LMFDB - Embedded newform 338.4.e.h.23.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [338,4,Mod(23,338)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(338, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("338.23");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	338.e (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$19.9426455819$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.17213603549184.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 $ x^12 - 5x^10 + 19x^8 - 28x^6 + 31x^4 - 6*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.1
Root			$-0.385418 + 0.222521i$ of defining polynomial
Character	$\chi$	$=$	338.23
Dual form			338.4.e.h.147.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.73205 + 1.00000i) q^{2} +(-0.202907 - 0.351445i) q^{3} +(2.00000 - 3.46410i) q^{4} +6.36227i q^{5} +(0.702889 + 0.405813i) q^{6} +(-2.20892 - 1.27532i) q^{7} +8.00000i q^{8} +(13.4177 - 23.2401i) q^{9} +(-6.36227 - 11.0198i) q^{10} +(-22.6214 + 13.0605i) q^{11} -1.62325 q^{12} +5.10129 q^{14} +(2.23599 - 1.29095i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-46.8543 + 81.1540i) q^{17} +53.6706i q^{18} +(32.2446 + 18.6164i) q^{19} +(22.0396 + 12.7245i) q^{20} +1.03509i q^{21} +(26.1209 - 45.2428i) q^{22} +(-52.4630 - 90.8686i) q^{23} +(2.81156 - 1.62325i) q^{24} +84.5215 q^{25} -21.8471 q^{27} +(-8.83570 + 5.10129i) q^{28} +(-124.772 - 216.112i) q^{29} +(-2.58189 + 4.47197i) q^{30} +278.993i q^{31} +(27.7128 + 16.0000i) q^{32} +(9.18006 + 5.30011i) q^{33} -187.417i q^{34} +(8.11395 - 14.0538i) q^{35} +(-53.6706 - 92.9603i) q^{36} +(9.43976 - 5.45005i) q^{37} -74.4658 q^{38} -50.8982 q^{40} +(-321.621 + 185.688i) q^{41} +(-1.03509 - 1.79282i) q^{42} +(-206.859 + 358.290i) q^{43} +104.484i q^{44} +(147.860 + 85.3668i) q^{45} +(181.737 + 104.926i) q^{46} -238.631i q^{47} +(-3.24651 + 5.62311i) q^{48} +(-168.247 - 291.413i) q^{49} +(-146.396 + 84.5215i) q^{50} +38.0282 q^{51} -424.907 q^{53} +(37.8403 - 21.8471i) q^{54} +(-83.0942 - 143.923i) q^{55} +(10.2026 - 17.6714i) q^{56} -15.1096i q^{57} +(432.224 + 249.544i) q^{58} +(-670.696 - 387.226i) q^{59} -10.3276i q^{60} +(61.7113 - 106.887i) q^{61} +(-278.993 - 483.229i) q^{62} +(-59.2772 + 34.2237i) q^{63} -64.0000 q^{64} -21.2004 q^{66} +(-763.491 + 440.802i) q^{67} +(187.417 + 324.616i) q^{68} +(-21.2902 + 36.8757i) q^{69} +32.4558i q^{70} +(-102.854 - 59.3826i) q^{71} +(185.921 + 107.341i) q^{72} -209.319i q^{73} +(-10.9001 + 18.8795i) q^{74} +(-17.1500 - 29.7046i) q^{75} +(128.978 - 74.4658i) q^{76} +66.6253 q^{77} -532.358 q^{79} +(88.1582 - 50.8982i) q^{80} +(-357.844 - 619.804i) q^{81} +(371.375 - 643.241i) q^{82} -376.511i q^{83} +(3.58564 + 2.07017i) q^{84} +(-516.324 - 298.100i) q^{85} -827.436i q^{86} +(-50.6342 + 87.7010i) q^{87} +(-104.484 - 180.971i) q^{88} +(-36.9218 + 21.3168i) q^{89} -341.467 q^{90} -419.704 q^{92} +(98.0505 - 56.6095i) q^{93} +(238.631 + 413.321i) q^{94} +(-118.443 + 205.149i) q^{95} -12.9860i q^{96} +(-553.666 - 319.659i) q^{97} +(582.825 + 336.494i) q^{98} +700.963i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 24 q^{3} + 24 q^{4} - 18 q^{9} - 48 q^{10} + 192 q^{12} + 216 q^{14} - 96 q^{16} - 180 q^{17} + 328 q^{22} + 38 q^{23} + 244 q^{25} - 276 q^{27} + 202 q^{29} + 360 q^{30} + 916 q^{35} + 72 q^{36}+ \cdots + 3658 q^{95}+O(q^{100}) $ 12 * q + 24 * q^3 + 24 * q^4 - 18 * q^9 - 48 * q^10 + 192 * q^12 + 216 * q^14 - 96 * q^16 - 180 * q^17 + 328 * q^22 + 38 * q^23 + 244 * q^25 - 276 * q^27 + 202 * q^29 + 360 * q^30 + 916 * q^35 + 72 * q^36 + 1040 * q^38 - 384 * q^40 + 936 * q^42 - 2410 * q^43 + 384 * q^48 - 368 * q^49 + 828 * q^51 - 4380 * q^53 + 1052 * q^55 + 432 * q^56 + 2216 * q^61 - 2076 * q^62 - 768 * q^64 + 1168 * q^66 + 720 * q^68 - 628 * q^69 + 336 * q^74 - 1010 * q^75 - 1920 * q^77 - 7844 * q^79 - 1830 * q^81 - 748 * q^82 - 3272 * q^87 - 1312 * q^88 + 5160 * q^90 + 304 * q^92 - 2144 * q^94 + 3658 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/338\mathbb{Z}\right)^\times$.

$n$	$171$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.73205	+	1.00000i	−0.612372	+	0.353553i
$2$	−1.73205	+	1.00000i	−0.612372	+	0.353553i
$3$	−0.202907	−	0.351445i	−0.0390494	−	0.0676355i	0.845840	−	0.533436i	$-0.179100\pi$
$3$	−0.202907	−	0.351445i	−0.0390494	−	0.0676355i	−0.884890	+	0.465801i	$0.845766\pi$
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$			6.36227i			0.569059i	0.958667	+	0.284529i	$0.0918374\pi$
$5$			6.36227i			0.569059i	−0.958667	+	0.284529i	$0.908163\pi$
$6$	0.702889	+	0.405813i	0.0478255	+	0.0276121i
$7$	−2.20892	−	1.27532i	−0.119271	−	0.0688610i	0.439178	−	0.898400i	$-0.355270\pi$
$7$	−2.20892	−	1.27532i	−0.119271	−	0.0688610i	−0.558448	+	0.829539i	$0.688603\pi$
$8$			8.00000i			0.353553i
$9$	13.4177	−	23.2401i	0.496950	−	0.860743i
$10$	−6.36227	−	11.0198i	−0.201193	−	0.348476i
$11$	−22.6214	+	13.0605i	−0.620055	+	0.357989i	−0.776890	−	0.629636i	$-0.783204\pi$
$11$	−22.6214	+	13.0605i	−0.620055	+	0.357989i	0.156835	+	0.987625i	$0.449871\pi$
$12$	−1.62325			−0.0390494
$13$		0			0
$13$		0			0
$14$	5.10129			0.0973841
$15$	2.23599	−	1.29095i	0.0384886	−	0.0222214i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−46.8543	+	81.1540i	−0.668461	+	1.15781i	0.309874	+	0.950778i	$0.399713\pi$
$17$	−46.8543	+	81.1540i	−0.668461	+	1.15781i	−0.978335	+	0.207030i	$0.933620\pi$
$18$			53.6706i			0.702794i
$19$	32.2446	+	18.6164i	0.389338	+	0.224784i	0.681873	−	0.731470i	$-0.261166\pi$
$19$	32.2446	+	18.6164i	0.389338	+	0.224784i	−0.292535	+	0.956255i	$0.594499\pi$
$20$	22.0396	+	12.7245i	0.246410	+	0.142265i
$21$			1.03509i			0.0107559i
$22$	26.1209	−	45.2428i	0.253136	−	0.438445i
$23$	−52.4630	−	90.8686i	−0.475622	−	0.823801i	0.523988	−	0.851725i	$-0.324443\pi$
$23$	−52.4630	−	90.8686i	−0.475622	−	0.823801i	−0.999610	+	0.0279247i	$0.991110\pi$
$24$	2.81156	−	1.62325i	0.0239128	−	0.0138060i
$25$	84.5215			0.676172
$26$		0			0
$27$	−21.8471			−0.155721
$28$	−8.83570	+	5.10129i	−0.0596354	+	0.0344305i
$29$	−124.772	−	216.112i	−0.798953	−	1.38383i	−0.920299	−	0.391216i	$-0.872054\pi$
$29$	−124.772	−	216.112i	−0.798953	−	1.38383i	0.121346	−	0.992610i	$-0.461279\pi$
$30$	−2.58189	+	4.47197i	−0.0157129	+	0.0272156i
$31$			278.993i			1.61641i	0.588904	+	0.808203i	$0.299559\pi$
$31$			278.993i			1.61641i	−0.588904	+	0.808203i	$0.700441\pi$
$32$	27.7128	+	16.0000i	0.153093	+	0.0883883i
$33$	9.18006	+	5.30011i	0.0484256	+	0.0279585i
$34$		−	187.417i		−	0.945346i
$35$	8.11395	−	14.0538i	0.0391860	−	0.0678721i
$36$	−53.6706	−	92.9603i	−0.248475	−	0.430372i
$37$	9.43976	−	5.45005i	0.0419429	−	0.0242157i	−0.478882	−	0.877879i	$-0.658958\pi$
$37$	9.43976	−	5.45005i	0.0419429	−	0.0242157i	0.520825	+	0.853664i	$0.325624\pi$
$38$	−74.4658			−0.317893
$39$		0			0
$40$	−50.8982			−0.201193
$41$	−321.621	+	185.688i	−1.22509	+	0.707306i	−0.965999	−	0.258547i	$-0.916756\pi$
$41$	−321.621	+	185.688i	−1.22509	+	0.707306i	−0.259091	+	0.965853i	$0.583423\pi$
$42$	−1.03509	−	1.79282i	−0.00380279	−	0.00658663i
$43$	−206.859	+	358.290i	−0.733621	+	1.27067i	0.221705	+	0.975114i	$0.428838\pi$
$43$	−206.859	+	358.290i	−0.733621	+	1.27067i	−0.955326	+	0.295555i	$0.904496\pi$
$44$			104.484i			0.357989i
$45$	147.860	+	85.3668i	0.489814	+	0.282794i
$46$	181.737	+	104.926i	0.582515	+	0.336315i
$47$		−	238.631i		−	0.740595i	−0.928913	−	0.370297i	$-0.879256\pi$
$47$		−	238.631i		−	0.740595i	0.928913	−	0.370297i	$-0.120744\pi$
$48$	−3.24651	+	5.62311i	−0.00976235	+	0.0169089i
$49$	−168.247	−	291.413i	−0.490516	−	0.849599i
$50$	−146.396	+	84.5215i	−0.414069	+	0.239063i
$51$	38.0282			0.104412
$52$		0			0
$53$	−424.907			−1.10124			−0.550618	−	0.834757i	$-0.685608\pi$
$53$	−424.907			−1.10124			−0.550618	+	0.834757i	$0.685608\pi$
$54$	37.8403	−	21.8471i	0.0953594	−	0.0550558i
$55$	−83.0942	−	143.923i	−0.203717	−	0.352848i
$56$	10.2026	−	17.6714i	0.0243460	−	0.0421686i
$57$		−	15.1096i		−	0.0351108i
$58$	432.224	+	249.544i	0.978513	+	0.564945i
$59$	−670.696	−	387.226i	−1.47995	−	0.854451i	−0.480210	−	0.877154i	$-0.659439\pi$
$59$	−670.696	−	387.226i	−1.47995	−	0.854451i	−0.999742	+	0.0227031i	$0.992773\pi$
$60$		−	10.3276i		−	0.0222214i
$61$	61.7113	−	106.887i	0.129530	−	0.224352i	−0.793965	−	0.607964i	$-0.791987\pi$
$61$	61.7113	−	106.887i	0.129530	−	0.224352i	0.923495	+	0.383612i	$0.125320\pi$
$62$	−278.993	−	483.229i	−0.571486	−	0.989842i
$63$	−59.2772	+	34.2237i	−0.118543	+	0.0684410i
$64$	−64.0000			−0.125000
$65$		0			0
$66$	−21.2004			−0.0395393
$67$	−763.491	+	440.802i	−1.39217	+	0.803769i	−0.993555	−	0.113350i	$-0.963842\pi$
$67$	−763.491	+	440.802i	−1.39217	+	0.803769i	−0.398614	+	0.917119i	$0.630509\pi$
$68$	187.417	+	324.616i	0.334230	+	0.578904i
$69$	−21.2902	+	36.8757i	−0.0371455	+	0.0643378i
$70$			32.4558i			0.0554173i
$71$	−102.854	−	59.3826i	−0.171922	−	0.0992593i	0.411570	−	0.911378i	$-0.364981\pi$
$71$	−102.854	−	59.3826i	−0.171922	−	0.0992593i	−0.583492	+	0.812119i	$0.698314\pi$
$72$	185.921	+	107.341i	0.304319	+	0.175698i
$73$		−	209.319i		−	0.335602i	−0.985821	−	0.167801i	$-0.946333\pi$
$73$		−	209.319i		−	0.335602i	0.985821	−	0.167801i	$-0.0536666\pi$
$74$	−10.9001	+	18.8795i	−0.0171231	+	0.0296581i
$75$	−17.1500	−	29.7046i	−0.0264041	−	0.0457332i
$76$	128.978	−	74.4658i	0.194669	−	0.112392i
$77$	66.6253			0.0986059
$78$		0			0
$79$	−532.358			−0.758164			−0.379082	−	0.925363i	$-0.623760\pi$
$79$	−532.358			−0.758164			−0.379082	+	0.925363i	$0.623760\pi$
$80$	88.1582	−	50.8982i	0.123205	−	0.0711324i
$81$	−357.844	−	619.804i	−0.490869	−	0.850211i
$82$	371.375	−	643.241i	0.500141	−	0.866270i
$83$		−	376.511i		−	0.497921i	−0.968514	−	0.248960i	$-0.919911\pi$
$83$		−	376.511i		−	0.497921i	0.968514	−	0.248960i	$-0.0800889\pi$
$84$	3.58564	+	2.07017i	0.00465745	+	0.00268898i
$85$	−516.324	−	298.100i	−0.658861	−	0.380393i
$86$		−	827.436i		−	1.03750i
$87$	−50.6342	+	87.7010i	−0.0623972	+	0.108075i
$88$	−104.484	−	180.971i	−0.126568	−	0.219223i
$89$	−36.9218	+	21.3168i	−0.0439742	+	0.0253885i	−0.521826	−	0.853052i	$-0.674749\pi$
$89$	−36.9218	+	21.3168i	−0.0439742	+	0.0253885i	0.477852	+	0.878441i	$0.341416\pi$
$90$	−341.467			−0.399931
$91$		0			0
$92$	−419.704			−0.475622
$93$	98.0505	−	56.6095i	0.109326	−	0.0631196i
$94$	238.631	+	413.321i	0.261840	+	0.453520i
$95$	−118.443	+	205.149i	−0.127916	+	0.221556i
$96$		−	12.9860i		−	0.0138060i
$97$	−553.666	−	319.659i	−0.579550	−	0.334603i	0.181405	−	0.983409i	$-0.441936\pi$
$97$	−553.666	−	319.659i	−0.579550	−	0.334603i	−0.760954	+	0.648805i	$0.775269\pi$
$98$	582.825	+	336.494i	0.600757	+	0.346847i
$99$			700.963i			0.711611i
$100$	169.043	−	292.791i	0.169043	−	0.292791i
$101$	237.419	+	411.222i	0.233902	+	0.405130i	0.958953	−	0.283565i	$-0.0915172\pi$
$101$	237.419	+	411.222i	0.233902	+	0.405130i	−0.725051	+	0.688695i	$0.758184\pi$
$102$	−65.8667	+	38.0282i	−0.0639390	+	0.0369152i
$103$	1100.53			1.05280			0.526402	−	0.850236i	$-0.323541\pi$
$103$	1100.53			1.05280			0.526402	+	0.850236i	$0.323541\pi$
$104$		0			0
$105$	−6.58550			−0.00612075
$106$	735.961	−	424.907i	0.674367	−	0.389346i
$107$	285.191	+	493.966i	0.257668	+	0.446294i	0.965617	−	0.259970i	$-0.0837126\pi$
$107$	285.191	+	493.966i	0.257668	+	0.446294i	−0.707949	+	0.706264i	$0.750379\pi$
$108$	−43.6942	+	75.6805i	−0.0389303	+	0.0674293i
$109$		−	593.029i		−	0.521118i	−0.965458	−	0.260559i	$-0.916093\pi$
$109$		−	593.029i		−	0.521118i	0.965458	−	0.260559i	$-0.0839069\pi$
$110$	287.847	+	166.188i	0.249501	+	0.144050i
$111$	−3.83078	−	2.21170i	−0.00327569	−	0.00189122i
$112$			40.8103i			0.0344305i
$113$	−919.559	+	1592.72i	−0.765529	+	1.32594i	0.174437	+	0.984668i	$0.444189\pi$
$113$	−919.559	+	1592.72i	−0.765529	+	1.32594i	−0.939966	+	0.341267i	$0.889144\pi$
$114$	15.1096	+	26.1706i	0.0124135	+	0.0215009i
$115$	578.131	−	333.784i	0.468791	−	0.270657i
$116$	−998.178			−0.798953
$117$		0			0
$118$	1548.91			1.20838
$119$	206.995	−	119.509i	0.159456	−	0.0920617i
$120$	10.3276	+	17.8879i	0.00785645	+	0.0136078i
$121$	−324.348	+	561.788i	−0.243688	+	0.422080i
$122$			246.845i			0.183183i
$123$	130.518	+	75.3545i	0.0956781	+	0.0552398i
$124$	966.459	+	557.985i	0.699924	+	0.404101i
$125$			1333.03i			0.953841i
$126$	68.4474	−	118.554i	0.0483951	−	0.0838227i
$127$	1234.26	+	2137.79i	0.862382	+	1.49369i	0.869623	+	0.493716i	$0.164362\pi$
$127$	1234.26	+	2137.79i	0.862382	+	1.49369i	−0.00724155	+	0.999974i	$0.502305\pi$
$128$	110.851	−	64.0000i	0.0765466	−	0.0441942i
$129$	167.892			0.114590
$130$		0			0
$131$	2279.82			1.52053			0.760264	−	0.649615i	$-0.225070\pi$
$131$	2279.82			1.52053			0.760264	+	0.649615i	$0.225070\pi$
$132$	36.7202	−	21.2004i	0.0242128	−	0.0139793i
$133$	−47.4840	−	82.2446i	−0.0309578	−	0.0536204i
$134$	881.604	−	1526.98i	0.568351	−	0.984412i
$135$		−	138.997i		−	0.0886146i
$136$	−649.232	−	374.834i	−0.409347	−	0.236336i
$137$	−380.453	−	219.654i	−0.237257	−	0.136981i	0.376658	−	0.926352i	$-0.377073\pi$
$137$	−380.453	−	219.654i	−0.237257	−	0.136981i	−0.613916	+	0.789372i	$0.710406\pi$
$138$		−	85.1607i		−	0.0525316i
$139$	1089.47	−	1887.02i	0.664803	−	1.15147i	−0.314536	−	0.949246i	$-0.601849\pi$
$139$	1089.47	−	1887.02i	0.664803	−	1.15147i	0.979339	−	0.202227i	$-0.0648178\pi$
$140$	−32.4558	−	56.2151i	−0.0195930	−	0.0339360i
$141$	−83.8657	+	48.4199i	−0.0500905	+	0.0289198i
$142$	237.530			0.140374
$143$		0			0
$144$	−429.365			−0.248475
$145$	1374.96	−	793.835i	0.787479	−	0.454651i
$146$	209.319	+	362.552i	0.118653	+	0.205514i
$147$	−68.2769	+	118.259i	−0.0383087	+	0.0663527i
$148$		−	43.6004i		−	0.0242157i
$149$	−2484.17	−	1434.24i	−1.36585	−	0.788572i	−0.375453	−	0.926842i	$-0.622513\pi$
$149$	−2484.17	−	1434.24i	−1.36585	−	0.788572i	−0.990395	+	0.138269i	$0.955846\pi$
$150$	59.4092	+	34.2999i	0.0323383	+	0.0186705i
$151$			2202.00i			1.18673i	0.804933	+	0.593366i	$0.202201\pi$
$151$			2202.00i			1.18673i	−0.804933	+	0.593366i	$0.797799\pi$
$152$	−148.932	+	257.957i	−0.0794733	+	0.137652i
$153$	1257.35	+	2177.79i	0.664383	+	1.15075i
$154$	−115.398	+	66.6253i	−0.0603835	+	0.0348624i
$155$	−1775.03			−0.919830
$156$		0			0
$157$	865.139			0.439781			0.219890	−	0.975525i	$-0.429430\pi$
$157$	865.139			0.439781			0.219890	+	0.975525i	$0.429430\pi$
$158$	922.071	−	532.358i	0.464278	−	0.268051i
$159$	86.2165	+	149.331i	0.0430026	+	0.0744827i
$160$	−101.796	+	176.316i	−0.0502982	+	0.0871190i
$161$			267.629i			0.131007i
$162$	1239.61	+	715.688i	0.601190	+	0.347097i
$163$	918.712	+	530.419i	0.441467	+	0.254881i	0.704220	−	0.709982i	$-0.251297\pi$
$163$	918.712	+	530.419i	0.441467	+	0.254881i	−0.262753	+	0.964863i	$0.584630\pi$
$164$			1485.50i			0.707306i
$165$	−33.7207	+	58.4060i	−0.0159100	+	0.0275570i
$166$	376.511	+	652.136i	0.176042	+	0.304913i
$167$	−1215.97	+	702.043i	−0.563443	+	0.325304i	−0.754526	−	0.656270i	$-0.772133\pi$
$167$	−1215.97	+	702.043i	−0.563443	+	0.325304i	0.191083	+	0.981574i	$0.438800\pi$
$168$	−8.28069			−0.00380279
$169$		0			0
$170$	1192.40			0.537958
$171$	865.295	−	499.578i	0.386963	−	0.223413i
$172$	827.436	+	1433.16i	0.366810	+	0.635334i
$173$	511.110	−	885.268i	0.224618	−	0.389050i	−0.731587	−	0.681749i	$-0.761220\pi$
$173$	511.110	−	885.268i	0.224618	−	0.389050i	0.956205	+	0.292698i	$0.0945532\pi$
$174$		−	202.537i		−	0.0882430i
$175$	−186.702	−	107.792i	−0.0806475	−	0.0465619i
$176$	361.942	+	208.967i	0.155014	+	0.0894972i
$177$			314.283i			0.133463i
$178$	42.6336	−	73.8436i	0.0179524	−	0.0310945i
$179$	209.112	+	362.192i	0.0873169	+	0.151237i	0.906376	−	0.422472i	$-0.138837\pi$
$179$	209.112	+	362.192i	0.0873169	+	0.151237i	−0.819059	+	0.573709i	$0.805504\pi$
$180$	591.439	−	341.467i	0.244907	−	0.141397i
$181$	2816.05			1.15644			0.578219	−	0.815882i	$-0.303748\pi$
$181$	2816.05			1.15644			0.578219	+	0.815882i	$0.303748\pi$
$182$		0			0
$183$	−50.0865			−0.0202322
$184$	726.949	−	419.704i	0.291258	−	0.168158i
$185$	34.6747	+	60.0584i	0.0137802	+	0.0238680i
$186$	−113.219	+	196.101i	−0.0446323	+	0.0773055i
$187$		−	2447.75i		−	0.957206i
$188$	−826.643	−	477.263i	−0.320687	−	0.185149i
$189$	48.2586	+	27.8621i	0.0185730	+	0.0107231i
$190$		−	473.772i		−	0.180900i
$191$	−807.053	+	1397.86i	−0.305740	+	0.529557i	−0.977426	−	0.211279i	$-0.932237\pi$
$191$	−807.053	+	1397.86i	−0.305740	+	0.529557i	0.671686	+	0.740836i	$0.265570\pi$
$192$	12.9860	+	22.4925i	0.00488117	+	0.00845444i
$193$	2131.39	−	1230.56i	0.794926	−	0.458951i	−0.0467677	−	0.998906i	$-0.514892\pi$
$193$	2131.39	−	1230.56i	0.794926	−	0.458951i	0.841694	+	0.539955i	$0.181559\pi$
$194$	1278.64			0.473200
$195$		0			0
$196$	−1345.98			−0.490516
$197$	2984.24	−	1722.95i	1.07928	−	0.623123i	0.148579	−	0.988901i	$-0.452530\pi$
$197$	2984.24	−	1722.95i	1.07928	−	0.623123i	0.930702	+	0.365777i	$0.119197\pi$
$198$	−700.963	−	1214.10i	−0.251592	−	0.435771i
$199$	1102.51	−	1909.61i	0.392739	−	0.680243i	−0.600071	−	0.799947i	$-0.704861\pi$
$199$	1102.51	−	1909.61i	0.392739	−	0.680243i	0.992810	+	0.119704i	$0.0381944\pi$
$200$			676.172i			0.239063i
$201$	309.835	+	178.883i	0.108727	+	0.0627734i
$202$	−822.445	−	474.839i	−0.286470	−	0.165394i
$203$			636.500i			0.220067i
$204$	76.0563	−	131.733i	0.0261030	−	0.0452117i
$205$	−1181.40	−	2046.24i	−0.402499	−	0.697149i
$206$	−1906.18	+	1100.53i	−0.644708	+	0.372222i
$207$	−2815.72			−0.945441
$208$		0			0
$209$	−972.558			−0.321881
$210$	11.4064	−	6.58550i	0.00374818	−	0.00216401i
$211$	466.596	+	808.169i	0.152236	+	0.263681i	0.932049	−	0.362332i	$-0.118019\pi$
$211$	466.596	+	808.169i	0.152236	+	0.263681i	−0.779813	+	0.626012i	$0.784686\pi$
$212$	−849.815	+	1471.92i	−0.275309	+	0.476849i
$213$			48.1964i			0.0155041i
$214$	−987.932	−	570.383i	−0.315578	−	0.182199i
$215$	−2279.54	−	1316.09i	−0.723085	−	0.417473i
$216$		−	174.777i		−	0.0550558i
$217$	355.806	−	616.274i	0.111307	−	0.192790i
$218$	593.029	+	1027.16i	0.184243	+	0.319118i
$219$	−73.5641	+	42.4723i	−0.0226986	+	0.0131051i
$220$	−664.754			−0.203717
$221$		0			0
$222$	8.84681			0.00267459
$223$	−5511.05	+	3181.81i	−1.65492	+	0.955469i	−0.679915	+	0.733290i	$0.737984\pi$
$223$	−5511.05	+	3181.81i	−1.65492	+	0.955469i	−0.975006	+	0.222179i	$0.928683\pi$
$224$	−40.8103	−	70.6856i	−0.0121730	−	0.0210843i
$225$	1134.08	−	1964.28i	0.336024	−	0.582010i
$226$		−	3678.23i		−	1.08262i
$227$	718.377	+	414.755i	0.210046	+	0.121270i	0.601333	−	0.798999i	$-0.294637\pi$
$227$	718.377	+	414.755i	0.210046	+	0.121270i	−0.391287	+	0.920269i	$0.627970\pi$
$228$	−52.3412	−	30.2192i	−0.0152034	−	0.00877770i
$229$		−	5789.35i		−	1.67062i	−0.549782	−	0.835308i	$-0.685289\pi$
$229$		−	5789.35i		−	1.67062i	0.549782	−	0.835308i	$-0.314711\pi$
$230$	−667.568	+	1156.26i	−0.191383	+	0.331485i
$231$	−13.5187	−	23.4151i	−0.00385050	−	0.00666926i
$232$	1728.89	−	998.178i	0.489256	−	0.282472i
$233$	−320.751			−0.0901849			−0.0450924	−	0.998983i	$-0.514358\pi$
$233$	−320.751			−0.0901849			−0.0450924	+	0.998983i	$0.514358\pi$
$234$		0			0
$235$	1518.24			0.421442
$236$	−2682.78	+	1548.91i	−0.739976	+	0.427225i
$237$	108.019	+	187.094i	0.0296058	+	0.0512788i
$238$	−239.017	+	413.990i	−0.0650974	+	0.112752i
$239$			3582.11i			0.969487i	0.874656	+	0.484744i	$0.161087\pi$
$239$			3582.11i			0.969487i	−0.874656	+	0.484744i	$0.838913\pi$
$240$	−35.7758	−	20.6552i	−0.00962215	−	0.00555535i
$241$	4226.41	+	2440.12i	1.12966	+	0.652207i	0.943848	−	0.330379i	$-0.107177\pi$
$241$	4226.41	+	2440.12i	1.12966	+	0.652207i	0.185808	+	0.982586i	$0.440510\pi$
$242$		−	1297.39i		−	0.344627i
$243$	−440.153	+	762.368i	−0.116197	+	0.201259i
$244$	−246.845	−	427.548i	−0.0647649	−	0.112176i
$245$	1854.05	−	1070.43i	0.483472	−	0.279133i
$246$	−301.418			−0.0781208
$247$		0			0
$248$	−2231.94			−0.571486
$249$	−132.323	+	76.3965i	−0.0336772	+	0.0194435i
$250$	−1333.03	−	2308.88i	−0.337234	−	0.584106i
$251$	−1490.11	+	2580.95i	−0.374721	+	0.649036i	−0.990285	−	0.139051i	$-0.955595\pi$
$251$	−1490.11	+	2580.95i	−0.374721	+	0.649036i	0.615564	+	0.788087i	$0.288928\pi$
$252$			273.790i			0.0684410i
$253$	2373.57	+	1370.38i	0.589823	+	0.340535i
$254$	−4275.59	−	2468.51i	−1.05620	−	0.609796i
$255$			241.946i			0.0594165i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−1927.96	−	3339.33i	−0.467950	−	0.810513i	0.531379	−	0.847134i	$-0.321674\pi$
$257$	−1927.96	−	3339.33i	−0.467950	−	0.810513i	−0.999329	+	0.0366210i	$0.988341\pi$
$258$	−290.798	+	167.892i	−0.0701716	+	0.0405136i
$259$	−27.8023			−0.00667008
$260$		0			0
$261$	−6696.60			−1.58816
$262$	−3948.77	+	2279.82i	−0.931129	+	0.537588i
$263$	2215.59	+	3837.51i	0.519464	+	0.899738i	0.999744	+	0.0226228i	$0.00720168\pi$
$263$	2215.59	+	3837.51i	0.519464	+	0.899738i	−0.480280	+	0.877115i	$0.659465\pi$
$264$	−42.4009	+	73.4405i	−0.00988482	+	0.0171210i
$265$		−	2703.38i		−	0.626668i
$266$	164.489	+	94.9679i	0.0379154	+	0.0218904i
$267$	14.9834	+	8.65065i	0.00343433	+	0.00198281i
$268$			3526.42i			0.803769i
$269$	−630.667	+	1092.35i	−0.142946	+	0.247589i	−0.928605	−	0.371071i	$-0.878991\pi$
$269$	−630.667	+	1092.35i	−0.142946	+	0.247589i	0.785659	+	0.618660i	$0.212324\pi$
$270$	138.997	+	240.750i	0.0313300	+	0.0542651i
$271$	−5370.00	+	3100.37i	−1.20371	+	0.694960i	−0.961377	−	0.275234i	$-0.911245\pi$
$271$	−5370.00	+	3100.37i	−1.20371	+	0.694960i	−0.242329	+	0.970194i	$0.577911\pi$
$272$	1499.34			0.334230
$273$		0			0
$274$	878.618			0.193720
$275$	−1911.99	+	1103.89i	−0.419264	+	0.242062i
$276$	85.1607	+	147.503i	0.0185727	+	0.0321689i
$277$	−578.785	+	1002.48i	−0.125544	+	0.217449i	−0.921946	−	0.387319i	$-0.873401\pi$
$277$	−578.785	+	1002.48i	−0.125544	+	0.217449i	0.796401	+	0.604769i	$0.206734\pi$
$278$			4357.88i			0.940173i
$279$	6483.81	+	3743.43i	1.39131	+	0.803273i
$280$	112.430	+	64.9116i	0.0239964	+	0.0138543i
$281$		−	6322.71i		−	1.34228i	−0.741330	−	0.671141i	$-0.765805\pi$
$281$		−	6322.71i		−	1.34228i	0.741330	−	0.671141i	$-0.234195\pi$
$282$	96.8397	−	167.731i	0.0204494	−	0.0354193i
$283$	−4654.17	−	8061.26i	−0.977604	−	1.69326i	−0.671060	−	0.741403i	$-0.734161\pi$
$283$	−4654.17	−	8061.26i	−0.977604	−	1.69326i	−0.306544	−	0.951857i	$-0.599173\pi$
$284$	−411.414	+	237.530i	−0.0859611	+	0.0496297i
$285$	96.1314			0.0199801
$286$		0			0
$287$	947.247			0.194823
$288$	743.682	−	429.365i	0.152159	−	0.0878492i
$289$	−1934.14	−	3350.04i	−0.393679	−	0.681872i
$290$	−1587.67	+	2749.93i	−0.321487	+	0.556832i
$291$			259.444i			0.0522642i
$292$	−725.103	−	418.638i	−0.145320	−	0.0839006i
$293$	−438.378	−	253.098i	−0.0874073	−	0.0504646i	0.455659	−	0.890154i	$-0.349404\pi$
$293$	−438.378	−	253.098i	−0.0874073	−	0.0504646i	−0.543067	+	0.839690i	$0.682737\pi$
$294$		−	273.108i		−	0.0541767i
$295$	2463.64	−	4267.15i	0.486233	−	0.842180i
$296$	43.6004	+	75.5181i	0.00856156	+	0.0148291i
$297$	494.211	−	285.333i	0.0965557	−	0.0557465i
$298$	5736.95			1.11521
$299$		0			0
$300$	−137.200			−0.0264041
$301$	913.871	−	527.624i	0.174999	−	0.101036i
$302$	−2202.00	−	3813.98i	−0.419573	−	0.726722i
$303$	96.3479	−	166.879i	0.0182675	−	0.0316402i
$304$		−	595.726i		−	0.112392i
$305$	680.045	+	392.624i	0.127670	+	0.0737101i
$306$	−4355.58	−	2514.70i	−0.813700	−	0.469790i
$307$		−	4094.64i		−	0.761217i	−0.924736	−	0.380608i	$-0.875715\pi$
$307$		−	4094.64i		−	0.761217i	0.924736	−	0.380608i	$-0.124285\pi$
$308$	133.251	−	230.797i	0.0246515	−	0.0426976i
$309$	−223.305	−	386.776i	−0.0411113	−	0.0712069i
$310$	3074.44	−	1775.03i	0.563278	−	0.325209i
$311$	−8705.00			−1.58719			−0.793594	−	0.608448i	$-0.791792\pi$
$311$	−8705.00			−1.58719			−0.793594	+	0.608448i	$0.791792\pi$
$312$		0			0
$313$	−3144.78			−0.567903			−0.283951	−	0.958839i	$-0.591645\pi$
$313$	−3144.78			−0.567903			−0.283951	+	0.958839i	$0.591645\pi$
$314$	−1498.46	+	865.139i	−0.269310	+	0.155486i
$315$	−217.741	−	377.138i	−0.0389469	−	0.0674581i
$316$	−1064.72	+	1844.14i	−0.189541	+	0.328294i
$317$			9902.03i			1.75443i	0.480100	+	0.877214i	$0.340600\pi$
$317$			9902.03i			1.75443i	−0.480100	+	0.877214i	$0.659400\pi$
$318$	−298.663	−	172.433i	−0.0526672	−	0.0304074i
$319$	5645.04	+	3259.17i	0.990789	+	0.572032i
$320$		−	407.185i		−	0.0711324i
$321$	115.734	−	200.458i	0.0201236	−	0.0348550i
$322$	−267.629	−	463.547i	−0.0463180	−	0.0802251i
$323$	−3021.60	+	1744.52i	−0.520514	+	0.300519i
$324$	−2862.75			−0.490869
$325$		0			0
$326$	−2121.67			−0.360456
$327$	−208.417	+	120.330i	−0.0352461	+	0.0203494i
$328$	−1485.50	−	2572.96i	−0.250070	−	0.433135i
$329$	−304.332	+	527.118i	−0.0509981	+	0.0883312i
$330$		−	134.883i		−	0.0225002i
$331$	−1702.93	−	983.184i	−0.282783	−	0.163265i	0.351900	−	0.936038i	$-0.385536\pi$
$331$	−1702.93	−	983.184i	−0.282783	−	0.163265i	−0.634683	+	0.772773i	$0.718869\pi$
$332$	−1304.27	−	753.022i	−0.215606	−	0.124480i
$333$		−	292.508i		−	0.0481361i
$334$	1404.09	−	2431.95i	0.230025	−	0.398414i
$335$	−2804.50	−	4857.54i	−0.457392	−	0.792226i
$336$	14.3426	−	8.28069i	0.00232872	−	0.00134449i
$337$	9570.83			1.54705			0.773526	−	0.633765i	$-0.218491\pi$
$337$	9570.83			1.54705			0.773526	+	0.633765i	$0.218491\pi$
$338$		0			0
$339$	746.338			0.119574
$340$	−2065.29	+	1192.40i	−0.329430	+	0.190197i
$341$	−3643.77	−	6311.20i	−0.578655	−	1.00226i
$342$	−999.156	+	1730.59i	−0.157977	+	0.273624i
$343$			1733.15i			0.272832i
$344$	−2866.32	−	1654.87i	−0.449249	−	0.259374i
$345$	−234.613	−	135.454i	−0.0366120	−	0.0211380i
$346$			2044.44i			0.317658i
$347$	3227.11	−	5589.51i	0.499251	−	0.864728i	−0.500748	−	0.865593i	$-0.666942\pi$
$347$	3227.11	−	5589.51i	0.499251	−	0.864728i	1.00000		0.000864443i	$0.000275161\pi$
$348$	202.537	+	350.804i	0.0311986	+	0.0540376i
$349$	2407.14	−	1389.76i	0.369201	−	0.213158i	−0.303908	−	0.952701i	$-0.598292\pi$
$349$	2407.14	−	1389.76i	0.369201	−	0.213158i	0.673109	+	0.739543i	$0.264958\pi$
$350$	431.169			0.0658484
$351$		0			0
$352$	−835.870			−0.126568
$353$	9653.88	−	5573.67i	1.45559	−	0.840387i	0.456803	−	0.889568i	$-0.348994\pi$
$353$	9653.88	−	5573.67i	1.45559	−	0.840387i	0.998790	+	0.0491807i	$0.0156610\pi$
$354$	−314.283	−	544.354i	−0.0471863	−	0.0817291i
$355$	377.808	−	654.383i	0.0564844	−	0.0978339i
$356$			170.535i			0.0253885i
$357$	−84.0013	−	48.4982i	−0.0124533	−	0.00718991i
$358$	−724.384	−	418.223i	−0.106941	−	0.0617424i
$359$			4313.27i			0.634111i	0.948407	+	0.317056i	$0.102694\pi$
$359$			4313.27i			0.634111i	−0.948407	+	0.317056i	$0.897306\pi$
$360$	−682.934	+	1182.88i	−0.0999828	+	0.173175i
$361$	−2736.36	−	4739.51i	−0.398944	−	0.690991i
$362$	−4877.54	+	2816.05i	−0.708171	+	0.408863i
$363$	263.250			0.0380634
$364$		0			0
$365$	1331.75			0.190977
$366$	86.7524	−	50.0865i	0.0123897	−	0.00715318i
$367$	3454.76	+	5983.81i	0.491381	+	0.851097i	0.999951	−	0.00992401i	$-0.00315896\pi$
$367$	3454.76	+	5983.81i	0.491381	+	0.851097i	−0.508570	+	0.861021i	$0.669826\pi$
$368$	−839.408	+	1453.90i	−0.118905	+	0.205950i
$369$			9965.98i			1.40598i
$370$	−120.117	−	69.3494i	−0.0168772	−	0.00974407i
$371$	938.588	+	541.894i	0.131345	+	0.0758322i
$372$		−	452.876i		−	0.0631196i
$373$	−1158.10	+	2005.88i	−0.160761	+	0.278447i	−0.935142	−	0.354273i	$-0.884728\pi$
$373$	−1158.10	+	2005.88i	−0.160761	+	0.278447i	0.774381	+	0.632720i	$0.218062\pi$
$374$	2447.75	+	4239.63i	0.338423	+	0.586167i
$375$	468.487	−	270.481i	0.0645135	−	0.0372469i
$376$	1909.05			0.261840
$377$		0			0
$378$	−111.448			−0.0151648
$379$	−9866.69	+	5696.54i	−1.33725	+	0.772062i	−0.986399	−	0.164369i	$-0.947441\pi$
$379$	−9866.69	+	5696.54i	−1.33725	+	0.772062i	−0.350852	+	0.936431i	$0.614108\pi$
$380$	473.772	+	820.596i	0.0639578	+	0.110778i
$381$	500.877	−	867.545i	0.0673510	−	0.116655i
$382$		−	3228.21i		−	0.432381i
$383$	10351.4	+	5976.39i	1.38102	+	0.797335i	0.992281	−	0.124011i	$-0.0395759\pi$
$383$	10351.4	+	5976.39i	1.38102	+	0.797335i	0.388744	+	0.921346i	$0.372909\pi$
$384$	−44.9849	−	25.9720i	−0.00597819	−	0.00345151i
$385$			423.888i			0.0561126i
$386$	−2461.12	+	4262.78i	−0.324527	+	0.562098i
$387$	5551.12	+	9614.83i	0.729146	+	1.26292i
$388$	−2214.67	+	1278.64i	−0.289775	+	0.167302i
$389$	−5282.24			−0.688484			−0.344242	−	0.938881i	$-0.611864\pi$
$389$	−5282.24			−0.688484			−0.344242	+	0.938881i	$0.611864\pi$
$390$		0			0
$391$	9832.46			1.27174
$392$	2331.30	−	1345.98i	0.300379	−	0.173424i
$393$	−462.591	−	801.231i	−0.0593757	−	0.102842i
$394$	−3445.91	+	5968.48i	−0.440615	+	0.763167i
$395$		−	3387.01i		−	0.431440i
$396$	2428.21	+	1401.93i	0.308137	+	0.177903i
$397$	7890.86	+	4555.79i	0.997559	+	0.575941i	0.907525	−	0.419997i	$-0.137969\pi$
$397$	7890.86	+	4555.79i	0.997559	+	0.575941i	0.0900341	+	0.995939i	$0.471302\pi$
$398$			4410.05i			0.555416i
$399$	−19.2696	+	33.3760i	−0.00241776	+	0.00418769i
$400$	−676.172	−	1171.16i	−0.0845215	−	0.146396i
$401$	432.633	−	249.781i	0.0538770	−	0.0311059i	−0.472820	−	0.881159i	$-0.656764\pi$
$401$	432.633	−	249.781i	0.0538770	−	0.0311059i	0.526697	+	0.850053i	$0.323430\pi$
$402$	−715.533			−0.0887750
$403$		0			0
$404$	1899.35			0.233902
$405$	3943.36	−	2276.70i	0.483820	−	0.279334i
$406$	−636.500	−	1102.45i	−0.0778053	−	0.134763i
$407$	−142.360	+	246.575i	−0.0173379	+	0.0300302i
$408$			304.225i			0.0369152i
$409$	−11087.9	−	6401.61i	−1.34049	−	0.773934i	−0.353614	−	0.935392i	$-0.615047\pi$
$409$	−11087.9	−	6401.61i	−1.34049	−	0.773934i	−0.986880	+	0.161457i	$0.948381\pi$
$410$	4092.48	+	2362.79i	0.492958	+	0.284610i
$411$			178.277i			0.0213960i
$412$	2201.07	−	3812.36i	0.263201	−	0.455877i
$413$	987.678	+	1710.71i	0.117677	+	0.203822i
$414$	4876.98	−	2815.72i	0.578962	−	0.334264i
$415$	2395.47			0.283346
$416$		0			0
$417$	−884.242			−0.103841
$418$	1684.52	−	972.558i	0.197111	−	0.113802i
$419$	3684.14	+	6381.11i	0.429551	+	0.744004i	0.996833	−	0.0795194i	$-0.0253386\pi$
$419$	3684.14	+	6381.11i	0.429551	+	0.744004i	−0.567282	+	0.823523i	$0.692005\pi$
$420$	−13.1710	+	22.8128i	−0.00153019	+	0.00265036i
$421$		−	15266.9i		−	1.76737i	−0.468080	−	0.883686i	$-0.655054\pi$
$421$		−	15266.9i		−	1.76737i	0.468080	−	0.883686i	$-0.344946\pi$
$422$	−1616.34	−	933.193i	−0.186450	−	0.107647i
$423$	−5545.81	−	3201.87i	−0.637462	−	0.368039i
$424$		−	3399.26i		−	0.389346i
$425$	−3960.19	+	6859.25i	−0.451994	+	0.782877i
$426$	−48.1964	−	83.4787i	−0.00548152	−	0.00949426i
$427$	−272.631	+	157.404i	−0.0308982	+	0.0178391i
$428$	2281.53			0.257668
$429$		0			0
$430$	5264.37			0.590397
$431$	−18.1367	+	10.4712i	−0.00202694	+	0.00117026i	−0.501013	−	0.865440i	$-0.667039\pi$
$431$	−18.1367	+	10.4712i	−0.00202694	+	0.00117026i	0.498986	+	0.866610i	$0.333706\pi$
$432$	174.777	+	302.722i	0.0194652	+	0.0337146i
$433$	3729.06	−	6458.92i	0.413873	−	0.716849i	−0.581436	−	0.813592i	$-0.697509\pi$
$433$	3729.06	−	6458.92i	0.413873	−	0.716849i	0.995309	+	0.0967427i	$0.0308424\pi$
$434$			1423.22i			0.157412i
$435$	−557.978	−	322.149i	−0.0615011	−	0.0355077i
$436$	−2054.31	−	1186.06i	−0.225651	−	0.130280i
$437$		−	3906.70i		−	0.427649i
$438$	84.9445	−	147.128i	0.00926668	−	0.0160504i
$439$	4507.17	+	7806.65i	0.490012	+	0.848726i	0.999934	−	0.0114946i	$-0.00365891\pi$
$439$	4507.17	+	7806.65i	0.490012	+	0.848726i	−0.509922	+	0.860221i	$0.670326\pi$
$440$	1151.39	−	664.754i	0.124751	−	0.0720248i
$441$	−9029.93			−0.975049
$442$		0			0
$443$	1787.12			0.191668			0.0958339	−	0.995397i	$-0.469448\pi$
$443$	1787.12			0.191668			0.0958339	+	0.995397i	$0.469448\pi$
$444$	−15.3231	+	8.84681i	−0.00163785	+	0.000945610i
$445$	−135.623	−	234.907i	−0.0144476	−	0.0250239i
$446$	6363.62	−	11022.1i	0.675619	−	1.17021i
$447$			1164.06i			0.123173i
$448$	141.371	+	81.6207i	0.0149088	+	0.00860762i
$449$	−3932.57	−	2270.47i	−0.413340	−	0.238642i	0.278884	−	0.960325i	$-0.410036\pi$
$449$	−3932.57	−	2270.47i	−0.413340	−	0.238642i	−0.692224	+	0.721683i	$0.743369\pi$
$450$			4536.32i			0.475209i
$451$	4850.34	−	8401.03i	0.506416	−	0.877138i
$452$	3678.23	+	6370.89i	0.382765	+	0.662968i
$453$	773.882	−	446.801i	0.0802652	−	0.0463411i
$454$	−1659.02			−0.171501
$455$		0			0
$456$	120.877			0.0124135
$457$	5952.95	−	3436.93i	0.609337	−	0.351801i	−0.163369	−	0.986565i	$-0.552236\pi$
$457$	5952.95	−	3436.93i	0.609337	−	0.351801i	0.772706	+	0.634764i	$0.218903\pi$
$458$	5789.35	+	10027.4i	0.590652	+	1.02304i
$459$	1023.63	−	1772.98i	0.104093	−	0.180295i
$460$		−	2670.27i		−	0.270657i
$461$	−8061.47	−	4654.29i	−0.814447	−	0.470221i	0.0340507	−	0.999420i	$-0.489159\pi$
$461$	−8061.47	−	4654.29i	−0.814447	−	0.470221i	−0.848498	+	0.529199i	$0.822493\pi$
$462$	46.8302	+	27.0374i	0.00471588	+	0.00272271i
$463$			14763.5i			1.48190i	0.671560	+	0.740950i	$0.265625\pi$
$463$			14763.5i			1.48190i	−0.671560	+	0.740950i	$0.734375\pi$
$464$	−1996.36	+	3457.79i	−0.199738	+	0.345957i
$465$	360.165	+	623.824i	0.0359188	+	0.0622132i
$466$	555.556	−	320.751i	0.0552267	−	0.0318852i
$467$	−7397.81			−0.733040			−0.366520	−	0.930410i	$-0.619451\pi$
$467$	−7397.81			−0.733040			−0.366520	+	0.930410i	$0.619451\pi$
$468$		0			0
$469$	2248.66			0.221393
$470$	−2629.66	+	1518.24i	−0.258079	+	0.149002i
$471$	−175.542	−	304.048i	−0.0171732	−	0.0297448i
$472$	3097.81	−	5365.57i	0.302094	−	0.523242i
$473$		−	10806.7i		−	1.05051i
$474$	−374.188	−	216.038i	−0.0362596	−	0.0209345i
$475$	2725.36	+	1573.49i	0.263259	+	0.151993i
$476$		−	956.069i		−	0.0920617i
$477$	−5701.26	+	9874.88i	−0.547260	+	0.947882i
$478$	−3582.11	−	6204.40i	−0.342765	−	0.593687i
$479$	10708.4	−	6182.49i	1.02146	−	0.589740i	0.106933	−	0.994266i	$-0.465897\pi$
$479$	10708.4	−	6182.49i	1.02146	−	0.589740i	0.914526	+	0.404526i	$0.132564\pi$
$480$	82.6206			0.00785645
$481$		0			0
$482$	−9760.48			−0.922360
$483$	94.0568	−	54.3037i	0.00886073	−	0.00511575i
$484$	1297.39	+	2247.15i	0.121844	+	0.211040i
$485$	2033.76	−	3522.58i	0.190409	−	0.329798i
$486$		−	1760.61i		−	0.164327i
$487$	−7315.63	−	4223.68i	−0.680704	−	0.393005i	0.119416	−	0.992844i	$-0.461898\pi$
$487$	−7315.63	−	4223.68i	−0.680704	−	0.393005i	−0.800120	+	0.599840i	$0.795231\pi$
$488$	855.096	+	493.690i	0.0793205	+	0.0457957i
$489$		−	430.502i		−	0.0398118i
$490$	−2140.87	+	3708.09i	−0.197377	+	0.341866i
$491$	7091.49	+	12282.8i	0.651801	+	1.12895i	0.982686	+	0.185281i	$0.0593196\pi$
$491$	7091.49	+	12282.8i	0.651801	+	1.12895i	−0.330884	+	0.943671i	$0.607347\pi$
$492$	522.072	−	301.418i	0.0478390	−	0.0276199i
$493$	23384.4			2.13627
$494$		0			0
$495$	−4459.72			−0.404949
$496$	3865.84	−	2231.94i	0.349962	−	0.202051i
$497$	151.464	+	262.343i	0.0136702	+	0.0236775i
$498$	152.793	−	264.645i	0.0137486	−	0.0238133i
$499$		−	14029.9i		−	1.25865i	−0.777143	−	0.629324i	$-0.783332\pi$
$499$		−	14029.9i		−	1.25865i	0.777143	−	0.629324i	$-0.216668\pi$
$500$	4617.76	+	2666.07i	0.413025	+	0.238460i
$501$	493.459	+	284.899i	0.0440042	+	0.0254058i
$502$		−	5960.44i		−	0.529935i
$503$	−4874.22	+	8442.40i	−0.432069	+	0.748366i	−0.997051	−	0.0767373i	$-0.975550\pi$
$503$	−4874.22	+	8442.40i	−0.432069	+	0.748366i	0.564982	+	0.825103i	$0.308883\pi$
$504$	−273.790	−	474.217i	−0.0241975	−	0.0419114i
$505$	−2616.31	+	1510.53i	−0.230543	+	0.133104i
$506$	−5481.53			−0.481589
$507$		0			0
$508$	9874.05			0.862382
$509$	9933.06	−	5734.85i	0.864981	−	0.499397i	−0.000696453	−	1.00000i	$-0.500222\pi$
$509$	9933.06	−	5734.85i	0.864981	−	0.499397i	0.865677	+	0.500603i	$0.166888\pi$
$510$	−241.946	−	419.062i	−0.0210069	−	0.0363850i
$511$	−266.950	+	462.370i	−0.0231099	+	0.0400275i
$512$		−	512.000i		−	0.0441942i
$513$	−704.451	−	406.715i	−0.0606282	−	0.0350037i
$514$	6678.66	+	3855.93i	0.573119	+	0.330891i
$515$			7001.89i			0.599107i
$516$	335.784	−	581.596i	0.0286474	−	0.0496188i
$517$	3116.64	+	5398.17i	0.265125	+	0.459209i
$518$	48.1550	−	27.8023i	0.00408457	−	0.00235823i
$519$	−414.830			−0.0350848
$520$		0			0
$521$	−8428.10			−0.708717			−0.354359	−	0.935110i	$-0.615301\pi$
$521$	−8428.10			−0.708717			−0.354359	+	0.935110i	$0.615301\pi$
$522$	11598.9	−	6696.60i	0.972545	−	0.561499i
$523$	8586.33	+	14872.0i	0.717885	+	1.24341i	0.961836	+	0.273626i	$0.0882230\pi$
$523$	8586.33	+	14872.0i	0.717885	+	1.24341i	−0.243951	+	0.969788i	$0.578444\pi$
$524$	4559.65	−	7897.54i	0.380132	−	0.658408i
$525$			87.4870i			0.00727285i
$526$	−7675.02	−	4431.18i	−0.636211	−	0.367316i
$527$	−22641.4	−	13072.0i	−1.87149	−	1.08050i
$528$		−	169.604i		−	0.0139793i
$529$	578.763	−	1002.45i	0.0475683	−	0.0823907i
$530$	2703.38	+	4682.39i	0.221561	+	0.383754i
$531$	−17998.3	+	10391.3i	−1.47093	+	0.849239i
$532$	−379.872			−0.0309578
$533$		0			0
$534$	−34.6026			−0.00280412
$535$	−3142.75	+	1814.46i	−0.253968	+	0.146628i
$536$	−3526.42	−	6107.93i	−0.284175	−	0.492206i
$537$	84.8602	−	146.982i	0.00681935	−	0.0118115i
$538$		−	2522.67i		−	0.202156i
$539$	7611.97	+	4394.77i	0.608294	+	0.351199i
$540$	−481.500	−	277.994i	−0.0383712	−	0.0221536i
$541$			3228.20i			0.256546i	0.991739	+	0.128273i	$0.0409434\pi$
$541$			3228.20i			0.256546i	−0.991739	+	0.128273i	$0.959057\pi$
$542$	6200.75	−	10740.0i	0.491411	−	0.851149i
$543$	−571.395	−	989.685i	−0.0451582	−	0.0782163i
$544$	−2596.93	+	1499.34i	−0.204673	+	0.118168i
$545$	3773.01			0.296547
$546$		0			0
$547$	6923.31			0.541169			0.270584	−	0.962696i	$-0.412783\pi$
$547$	6923.31			0.541169			0.270584	+	0.962696i	$0.412783\pi$
$548$	−1521.81	+	878.618i	−0.118629	+	0.0684903i
$549$	−1656.04	−	2868.35i	−0.128740	−	0.222984i
$550$	2207.78	−	3823.99i	0.171164	−	0.296464i
$551$		−	9291.26i		−	0.718368i
$552$	−295.005	−	170.321i	−0.0227469	−	0.0131329i
$553$	1175.94	+	678.928i	0.0904267	+	0.0522079i
$554$		−	2315.14i		−	0.177547i
$555$	14.0715	−	24.3725i	0.00107622	−	0.00186406i
$556$	−4357.88	−	7548.07i	−0.332401	−	0.575736i
$557$	15306.0	−	8836.91i	1.16434	−	0.672229i	0.211996	−	0.977271i	$-0.432004\pi$
$557$	15306.0	−	8836.91i	1.16434	−	0.672229i	0.952339	+	0.305041i	$0.0986703\pi$
$558$	−14973.7			−1.13600
$559$		0			0
$560$	−259.647			−0.0195930
$561$	−860.250	+	496.666i	−0.0647411	+	0.0373783i
$562$	6322.71	+	10951.3i	0.474568	+	0.821976i
$563$	−1221.09	+	2115.00i	−0.0914085	+	0.158324i	−0.908104	−	0.418745i	$-0.862470\pi$
$563$	−1221.09	+	2115.00i	−0.0914085	+	0.158324i	0.816696	+	0.577069i	$0.195804\pi$
$564$			387.359i			0.0289198i
$565$	−10133.3	−	5850.48i	−0.754535	−	0.435631i
$566$	16122.5	+	9308.35i	1.19732	+	0.691270i
$567$			1825.47i			0.135207i
$568$	475.060	−	822.829i	0.0350935	−	0.0607837i
$569$	3487.06	+	6039.77i	0.256916	+	0.444992i	0.965414	−	0.260721i	$-0.0839603\pi$
$569$	3487.06	+	6039.77i	0.256916	+	0.444992i	−0.708498	+	0.705713i	$0.750627\pi$
$570$	−166.504	+	96.1314i	−0.0122353	+	0.00706404i
$571$	−5061.39			−0.370950			−0.185475	−	0.982649i	$-0.559382\pi$
$571$	−5061.39			−0.370950			−0.185475	+	0.982649i	$0.559382\pi$
$572$		0			0
$573$	655.026			0.0477558
$574$	−1640.68	+	947.247i	−0.119304	+	0.0688804i
$575$	−4434.25	−	7680.35i	−0.321602	−	0.557031i
$576$	−858.730	+	1487.36i	−0.0621188	+	0.107593i
$577$			3849.90i			0.277771i	0.990308	+	0.138885i	$0.0443519\pi$
$577$			3849.90i			0.277771i	−0.990308	+	0.138885i	$0.955648\pi$
$578$	6700.07	+	3868.29i	0.482156	+	0.278373i
$579$	−864.946	−	499.377i	−0.0620828	−	0.0358435i
$580$		−	6350.68i		−	0.454651i
$581$	−480.173	+	831.684i	−0.0342873	+	0.0593874i
$582$	−259.444	−	449.370i	−0.0184782	−	0.0320052i
$583$	9612.00	−	5549.49i	0.682827	−	0.394230i
$584$	1674.55			0.118653
$585$		0			0
$586$	1012.39			0.0713677
$587$	−10117.0	+	5841.06i	−0.711369	+	0.410709i	−0.811568	−	0.584258i	$-0.801385\pi$
$587$	−10117.0	+	5841.06i	−0.711369	+	0.410709i	0.100199	+	0.994967i	$0.468052\pi$
$588$	273.108	+	473.036i	0.0191544	+	0.0331763i
$589$	−5193.85	+	8996.01i	−0.363343	+	0.629328i
$590$			9854.56i			0.687637i
$591$	−1211.04	−	699.197i	−0.0842906	−	0.0486652i
$592$	−151.036	−	87.2008i	−0.0104857	−	0.00605394i
$593$			14539.7i			1.00687i	0.864033	+	0.503435i	$0.167931\pi$
$593$			14539.7i			1.00687i	−0.864033	+	0.503435i	$0.832069\pi$
$594$	−570.666	+	988.423i	−0.0394187	+	0.0682752i
$595$	760.347	+	1316.96i	0.0523885	+	0.0907396i
$596$	−9936.69	+	5736.95i	−0.682924	+	0.394286i
$597$	−894.827			−0.0613448
$598$		0			0
$599$	8414.92			0.573997			0.286998	−	0.957931i	$-0.407343\pi$
$599$	8414.92			0.573997			0.286998	+	0.957931i	$0.407343\pi$
$600$	237.637	−	137.200i	0.0161691	−	0.00933526i
$601$	−9135.37	−	15822.9i	−0.620032	−	1.07393i	−0.989479	−	0.144675i	$-0.953786\pi$
$601$	−9135.37	−	15822.9i	−0.620032	−	1.07393i	0.369447	−	0.929252i	$-0.379547\pi$
$602$	−1055.25	+	1827.74i	−0.0714430	+	0.123743i
$603$			23658.1i			1.59773i
$604$	7627.96	+	4404.01i	0.513870	+	0.296683i
$605$	−3574.25	−	2063.59i	−0.240188	−	0.138673i
$606$			385.392i			0.0258341i
$607$	2833.59	−	4907.93i	0.189476	−	0.328182i	−0.755600	−	0.655034i	$-0.772654\pi$
$607$	2833.59	−	4907.93i	0.189476	−	0.328182i	0.945076	+	0.326851i	$0.105988\pi$
$608$	595.726	+	1031.83i	0.0397367	+	0.0688259i
$609$	223.694	−	129.150i	0.0148843	−	0.00859347i
$610$	−1570.50			−0.104242
$611$		0			0
$612$	10058.8			0.664383
$613$	−12585.6	+	7266.32i	−0.829248	+	0.478767i	−0.853595	−	0.520937i	$-0.825583\pi$
$613$	−12585.6	+	7266.32i	−0.829248	+	0.478767i	0.0243470	+	0.999704i	$0.492249\pi$
$614$	4094.64	+	7092.13i	0.269131	+	0.466148i
$615$	−479.426	+	830.390i	−0.0314347	+	0.0544465i
$616$			533.002i			0.0348624i
$617$	9919.56	+	5727.06i	0.647239	+	0.373684i	0.787398	−	0.616445i	$-0.211428\pi$
$617$	9919.56	+	5727.06i	0.647239	+	0.373684i	−0.140158	+	0.990129i	$0.544761\pi$
$618$	773.553	+	446.611i	0.0503509	+	0.0290701i
$619$		−	10052.7i		−	0.652751i	−0.945240	−	0.326376i	$-0.894173\pi$
$619$		−	10052.7i		−	0.652751i	0.945240	−	0.326376i	$-0.105827\pi$
$620$	−3550.05	+	6148.88i	−0.229957	+	0.398298i
$621$	1146.16	+	1985.21i	0.0740644	+	0.128283i
$622$	15077.5	−	8705.00i	0.971950	−	0.561155i
$623$	108.743			0.00699311
$624$		0			0
$625$	2084.07			0.133380
$626$	5446.92	−	3144.78i	0.347768	−	0.200784i
$627$	197.338	+	341.800i	0.0125693	+	0.0217706i
$628$	1730.28	−	2996.93i	0.109945	−	0.190431i
$629$			1021.43i			0.0647491i
$630$	754.275	+	435.481i	0.0477001	+	0.0275396i
$631$	10433.6	+	6023.82i	0.658247	+	0.380039i	0.791609	−	0.611028i	$-0.209244\pi$
$631$	10433.6	+	6023.82i	0.658247	+	0.380039i	−0.133362	+	0.991067i	$0.542577\pi$
$632$		−	4258.86i		−	0.268051i
$633$	189.351	−	327.966i	0.0118895	−	0.0205931i
$634$	−9902.03	−	17150.8i	−0.620284	−	1.07436i
$635$	−13601.2	+	7852.67i	−0.849997	+	0.490746i
$636$	689.732			0.0430026
$637$		0			0
$638$	−13036.7			−0.808976
$639$	−2760.11	+	1593.55i	−0.170874	+	0.0986539i
$640$	407.185	+	705.266i	0.0251491	+	0.0435595i
$641$	−10575.4	+	18317.1i	−0.651643	+	1.12868i	0.331082	+	0.943602i	$0.392586\pi$
$641$	−10575.4	+	18317.1i	−0.651643	+	1.12868i	−0.982724	+	0.185076i	$0.940747\pi$
$642$			462.938i			0.0284590i
$643$	−13275.7	−	7664.72i	−0.814217	−	0.470089i	0.0342009	−	0.999415i	$-0.489111\pi$
$643$	−13275.7	−	7664.72i	−0.814217	−	0.470089i	−0.848418	+	0.529326i	$0.822445\pi$
$644$	927.095	+	535.258i	0.0567277	+	0.0327518i
$645$			1068.18i			0.0652083i
$646$	3489.04	−	6043.19i	0.212499	−	0.368059i
$647$	−7259.97	−	12574.6i	−0.441142	−	0.764080i	0.556633	−	0.830759i	$-0.312093\pi$
$647$	−7259.97	−	12574.6i	−0.441142	−	0.764080i	−0.997774	+	0.0666787i	$0.978760\pi$
$648$	4958.43	−	2862.75i	0.300595	−	0.173549i
$649$	20229.4			1.22354
$650$		0			0
$651$	−288.781			−0.0173859
$652$	3674.85	−	2121.67i	0.220733	−	0.127440i
$653$	−13807.8	−	23915.8i	−0.827475	−	1.43323i	−0.900013	−	0.435863i	$-0.856443\pi$
$653$	−13807.8	−	23915.8i	−0.827475	−	1.43323i	0.0725376	−	0.997366i	$-0.476890\pi$
$654$	240.659	−	416.834i	0.0143892	−	0.0249228i
$655$			14504.9i			0.865270i
$656$	5145.93	+	2971.00i	0.306273	+	0.176827i
$657$	−4864.59	−	2808.57i	−0.288867	−	0.166778i
$658$		−	1217.33i		−	0.0721222i
$659$	6949.24	−	12036.4i	0.410780	−	0.711492i	−0.584195	−	0.811613i	$-0.698590\pi$
$659$	6949.24	−	12036.4i	0.410780	−	0.711492i	0.994975	+	0.100121i	$0.0319231\pi$
$660$	134.883	+	233.624i	0.00795502	+	0.0137785i
$661$	−15020.6	+	8672.14i	−0.883862	+	0.510298i	−0.871930	−	0.489631i	$-0.837132\pi$
$661$	−15020.6	+	8672.14i	−0.883862	+	0.510298i	−0.0119324	+	0.999929i	$0.503798\pi$
$662$	3932.74			0.230892
$663$		0			0
$664$	3012.09			0.176042
$665$	523.263	−	302.106i	0.0305132	−	0.0176168i
$666$	292.508	+	506.638i	0.0170187	+	0.0294772i
$667$	−13091.9	+	22675.8i	−0.759998	+	1.31636i
$668$			5616.35i			0.325304i
$669$	2236.46	+	1291.22i	0.129247	+	0.0746210i
$670$	9715.08	+	5609.00i	0.560189	+	0.323425i
$671$			3223.91i			0.185481i
$672$	−16.5614	+	28.6851i	−0.000950698	+	0.00164666i
$673$	−1328.00	−	2300.15i	−0.0760631	−	0.131745i	0.825485	−	0.564424i	$-0.190902\pi$
$673$	−1328.00	−	2300.15i	−0.0760631	−	0.131745i	−0.901548	+	0.432679i	$0.857568\pi$
$674$	−16577.2	+	9570.83i	−0.947372	+	0.546965i
$675$	−1846.55			−0.105294
$676$		0			0
$677$	−18853.1			−1.07029			−0.535143	−	0.844761i	$-0.679742\pi$
$677$	−18853.1			−1.07029			−0.535143	+	0.844761i	$0.679742\pi$
$678$	−1292.70	+	746.338i	−0.0732237	+	0.0422757i
$679$	815.338	+	1412.21i	0.0460822	+	0.0798167i
$680$	2384.80	−	4130.59i	0.134489	−	0.232942i
$681$		−	336.626i		−	0.0189421i
$682$	12622.4	+	7287.55i	0.708705	+	0.409171i
$683$	−1455.14	−	840.126i	−0.0815218	−	0.0470666i	0.458685	−	0.888599i	$-0.348321\pi$
$683$	−1455.14	−	840.126i	−0.0815218	−	0.0470666i	−0.540207	+	0.841532i	$0.681654\pi$
$684$		−	3996.62i		−	0.223413i
$685$	1397.50	−	2420.54i	0.0779501	−	0.135013i
$686$	−1733.15	−	3001.90i	−0.0964606	−	0.167075i
$687$	−2034.64	+	1174.70i	−0.112993	+	0.0652365i
$688$	6619.49			0.366810
$689$		0			0
$690$	541.816			0.0298936
$691$	−9472.95	+	5469.21i	−0.521516	+	0.301098i	−0.737555	−	0.675287i	$-0.764020\pi$
$691$	−9472.95	+	5469.21i	−0.521516	+	0.301098i	0.216038	+	0.976385i	$0.430686\pi$
$692$	−2044.44	−	3541.07i	−0.112309	−	0.194525i
$693$	893.955	−	1548.38i	0.0490022	−	0.0848743i
$694$			12908.4i			0.706048i
$695$	12005.7	+	6931.50i	0.655256	+	0.378312i
$696$	−701.608	−	405.074i	−0.0382103	−	0.0220607i
$697$		−	34801.0i		−	1.89122i
$698$	−2779.52	+	4814.28i	−0.150726	+	0.261064i
$699$	65.0824	+	112.726i	0.00352166	+	0.00609970i
$700$	−746.806	+	431.169i	−0.0403238	+	0.0232809i
$701$	−19632.4			−1.05778			−0.528892	−	0.848689i	$-0.677392\pi$
$701$	−19632.4			−1.05778			−0.528892	+	0.848689i	$0.677392\pi$
$702$		0			0
$703$	405.842			0.0217733
$704$	1447.77	−	835.870i	0.0775069	−	0.0447486i
$705$	−308.060	−	533.576i	−0.0164571	−	0.0285045i
$706$	−11147.3	+	19307.8i	−0.594243	+	1.02926i
$707$		−	1211.15i		−	0.0644269i
$708$	1088.71	+	628.566i	0.0577912	+	0.0333658i
$709$	−16868.3	−	9738.89i	−0.893513	−	0.515870i	−0.0184228	−	0.999830i	$-0.505865\pi$
$709$	−16868.3	−	9738.89i	−0.893513	−	0.515870i	−0.875090	+	0.483960i	$0.839198\pi$
$710$			1511.23i			0.0798810i
$711$	−7142.99	+	12372.0i	−0.376770	+	0.652584i
$712$	−170.535	−	295.374i	−0.00897620	−	0.0155472i
$713$	25351.7	−	14636.8i	1.33160	−	0.768797i
$714$	193.993			0.0101681
$715$		0			0
$716$	1672.89			0.0873169
$717$	1258.91	−	726.834i	0.0655718	−	0.0378579i
$718$	−4313.27	−	7470.81i	−0.224192	−	0.388312i
$719$	−201.611	+	349.201i	−0.0104573	+	0.0181126i	−0.871207	−	0.490916i	$-0.836662\pi$
$719$	−201.611	+	349.201i	−0.0104573	+	0.0181126i	0.860749	+	0.509029i	$0.169995\pi$
$720$		−	2731.74i		−	0.141397i
$721$	−2430.99	−	1403.54i	−0.125569	−	0.0724971i
$722$	9479.02	+	5472.71i	0.488604	+	0.282096i
$723$		−	1980.47i		−	0.101873i
$724$	5632.10	−	9755.08i	0.289110	−	0.500752i
$725$	−10545.9	−	18266.1i	−0.540229	−	0.935704i
$726$	−455.962	+	263.250i	−0.0233090	+	0.0134575i
$727$	29051.3			1.48206			0.741028	−	0.671474i	$-0.234339\pi$
$727$	29051.3			1.48206			0.741028	+	0.671474i	$0.234339\pi$
$728$		0			0
$729$	−18966.3			−0.963589
$730$	−2306.65	+	1331.75i	−0.116949	+	0.0675207i
$731$	−19384.4	−	33574.8i	−0.980793	−	1.69878i
$732$	−100.173	+	173.505i	−0.00505806	+	0.00876082i
$733$			25289.5i			1.27434i	0.770724	+	0.637169i	$0.219895\pi$
$733$			25289.5i			1.27434i	−0.770724	+	0.637169i	$0.780105\pi$
$734$	−11967.6	−	6909.51i	−0.601816	−	0.347459i
$735$	−752.396	−	434.396i	−0.0377586	−	0.0217999i
$736$		−	3357.63i		−	0.168158i
$737$	11514.2	−	19943.1i	0.575481	−	0.996762i
$738$	−9965.98	−	17261.6i	−0.497090	−	0.860986i
$739$	219.893	−	126.956i	0.0109458	−	0.00631953i	−0.494517	−	0.869168i	$-0.664655\pi$
$739$	219.893	−	126.956i	0.0109458	−	0.00631953i	0.505463	+	0.862848i	$0.331322\pi$
$740$	277.398			0.0137802
$741$		0			0
$742$	−2167.58			−0.107243
$743$	−11174.8	+	6451.78i	−0.551768	+	0.318564i	−0.749835	−	0.661625i	$-0.769867\pi$
$743$	−11174.8	+	6451.78i	−0.551768	+	0.318564i	0.198066	+	0.980189i	$0.436534\pi$
$744$	452.876	+	784.404i	0.0223162	+	0.0386527i
$745$	9125.01	−	15805.0i	0.448744	−	0.777248i
$746$		−	4632.39i		−	0.227351i
$747$	−8750.14	−	5051.89i	−0.428582	−	0.247442i
$748$	−8479.27	−	4895.51i	−0.414482	−	0.239301i
$749$		−	1454.84i		−	0.0709731i
$750$	−540.962	+	936.974i	−0.0263375	+	0.0456179i
$751$	−16912.6	−	29293.5i	−0.821771	−	1.42335i	−0.904362	−	0.426766i	$-0.859653\pi$
$751$	−16912.6	−	29293.5i	−0.821771	−	1.42335i	0.0825911	−	0.996584i	$-0.473680\pi$
$752$	−3306.57	+	1909.05i	−0.160343	+	0.0925743i
$753$	1209.41			0.0585305
$754$		0			0
$755$	−14009.7			−0.675320
$756$	193.034	−	111.448i	0.00928649	−	0.00536156i
$757$	16928.8	+	29321.5i	0.812796	+	1.40780i	0.910899	+	0.412629i	$0.135389\pi$
$757$	16928.8	+	29321.5i	0.812796	+	1.40780i	−0.0981029	+	0.995176i	$0.531277\pi$
$758$	11393.1	−	19733.4i	0.545930	−	0.945579i
$759$		−	1112.24i		−	0.0531907i
$760$	−1641.19	−	947.543i	−0.0783320	−	0.0452250i
$761$	10255.2	+	5920.81i	0.488501	+	0.282036i	0.723952	−	0.689850i	$-0.242324\pi$
$761$	10255.2	+	5920.81i	0.488501	+	0.282036i	−0.235452	+	0.971886i	$0.575657\pi$
$762$			2003.51i			0.0952487i
$763$	−756.304	+	1309.96i	−0.0358847	+	0.0621542i
$764$	3228.21	+	5591.43i	0.152870	+	0.264778i
$765$	−13855.7	+	7999.60i	−0.654842	+	0.378073i
$766$	−23905.6			−1.12760
$767$		0			0
$768$	103.888			0.00488117
$769$	−8494.96	+	4904.57i	−0.398356	+	0.229991i	−0.685775	−	0.727814i	$-0.740536\pi$
$769$	−8494.96	+	4904.57i	−0.398356	+	0.229991i	0.287418	+	0.957805i	$0.407203\pi$
$770$	−423.888	−	734.196i	−0.0198388	−	0.0343618i
$771$	−782.393	+	1355.15i	−0.0365463	+	0.0633001i
$772$		−	9844.47i		−	0.458951i
$773$	23488.0	+	13560.8i	1.09289	+	0.630982i	0.934345	−	0.356369i	$-0.115985\pi$
$773$	23488.0	+	13560.8i	1.09289	+	0.630982i	0.158548	+	0.987351i	$0.449319\pi$
$774$	−19229.7	−	11102.2i	−0.893018	−	0.515584i
$775$			23580.9i			1.09297i
$776$	2557.28	−	4429.33i	0.118300	−	0.204902i
$777$	5.64127	+	9.77097i	0.000260463	+	0.000451134i
$778$	9149.11	−	5282.24i	0.421609	−	0.243416i
$779$	−13827.4			−0.635966
$780$		0			0
$781$	3102.26			0.142135
$782$	−17030.3	+	9832.46i	−0.778777	+	0.449627i
$783$	2725.91	+	4721.41i	0.124414	+	0.215491i
$784$	−2691.95	+	4662.60i	−0.122629	+	0.212400i
$785$			5504.25i			0.250261i
$786$	1602.46	+	925.182i	0.0727201	+	0.0419849i
$787$	−15982.9	−	9227.71i	−0.723923	−	0.417957i	0.0922719	−	0.995734i	$-0.470587\pi$
$787$	−15982.9	−	9227.71i	−0.723923	−	0.417957i	−0.816195	+	0.577777i	$0.803920\pi$
$788$		−	13783.6i		−	0.623123i
$789$	899.115	−	1557.31i	0.0405695	−	0.0702684i
$790$	3387.01	+	5866.46i	0.152537	+	0.264202i
$791$	4062.47	−	2345.47i	0.182610	−	0.105430i
$792$	−5607.71			−0.251592
$793$		0			0
$794$	−18223.2			−0.814504
$795$	−950.087	+	548.533i	−0.0423850	+	0.0244710i
$796$	−4410.05	−	7638.42i	−0.196369	−	0.340122i
$797$	−7025.68	+	12168.8i	−0.312249	+	0.540831i	−0.978849	−	0.204585i	$-0.934416\pi$
$797$	−7025.68	+	12168.8i	−0.312249	+	0.540831i	0.666600	+	0.745416i	$0.267749\pi$
$798$		−	77.0785i		−	0.00341923i
$799$	19365.9	+	11180.9i	0.857466	+	0.495058i
$800$	2342.33	+	1352.34i	0.103517	+	0.0597657i
$801$			1144.09i			0.0504673i
$802$	−499.562	+	865.266i	−0.0219952	+	0.0380968i
$803$	2733.81	+	4735.09i	0.120142	+	0.208092i
$804$	1239.34	−	715.533i	0.0543634	−	0.0313867i
$805$	−1702.73			−0.0745507
$806$		0			0
$807$	511.866			0.0223278
$808$	−3289.78	+	1899.35i	−0.143235	+	0.0826968i
$809$	12193.2	+	21119.3i	0.529902	+	0.917818i	0.999392	+	0.0348794i	$0.0111047\pi$
$809$	12193.2	+	21119.3i	0.529902	+	0.917818i	−0.469489	+	0.882938i	$0.655562\pi$
$810$	−4553.40	+	7886.72i	−0.197519	+	0.342112i
$811$		−	34306.9i		−	1.48542i	−0.669612	−	0.742711i	$-0.733540\pi$
$811$		−	34306.9i		−	1.48542i	0.669612	−	0.742711i	$-0.266460\pi$
$812$	2204.90	+	1273.00i	0.0952916	+	0.0550167i
$813$	2179.22	+	1258.17i	0.0940080	+	0.0542756i
$814$		−	569.442i		−	0.0245196i
$815$	−3374.67	+	5845.10i	−0.145042	+	0.251221i
$816$	−304.225	−	526.934i	−0.0130515	−	0.0226058i
$817$	−13340.2	+	7701.95i	−0.571253	+	0.329813i
$818$	25606.4			1.09451
$819$		0			0
$820$	−9451.17			−0.402499
$821$	2835.84	−	1637.27i	0.120550	−	0.0695995i	−0.438513	−	0.898725i	$-0.644495\pi$
$821$	2835.84	−	1637.27i	0.120550	−	0.0695995i	0.559062	+	0.829126i	$0.311161\pi$
$822$	−178.277	−	308.785i	−0.00756464	−	0.0131023i
$823$	8607.39	−	14908.4i	0.364562	−	0.631440i	−0.624144	−	0.781310i	$-0.714552\pi$
$823$	8607.39	−	14908.4i	0.364562	−	0.631440i	0.988706	+	0.149869i	$0.0478853\pi$
$824$			8804.26i			0.372222i
$825$	775.912	+	447.973i	0.0327440	+	0.0189048i
$826$	−3421.42	−	1975.36i	−0.144124	−	0.0832099i
$827$		−	40718.9i		−	1.71213i	−0.516864	−	0.856067i	$-0.672901\pi$
$827$		−	40718.9i		−	1.71213i	0.516864	−	0.856067i	$-0.327099\pi$
$828$	−5631.45	+	9753.95i	−0.236360	+	0.409388i
$829$	813.632	+	1409.25i	0.0340876	+	0.0590414i	0.882566	−	0.470189i	$-0.155814\pi$
$829$	813.632	+	1409.25i	0.0340876	+	0.0590414i	−0.848478	+	0.529230i	$0.822481\pi$
$830$	−4149.07	+	2395.47i	−0.173514	+	0.100178i
$831$	469.757			0.0196097
$832$		0			0
$833$	31532.4			1.31156
$834$	1531.55	−	884.242i	0.0635891	−	0.0367132i
$835$	−4466.59	−	7736.36i	−0.185117	−	0.320632i
$836$	−1945.12	+	3369.04i	−0.0804704	+	0.139379i
$837$		−	6095.18i		−	0.251709i
$838$	−12762.2	−	7368.27i	−0.526090	−	0.303738i
$839$	14827.4	+	8560.59i	0.610128	+	0.352258i	0.773016	−	0.634387i	$-0.218747\pi$
$839$	14827.4	+	8560.59i	0.610128	+	0.352258i	−0.162887	+	0.986645i	$0.552081\pi$
$840$		−	52.6840i		−	0.00216401i
$841$	−18941.7	+	32808.0i	−0.776650	+	1.34520i
$842$	15266.9	+	26443.1i	0.624861	+	1.08229i
$843$	−2222.08	+	1282.92i	−0.0907859	+	0.0524153i
$844$	3732.77			0.152236
$845$		0			0
$846$	12807.5			0.520485
$847$	1432.92	−	827.298i	0.0581296	−	0.0335612i
$848$	3399.26	+	5887.69i	0.137655	+	0.238425i
$849$	−1888.73	+	3271.37i	−0.0763497	+	0.132242i
$850$		−	15840.8i		−	0.639216i
$851$	−990.477	−	571.852i	−0.0398979	−	0.0230351i
$852$	166.957	+	96.3929i	0.00671346	+	0.00387602i
$853$		−	4791.65i		−	0.192336i	−0.995365	−	0.0961682i	$-0.969341\pi$
$853$		−	4791.65i		−	0.192336i	0.995365	−	0.0961682i	$-0.0306587\pi$
$854$	314.807	−	545.262i	0.0126141	−	0.0218483i
$855$	3178.45	+	5505.24i	0.127135	+	0.220205i
$856$	−3951.73	+	2281.53i	−0.157789	+	0.0910994i
$857$	−12689.7			−0.505802			−0.252901	−	0.967492i	$-0.581385\pi$
$857$	−12689.7			−0.505802			−0.252901	+	0.967492i	$0.581385\pi$
$858$		0			0
$859$	−35646.1			−1.41586			−0.707932	−	0.706280i	$-0.750372\pi$
$859$	−35646.1			−1.41586			−0.707932	+	0.706280i	$0.750372\pi$
$860$	−9118.16	+	5264.37i	−0.361543	+	0.208737i
$861$	−192.203	−	332.905i	−0.00760773	−	0.0131770i
$862$	20.9424	−	36.2734i	0.000827497	−	0.00143327i
$863$		−	10664.4i		−	0.420650i	−0.977631	−	0.210325i	$-0.932548\pi$
$863$		−	10664.4i		−	0.420650i	0.977631	−	0.210325i	$-0.0674523\pi$
$864$	−605.444	−	349.553i	−0.0238398	−	0.0137639i
$865$	5632.32	+	3251.82i	0.221393	+	0.127821i
$866$			14916.2i			0.585305i
$867$	−784.901	+	1359.49i	−0.0307458	+	0.0532534i
$868$	−1423.22	−	2465.09i	−0.0556536	−	0.0963949i
$869$	12042.7	−	6952.84i	0.470103	−	0.271414i
$870$	1288.59			0.0502155
$871$		0			0
$872$	4744.23			0.184243
$873$	−14857.8	+	8578.16i	−0.576015	+	0.332562i
$874$	3906.70	+	6766.60i	0.151197	+	0.261881i
$875$	1700.05	−	2944.57i	0.0656824	−	0.113765i
$876$			339.778i			0.0131051i
$877$	−9538.83	−	5507.25i	−0.367279	−	0.212048i	0.304990	−	0.952355i	$-0.401347\pi$
$877$	−9538.83	−	5507.25i	−0.367279	−	0.212048i	−0.672269	+	0.740307i	$0.734680\pi$
$878$	−15613.3	−	9014.34i	−0.600140	−	0.346491i
$879$			205.421i			0.00788245i
$880$	−1329.51	+	2302.78i	−0.0509292	+	0.0882120i
$881$	−2271.51	−	3934.36i	−0.0868660	−	0.150456i	0.819319	−	0.573338i	$-0.194352\pi$
$881$	−2271.51	−	3934.36i	−0.0868660	−	0.150456i	−0.906185	+	0.422882i	$0.861019\pi$
$882$	15640.3	−	9029.93i	0.597093	−	0.344732i
$883$	−28212.2			−1.07522			−0.537608	−	0.843195i	$-0.680672\pi$
$883$	−28212.2			−1.07522			−0.537608	+	0.843195i	$0.680672\pi$
$884$		0			0
$885$	−1999.56			−0.0759484
$886$	−3095.39	+	1787.12i	−0.117372	+	0.0677648i
$887$	15348.0	+	26583.5i	0.580987	+	1.00630i	0.995363	+	0.0961927i	$0.0306665\pi$
$887$	15348.0	+	26583.5i	0.580987	+	1.00630i	−0.414376	+	0.910106i	$0.636000\pi$
$888$	17.6936	−	30.6462i	0.000668647	−	0.00115813i
$889$		−	6296.30i		−	0.237538i
$890$	469.813	+	271.247i	0.0176946	+	0.0102160i
$891$	16189.9	+	9347.22i	0.608732	+	0.351452i
$892$			25454.5i			0.955469i
$893$	4442.47	−	7694.58i	0.166474	−	0.288342i
$894$	−1164.06	−	2016.22i	−0.0435483	−	0.0754278i
$895$	−2304.36	+	1330.42i	−0.0860630	+	0.0496885i
$896$	−326.483			−0.0121730
$897$		0			0
$898$	9081.89			0.337491
$899$	60293.6	−	34810.5i	2.23682	−	1.29143i
$900$	−4536.32	−	7857.14i	−0.168012	−	0.291005i
$901$	19908.7	−	34482.9i	0.736133	−	1.27502i
$902$			19401.3i			0.716180i
$903$	−370.861	−	214.117i	−0.0136672	−	0.00789076i
$904$	−12741.8	−	7356.47i	−0.468789	−	0.270655i
$905$			17916.5i			0.658082i
$906$	−893.602	+	1547.76i	−0.0327681	+	0.0567561i
$907$	15138.6	+	26220.9i	0.554211	+	0.959922i	0.997964	+	0.0637731i	$0.0203134\pi$
$907$	15138.6	+	26220.9i	0.554211	+	0.959922i	−0.443753	+	0.896149i	$0.646353\pi$
$908$	2873.51	−	1659.02i	0.105023	−	0.0606349i
$909$	12742.4			0.464951
$910$		0			0
$911$	18833.6			0.684946			0.342473	−	0.939528i	$-0.388736\pi$
$911$	18833.6			0.684946			0.342473	+	0.939528i	$0.388736\pi$
$912$	−209.365	+	120.877i	−0.00760171	+	0.00438885i
$913$	4917.41	+	8517.20i	0.178250	+	0.308738i
$914$	−6873.87	+	11905.9i	−0.248761	+	0.430866i
$915$		−	318.664i		−	0.0115133i
$916$	−20054.9	−	11578.7i	−0.723398	−	0.417654i
$917$	−5035.96	−	2907.51i	−0.181354	−	0.104705i
$918$			4094.52i			0.147210i
$919$	1279.32	−	2215.85i	0.0459206	−	0.0795367i	−0.842152	−	0.539241i	$-0.818711\pi$
$919$	1279.32	−	2215.85i	0.0459206	−	0.0795367i	0.888072	+	0.459704i	$0.152045\pi$
$920$	2670.27	+	4625.05i	0.0956916	+	0.165743i
$921$	−1439.04	+	830.830i	−0.0514853	+	0.0297250i
$922$	18617.2			0.664993
$923$		0			0
$924$	−108.150			−0.00385050
$925$	797.863	−	460.646i	0.0283606	−	0.0163740i
$926$	−14763.5	−	25571.2i	−0.523931	−	0.907475i
$927$	14766.6	−	25576.5i	0.523191	−	0.906193i
$928$		−	7985.42i		−	0.282472i
$929$	−14196.7	−	8196.45i	−0.501375	−	0.289469i	0.227906	−	0.973683i	$-0.426812\pi$
$929$	−14196.7	−	8196.45i	−0.501375	−	0.289469i	−0.729281	+	0.684214i	$0.760145\pi$
$930$	−1247.65	−	720.330i	−0.0439914	−	0.0253984i
$931$		−	12528.7i		−	0.441042i
$932$	−641.501	+	1111.11i	−0.0225462	+	0.0390512i
$933$	1766.30	+	3059.32i	0.0619787	+	0.107350i
$934$	12813.4	−	7397.81i	0.448894	−	0.259169i
$935$	15573.3			0.544707
$936$		0			0
$937$	24289.2			0.846845			0.423422	−	0.905932i	$-0.360829\pi$
$937$	24289.2			0.846845			0.423422	+	0.905932i	$0.360829\pi$
$938$	−3894.79	+	2248.66i	−0.135575	+	0.0782744i
$939$	638.097	+	1105.22i	0.0221763	+	0.0384104i
$940$	3036.47	−	5259.33i	0.105361	−	0.182490i
$941$		−	31263.6i		−	1.08306i	−0.840680	−	0.541532i	$-0.817844\pi$
$941$		−	31263.6i		−	1.08306i	0.840680	−	0.541532i	$-0.182156\pi$
$942$	608.096	+	351.085i	0.0210328	+	0.0121433i
$943$	33746.4	+	19483.5i	1.16536	+	0.672820i
$944$			12391.2i			0.427225i
$945$	−177.266	+	307.034i	−0.00610208	+	0.0105691i
$946$	10806.7	+	18717.7i	0.371412	+	0.643305i
$947$	38179.5	−	22043.0i	1.31010	−	0.756389i	0.327991	−	0.944681i	$-0.393628\pi$
$947$	38179.5	−	22043.0i	1.31010	−	0.756389i	0.982113	+	0.188292i	$0.0602951\pi$
$948$	864.151			0.0296058
$949$		0			0
$950$	−6293.96			−0.214950
$951$	3480.01	−	2009.19i	0.118662	−	0.0685093i
$952$	956.069	+	1655.96i	0.0325487	+	0.0563760i
$953$	−317.041	+	549.131i	−0.0107765	+	0.0186654i	−0.871363	−	0.490638i	$-0.836764\pi$
$953$	−317.041	+	549.131i	−0.0107765	+	0.0186654i	0.860587	+	0.509304i	$0.170097\pi$
$954$		−	22805.0i		−	0.773942i
$955$	−8893.55	−	5134.69i	−0.301349	−	0.173984i
$956$	12408.8	+	7164.22i	0.419800	+	0.242372i
$957$		−	2645.23i		−	0.0893501i
$958$	−12365.0	+	21416.8i	−0.417009	+	0.722281i
$959$	560.261	+	970.400i	0.0188652	+	0.0326756i
$960$	−143.103	+	82.6206i	−0.00481108	+	0.00277768i
$961$	−48045.9			−1.61277
$962$		0			0
$963$	15306.4			0.512193
$964$	16905.6	−	9760.48i	0.564828	−	0.326104i
$965$	7829.15	+	13560.5i	0.261170	+	0.452360i
$966$	−108.607	+	188.114i	−0.00361738	+	0.00626548i
$967$			58557.1i			1.94733i	0.227981	+	0.973666i	$0.426788\pi$
$967$			58557.1i			1.94733i	−0.227981	+	0.973666i	$0.573212\pi$
$968$	−4494.30	−	2594.79i	−0.149228	−	0.0861566i
$969$	1226.20	+	707.949i	0.0406515	+	0.0234702i
$970$			8135.04i			0.269279i
$971$	1667.84	−	2888.79i	0.0551222	−	0.0954745i	−0.837148	−	0.546977i	$-0.815778\pi$
$971$	1667.84	−	2888.79i	0.0551222	−	0.0954745i	0.892270	+	0.451503i	$0.149112\pi$
$972$	1760.61	+	3049.47i	0.0580985	+	0.100629i
$973$	−4813.11	+	2778.85i	−0.158583	+	0.0915579i
$974$	16894.7			0.555793
$975$		0			0
$976$	−1974.76			−0.0647649
$977$	20531.4	−	11853.8i	0.672323	−	0.388166i	−0.124633	−	0.992203i	$-0.539775\pi$
$977$	20531.4	−	11853.8i	0.672323	−	0.388166i	0.796956	+	0.604037i	$0.206442\pi$
$978$	430.502	+	745.651i	0.0140756	+	0.0243796i
$979$	556.815	−	964.432i	0.0181776	−	0.0314846i
$980$		−	8563.47i		−	0.279133i
$981$	−13782.0	−	7957.06i	−0.448549	−	0.258970i
$982$	−24565.6	−	14183.0i	−0.798290	−	0.460893i
$983$			34833.6i			1.13023i	0.825011	+	0.565117i	$0.191169\pi$
$983$			34833.6i			1.13023i	−0.825011	+	0.565117i	$0.808831\pi$
$984$	−602.836	+	1044.14i	−0.0195302	+	0.0338273i
$985$	10961.9	+	18986.6i	0.354594	+	0.614175i
$986$	−40503.0	+	23384.4i	−1.30819	+	0.755286i
$987$	247.004			0.00796577
$988$		0			0
$989$	43409.8			1.39570
$990$	7724.46	−	4459.72i	0.247979	−	0.143171i
$991$	−11978.8	−	20747.8i	−0.383974	−	0.665062i	0.607652	−	0.794203i	$-0.292111\pi$
$991$	−11978.8	−	20747.8i	−0.383974	−	0.665062i	−0.991626	+	0.129141i	$0.958778\pi$
$992$	−4463.88	+	7731.67i	−0.142871	+	0.247461i
$993$			797.979i			0.0255016i
$994$	−524.686	−	302.928i	−0.0167425	−	0.00966628i
$995$	12149.4	+	7014.48i	0.387098	+	0.223491i
$996$			611.172i			0.0194435i
$997$	21680.9	−	37552.5i	0.688708	−	1.19288i	−0.283547	−	0.958958i	$-0.591511\pi$
$997$	21680.9	−	37552.5i	0.688708	−	1.19288i	0.972256	−	0.233920i	$-0.0751553\pi$
$998$	14029.9	+	24300.5i	0.444999	+	0.770761i
$999$	−206.231	+	119.068i	−0.00653140	+	0.00377091i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.4.e.h.23.1		12
13.2	odd	12		338.4.a.j.1.3	✓	3
13.3	even	3		338.4.b.f.337.3		6
13.4	even	6	inner	338.4.e.h.147.1		12
13.5	odd	4		338.4.c.l.315.1		6
13.6	odd	12		338.4.c.l.191.1		6
13.7	odd	12		338.4.c.k.191.1		6
13.8	odd	4		338.4.c.k.315.1		6
13.9	even	3	inner	338.4.e.h.147.4		12
13.10	even	6		338.4.b.f.337.6		6
13.11	odd	12		338.4.a.k.1.3	yes	3
13.12	even	2	inner	338.4.e.h.23.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
338.4.a.j.1.3	✓	3	13.2	odd	12
338.4.a.k.1.3	yes	3	13.11	odd	12
338.4.b.f.337.3		6	13.3	even	3
338.4.b.f.337.6		6	13.10	even	6
338.4.c.k.191.1		6	13.7	odd	12
338.4.c.k.315.1		6	13.8	odd	4
338.4.c.l.191.1		6	13.6	odd	12
338.4.c.l.315.1		6	13.5	odd	4
338.4.e.h.23.1		12	1.1	even	1	trivial
338.4.e.h.23.4		12	13.12	even	2	inner
338.4.e.h.147.1		12	13.4	even	6	inner
338.4.e.h.147.4		12	13.9	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	338.e (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.73205 + 1.00000i) q^{2} +(-0.202907 - 0.351445i) q^{3} +(2.00000 - 3.46410i) q^{4} +6.36227i q^{5} +(0.702889 + 0.405813i) q^{6} +(-2.20892 - 1.27532i) q^{7} +8.00000i q^{8} +(13.4177 - 23.2401i) q^{9} +(-6.36227 - 11.0198i) q^{10} +(-22.6214 + 13.0605i) q^{11} -1.62325 q^{12} +5.10129 q^{14} +(2.23599 - 1.29095i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-46.8543 + 81.1540i) q^{17} +53.6706i q^{18} +(32.2446 + 18.6164i) q^{19} +(22.0396 + 12.7245i) q^{20} +1.03509i q^{21} +(26.1209 - 45.2428i) q^{22} +(-52.4630 - 90.8686i) q^{23} +(2.81156 - 1.62325i) q^{24} +84.5215 q^{25} -21.8471 q^{27} +(-8.83570 + 5.10129i) q^{28} +(-124.772 - 216.112i) q^{29} +(-2.58189 + 4.47197i) q^{30} +278.993i q^{31} +(27.7128 + 16.0000i) q^{32} +(9.18006 + 5.30011i) q^{33} -187.417i q^{34} +(8.11395 - 14.0538i) q^{35} +(-53.6706 - 92.9603i) q^{36} +(9.43976 - 5.45005i) q^{37} -74.4658 q^{38} -50.8982 q^{40} +(-321.621 + 185.688i) q^{41} +(-1.03509 - 1.79282i) q^{42} +(-206.859 + 358.290i) q^{43} +104.484i q^{44} +(147.860 + 85.3668i) q^{45} +(181.737 + 104.926i) q^{46} -238.631i q^{47} +(-3.24651 + 5.62311i) q^{48} +(-168.247 - 291.413i) q^{49} +(-146.396 + 84.5215i) q^{50} +38.0282 q^{51} -424.907 q^{53} +(37.8403 - 21.8471i) q^{54} +(-83.0942 - 143.923i) q^{55} +(10.2026 - 17.6714i) q^{56} -15.1096i q^{57} +(432.224 + 249.544i) q^{58} +(-670.696 - 387.226i) q^{59} -10.3276i q^{60} +(61.7113 - 106.887i) q^{61} +(-278.993 - 483.229i) q^{62} +(-59.2772 + 34.2237i) q^{63} -64.0000 q^{64} -21.2004 q^{66} +(-763.491 + 440.802i) q^{67} +(187.417 + 324.616i) q^{68} +(-21.2902 + 36.8757i) q^{69} +32.4558i q^{70} +(-102.854 - 59.3826i) q^{71} +(185.921 + 107.341i) q^{72} -209.319i q^{73} +(-10.9001 + 18.8795i) q^{74} +(-17.1500 - 29.7046i) q^{75} +(128.978 - 74.4658i) q^{76} +66.6253 q^{77} -532.358 q^{79} +(88.1582 - 50.8982i) q^{80} +(-357.844 - 619.804i) q^{81} +(371.375 - 643.241i) q^{82} -376.511i q^{83} +(3.58564 + 2.07017i) q^{84} +(-516.324 - 298.100i) q^{85} -827.436i q^{86} +(-50.6342 + 87.7010i) q^{87} +(-104.484 - 180.971i) q^{88} +(-36.9218 + 21.3168i) q^{89} -341.467 q^{90} -419.704 q^{92} +(98.0505 - 56.6095i) q^{93} +(238.631 + 413.321i) q^{94} +(-118.443 + 205.149i) q^{95} -12.9860i q^{96} +(-553.666 - 319.659i) q^{97} +(582.825 + 336.494i) q^{98} +700.963i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 24 q^{3} + 24 q^{4} - 18 q^{9} - 48 q^{10} + 192 q^{12} + 216 q^{14} - 96 q^{16} - 180 q^{17} + 328 q^{22} + 38 q^{23} + 244 q^{25} - 276 q^{27} + 202 q^{29} + 360 q^{30} + 916 q^{35} + 72 q^{36}+ \cdots + 3658 q^{95}+O(q^{100}) \) 12 * q + 24 * q^3 + 24 * q^4 - 18 * q^9 - 48 * q^10 + 192 * q^12 + 216 * q^14 - 96 * q^16 - 180 * q^17 + 328 * q^22 + 38 * q^23 + 244 * q^25 - 276 * q^27 + 202 * q^29 + 360 * q^30 + 916 * q^35 + 72 * q^36 + 1040 * q^38 - 384 * q^40 + 936 * q^42 - 2410 * q^43 + 384 * q^48 - 368 * q^49 + 828 * q^51 - 4380 * q^53 + 1052 * q^55 + 432 * q^56 + 2216 * q^61 - 2076 * q^62 - 768 * q^64 + 1168 * q^66 + 720 * q^68 - 628 * q^69 + 336 * q^74 - 1010 * q^75 - 1920 * q^77 - 7844 * q^79 - 1830 * q^81 - 748 * q^82 - 3272 * q^87 - 1312 * q^88 + 5160 * q^90 + 304 * q^92 - 2144 * q^94 + 3658 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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