LMFDB - Embedded newform 338.4.e.h.23.4

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			23.4
Root			$0.385418 - 0.222521i$ of defining polynomial
Character	$\chi$	$=$	338.23
Dual form			338.4.e.h.147.4

$q$-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	$-0.908163\pi$
$5$		−	6.36227i		−	0.569059i	0.958667	−	0.284529i	$-0.0918374\pi$
$6$	−0.702889	−	0.405813i	−0.0478255	−	0.0276121i
$7$	2.20892	+	1.27532i	0.119271	+	0.0688610i	0.558448	−	0.829539i	$-0.311397\pi$
$7$	2.20892	+	1.27532i	0.119271	+	0.0688610i	−0.439178	+	0.898400i	$0.644730\pi$
$8$		−	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	−0.156835	−	0.987625i	$-0.550129\pi$
$11$	22.6214	−	13.0605i	0.620055	−	0.357989i	0.776890	+	0.629636i	$0.216796\pi$
$12$	−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	0.292535	−	0.956255i	$-0.405501\pi$
$19$	−32.2446	−	18.6164i	−0.389338	−	0.224784i	−0.681873	+	0.731470i	$0.738834\pi$
$20$	−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	$-0.700441\pi$
$31$		−	278.993i		−	1.61641i	0.588904	−	0.808203i	$-0.299559\pi$
$32$	−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	−0.520825	−	0.853664i	$-0.674376\pi$
$37$	−9.43976	+	5.45005i	−0.0419429	+	0.0242157i	0.478882	+	0.877879i	$0.341042\pi$
$38$	−74.4658			−0.317893
$39$		0			0
$40$	−50.8982			−0.201193
$41$	321.621	−	185.688i	1.22509	−	0.707306i	0.259091	−	0.965853i	$-0.416577\pi$
$41$	321.621	−	185.688i	1.22509	−	0.707306i	0.965999	+	0.258547i	$0.0832436\pi$
$42$	−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	$0.120744\pi$
$47$			238.631i			0.740595i	−0.928913	+	0.370297i	$0.879256\pi$
$48$	−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	0.999742	−	0.0227031i	$-0.00722724\pi$
$59$	670.696	+	387.226i	1.47995	+	0.854451i	0.480210	+	0.877154i	$0.340561\pi$
$60$			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	0.398614	−	0.917119i	$-0.369491\pi$
$67$	763.491	−	440.802i	1.39217	−	0.803769i	0.993555	+	0.113350i	$0.0361580\pi$
$68$	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	0.583492	−	0.812119i	$-0.301686\pi$
$71$	102.854	+	59.3826i	0.171922	+	0.0992593i	−0.411570	+	0.911378i	$0.635019\pi$
$72$	−185.921	−	107.341i	−0.304319	−	0.175698i
$73$			209.319i			0.335602i	0.985821	+	0.167801i	$0.0536666\pi$
$73$			209.319i			0.335602i	−0.985821	+	0.167801i	$0.946333\pi$
$74$	−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	$0.0800889\pi$
$83$			376.511i			0.497921i	−0.968514	+	0.248960i	$0.919911\pi$
$84$	−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	−0.477852	−	0.878441i	$-0.658584\pi$
$89$	36.9218	−	21.3168i	0.0439742	−	0.0253885i	0.521826	+	0.853052i	$0.325251\pi$
$90$	−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	0.760954	−	0.648805i	$-0.224731\pi$
$97$	553.666	+	319.659i	0.579550	+	0.334603i	−0.181405	+	0.983409i	$0.558064\pi$
$98$	−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	$0.0839069\pi$
$109$			593.029i			0.521118i	−0.965458	+	0.260559i	$0.916093\pi$
$110$	−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	0.613916	−	0.789372i	$-0.289594\pi$
$137$	380.453	+	219.654i	0.237257	+	0.136981i	−0.376658	+	0.926352i	$0.622927\pi$
$138$			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	0.990395	−	0.138269i	$-0.0441539\pi$
$149$	2484.17	+	1434.24i	1.36585	+	0.788572i	0.375453	+	0.926842i	$0.377487\pi$
$150$	−59.4092	−	34.2999i	−0.0323383	−	0.0186705i
$151$		−	2202.00i		−	1.18673i	−0.804933	−	0.593366i	$-0.797799\pi$
$151$		−	2202.00i		−	1.18673i	0.804933	−	0.593366i	$-0.202201\pi$
$152$	−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	0.262753	−	0.964863i	$-0.415370\pi$
$163$	−918.712	−	530.419i	−0.441467	−	0.254881i	−0.704220	+	0.709982i	$0.748703\pi$
$164$		−	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	−0.191083	−	0.981574i	$-0.561200\pi$
$167$	1215.97	−	702.043i	0.563443	−	0.325304i	0.754526	+	0.656270i	$0.227867\pi$
$168$	−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	−0.841694	−	0.539955i	$-0.818441\pi$
$193$	−2131.39	+	1230.56i	−0.794926	+	0.458951i	0.0467677	+	0.998906i	$0.485108\pi$
$194$	1278.64			0.473200
$195$		0			0
$196$	−1345.98			−0.490516
$197$	−2984.24	+	1722.95i	−1.07928	+	0.623123i	−0.930702	−	0.365777i	$-0.880803\pi$
$197$	−2984.24	+	1722.95i	−1.07928	+	0.623123i	−0.148579	+	0.988901i	$0.547470\pi$
$198$	−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	$-0.262016\pi$
$223$	5511.05	−	3181.81i	1.65492	−	0.955469i	0.975006	−	0.222179i	$-0.0713169\pi$
$224$	−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	0.391287	−	0.920269i	$-0.372030\pi$
$227$	−718.377	−	414.755i	−0.210046	−	0.121270i	−0.601333	+	0.798999i	$0.705363\pi$
$228$	52.3412	+	30.2192i	0.0152034	+	0.00877770i
$229$			5789.35i			1.67062i	0.549782	+	0.835308i	$0.314711\pi$
$229$			5789.35i			1.67062i	−0.549782	+	0.835308i	$0.685289\pi$
$230$	−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	$-0.838913\pi$
$239$		−	3582.11i		−	0.969487i	0.874656	−	0.484744i	$-0.161087\pi$
$240$	35.7758	+	20.6552i	0.00962215	+	0.00555535i
$241$	−4226.41	−	2440.12i	−1.12966	−	0.652207i	−0.185808	−	0.982586i	$-0.559490\pi$
$241$	−4226.41	−	2440.12i	−1.12966	−	0.652207i	−0.943848	+	0.330379i	$0.892823\pi$
$242$			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	0.242329	−	0.970194i	$-0.422089\pi$
$271$	5370.00	−	3100.37i	1.20371	−	0.694960i	0.961377	+	0.275234i	$0.0887552\pi$
$272$	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	$0.234195\pi$
$281$			6322.71i			1.34228i	−0.741330	+	0.671141i	$0.765805\pi$
$282$	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	0.543067	−	0.839690i	$-0.317263\pi$
$293$	438.378	+	253.098i	0.0874073	+	0.0504646i	−0.455659	+	0.890154i	$0.650596\pi$
$294$			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	$0.124285\pi$
$307$			4094.64i			0.761217i	−0.924736	+	0.380608i	$0.875715\pi$
$308$	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	$-0.659400\pi$
$317$		−	9902.03i		−	1.75443i	0.480100	−	0.877214i	$-0.340600\pi$
$318$	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	0.634683	−	0.772773i	$-0.281131\pi$
$331$	1702.93	+	983.184i	0.282783	+	0.163265i	−0.351900	+	0.936038i	$0.614464\pi$
$332$	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	−0.673109	−	0.739543i	$-0.735042\pi$
$349$	−2407.14	+	1389.76i	−0.369201	+	0.213158i	0.303908	+	0.952701i	$0.401708\pi$
$350$	431.169			0.0658484
$351$		0			0
$352$	−835.870			−0.126568
$353$	−9653.88	+	5573.67i	−1.45559	+	0.840387i	−0.998790	−	0.0491807i	$-0.984339\pi$
$353$	−9653.88	+	5573.67i	−1.45559	+	0.840387i	−0.456803	+	0.889568i	$0.651006\pi$
$354$	−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	$-0.897306\pi$
$359$		−	4313.27i		−	0.634111i	0.948407	−	0.317056i	$-0.102694\pi$
$360$	−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	0.350852	−	0.936431i	$-0.385892\pi$
$379$	9866.69	−	5696.54i	1.33725	−	0.772062i	0.986399	+	0.164369i	$0.0525588\pi$
$380$	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	−0.388744	−	0.921346i	$-0.627091\pi$
$383$	−10351.4	−	5976.39i	−1.38102	−	0.797335i	−0.992281	+	0.124011i	$0.960424\pi$
$384$	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	−0.0900341	−	0.995939i	$-0.528698\pi$
$397$	−7890.86	−	4555.79i	−0.997559	−	0.575941i	−0.907525	+	0.419997i	$0.862031\pi$
$398$		−	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	−0.526697	−	0.850053i	$-0.676570\pi$
$401$	−432.633	+	249.781i	−0.0538770	+	0.0311059i	0.472820	+	0.881159i	$0.343236\pi$
$402$	−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	0.986880	−	0.161457i	$-0.0516194\pi$
$409$	11087.9	+	6401.61i	1.34049	+	0.773934i	0.353614	+	0.935392i	$0.384953\pi$
$410$	−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	$0.344946\pi$
$421$			15266.9i			1.76737i	−0.468080	+	0.883686i	$0.655054\pi$
$422$	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	−0.498986	−	0.866610i	$-0.666294\pi$
$431$	18.1367	−	10.4712i	0.00202694	−	0.00117026i	0.501013	+	0.865440i	$0.332961\pi$
$432$	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	0.692224	−	0.721683i	$-0.256631\pi$
$449$	3932.57	+	2270.47i	0.413340	+	0.238642i	−0.278884	+	0.960325i	$0.589964\pi$
$450$		−	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	−0.772706	−	0.634764i	$-0.781097\pi$
$457$	−5952.95	+	3436.93i	−0.609337	+	0.351801i	0.163369	+	0.986565i	$0.447764\pi$
$458$	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	0.848498	−	0.529199i	$-0.177507\pi$
$461$	8061.47	+	4654.29i	0.814447	+	0.470221i	−0.0340507	+	0.999420i	$0.510841\pi$
$462$	−46.8302	−	27.0374i	−0.00471588	−	0.00272271i
$463$		−	14763.5i		−	1.48190i	−0.671560	−	0.740950i	$-0.734375\pi$
$463$		−	14763.5i		−	1.48190i	0.671560	−	0.740950i	$-0.265625\pi$
$464$	−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	−0.914526	−	0.404526i	$-0.867436\pi$
$479$	−10708.4	+	6182.49i	−1.02146	+	0.589740i	−0.106933	+	0.994266i	$0.534103\pi$
$480$	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	0.800120	−	0.599840i	$-0.204769\pi$
$487$	7315.63	+	4223.68i	0.680704	+	0.393005i	−0.119416	+	0.992844i	$0.538102\pi$
$488$	−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	$0.216668\pi$
$499$			14029.9i			1.25865i	−0.777143	+	0.629324i	$0.783332\pi$
$500$	−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	−0.865677	−	0.500603i	$-0.833112\pi$
$509$	−9933.06	+	5734.85i	−0.864981	+	0.499397i	0.000696453		1.00000i	$0.499778\pi$
$510$	−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	$-0.959057\pi$
$541$		−	3228.20i		−	0.256546i	0.991739	−	0.128273i	$-0.0409434\pi$
$542$	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	−0.952339	−	0.305041i	$-0.901330\pi$
$557$	−15306.0	+	8836.91i	−1.16434	+	0.672229i	−0.211996	+	0.977271i	$0.567996\pi$
$558$	−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	$-0.955648\pi$
$577$		−	3849.90i		−	0.277771i	0.990308	−	0.138885i	$-0.0443519\pi$
$578$	−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	−0.100199	−	0.994967i	$-0.531948\pi$
$587$	10117.0	−	5841.06i	0.711369	−	0.410709i	0.811568	+	0.584258i	$0.198615\pi$
$588$	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	$-0.832069\pi$
$593$		−	14539.7i		−	1.00687i	0.864033	−	0.503435i	$-0.167931\pi$
$594$	−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	−0.0243470	−	0.999704i	$-0.507751\pi$
$613$	12585.6	−	7266.32i	0.829248	−	0.478767i	0.853595	+	0.520937i	$0.174417\pi$
$614$	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	0.140158	−	0.990129i	$-0.455239\pi$
$617$	−9919.56	−	5727.06i	−0.647239	−	0.373684i	−0.787398	+	0.616445i	$0.788572\pi$
$618$	−773.553	−	446.611i	−0.0503509	−	0.0290701i
$619$			10052.7i			0.652751i	0.945240	+	0.326376i	$0.105827\pi$
$619$			10052.7i			0.652751i	−0.945240	+	0.326376i	$0.894173\pi$
$620$	−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	0.133362	−	0.991067i	$-0.457423\pi$
$631$	−10433.6	−	6023.82i	−0.658247	−	0.380039i	−0.791609	+	0.611028i	$0.790756\pi$
$632$			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	0.848418	−	0.529326i	$-0.177555\pi$
$643$	13275.7	+	7664.72i	0.814217	+	0.470089i	−0.0342009	+	0.999415i	$0.510889\pi$
$644$	−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	0.0119324	−	0.999929i	$-0.496202\pi$
$661$	15020.6	−	8672.14i	0.883862	−	0.510298i	0.871930	+	0.489631i	$0.162868\pi$
$662$	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	0.540207	−	0.841532i	$-0.318346\pi$
$683$	1455.14	+	840.126i	0.0815218	+	0.0470666i	−0.458685	+	0.888599i	$0.651679\pi$
$684$			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	−0.216038	−	0.976385i	$-0.569314\pi$
$691$	9472.95	−	5469.21i	0.521516	−	0.301098i	0.737555	+	0.675287i	$0.235980\pi$
$692$	−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	0.875090	−	0.483960i	$-0.160802\pi$
$709$	16868.3	+	9738.89i	0.893513	+	0.515870i	0.0184228	+	0.999830i	$0.494135\pi$
$710$		−	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	$-0.780105\pi$
$733$		−	25289.5i		−	1.27434i	0.770724	−	0.637169i	$-0.219895\pi$
$734$	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	−0.505463	−	0.862848i	$-0.668678\pi$
$739$	−219.893	+	126.956i	−0.0109458	+	0.00631953i	0.494517	+	0.869168i	$0.335345\pi$
$740$	277.398			0.0137802
$741$		0			0
$742$	−2167.58			−0.107243
$743$	11174.8	−	6451.78i	0.551768	−	0.318564i	−0.198066	−	0.980189i	$-0.563466\pi$
$743$	11174.8	−	6451.78i	0.551768	−	0.318564i	0.749835	+	0.661625i	$0.230133\pi$
$744$	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	0.235452	−	0.971886i	$-0.424343\pi$
$761$	−10255.2	−	5920.81i	−0.488501	−	0.282036i	−0.723952	+	0.689850i	$0.757676\pi$
$762$		−	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	−0.287418	−	0.957805i	$-0.592797\pi$
$769$	8494.96	−	4904.57i	0.398356	−	0.229991i	0.685775	+	0.727814i	$0.259464\pi$
$770$	−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	−0.158548	−	0.987351i	$-0.550681\pi$
$773$	−23488.0	−	13560.8i	−1.09289	−	0.630982i	−0.934345	+	0.356369i	$0.884015\pi$
$774$	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	0.816195	−	0.577777i	$-0.196080\pi$
$787$	15982.9	+	9227.71i	0.723923	+	0.417957i	−0.0922719	+	0.995734i	$0.529413\pi$
$788$			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	$0.266460\pi$
$811$			34306.9i			1.48542i	−0.669612	+	0.742711i	$0.733540\pi$
$812$	−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	−0.559062	−	0.829126i	$-0.688839\pi$
$821$	−2835.84	+	1637.27i	−0.120550	+	0.0695995i	0.438513	+	0.898725i	$0.355505\pi$
$822$	−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	$0.327099\pi$
$827$			40718.9i			1.71213i	−0.516864	+	0.856067i	$0.672901\pi$
$828$	−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	0.162887	−	0.986645i	$-0.447919\pi$
$839$	−14827.4	−	8560.59i	−0.610128	−	0.352258i	−0.773016	+	0.634387i	$0.781253\pi$
$840$			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	$0.0306587\pi$
$853$			4791.65i			0.192336i	−0.995365	+	0.0961682i	$0.969341\pi$
$854$	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	$0.0674523\pi$
$863$			10664.4i			0.420650i	−0.977631	+	0.210325i	$0.932548\pi$
$864$	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	0.672269	−	0.740307i	$-0.265320\pi$
$877$	9538.83	+	5507.25i	0.367279	+	0.212048i	−0.304990	+	0.952355i	$0.598653\pi$
$878$	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	0.729281	−	0.684214i	$-0.239855\pi$
$929$	14196.7	+	8196.45i	0.501375	+	0.289469i	−0.227906	+	0.973683i	$0.573188\pi$
$930$	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	$0.182156\pi$
$941$			31263.6i			1.08306i	−0.840680	+	0.541532i	$0.817844\pi$
$942$	−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	−0.982113	−	0.188292i	$-0.939705\pi$
$947$	−38179.5	+	22043.0i	−1.31010	+	0.756389i	−0.327991	+	0.944681i	$0.606372\pi$
$948$	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	$-0.573212\pi$
$967$		−	58557.1i		−	1.94733i	0.227981	−	0.973666i	$-0.426788\pi$
$968$	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	−0.796956	−	0.604037i	$-0.793558\pi$
$977$	−20531.4	+	11853.8i	−0.672323	+	0.388166i	0.124633	+	0.992203i	$0.460225\pi$
$978$	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	$-0.808831\pi$
$983$		−	34833.6i		−	1.13023i	0.825011	−	0.565117i	$-0.191169\pi$
$984$	−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.23.4		12
13.2	odd	12		338.4.a.k.1.3	yes	3
13.3	even	3		338.4.b.f.337.6		6
13.4	even	6	inner	338.4.e.h.147.4		12
13.5	odd	4		338.4.c.k.315.1		6
13.6	odd	12		338.4.c.k.191.1		6
13.7	odd	12		338.4.c.l.191.1		6
13.8	odd	4		338.4.c.l.315.1		6
13.9	even	3	inner	338.4.e.h.147.1		12
13.10	even	6		338.4.b.f.337.3		6
13.11	odd	12		338.4.a.j.1.3	✓	3
13.12	even	2	inner	338.4.e.h.23.1		12

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