LMFDB - Embedded newform 819.2.j.h.235.5

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			235.5
Root			$-0.862625 - 1.49411i$ of defining polynomial
Character	$\chi$	$=$	819.235
Dual form			819.2.j.h.352.5

$q$-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 $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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	0.713536	+	0.700619i	$0.247093\pi$
$2$	1.36263	+	2.36014i	0.963521	+	1.66887i	0.249986	+	0.968250i	$0.419574\pi$
$3$		0			0
$3$		0			0
$4$	−2.71349	+	4.69991i	−1.35675	+	2.34996i
$5$	1.09358	+	1.89414i	0.489065	+	0.847085i	0.999921	−	0.0125813i	$-0.00400485\pi$
$5$	1.09358	+	1.89414i	0.489065	+	0.847085i	−0.510856	+	0.859666i	$0.670672\pi$
$6$		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	−0.934153	−	0.356873i	$-0.883843\pi$
$11$	−0.524077	+	0.907729i	−0.158015	+	0.273691i	0.776138	+	0.630564i	$0.217176\pi$
$12$		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	0.343404	+	0.939188i	$0.388420\pi$
$17$	−2.64562	+	4.58236i	−0.641658	+	1.11138i	−0.985063	+	0.172197i	$0.944913\pi$
$18$		0			0
$19$	−0.378453	−	0.655500i	−0.0868231	−	0.150382i	0.819344	−	0.573303i	$-0.194338\pi$
$19$	−0.378453	−	0.655500i	−0.0868231	−	0.150382i	−0.906167	+	0.422921i	$0.861005\pi$
$20$	−11.8697			−2.65415
$21$		0			0
$22$	−2.85648			−0.609005
$23$	0.326792	+	0.566020i	0.0681408	+	0.118023i	0.898083	−	0.439826i	$-0.144960\pi$
$23$	0.326792	+	0.566020i	0.0681408	+	0.118023i	−0.829942	+	0.557850i	$0.811627\pi$
$24$		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	−0.908482	−	0.417923i	$-0.862758\pi$
$31$	−0.513956	+	0.890198i	−0.0923092	+	0.159884i	0.816173	+	0.577807i	$0.196091\pi$
$32$	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	0.833287	+	0.552841i	$0.186456\pi$
$37$	5.44661	+	9.43381i	0.895418	+	1.55091i	0.0621309	+	0.998068i	$0.480210\pi$
$38$	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	0.938588	−	0.345040i	$-0.112135\pi$
$47$	1.16875	+	2.02434i	0.170480	+	0.295281i	−0.768108	+	0.640321i	$0.778801\pi$
$48$		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	−0.647904	−	0.761722i	$-0.724354\pi$
$53$	2.44407	−	4.23325i	0.335719	−	0.581482i	0.983623	+	0.180240i	$0.0576875\pi$
$54$		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	−0.898122	−	0.439747i	$-0.855068\pi$
$59$	−0.524077	+	0.907729i	−0.0682291	+	0.118176i	0.829893	+	0.557923i	$0.188402\pi$
$60$		0			0
$61$	6.24989	+	10.8251i	0.800217	+	1.38602i	0.919473	+	0.393153i	$0.128616\pi$
$61$	6.24989	+	10.8251i	0.800217	+	1.38602i	−0.119256	+	0.992864i	$0.538051\pi$
$62$	−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	−0.969779	−	0.243986i	$-0.921545\pi$
$67$	−2.23944	+	3.87883i	−0.273592	+	0.473875i	0.696187	+	0.717860i	$0.254878\pi$
$68$	−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	−0.515093	−	0.857134i	$-0.672243\pi$
$73$	4.14174	−	7.17370i	0.484754	−	0.839618i	0.999847	+	0.0175164i	$0.00557593\pi$
$74$	−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	0.799530	−	0.600626i	$-0.205082\pi$
$79$	−1.07007	−	1.85342i	−0.120392	−	0.208526i	−0.919922	+	0.392100i	$0.871749\pi$
$80$	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	0.671724	−	0.740802i	$-0.265554\pi$
$89$	−2.88388	−	4.99503i	−0.305691	−	0.529472i	−0.977415	+	0.211329i	$0.932221\pi$
$90$		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	0.437579	+	0.899180i	$0.355836\pi$
$101$	−5.62716	+	9.74653i	−0.559924	+	0.969816i	−0.997502	+	0.0706359i	$0.977497\pi$
$102$		0			0
$103$	−10.1167	−	17.5226i	−0.996828	−	1.72656i	−0.567341	−	0.823483i	$-0.692028\pi$
$103$	−10.1167	−	17.5226i	−0.996828	−	1.72656i	−0.429487	−	0.903073i	$-0.641306\pi$
$104$	−9.33940			−0.915804
$105$		0			0
$106$	13.3214			1.29389
$107$	4.52758	+	7.84201i	0.437698	+	0.758115i	0.997512	−	0.0705034i	$-0.0224606\pi$
$107$	4.52758	+	7.84201i	0.437698	+	0.758115i	−0.559813	+	0.828619i	$0.689127\pi$
$108$		0			0
$109$	−7.55070	+	13.0782i	−0.723226	+	1.25266i	0.236474	+	0.971638i	$0.424008\pi$
$109$	−7.55070	+	13.0782i	−0.723226	+	1.25266i	−0.959700	+	0.281026i	$0.909325\pi$
$110$	−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	0.539599	−	0.841922i	$-0.318576\pi$
$131$	−5.25723	−	9.10580i	−0.459327	−	0.795577i	−0.998925	+	0.0463451i	$0.985243\pi$
$132$		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	−0.617028	−	0.786942i	$-0.711663\pi$
$137$	4.36583	−	7.56183i	0.372998	−	0.646051i	0.990025	+	0.140891i	$0.0449966\pi$
$138$		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	0.987448	+	0.157944i	$0.0504864\pi$
$149$	7.69632	+	13.3304i	0.630507	+	1.09207i	−0.356941	+	0.934127i	$0.616180\pi$
$150$		0			0
$151$	6.83786	−	11.8435i	0.556457	−	0.963812i	−0.441331	−	0.897344i	$-0.645494\pi$
$151$	6.83786	−	11.8435i	0.556457	−	0.963812i	0.997789	−	0.0664680i	$-0.0211730\pi$
$152$	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	−0.925666	−	0.378343i	$-0.876494\pi$
$157$	−1.69378	+	2.93371i	−0.135178	+	0.234136i	0.790487	+	0.612478i	$0.209827\pi$
$158$	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	0.998856	+	0.0478219i	$0.0152280\pi$
$163$	6.90502	+	11.9598i	0.540843	+	0.936767i	−0.458013	+	0.888946i	$0.651439\pi$
$164$	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	0.933723	−	0.357997i	$-0.116540\pi$
$173$	2.06273	+	3.57275i	0.156826	+	0.271631i	−0.776896	+	0.629629i	$0.783207\pi$
$174$		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	−0.460316	−	0.887755i	$-0.652264\pi$
$179$	7.20679	−	12.4825i	0.538661	−	0.932988i	0.998976	−	0.0452324i	$-0.0144028\pi$
$180$		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	0.948683	−	0.316229i	$-0.102417\pi$
$191$	2.77068	+	4.79895i	0.200479	+	0.347240i	−0.748204	+	0.663469i	$0.769083\pi$
$192$		0			0
$193$	4.37044	−	7.56983i	0.314591	−	0.544888i	−0.664759	−	0.747058i	$-0.731466\pi$
$193$	4.37044	−	7.56983i	0.314591	−	0.544888i	0.979351	+	0.202170i	$0.0647992\pi$
$194$	−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	0.278566	+	0.960417i	$0.410141\pi$
$199$	−9.76839	+	16.9193i	−0.692463	+	1.19938i	−0.971029	+	0.238963i	$0.923192\pi$
$200$	−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	−0.310774	−	0.950484i	$-0.600588\pi$
$227$	10.0608	−	17.4258i	0.667757	−	1.15659i	0.978530	−	0.206104i	$-0.0660786\pi$
$228$		0			0
$229$	−12.6249	−	21.8669i	−0.834275	−	1.44501i	−0.894619	−	0.446829i	$-0.852553\pi$
$229$	−12.6249	−	21.8669i	−0.834275	−	1.44501i	0.0603445	−	0.998178i	$-0.480780\pi$
$230$	−3.89573			−0.256877
$231$		0			0
$232$	−28.9903			−1.90331
$233$	−0.396678	−	0.687066i	−0.0259872	−	0.0450112i	0.852739	−	0.522337i	$-0.174940\pi$
$233$	−0.396678	−	0.687066i	−0.0259872	−	0.0450112i	−0.878727	+	0.477326i	$0.841606\pi$
$234$		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	−0.998042	−	0.0625446i	$-0.980078\pi$
$241$	−6.90602	+	11.9616i	−0.444856	+	0.770513i	0.553186	+	0.833058i	$0.313412\pi$
$242$	−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	0.982752	−	0.184930i	$-0.0592057\pi$
$257$	5.30990	+	9.19701i	0.331222	+	0.573694i	−0.651530	+	0.758623i	$0.725872\pi$
$258$		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	−0.661008	−	0.750379i	$-0.729871\pi$
$263$	5.17888	−	8.97008i	0.319343	−	0.553119i	0.980351	+	0.197260i	$0.0632044\pi$
$264$		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	−0.623849	−	0.781545i	$-0.714432\pi$
$269$	5.98503	−	10.3664i	0.364914	−	0.632049i	0.988762	+	0.149496i	$0.0477652\pi$
$270$		0			0
$271$	1.37845	+	2.38755i	0.0837351	+	0.145033i	0.904852	−	0.425727i	$-0.139982\pi$
$271$	1.37845	+	2.38755i	0.0837351	+	0.145033i	−0.821116	+	0.570761i	$0.806648\pi$
$272$	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	−0.242632	−	0.970118i	$-0.578011\pi$
$277$	11.9637	−	20.7218i	0.718831	−	1.24505i	0.961463	−	0.274933i	$-0.0886558\pi$
$278$	−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	−0.758860	−	0.651254i	$-0.774243\pi$
$283$	3.10499	−	5.37801i	0.184573	−	0.319689i	0.943432	+	0.331565i	$0.107577\pi$
$284$	−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	−0.394514	−	0.918890i	$-0.629087\pi$
$311$	10.5551	−	18.2820i	0.598525	−	1.03668i	0.993039	−	0.117785i	$-0.0375795\pi$
$312$		0			0
$313$	−0.990260	−	1.71518i	−0.0559728	−	0.0969477i	0.836681	−	0.547690i	$-0.184493\pi$
$313$	−0.990260	−	1.71518i	−0.0559728	−	0.0969477i	−0.892654	+	0.450742i	$0.851159\pi$
$314$	−9.23194			−0.520989
$315$		0			0
$316$	11.6145			0.653368
$317$	−9.02297	−	15.6282i	−0.506781	−	0.877770i	−0.999969	−	0.00784727i	$-0.997502\pi$
$317$	−9.02297	−	15.6282i	−0.506781	−	0.877770i	0.493189	−	0.869922i	$-0.335831\pi$
$318$		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	0.994119	−	0.108296i	$-0.0345395\pi$
$331$	7.33689	+	12.7079i	0.403272	+	0.698488i	−0.590847	+	0.806784i	$0.701206\pi$
$332$	−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	−0.456428	−	0.889761i	$-0.650871\pi$
$347$	10.1027	−	17.4984i	0.542342	−	0.939363i	0.998769	−	0.0496025i	$-0.0157954\pi$
$348$		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	−0.953810	−	0.300412i	$-0.902876\pi$
$353$	−4.07218	+	7.05322i	−0.216740	+	0.375405i	0.737069	+	0.675817i	$0.236209\pi$
$354$		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	−0.871404	−	0.490566i	$-0.836790\pi$
$359$	−16.3050	−	28.2411i	−0.860545	−	1.49051i	0.0108595	−	0.999941i	$-0.496543\pi$
$360$		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	−0.821835	−	0.569725i	$-0.807050\pi$
$367$	1.58006	−	2.73675i	0.0824786	−	0.142857i	0.904314	+	0.426868i	$0.140383\pi$
$368$	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	0.884520	−	0.466503i	$-0.154486\pi$
$373$	0.738849	+	1.27972i	0.0382561	+	0.0662616i	−0.846263	+	0.532765i	$0.821153\pi$
$374$	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	−0.998477	−	0.0551766i	$-0.982428\pi$
$383$	−10.7054	−	18.5424i	−0.547023	−	0.947471i	0.451454	−	0.892294i	$-0.350906\pi$
$384$		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	0.0323675	−	0.999476i	$-0.489695\pi$
$389$	17.3909	−	30.1220i	0.881755	−	1.52725i	0.849388	−	0.527769i	$-0.176971\pi$
$390$		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	0.804742	−	0.593624i	$-0.202303\pi$
$397$	−2.22605	−	3.85564i	−0.111722	−	0.193509i	−0.916465	+	0.400115i	$0.868970\pi$
$398$	−53.2426			−2.66881
$399$		0			0
$400$	−3.15780			−0.157890
$401$	−6.87687	−	11.9111i	−0.343415	−	0.594811i	0.641650	−	0.766998i	$-0.278250\pi$
$401$	−6.87687	−	11.9111i	−0.343415	−	0.594811i	−0.985064	+	0.172186i	$0.944917\pi$
$402$		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	−0.819624	−	0.572902i	$-0.805818\pi$
$409$	1.74603	−	3.02422i	0.0863358	−	0.149538i	0.905960	+	0.423364i	$0.139151\pi$
$410$	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	−0.969806	−	0.243879i	$-0.921580\pi$
$431$	−5.68211	+	9.84171i	−0.273698	+	0.474059i	0.696108	+	0.717937i	$0.254913\pi$
$432$		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	0.994916	+	0.100711i	$0.0321118\pi$
$439$	12.2503	+	21.2182i	0.584676	+	1.01269i	−0.410239	+	0.911978i	$0.634555\pi$
$440$	21.4105			1.02070
$441$		0			0
$442$	−14.4200			−0.685888
$443$	20.2344	+	35.0470i	0.961366	+	1.66513i	0.719077	+	0.694930i	$0.244565\pi$
$443$	20.2344	+	35.0470i	0.961366	+	1.66513i	0.242288	+	0.970204i	$0.422102\pi$
$444$		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	0.966724	−	0.255821i	$-0.0823457\pi$
$457$	5.59696	+	9.69422i	0.261815	+	0.453476i	−0.704910	+	0.709297i	$0.749012\pi$
$458$	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	0.999847	+	0.0174663i	$0.00555997\pi$
$467$	11.1303	+	19.2783i	0.515050	+	0.892093i	−0.484797	+	0.874626i	$0.661107\pi$
$468$		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	0.196219	+	0.980560i	$0.437134\pi$
$479$	−16.4382	+	28.4718i	−0.751081	+	1.30091i	−0.947299	+	0.320350i	$0.896200\pi$
$480$		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	−0.355188	−	0.934795i	$-0.615583\pi$
$487$	13.9462	−	24.1555i	0.631962	−	1.09459i	0.987150	−	0.159796i	$-0.0510836\pi$
$488$	−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	0.998368	+	0.0571077i	$0.0181878\pi$
$499$	12.2557	+	21.2275i	0.548641	+	0.950274i	−0.449727	+	0.893166i	$0.648479\pi$
$500$	−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	0.847807	+	0.530305i	$0.177923\pi$
$509$	19.9250	+	34.5112i	0.883161	+	1.52968i	0.0353545	+	0.999375i	$0.488744\pi$
$510$		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	−0.996880	−	0.0789382i	$-0.974847\pi$
$521$	−9.81670	+	17.0030i	−0.430077	+	0.744916i	0.566802	+	0.823854i	$0.308180\pi$
$522$		0			0
$523$	−11.4162	−	19.7734i	−0.499195	−	0.864632i	0.500804	−	0.865561i	$-0.333038\pi$
$523$	−11.4162	−	19.7734i	−0.499195	−	0.864632i	−1.00000		0.000928862i	$0.999704\pi$
$524$	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	0.950886	−	0.309542i	$-0.100176\pi$
$541$	4.82334	+	8.35427i	0.207372	+	0.359178i	−0.743514	+	0.668720i	$0.766842\pi$
$542$	−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	−0.663586	−	0.748100i	$-0.730966\pi$
$557$	7.45977	−	12.9207i	0.316080	−	0.547467i	0.979667	+	0.200633i	$0.0642997\pi$
$558$		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	−0.988602	−	0.150555i	$-0.951894\pi$
$563$	−8.63486	+	14.9560i	−0.363916	+	0.630321i	0.624686	+	0.780876i	$0.285227\pi$
$564$		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	0.997813	+	0.0660972i	$0.0210547\pi$
$569$	13.2662	+	22.9777i	0.556148	+	0.963277i	−0.441665	+	0.897180i	$0.645612\pi$
$570$		0			0
$571$	0.992844	−	1.71966i	0.0415492	−	0.0719654i	−0.844503	−	0.535551i	$-0.820104\pi$
$571$	0.992844	−	1.71966i	0.0415492	−	0.0719654i	0.886052	+	0.463586i	$0.153437\pi$
$572$	−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	−0.962878	−	0.269937i	$-0.912997\pi$
$577$	−5.94915	+	10.3042i	−0.247666	+	0.428971i	0.715212	+	0.698908i	$0.246330\pi$
$578$	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	0.959213	+	0.282686i	$0.0912253\pi$
$593$	17.6408	+	30.5547i	0.724419	+	1.25473i	−0.234793	+	0.972045i	$0.575441\pi$
$594$		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	0.489045	+	0.872259i	$0.337345\pi$
$599$	−12.5034	+	21.6565i	−0.510876	+	0.884863i	−0.999921	+	0.0126040i	$0.995988\pi$
$600$		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	−0.956221	−	0.292646i	$-0.905464\pi$
$607$	−18.0234	−	31.2175i	−0.731549	−	1.26708i	0.224672	−	0.974434i	$-0.427869\pi$
$608$	−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	−0.989577	−	0.144006i	$-0.954001\pi$
$613$	−9.16264	+	15.8702i	−0.370075	+	0.640989i	0.619501	+	0.784996i	$0.287335\pi$
$614$	−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	−0.497407	−	0.867517i	$-0.665714\pi$
$619$	12.5043	−	21.6580i	0.502588	−	0.870509i	0.999996	−	0.00299144i	$-0.000952205\pi$
$620$	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	−0.995919	−	0.0902567i	$-0.971231\pi$
$641$	−10.6284	+	18.4088i	−0.419795	+	0.727106i	0.576124	+	0.817362i	$0.304565\pi$
$642$		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	−0.147490	−	0.989064i	$-0.547119\pi$
$647$	19.9117	−	34.4881i	0.782809	−	1.35587i	0.930299	−	0.366802i	$-0.119547\pi$
$648$		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	−0.986459	−	0.164008i	$-0.947558\pi$
$653$	−16.2335	−	28.1172i	−0.635265	−	1.10031i	0.351195	−	0.936303i	$-0.385776\pi$
$654$		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	−0.969635	−	0.244557i	$-0.921357\pi$
$661$	−7.01944	+	12.1580i	−0.273025	+	0.472893i	0.696610	+	0.717450i	$0.254691\pi$
$662$	−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	0.759065	−	0.651015i	$-0.225656\pi$
$677$	−4.79438	−	8.30411i	−0.184263	−	0.319153i	−0.943328	+	0.331862i	$0.892323\pi$
$678$		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	0.0846691	−	0.996409i	$-0.473017\pi$
$683$	23.6581	−	40.9769i	0.905250	−	1.56794i	0.820581	−	0.571530i	$-0.193650\pi$
$684$		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	0.999834	+	0.0182158i	$0.00579859\pi$
$691$	13.5559	+	23.4796i	0.515692	+	0.893205i	−0.484142	+	0.874990i	$0.660868\pi$
$692$	−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	0.999309	+	0.0371721i	$0.0118350\pi$
$709$	14.1615	+	24.5284i	0.531846	+	0.921185i	−0.467462	+	0.884013i	$0.654832\pi$
$710$	−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	−0.931215	−	0.364471i	$-0.881250\pi$
$719$	−20.9485	−	36.2839i	−0.781249	−	1.35316i	0.149966	−	0.988691i	$-0.452084\pi$
$720$		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	0.654212	−	0.756311i	$-0.273000\pi$
$733$	−8.87698	−	15.3754i	−0.327879	−	0.567902i	−0.982091	+	0.188409i	$0.939667\pi$
$734$	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	0.0942227	+	0.995551i	$0.469963\pi$
$739$	−22.1571	+	38.3772i	−0.815061	+	1.41173i	−0.909284	+	0.416176i	$0.863370\pi$
$740$	−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	0.989736	+	0.142911i	$0.0456462\pi$
$751$	16.9532	+	29.3639i	0.618632	+	1.07150i	−0.371103	+	0.928592i	$0.621020\pi$
$752$	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	0.989098	−	0.147258i	$-0.0470449\pi$
$761$	10.1247	+	17.5365i	0.367020	+	0.635697i	−0.622079	+	0.782955i	$0.713712\pi$
$762$		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	−0.941088	−	0.338163i	$-0.890194\pi$
$773$	−4.94018	+	8.55665i	−0.177686	+	0.307761i	0.763402	+	0.645924i	$0.223528\pi$
$774$		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	0.305836	+	0.952084i	$0.401064\pi$
$787$	−18.8411	+	32.6337i	−0.671611	+	1.16326i	−0.977447	+	0.211180i	$0.932269\pi$
$788$	−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	−0.950607	−	0.310396i	$-0.899539\pi$
$809$	−5.87327	+	10.1728i	−0.206493	+	0.357657i	0.744114	+	0.668052i	$0.232872\pi$
$810$		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	0.703875	−	0.710323i	$-0.251451\pi$
$821$	−7.54208	−	13.0633i	−0.263220	−	0.455911i	−0.967096	+	0.254412i	$0.918118\pi$
$822$		0			0
$823$	7.38828	−	12.7969i	0.257539	−	0.446071i	−0.708043	−	0.706170i	$-0.750422\pi$
$823$	7.38828	−	12.7969i	0.257539	−	0.446071i	0.965582	+	0.260098i	$0.0837550\pi$
$824$	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	−0.555746	−	0.831352i	$-0.687567\pi$
$829$	12.7291	−	22.0474i	0.442099	−	0.765738i	0.997845	+	0.0656144i	$0.0209007\pi$
$830$	−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	−0.677987	−	0.735074i	$-0.737147\pi$
$857$	8.71210	−	15.0898i	0.297600	−	0.515458i	0.975586	+	0.219616i	$0.0704806\pi$
$858$		0			0
$859$	17.7459	+	30.7367i	0.605481	+	1.04872i	0.991975	+	0.126432i	$0.0403524\pi$
$859$	17.7459	+	30.7367i	0.605481	+	1.04872i	−0.386495	+	0.922292i	$0.626314\pi$
$860$	−10.5376			−0.359329
$861$		0			0
$862$	−30.9704			−1.05486
$863$	28.0010	+	48.4991i	0.953164	+	1.65093i	0.738516	+	0.674236i	$0.235527\pi$
$863$	28.0010	+	48.4991i	0.953164	+	1.65093i	0.214648	+	0.976691i	$0.431140\pi$
$864$		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	0.570898	−	0.821021i	$-0.306595\pi$
$877$	−12.6031	−	21.8292i	−0.425577	−	0.737120i	−0.996474	+	0.0839011i	$0.973262\pi$
$878$	−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	−0.981057	−	0.193717i	$-0.937946\pi$
$887$	−19.6056	−	33.9579i	−0.658292	−	1.14020i	0.322765	−	0.946479i	$-0.395388\pi$
$888$		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	−0.987720	−	0.156234i	$-0.950065\pi$
$907$	−10.7985	+	18.7035i	−0.358558	+	0.621040i	0.629162	+	0.777274i	$0.283398\pi$
$908$	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	−0.994307	−	0.106552i	$-0.966019\pi$
$919$	−17.8686	−	30.9493i	−0.589430	−	1.02092i	0.404877	−	0.914371i	$-0.367314\pi$
$920$	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	0.946307	−	0.323269i	$-0.104782\pi$
$929$	5.88847	+	10.1991i	0.193194	+	0.334622i	−0.753113	+	0.657891i	$0.771449\pi$
$930$		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	−0.805090	−	0.593153i	$-0.797883\pi$
$941$	3.40932	−	5.90511i	0.111141	−	0.192501i	0.916230	+	0.400652i	$0.131216\pi$
$942$		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	0.874508	−	0.485012i	$-0.161185\pi$
$947$	0.529958	+	0.917914i	0.0172213	+	0.0298282i	−0.857286	+	0.514840i	$0.827851\pi$
$948$		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	0.641106	−	0.767452i	$-0.278476\pi$
$971$	−10.7218	−	18.5708i	−0.344080	−	0.595964i	−0.985186	+	0.171488i	$0.945142\pi$
$972$		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	0.348966	+	0.937135i	$0.386533\pi$
$977$	−19.9138	+	34.4918i	−0.637100	+	1.10349i	−0.986066	+	0.166354i	$0.946801\pi$
$978$		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	−0.711155	−	0.703036i	$-0.751827\pi$
$983$	7.94071	−	13.7537i	0.253269	−	0.438675i	0.964424	+	0.264360i	$0.0851608\pi$
$984$		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	−0.690908	−	0.722943i	$-0.742789\pi$
$991$	8.83435	−	15.3016i	0.280633	−	0.486070i	0.971541	+	0.236873i	$0.0761225\pi$
$992$	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	−0.599256	−	0.800558i	$-0.704537\pi$
$997$	12.4304	−	21.5301i	0.393675	−	0.681865i	0.992931	+	0.118692i	$0.0378701\pi$
$998$	−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.235.5		10
3.2	odd	2		91.2.e.c.53.1	✓	10
7.2	even	3	inner	819.2.j.h.352.5		10
7.3	odd	6		5733.2.a.bm.1.1		5
7.4	even	3		5733.2.a.bl.1.1		5
12.11	even	2		1456.2.r.p.417.2		10
21.2	odd	6		91.2.e.c.79.1	yes	10
21.5	even	6		637.2.e.m.79.1		10
21.11	odd	6		637.2.a.l.1.5		5
21.17	even	6		637.2.a.k.1.5		5
21.20	even	2		637.2.e.m.508.1		10
39.38	odd	2		1183.2.e.f.508.5		10
84.23	even	6		1456.2.r.p.625.2		10
273.38	even	6		8281.2.a.bx.1.1		5
273.116	odd	6		8281.2.a.bw.1.1		5
273.233	odd	6		1183.2.e.f.170.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.e.c.53.1	✓	10	3.2	odd	2
91.2.e.c.79.1	yes	10	21.2	odd	6
637.2.a.k.1.5		5	21.17	even	6
637.2.a.l.1.5		5	21.11	odd	6
637.2.e.m.79.1		10	21.5	even	6
637.2.e.m.508.1		10	21.20	even	2
819.2.j.h.235.5		10	1.1	even	1	trivial
819.2.j.h.352.5		10	7.2	even	3	inner
1183.2.e.f.170.5		10	273.233	odd	6
1183.2.e.f.508.5		10	39.38	odd	2
1456.2.r.p.417.2		10	12.11	even	2
1456.2.r.p.625.2		10	84.23	even	6
5733.2.a.bl.1.1		5	7.4	even	3
5733.2.a.bm.1.1		5	7.3	odd	6
8281.2.a.bw.1.1		5	273.116	odd	6
8281.2.a.bx.1.1		5	273.38	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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