205i
$671$	−13.1017			−0.505786
$672$		0			0
$673$	−47.1937			−1.81918			−0.909592	−	0.415502i	$-0.863606\pi$
$673$	−47.1937			−1.81918			−0.909592	+	0.415502i	$0.863606\pi$
$674$	17.4526	−	30.2287i	0.672247	−	1.16437i
$675$		0			0
$676$	−2.71349	−	4.69991i	−0.104365	−	0.180766i
$677$	−4.79438	+	8.30411i	−0.184263	+	0.319153i	−0.943328	−	0.331862i	$-0.892323\pi$
$677$	−4.79438	+	8.30411i	−0.184263	+	0.319153i	0.759065	+	0.651015i	$0.225656\pi$
$678$		0			0
$679$	6.34526	−	4.25585i	0.243509	−	0.163325i
$680$	108.083			4.14481
$681$		0			0
$682$	1.46811	+	2.54284i	0.0562167	+	0.0973702i
$683$	23.6581	+	40.9769i	0.905250	+	1.56794i	0.820581	+	0.571530i	$0.193650\pi$
$683$	23.6581	+	40.9769i	0.905250	+	1.56794i	0.0846691	+	0.996409i	$0.473017\pi$
$684$		0			0
$685$	19.0976			0.729680
$686$	47.8783	+	15.9726i	1.82800	+	0.609837i
$687$		0			0
$688$	−6.47994	+	11.2236i	−0.247045	+	0.427895i
$689$	2.44407	+	4.23325i	0.0931117	+	0.161274i
$690$		0			0
$691$	13.5559	−	23.4796i	0.515692	−	0.893205i	−0.484142	−	0.874990i	$-0.660868\pi$
$691$	13.5559	−	23.4796i	0.515692	−	0.893205i	0.999834	−	0.0182158i	$-0.00579859\pi$
$692$	−22.3888			−0.851095
$693$		0			0
$694$	55.0648			2.09023
$695$	−4.37433	+	7.57656i	−0.165928	+	0.287395i
$696$		0			0
$697$	19.3670	+	33.5447i	0.733578	+	1.27059i
$698$	−25.1314	+	43.5289i	−0.951238	+	1.64759i
$699$		0			0
$700$	0.208563	+	3.09893i	0.00788293	+	0.117128i
$701$	1.79821			0.0679176			0.0339588	−	0.999423i	$-0.489189\pi$
$701$	1.79821			0.0679176			0.0339588	+	0.999423i	$0.489189\pi$
$702$		0			0
$703$	4.12258	+	7.14051i	0.155486	+	0.269310i
$704$	−14.8419	−	25.7069i	−0.559375	−	0.968866i
$705$		0			0
$706$	−22.1954			−0.835336
$707$	26.7284	+	13.1229i	1.00523	+	0.493537i
$708$		0			0
$709$	14.1615	−	24.5284i	0.531846	−	0.921185i	−0.467462	−	0.884013i	$-0.654832\pi$
$709$	14.1615	−	24.5284i	0.531846	−	0.921185i	0.999309	−	0.0371721i	$-0.0118350\pi$
$710$	−19.6780	−	34.0834i	−0.738504	−	1.27913i
$711$		0			0
$712$	26.9337	−	46.6506i	1.00938	−	1.74831i
$713$	−0.671827			−0.0251601
$714$		0			0
$715$	−2.29249			−0.0857341
$716$	39.1112	−	67.7425i	1.46165	−	2.53166i
$717$		0			0
$718$	44.4352	+	76.9640i	1.65831	+	2.87227i
$719$	−20.9485	+	36.2839i	−0.781249	+	1.35316i	0.149966	+	0.988691i	$0.452084\pi$
$719$	−20.9485	+	36.2839i	−0.781249	+	1.35316i	−0.931215	+	0.364471i	$0.881250\pi$
$720$		0			0
$721$	−3.59469	−	53.4117i	−0.133873	−	1.98916i
$722$	50.2184			1.86894
$723$		0			0
$724$	−49.1180	−	85.0749i	−1.82546	−	3.16179i
$725$	0.335728	+	0.581499i	0.0124686	+	0.0215963i
$726$		0			0
$727$	19.5123			0.723670			0.361835	−	0.932242i	$-0.382150\pi$
$727$	19.5123			0.723670			0.361835	+	0.932242i	$0.382150\pi$
$728$	20.5213	−	13.7639i	0.760571	−	0.510125i
$729$		0			0
$730$	24.6871	−	42.7593i	0.913711	−	1.58259i
$731$	−2.34871	−	4.06808i	−0.0868701	−	0.150463i
$732$		0			0
$733$	−8.87698	+	15.3754i	−0.327879	+	0.567902i	−0.982091	−	0.188409i	$-0.939667\pi$
$733$	−8.87698	+	15.3754i	−0.327879	+	0.567902i	0.654212	+	0.756311i	$0.273000\pi$
$734$	8.61213			0.317880
$735$		0			0
$736$	13.7939			0.508450
$737$	−2.34728	+	4.06562i	−0.0864633	+	0.149759i
$738$		0			0
$739$	−22.1571	−	38.3772i	−0.815061	−	1.41173i	−0.909284	−	0.416176i	$-0.863370\pi$
$739$	−22.1571	−	38.3772i	−0.815061	−	1.41173i	0.0942227	−	0.995551i	$-0.469963\pi$
$740$	−64.6497	+	111.977i	−2.37657	+	4.11634i
$741$		0			0
$742$	−29.2709	+	19.6324i	−1.07457	+	0.720729i
$743$	7.16727			0.262941			0.131471	−	0.991320i	$-0.458030\pi$
$743$	7.16727			0.262941			0.131471	+	0.991320i	$0.458030\pi$
$744$		0			0
$745$	−16.8331	−	29.1558i	−0.616718	−	1.06819i
$746$	−2.01355	−	3.48757i	−0.0737212	−	0.127689i
$747$		0			0
$748$	30.0983			1.10050
$749$	1.60875	+	23.9036i	0.0587826	+	0.873420i
$750$		0			0
$751$	16.9532	−	29.3639i	0.618632	−	1.07150i	−0.371103	−	0.928592i	$-0.621020\pi$
$751$	16.9532	−	29.3639i	0.618632	−	1.07150i	0.989736	−	0.142911i	$-0.0456462\pi$
$752$	17.0618	+	29.5518i	0.622178	+	1.07764i
$753$		0			0
$754$	4.22970	−	7.32606i	0.154037	−	0.266799i
$755$	29.9110			1.08857
$756$		0			0
$757$	−0.906670			−0.0329535			−0.0164767	−	0.999864i	$-0.505245\pi$
$757$	−0.906670			−0.0329535			−0.0164767	+	0.999864i	$0.505245\pi$
$758$	14.6147	−	25.3134i	0.530830	−	0.919424i
$759$		0			0
$760$	−7.73059	−	13.3898i	−0.280418	−	0.485698i
$761$	10.1247	−	17.5365i	0.367020	−	0.635697i	−0.622079	−	0.782955i	$-0.713712\pi$
$761$	10.1247	−	17.5365i	0.367020	−	0.635697i	0.989098	+	0.147258i	$0.0470449\pi$
$762$		0			0
$763$	35.8650	+	17.6087i	1.29840	+	0.637477i
$764$	−30.0729			−1.08800
$765$		0			0
$766$	29.1750	+	50.5326i	1.05414	+	1.82582i
$767$	−0.524077	−	0.907729i	−0.0189233	−	0.0327762i
$768$		0			0
$769$	−36.9094			−1.33099			−0.665494	−	0.746403i	$-0.731779\pi$
$769$	−36.9094			−1.33099			−0.665494	+	0.746403i	$0.731779\pi$
$770$	−1.10996	−	16.4923i	−0.0400001	−	0.594341i
$771$		0			0
$772$	23.7183	−	41.0814i	0.853642	−	1.47855i
$773$	−4.94018	−	8.55665i	−0.177686	−	0.307761i	0.763402	−	0.645924i	$-0.223528\pi$
$773$	−4.94018	−	8.55665i	−0.177686	−	0.307761i	−0.941088	+	0.338163i	$0.890194\pi$
$774$		0			0
$775$	0.111176	−	0.192562i	0.00399355	−	0.00691704i
$776$	26.9701			0.968169
$777$		0			0
$778$	94.7893			3.39836
$779$	2.77043	−	4.79852i	0.0992609	−	0.171925i
$780$		0			0
$781$	−3.46035	−	5.99350i	−0.123821	−	0.214464i
$782$	−4.71233	+	8.16200i	−0.168513	+	0.291873i
$783$		0			0
$784$	62.4913	+	80.8526i	2.23183	+	2.88759i
$785$	−7.40915			−0.264444
$786$		0			0
$787$	−18.8411	−	32.6337i	−0.671611	−	1.16326i	−0.977447	−	0.211180i	$-0.932269\pi$
$787$	−18.8411	−	32.6337i	−0.671611	−	1.16326i	0.305836	−	0.952084i	$-0.401064\pi$
$788$	−14.8394	−	25.7026i	−0.528632	−	0.915617i
$789$		0			0
$790$	12.7565			0.453854
$791$	6.82056	−	4.57464i	0.242511	−	0.162656i
$792$		0			0
$793$	6.24989	−	10.8251i	0.221940	−	0.384412i
$794$	6.06656	+	10.5076i	0.215294	+	0.372900i
$795$		0			0
$796$	−53.0129	+	91.8211i	−1.87899	+	3.25451i
$797$	−28.3837			−1.00540			−0.502701	−	0.864460i	$-0.667660\pi$
$797$	−28.3837			−1.00540			−0.502701	+	0.864460i	$0.667660\pi$
$798$		0			0
$799$	−12.3683			−0.437560
$800$	−2.28266	+	3.95368i	−0.0807041	+	0.139784i
$801$		0			0
$802$	18.7412	+	32.4607i	0.661775	+	1.14623i
$803$	4.34118	−	7.51915i	0.153197	−	0.265345i
$804$		0			0
$805$	3.39498	+	1.66684i	0.119657	+	0.0587482i
$806$	−2.80132			−0.0986722
$807$		0			0
$808$	52.5543	+	91.0268i	1.84886	+	3.20231i
$809$	−5.87327	−	10.1728i	−0.206493	−	0.357657i	0.744114	−	0.668052i	$-0.232872\pi$
$809$	−5.87327	−	10.1728i	−0.206493	−	0.357657i	−0.950607	+	0.310396i	$0.899539\pi$
$810$		0			0
$811$	2.01940			0.0709108			0.0354554	−	0.999371i	$-0.488712\pi$
$811$	2.01940			0.0709108			0.0354554	+	0.999371i	$0.488712\pi$
$812$	40.0080	+	19.6428i	1.40400	+	0.689326i
$813$		0			0
$814$	−15.5582	+	26.9475i	−0.545313	+	0.944511i
$815$	−15.1024	−	26.1581i	−0.529014	−	0.916280i
$816$		0			0
$817$	−0.335980	+	0.581934i	−0.0117544	+	0.0203593i
$818$	9.51676			0.332746
$819$		0			0
$820$	86.8910			3.03437
$821$	−7.54208	+	13.0633i	−0.263220	+	0.455911i	−0.967096	−	0.254412i	$-0.918118\pi$
$821$	−7.54208	+	13.0633i	−0.263220	+	0.455911i	0.703875	+	0.710323i	$0.251451\pi$
$822$		0			0
$823$	7.38828	+	12.7969i	0.257539	+	0.446071i	0.965582	−	0.260098i	$-0.0837550\pi$
$823$	7.38828	+	12.7969i	0.257539	+	0.446071i	−0.708043	+	0.706170i	$0.750422\pi$
$824$	94.4839	−	163.651i	3.29150	−	5.70105i
$825$		0			0
$826$	6.27651	−	4.20974i	0.218388	−	0.146476i
$827$	−13.0407			−0.453471			−0.226736	−	0.973956i	$-0.572805\pi$
$827$	−13.0407			−0.453471			−0.226736	+	0.973956i	$0.572805\pi$
$828$		0			0
$829$	12.7291	+	22.0474i	0.442099	+	0.765738i	0.997845	−	0.0656144i	$-0.0209007\pi$
$829$	12.7291	+	22.0474i	0.442099	+	0.765738i	−0.555746	+	0.831352i	$0.687567\pi$
$830$	−19.8653	−	34.4077i	−0.689535	−	1.19431i
$831$		0			0
$832$	28.3200			0.981820
$833$	−36.7047	+	4.96305i	−1.27174	+	0.171960i
$834$		0			0
$835$	−17.9110	+	31.0228i	−0.619835	+	1.07359i
$836$	−2.15277	−	3.72870i	−0.0744549	−	0.128960i
$837$		0			0
$838$	4.86099	−	8.41948i	0.167920	−	0.290846i
$839$	−32.1703			−1.11064			−0.555321	−	0.831636i	$-0.687404\pi$
$839$	−32.1703			−1.11064			−0.555321	+	0.831636i	$0.687404\pi$
$840$		0			0
$841$	−19.3647			−0.667747
$842$	−13.6263	+	23.6014i	−0.469592	+	0.813357i
$843$		0			0
$844$	−45.2896	−	78.4439i	−1.55893	−	2.70015i
$845$	1.09358	−	1.89414i	0.0376204	−	0.0651604i
$846$		0			0
$847$	1.75909	+	26.1374i	0.0604431	+	0.898093i
$848$	−71.3582			−2.45045
$849$		0			0
$850$	−1.55962	−	2.70134i	−0.0534946	−	0.0926553i
$851$	−3.55982	−	6.16579i	−0.122029	−	0.211360i
$852$		0			0
$853$	−19.3910			−0.663934			−0.331967	−	0.943291i	$-0.607712\pi$
$853$	−19.3910			−0.663934			−0.331967	+	0.943291i	$0.607712\pi$
$854$	80.9027	+	39.7209i	2.76843	+	1.35922i
$855$		0			0
$856$	−42.2849	+	73.2396i	−1.44527	+	2.50328i
$857$	8.71210	+	15.0898i	0.297600	+	0.515458i	0.975586	−	0.219616i	$-0.0704806\pi$
$857$	8.71210	+	15.0898i	0.297600	+	0.515458i	−0.677987	+	0.735074i	$0.737147\pi$
$858$		0			0
$859$	17.7459	−	30.7367i	0.605481	−	1.04872i	−0.386495	−	0.922292i	$-0.626314\pi$
$859$	17.7459	−	30.7367i	0.605481	−	1.04872i	0.991975	−	0.126432i	$-0.0403524\pi$
$860$	−10.5376			−0.359329
$861$		0			0
$862$	−30.9704			−1.05486
$863$	28.0010	−	48.4991i	0.953164	−	1.65093i	0.214648	−	0.976691i	$-0.431140\pi$
$863$	28.0010	−	48.4991i	0.953164	−	1.65093i	0.738516	−	0.674236i	$-0.235527\pi$
$864$		0			0
$865$	−4.51153	−	7.81420i	−0.153397	−	0.265691i
$866$	−28.9062	+	50.0670i	−0.982273	+	1.70135i
$867$		0			0
$868$	−0.991079	−	14.7259i	−0.0336394	−	0.499830i
$869$	2.24320			0.0760953
$870$		0			0
$871$	−2.23944	−	3.87883i	−0.0758807	−	0.131429i
$872$	70.5190	+	122.143i	2.38808	+	4.13627i
$873$		0			0
$874$	1.34819			0.0456031
$875$	−25.0687	+	16.8139i	−0.847476	+	0.568414i
$876$		0			0
$877$	−12.6031	+	21.8292i	−0.425577	+	0.737120i	−0.996474	−	0.0839011i	$-0.973262\pi$
$877$	−12.6031	+	21.8292i	−0.425577	+	0.737120i	0.570898	+	0.821021i	$0.306595\pi$
$878$	−33.3852	−	57.8249i	−1.12670	−	1.95150i
$879$		0			0
$880$	16.7331	−	28.9826i	0.564074	−	0.977004i
$881$	18.6082			0.626925			0.313463	−	0.949601i	$-0.398511\pi$
$881$	18.6082			0.626925			0.313463	+	0.949601i	$0.398511\pi$
$882$		0			0
$883$	−11.2552			−0.378768			−0.189384	−	0.981903i	$-0.560649\pi$
$883$	−11.2552			−0.378768			−0.189384	+	0.981903i	$0.560649\pi$
$884$	−14.3578	+	24.8684i	−0.482904	+	0.836415i
$885$		0			0
$886$	−55.1438	−	95.5119i	−1.85259	−	3.20879i
$887$	−19.6056	+	33.9579i	−0.658292	+	1.14020i	0.322765	+	0.946479i	$0.395388\pi$
$887$	−19.6056	+	33.9579i	−0.658292	+	1.14020i	−0.981057	+	0.193717i	$0.937946\pi$
$888$		0			0
$889$	−19.3123	+	12.9530i	−0.647712	+	0.434429i
$890$	34.3792			1.15239
$891$		0			0
$892$	14.4959	+	25.1077i	0.485360	+	0.840668i
$893$	0.884638	+	1.53224i	0.0296033	+	0.0512744i
$894$		0			0
$895$	31.5249			1.05376
$896$	6.21266	+	92.3107i	0.207551	+	3.08389i
$897$		0			0
$898$	37.8316	−	65.5263i	1.26246	−	2.18664i
$899$	−1.59536	−	2.76325i	−0.0532083	−	0.0921595i
$900$		0			0
$901$	12.9322	−	22.3992i	0.430834	−	0.746226i
$902$	20.9106			0.696247
$903$		0			0
$904$	28.9903			0.964203
$905$	19.7954	−	34.2866i	0.658020	−	1.13972i
$906$		0			0
$907$	−10.7985	−	18.7035i	−0.358558	−	0.621040i	0.629162	−	0.777274i	$-0.283398\pi$
$907$	−10.7985	−	18.7035i	−0.358558	−	0.621040i	−0.987720	+	0.156234i	$0.950065\pi$
$908$	54.5997	−	94.5694i	1.81195	−	3.13840i
$909$		0			0
$910$	14.1560	+	6.95021i	0.469268	+	0.230397i
$911$	32.4434			1.07490			0.537449	−	0.843297i	$-0.319388\pi$
$911$	32.4434			1.07490			0.537449	+	0.843297i	$0.319388\pi$
$912$		0			0
$913$	−3.49328	−	6.05054i	−0.115611	−	0.200244i
$914$	−15.2531	−	26.4192i	−0.504528	−	0.873868i
$915$		0			0
$916$	137.030			4.52760
$917$	−1.86802	−	27.7559i	−0.0616873	−	0.916580i
$918$		0			0
$919$	−17.8686	+	30.9493i	−0.589430	+	1.02092i	0.404877	+	0.914371i	$0.367314\pi$
$919$	−17.8686	+	30.9493i	−0.589430	+	1.02092i	−0.994307	+	0.106552i	$0.966019\pi$
$920$	6.67532	+	11.5620i	0.220079	+	0.381187i
$921$		0			0
$922$	12.6693	−	21.9439i	0.417242	−	0.722684i
$923$	6.60274			0.217332
$924$		0			0
$925$	2.35636			0.0774765
$926$	38.4858	−	66.6594i	1.26472	−	2.19056i
$927$		0			0
$928$	32.7559	+	56.7349i	1.07527	+	1.86241i
$929$	5.88847	−	10.1991i	0.193194	−	0.334622i	−0.753113	−	0.657891i	$-0.771449\pi$
$929$	5.88847	−	10.1991i	0.193194	−	0.334622i	0.946307	+	0.323269i	$0.104782\pi$
$930$		0			0
$931$	3.24012	+	4.19214i	0.106191	+	0.137392i
$932$	4.30553			0.141032
$933$		0			0
$934$	−30.3329	−	52.5382i	−0.992523	−	1.71910i
$935$	6.06506	+	10.5050i	0.198349	+	0.343550i
$936$		0			0
$937$	18.9937			0.620497			0.310248	−	0.950655i	$-0.399588\pi$
$937$	18.9937			0.620497			0.310248	+	0.950655i	$0.399588\pi$
$938$	26.8203	−	17.9887i	0.875713	−	0.587352i
$939$		0			0
$940$	−13.8728	+	24.0284i	−0.452480	+	0.783719i
$941$	3.40932	+	5.90511i	0.111141	+	0.192501i	0.916230	−	0.400652i	$-0.131216\pi$
$941$	3.40932	+	5.90511i	0.111141	+	0.192501i	−0.805090	+	0.593153i	$0.797883\pi$
$942$		0			0
$943$	−2.39225	+	4.14349i	−0.0779023	+	0.134931i
$944$	15.3012			0.498012
$945$		0			0
$946$	−2.53590			−0.0824493
$947$	0.529958	−	0.917914i	0.0172213	−	0.0298282i	−0.857286	−	0.514840i	$-0.827851\pi$
$947$	0.529958	−	0.917914i	0.0172213	−	0.0298282i	0.874508	+	0.485012i	$0.161185\pi$
$948$		0			0
$949$	4.14174	+	7.17370i	0.134446	+	0.232868i
$950$	−0.223102	+	0.386424i	−0.00723838	+	0.0125372i
$951$		0			0
$952$	−117.363	−	57.6219i	−3.80376	−	1.86753i
$953$	40.4127			1.30910			0.654548	−	0.756020i	$-0.272859\pi$
$953$	40.4127			1.30910			0.654548	+	0.756020i	$0.272859\pi$
$954$		0			0
$955$	−6.05993	−	10.4961i	−0.196095	−	0.339646i
$956$	54.4023	+	94.2276i	1.75950	+	3.04754i
$957$		0			0
$958$	−89.5964			−2.89473
$959$	−20.7372	−	10.1814i	−0.669639	−	0.328774i
$960$		0			0
$961$	14.9717	−	25.9317i	0.482958	−	0.836508i
$962$	−14.8434	−	25.7095i	−0.478570	−	0.828907i
$963$		0			0
$964$	−37.4789	+	64.9154i	−1.20711	+	2.09078i
$965$	19.1177			0.615422
$966$		0			0
$967$	−36.2949			−1.16717			−0.583583	−	0.812053i	$-0.698350\pi$
$967$	−36.2949			−1.16717			−0.583583	+	0.812053i	$0.698350\pi$
$968$	−46.2365	+	80.0839i	−1.48610	+	2.57399i
$969$		0			0
$970$	8.60638	+	14.9067i	0.276334	+	0.478625i
$971$	−10.7218	+	18.5708i	−0.344080	+	0.595964i	−0.985186	−	0.171488i	$-0.945142\pi$
$971$	−10.7218	+	18.5708i	−0.344080	+	0.595964i	0.641106	+	0.767452i	$0.278476\pi$
$972$		0			0
$973$	8.78914	−	5.89500i	0.281767	−	0.188985i
$974$	76.0137			2.43564
$975$		0			0
$976$	91.2374	+	158.028i	2.92044	+	5.05835i
$977$	−19.9138	−	34.4918i	−0.637100	−	1.10349i	−0.986066	−	0.166354i	$-0.946801\pi$
$977$	−19.9138	−	34.4918i	−0.637100	−	1.10349i	0.348966	−	0.937135i	$-0.386533\pi$
$978$		0			0
$979$	6.04551			0.193215
$980$	−31.5275	+	76.8742i	−1.00711	+	2.45565i
$981$		0			0
$982$	−14.5216	+	25.1522i	−0.463403	+	0.802638i
$983$	7.94071	+	13.7537i	0.253269	+	0.438675i	0.964424	−	0.264360i	$-0.0851608\pi$
$983$	7.94071	+	13.7537i	0.253269	+	0.438675i	−0.711155	+	0.703036i	$0.751827\pi$
$984$		0			0
$985$	5.98052	−	10.3586i	0.190555	−	0.330051i
$986$	−44.7608			−1.42548
$987$		0			0
$988$	4.10772			0.130684
$989$	0.290116	−	0.502496i	0.00922516	−	0.0159785i
$990$		0			0
$991$	8.83435	+	15.3016i	0.280633	+	0.486070i	0.971541	−	0.236873i	$-0.0761225\pi$
$991$	8.83435	+	15.3016i	0.280633	+	0.486070i	−0.690908	+	0.722943i	$0.742789\pi$
$992$	10.8471	−	18.7877i	0.344394	−	0.596509i
$993$		0			0
$994$	3.19686	+	47.5005i	0.101398	+	1.50662i
$995$	−42.7301			−1.35464
$996$		0			0
$997$	12.4304	+	21.5301i	0.393675	+	0.681865i	0.992931	−	0.118692i	$-0.0378701\pi$
$997$	12.4304	+	21.5301i	0.393675	+	0.681865i	−0.599256	+	0.800558i	$0.704537\pi$
$998$	−33.3999	−	57.8503i	−1.05725	−	1.83122i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.j.h.352.5		10
3.2	odd	2		91.2.e.c.79.1	yes	10
7.2	even	3		5733.2.a.bl.1.1		5
7.4	even	3	inner	819.2.j.h.235.5		10
7.5	odd	6		5733.2.a.bm.1.1		5
12.11	even	2		1456.2.r.p.625.2		10
21.2	odd	6		637.2.a.l.1.5		5
21.5	even	6		637.2.a.k.1.5		5
21.11	odd	6		91.2.e.c.53.1	✓	10
21.17	even	6		637.2.e.m.508.1		10
21.20	even	2		637.2.e.m.79.1		10
39.38	odd	2		1183.2.e.f.170.5		10
84.11	even	6		1456.2.r.p.417.2		10
273.116	odd	6		1183.2.e.f.508.5		10
273.194	even	6		8281.2.a.bx.1.1		5
273.233	odd	6		8281.2.a.bw.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.e.c.53.1	✓	10	21.11	odd	6
91.2.e.c.79.1	yes	10	3.2	odd	2
637.2.a.k.1.5		5	21.5	even	6
637.2.a.l.1.5		5	21.2	odd	6
637.2.e.m.79.1		10	21.20	even	2
637.2.e.m.508.1		10	21.17	even	6
819.2.j.h.235.5		10	7.4	even	3	inner
819.2.j.h.352.5		10	1.1	even	1	trivial
1183.2.e.f.170.5		10	39.38	odd	2
1183.2.e.f.508.5		10	273.116	odd	6
1456.2.r.p.417.2		10	84.11	even	6
1456.2.r.p.625.2		10	12.11	even	2
5733.2.a.bl.1.1		5	7.2	even	3
5733.2.a.bm.1.1		5	7.5	odd	6
8281.2.a.bw.1.1		5	273.233	odd	6
8281.2.a.bx.1.1		5	273.194	even	6

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36263 - 2.36014i) q^{2} +(-2.71349 - 4.69991i) q^{4} +(1.09358 - 1.89414i) q^{5} +(-2.19729 + 1.47375i) q^{7} -9.33940 q^{8} +O(q^{10})\)	\(q+(1.36263 - 2.36014i) q^{2} +(-2.71349 - 4.69991i) q^{4} +(1.09358 - 1.89414i) q^{5} +(-2.19729 + 1.47375i) q^{7} -9.33940 q^{8} +(-2.98028 - 5.16200i) q^{10} +(-0.524077 - 0.907729i) q^{11} +1.00000 q^{13} +(0.484172 + 7.19406i) q^{14} +(-7.29912 + 12.6424i) q^{16} +(-2.64562 - 4.58236i) q^{17} +(-0.378453 + 0.655500i) q^{19} -11.8697 q^{20} -2.85648 q^{22} +(0.326792 - 0.566020i) q^{23} +(0.108157 + 0.187333i) q^{25} +(1.36263 - 2.36014i) q^{26} +(12.8888 + 6.32803i) q^{28} +3.10408 q^{29} +(-0.513956 - 0.890198i) q^{31} +(10.5525 + 18.2775i) q^{32} -14.4200 q^{34} +(0.388575 + 5.77363i) q^{35} +(5.44661 - 9.43381i) q^{37} +(1.03138 + 1.78640i) q^{38} +(-10.2134 + 17.6901i) q^{40} -7.32040 q^{41} +0.887771 q^{43} +(-2.84416 + 4.92623i) q^{44} +(-0.890590 - 1.54255i) q^{46} +(1.16875 - 2.02434i) q^{47} +(2.65613 - 6.47650i) q^{49} +0.589510 q^{50} +(-2.71349 - 4.69991i) q^{52} +(2.44407 + 4.23325i) q^{53} -2.29249 q^{55} +(20.5213 - 13.7639i) q^{56} +(4.22970 - 7.32606i) q^{58} +(-0.524077 - 0.907729i) q^{59} +(6.24989 - 10.8251i) q^{61} -2.80132 q^{62} +28.3200 q^{64} +(1.09358 - 1.89414i) q^{65} +(-2.23944 - 3.87883i) q^{67} +(-14.3578 + 24.8684i) q^{68} +(14.1560 + 6.95021i) q^{70} +6.60274 q^{71} +(4.14174 + 7.17370i) q^{73} +(-14.8434 - 25.7095i) q^{74} +4.10772 q^{76} +(2.48931 + 1.22218i) q^{77} +(-1.07007 + 1.85342i) q^{79} +(15.9644 + 27.6511i) q^{80} +(-9.97496 + 17.2771i) q^{82} +6.66558 q^{83} -11.5728 q^{85} +(1.20970 - 2.09526i) q^{86} +(4.89457 + 8.47765i) q^{88} +(-2.88388 + 4.99503i) q^{89} +(-2.19729 + 1.47375i) q^{91} -3.54699 q^{92} +(-3.18515 - 5.51684i) q^{94} +(0.827739 + 1.43369i) q^{95} -2.88777 q^{97} +(-11.6661 - 15.0939i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} - 8 q^{4} + 2 q^{5} + q^{7} - 18 q^{8}+O(q^{10}) \) 10 * q + 4 * q^2 - 8 * q^4 + 2 * q^5 + q^7 - 18 * q^8	\( 10 q + 4 q^{2} - 8 q^{4} + 2 q^{5} + q^{7} - 18 q^{8} + 5 q^{10} + 11 q^{11} + 10 q^{13} - 10 q^{14} - 10 q^{16} - 5 q^{17} - 9 q^{19} - 2 q^{20} + 16 q^{22} + 10 q^{23} - 9 q^{25} + 4 q^{26} + 37 q^{28} + 6 q^{29} + 6 q^{31} + 22 q^{32} - 44 q^{34} + 4 q^{35} - 4 q^{37} - 10 q^{38} - 28 q^{40} - 28 q^{41} + 4 q^{43} - 3 q^{46} + q^{47} - 11 q^{49} - 18 q^{50} - 8 q^{52} + 17 q^{53} + 21 q^{56} + 27 q^{58} + 11 q^{59} + 11 q^{61} + 46 q^{62} + 18 q^{64} + 2 q^{65} - 13 q^{67} - 32 q^{68} + 49 q^{70} - 30 q^{71} - 33 q^{74} + 16 q^{76} + 46 q^{77} - 2 q^{79} + 55 q^{80} - 34 q^{82} - 12 q^{83} - 44 q^{85} + 28 q^{86} + 3 q^{88} - 4 q^{89} + q^{91} - 42 q^{92} - 20 q^{94} - 12 q^{95} - 24 q^{97} + 7 q^{98}+O(q^{100}) \) 10 * q + 4 * q^2 - 8 * q^4 + 2 * q^5 + q^7 - 18 * q^8 + 5 * q^10 + 11 * q^11 + 10 * q^13 - 10 * q^14 - 10 * q^16 - 5 * q^17 - 9 * q^19 - 2 * q^20 + 16 * q^22 + 10 * q^23 - 9 * q^25 + 4 * q^26 + 37 * q^28 + 6 * q^29 + 6 * q^31 + 22 * q^32 - 44 * q^34 + 4 * q^35 - 4 * q^37 - 10 * q^38 - 28 * q^40 - 28 * q^41 + 4 * q^43 - 3 * q^46 + q^47 - 11 * q^49 - 18 * q^50 - 8 * q^52 + 17 * q^53 + 21 * q^56 + 27 * q^58 + 11 * q^59 + 11 * q^61 + 46 * q^62 + 18 * q^64 + 2 * q^65 - 13 * q^67 - 32 * q^68 + 49 * q^70 - 30 * q^71 - 33 * q^74 + 16 * q^76 + 46 * q^77 - 2 * q^79 + 55 * q^80 - 34 * q^82 - 12 * q^83 - 44 * q^85 + 28 * q^86 + 3 * q^88 - 4 * q^89 + q^91 - 42 * q^92 - 20 * q^94 - 12 * q^95 - 24 * q^97 + 7 * q^98

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