LMFDB - Embedded newform 207.4.i.b.73.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,4,Mod(55,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("207.55");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	207.i (of order $11$, degree $10$, 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:	$12.2133953712$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	no (minimal twist has level 69)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			73.1
Character	$\chi$	$=$	207.73
Dual form			207.4.i.b.190.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.23641 - 4.89704i) q^{2} +(-13.7407 + 15.8576i) q^{4} +(-9.26837 - 5.95642i) q^{5} +(-1.89824 - 13.2025i) q^{7} +(67.0611 + 19.6909i) q^{8} +O(q^{10})$	\(q+(-2.23641 - 4.89704i) q^{2} +(-13.7407 + 15.8576i) q^{4} +(-9.26837 - 5.95642i) q^{5} +(-1.89824 - 13.2025i) q^{7} +(67.0611 + 19.6909i) q^{8} +(-8.44102 + 58.7086i) q^{10} +(-17.2646 + 37.8043i) q^{11} +(-9.90258 + 68.8739i) q^{13} +(-60.4082 + 38.8220i) q^{14} +(-29.6594 - 206.286i) q^{16} +(38.6890 + 44.6495i) q^{17} +(70.8862 - 81.8071i) q^{19} +(221.808 - 65.1286i) q^{20} +223.740 q^{22} +(-59.2111 - 93.0648i) q^{23} +(-1.50314 - 3.29142i) q^{25} +(359.425 - 105.537i) q^{26} +(235.443 + 151.310i) q^{28} +(-86.8617 - 100.244i) q^{29} +(128.303 + 37.6731i) q^{31} +(-473.485 + 304.290i) q^{32} +(132.126 - 289.316i) q^{34} +(-61.0463 + 133.673i) q^{35} +(-129.270 + 83.0768i) q^{37} +(-559.143 - 164.179i) q^{38} +(-504.259 - 581.946i) q^{40} +(316.096 + 203.143i) q^{41} +(-97.6527 + 28.6734i) q^{43} +(-362.256 - 793.231i) q^{44} +(-323.322 + 498.090i) q^{46} +539.392 q^{47} +(158.402 - 46.5112i) q^{49} +(-12.7566 + 14.7219i) q^{50} +(-956.104 - 1103.40i) q^{52} +(72.8750 + 506.856i) q^{53} +(385.193 - 247.549i) q^{55} +(132.672 - 922.754i) q^{56} +(-296.640 + 649.551i) q^{58} +(-21.4261 + 149.022i) q^{59} +(121.174 + 35.5800i) q^{61} +(-102.450 - 712.557i) q^{62} +(1146.44 + 736.772i) q^{64} +(502.023 - 579.365i) q^{65} +(-197.636 - 432.763i) q^{67} -1239.64 q^{68} +791.125 q^{70} +(271.279 + 594.017i) q^{71} +(-141.209 + 162.964i) q^{73} +(695.931 + 447.248i) q^{74} +(323.237 + 2248.17i) q^{76} +(531.885 + 156.176i) q^{77} +(-196.021 + 1363.35i) q^{79} +(-953.831 + 2088.60i) q^{80} +(287.879 - 2002.25i) q^{82} +(186.957 - 120.150i) q^{83} +(-92.6328 - 644.276i) q^{85} +(358.806 + 414.084i) q^{86} +(-1902.19 + 2195.24i) q^{88} +(724.001 - 212.586i) q^{89} +928.108 q^{91} +(2289.38 + 339.828i) q^{92} +(-1206.30 - 2641.43i) q^{94} +(-1144.28 + 335.990i) q^{95} +(679.941 + 436.972i) q^{97} +(-582.019 - 671.686i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 4 q^{2} - 28 q^{4} + 6 q^{5} - 4 q^{7} + 52 q^{8}+O(q^{10}) $ 60 * q - 4 * q^2 - 28 * q^4 + 6 * q^5 - 4 * q^7 + 52 * q^8	$ 60 q - 4 q^{2} - 28 q^{4} + 6 q^{5} - 4 q^{7} + 52 q^{8} - 78 q^{10} - 10 q^{11} + 50 q^{13} + 224 q^{14} + 260 q^{16} + 662 q^{17} - 4 q^{19} + 735 q^{20} + 622 q^{22} + 438 q^{23} - 754 q^{25} + 40 q^{26} + 672 q^{28} - 1302 q^{29} + 1528 q^{31} - 1588 q^{32} + 29 q^{34} - 950 q^{35} + 316 q^{37} - 3122 q^{38} - 1939 q^{40} + 1500 q^{41} - 1316 q^{43} + 2901 q^{44} - 1980 q^{46} + 1440 q^{47} - 2310 q^{49} - 195 q^{50} + 6189 q^{52} + 148 q^{53} - 606 q^{55} + 432 q^{56} - 2623 q^{58} - 5264 q^{59} + 1482 q^{61} + 2299 q^{62} - 6780 q^{64} + 1446 q^{65} + 388 q^{67} - 5604 q^{68} + 2984 q^{70} + 3316 q^{71} + 2072 q^{73} + 6556 q^{74} + 9841 q^{76} - 9338 q^{77} + 268 q^{79} - 7980 q^{80} + 7742 q^{82} + 3494 q^{83} - 3842 q^{85} + 4792 q^{86} - 7960 q^{88} + 2754 q^{89} - 5436 q^{91} + 17609 q^{92} - 10961 q^{94} + 2396 q^{95} - 5654 q^{97} - 14411 q^{98}+O(q^{100}) $ 60 * q - 4 * q^2 - 28 * q^4 + 6 * q^5 - 4 * q^7 + 52 * q^8 - 78 * q^10 - 10 * q^11 + 50 * q^13 + 224 * q^14 + 260 * q^16 + 662 * q^17 - 4 * q^19 + 735 * q^20 + 622 * q^22 + 438 * q^23 - 754 * q^25 + 40 * q^26 + 672 * q^28 - 1302 * q^29 + 1528 * q^31 - 1588 * q^32 + 29 * q^34 - 950 * q^35 + 316 * q^37 - 3122 * q^38 - 1939 * q^40 + 1500 * q^41 - 1316 * q^43 + 2901 * q^44 - 1980 * q^46 + 1440 * q^47 - 2310 * q^49 - 195 * q^50 + 6189 * q^52 + 148 * q^53 - 606 * q^55 + 432 * q^56 - 2623 * q^58 - 5264 * q^59 + 1482 * q^61 + 2299 * q^62 - 6780 * q^64 + 1446 * q^65 + 388 * q^67 - 5604 * q^68 + 2984 * q^70 + 3316 * q^71 + 2072 * q^73 + 6556 * q^74 + 9841 * q^76 - 9338 * q^77 + 268 * q^79 - 7980 * q^80 + 7742 * q^82 + 3494 * q^83 - 3842 * q^85 + 4792 * q^86 - 7960 * q^88 + 2754 * q^89 - 5436 * q^91 + 17609 * q^92 - 10961 * q^94 + 2396 * q^95 - 5654 * q^97 - 14411 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{2}{11}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.23641	−	4.89704i	−0.790689	−	1.73137i	−0.674670	−	0.738120i	$-0.735714\pi$
$2$	−2.23641	−	4.89704i	−0.790689	−	1.73137i	−0.116019	−	0.993247i	$-0.537013\pi$
$3$		0			0
$3$		0			0
$4$	−13.7407	+	15.8576i	−1.71758	+	1.98219i
$5$	−9.26837	−	5.95642i	−0.828988	−	0.532758i	0.0559681	−	0.998433i	$-0.482175\pi$
$5$	−9.26837	−	5.95642i	−0.828988	−	0.532758i	−0.884956	+	0.465674i	$0.845812\pi$
$6$		0			0
$7$	−1.89824	−	13.2025i	−0.102495	−	0.712870i	−0.974666	−	0.223667i	$-0.928197\pi$
$7$	−1.89824	−	13.2025i	−0.102495	−	0.712870i	0.872170	−	0.489202i	$-0.162712\pi$
$8$	67.0611	+	19.6909i	2.96371	+	0.870223i
$9$		0			0
$10$	−8.44102	+	58.7086i	−0.266929	+	1.85653i
$11$	−17.2646	+	37.8043i	−0.473226	+	1.03622i	0.511045	+	0.859554i	$0.329259\pi$
$11$	−17.2646	+	37.8043i	−0.473226	+	1.03622i	−0.984271	+	0.176667i	$0.943469\pi$
$12$		0			0
$13$	−9.90258	+	68.8739i	−0.211268	+	1.46940i	0.557663	+	0.830067i	$0.311698\pi$
$13$	−9.90258	+	68.8739i	−0.211268	+	1.46940i	−0.768931	+	0.639332i	$0.779211\pi$
$14$	−60.4082	+	38.8220i	−1.15320	+	0.741115i
$15$		0			0
$16$	−29.6594	−	206.286i	−0.463429	−	3.22322i
$17$	38.6890	+	44.6495i	0.551968	+	0.637005i	0.961341	−	0.275362i	$-0.0887978\pi$
$17$	38.6890	+	44.6495i	0.551968	+	0.637005i	−0.409373	+	0.912367i	$0.634252\pi$
$18$		0			0
$19$	70.8862	−	81.8071i	0.855917	−	0.987781i	−0.144082	−	0.989566i	$-0.546023\pi$
$19$	70.8862	−	81.8071i	0.855917	−	0.987781i	0.999998	+	0.00178512i	$0.000568223\pi$
$20$	221.808	−	65.1286i	2.47989	−	0.728160i
$21$		0			0
$22$	223.740			2.16825
$23$	−59.2111	−	93.0648i	−0.536798	−	0.843711i
$23$	−59.2111	−	93.0648i	−0.536798	−	0.843711i
$24$		0			0
$25$	−1.50314	−	3.29142i	−0.0120251	−	0.0263313i
$26$	359.425	−	105.537i	2.71112	−	0.796055i
$27$		0			0
$28$	235.443	+	151.310i	1.58909	+	1.02125i
$29$	−86.8617	−	100.244i	−0.556200	−	0.641889i	0.406116	−	0.913821i	$-0.366883\pi$
$29$	−86.8617	−	100.244i	−0.556200	−	0.641889i	−0.962316	+	0.271932i	$0.912337\pi$
$30$		0			0
$31$	128.303	+	37.6731i	0.743350	+	0.218267i	0.631412	−	0.775448i	$-0.282476\pi$
$31$	128.303	+	37.6731i	0.743350	+	0.218267i	0.111939	+	0.993715i	$0.464294\pi$
$32$	−473.485	+	304.290i	−2.61566	+	1.68098i
$33$		0			0
$34$	132.126	−	289.316i	0.666455	−	1.45933i
$35$	−61.0463	+	133.673i	−0.294820	+	0.645566i
$36$		0			0
$37$	−129.270	+	83.0768i	−0.574375	+	0.369128i	−0.795349	−	0.606151i	$-0.792713\pi$
$37$	−129.270	+	83.0768i	−0.574375	+	0.369128i	0.220975	+	0.975280i	$0.429076\pi$
$38$	−559.143	−	164.179i	−2.38697	−	0.700879i
$39$		0			0
$40$	−504.259	−	581.946i	−1.99326	−	2.30035i
$41$	316.096	+	203.143i	1.20405	+	0.773794i	0.979652	−	0.200705i	$-0.0643231\pi$
$41$	316.096	+	203.143i	1.20405	+	0.773794i	0.224395	+	0.974498i	$0.427959\pi$
$42$		0			0
$43$	−97.6527	+	28.6734i	−0.346323	+	0.101690i	−0.450268	−	0.892893i	$-0.648672\pi$
$43$	−97.6527	+	28.6734i	−0.346323	+	0.101690i	0.103945	+	0.994583i	$0.466853\pi$
$44$	−362.256	−	793.231i	−1.24119	−	2.71782i
$45$		0			0
$46$	−323.322	+	498.090i	−1.03633	+	1.59651i
$47$	539.392			1.67401			0.837005	−	0.547195i	$-0.184304\pi$
$47$	539.392			1.67401			0.837005	+	0.547195i	$0.184304\pi$
$48$		0			0
$49$	158.402	−	46.5112i	0.461815	−	0.135601i
$50$	−12.7566	+	14.7219i	−0.0360811	+	0.0416398i
$51$		0			0
$52$	−956.104	−	1103.40i	−2.54977	−	2.94259i
$53$	72.8750	+	506.856i	0.188871	+	1.31362i	0.834938	+	0.550344i	$0.185503\pi$
$53$	72.8750	+	506.856i	0.188871	+	1.31362i	−0.646067	+	0.763280i	$0.723587\pi$
$54$		0			0
$55$	385.193	−	247.549i	0.944354	−	0.606899i
$56$	132.672	−	922.754i	0.316590	−	2.20193i
$57$		0			0
$58$	−296.640	+	649.551i	−0.671565	+	1.47052i
$59$	−21.4261	+	149.022i	−0.0472787	+	0.328831i	0.952431	+	0.304753i	$0.0985740\pi$
$59$	−21.4261	+	149.022i	−0.0472787	+	0.328831i	−0.999710	+	0.0240776i	$0.992335\pi$
$60$		0			0
$61$	121.174	+	35.5800i	0.254341	+	0.0746812i	0.406418	−	0.913687i	$-0.366778\pi$
$61$	121.174	+	35.5800i	0.254341	+	0.0746812i	−0.152077	+	0.988369i	$0.548596\pi$
$62$	−102.450	−	712.557i	−0.209858	−	1.45959i
$63$		0			0
$64$	1146.44	+	736.772i	2.23914	+	1.43901i
$65$	502.023	−	579.365i	0.957973	−	1.10556i
$66$		0			0
$67$	−197.636	−	432.763i	−0.360375	−	0.789110i	−0.999795	−	0.0202529i	$-0.993553\pi$
$67$	−197.636	−	432.763i	−0.360375	−	0.789110i	0.639420	−	0.768857i	$-0.279174\pi$
$68$	−1239.64			−2.21072
$69$		0			0
$70$	791.125			1.35082
$71$	271.279	+	594.017i	0.453449	+	0.992914i	0.988932	+	0.148368i	$0.0474021\pi$
$71$	271.279	+	594.017i	0.453449	+	0.992914i	−0.535484	+	0.844546i	$0.679871\pi$
$72$		0			0
$73$	−141.209	+	162.964i	−0.226401	+	0.261281i	−0.857573	−	0.514362i	$-0.828029\pi$
$73$	−141.209	+	162.964i	−0.226401	+	0.261281i	0.631172	+	0.775643i	$0.282574\pi$
$74$	695.931	+	447.248i	1.09325	+	0.702588i
$75$		0			0
$76$	323.237	+	2248.17i	0.487867	+	3.39319i
$77$	531.885	+	156.176i	0.787194	+	0.231141i
$78$		0			0
$79$	−196.021	+	1363.35i	−0.279165	+	1.94164i	0.0534427	+	0.998571i	$0.482981\pi$
$79$	−196.021	+	1363.35i	−0.279165	+	1.94164i	−0.332608	+	0.943065i	$0.607929\pi$
$80$	−953.831	+	2088.60i	−1.33302	+	2.91891i
$81$		0			0
$82$	287.879	−	2002.25i	0.387695	−	2.69648i
$83$	186.957	−	120.150i	0.247243	−	0.158894i	−0.411150	−	0.911568i	$-0.634873\pi$
$83$	186.957	−	120.150i	0.247243	−	0.158894i	0.658393	+	0.752674i	$0.271236\pi$
$84$		0			0
$85$	−92.6328	−	644.276i	−0.118205	−	0.822135i
$86$	358.806	+	414.084i	0.449896	+	0.519207i
$87$		0			0
$88$	−1902.19	+	2195.24i	−2.30425	+	2.65924i
$89$	724.001	−	212.586i	0.862292	−	0.253192i	0.179458	−	0.983766i	$-0.442566\pi$
$89$	724.001	−	212.586i	0.862292	−	0.253192i	0.682834	+	0.730574i	$0.260747\pi$
$90$		0			0
$91$	928.108			1.06914
$92$	2289.38	+	339.828i	2.59439	+	0.385103i
$93$		0			0
$94$	−1206.30	−	2641.43i	−1.32362	−	2.89833i
$95$	−1144.28	+	335.990i	−1.23579	+	0.362862i
$96$		0			0
$97$	679.941	+	436.972i	0.711728	+	0.457400i	0.845750	−	0.533579i	$-0.179153\pi$
$97$	679.941	+	436.972i	0.711728	+	0.457400i	−0.134023	+	0.990978i	$0.542790\pi$
$98$	−582.019	−	671.686i	−0.599927	−	0.692353i
$99$		0			0
$100$	72.8480	+	21.3901i	0.0728480	+	0.0213901i
$101$	−230.359	+	148.043i	−0.226947	+	0.145850i	−0.649173	−	0.760641i	$-0.724885\pi$
$101$	−230.359	+	148.043i	−0.226947	+	0.145850i	0.422227	+	0.906490i	$0.361249\pi$
$102$		0			0
$103$	−451.929	+	989.586i	−0.432329	+	0.946668i	0.560615	+	0.828077i	$0.310565\pi$
$103$	−451.929	+	989.586i	−0.432329	+	0.946668i	−0.992943	+	0.118591i	$0.962162\pi$
$104$	−2020.27	+	4423.77i	−1.90484	+	4.17102i
$105$		0			0
$106$	2319.12	−	1490.41i	2.12503	−	1.36567i
$107$	−482.219	−	141.592i	−0.435681	−	0.127927i	0.0565351	−	0.998401i	$-0.481995\pi$
$107$	−482.219	−	141.592i	−0.435681	−	0.127927i	−0.492216	+	0.870473i	$0.663813\pi$
$108$		0			0
$109$	540.443	+	623.704i	0.474909	+	0.548074i	0.941770	−	0.336256i	$-0.109161\pi$
$109$	540.443	+	623.704i	0.474909	+	0.548074i	−0.466862	+	0.884330i	$0.654615\pi$
$110$	−2073.71	−	1332.69i	−1.79746	−	1.15515i
$111$		0			0
$112$	−2667.20	+	783.160i	−2.25024	+	0.660729i
$113$	−100.861	−	220.854i	−0.0839663	−	0.183860i	0.862992	−	0.505218i	$-0.168588\pi$
$113$	−100.861	−	220.854i	−0.0839663	−	0.183860i	−0.946958	+	0.321358i	$0.895861\pi$
$114$		0			0
$115$	−5.54281	+	1215.24i	−0.00449452	+	0.985410i
$116$	2783.16			2.22767
$117$		0			0
$118$	777.685	−	228.349i	0.606709	−	0.178146i
$119$	516.045	−	595.548i	0.397528	−	0.458771i
$120$		0			0
$121$	−259.478	−	299.453i	−0.194950	−	0.224984i
$122$	−96.7582	−	672.968i	−0.0718039	−	0.499407i
$123$		0			0
$124$	−2360.37	+	1516.92i	−1.70941	+	1.09857i
$125$	−201.665	+	1402.61i	−0.144299	+	1.00362i
$126$		0			0
$127$	71.2278	−	155.967i	0.0497673	−	0.108975i	−0.883115	−	0.469157i	$-0.844558\pi$
$127$	71.2278	−	155.967i	0.0497673	−	0.108975i	0.932882	+	0.360181i	$0.117285\pi$
$128$	403.307	−	2805.06i	0.278497	−	1.93699i
$129$		0			0
$130$	−3959.90	−	1162.73i	−2.67159	−	0.784449i
$131$	−266.482	−	1853.43i	−0.177730	−	1.23614i	−0.861998	−	0.506911i	$-0.830787\pi$
$131$	−266.482	−	1853.43i	−0.177730	−	1.23614i	0.684268	−	0.729230i	$-0.260122\pi$
$132$		0			0
$133$	−1214.62	−	780.589i	−0.791886	−	0.508915i
$134$	−1677.26	+	1935.67i	−1.08130	+	1.24788i
$135$		0			0
$136$	1715.34	+	3756.06i	1.08154	+	2.36823i
$137$	343.908			0.214468			0.107234	−	0.994234i	$-0.465801\pi$
$137$	343.908			0.214468			0.107234	+	0.994234i	$0.465801\pi$
$138$		0			0
$139$	2686.10			1.63908			0.819539	−	0.573024i	$-0.194230\pi$
$139$	2686.10			1.63908			0.819539	+	0.573024i	$0.194230\pi$
$140$	−1280.91	−	2804.79i	−0.773260	−	1.69320i
$141$		0			0
$142$	2302.24	−	2656.93i	1.36056	−	1.57017i
$143$	−2432.77	−	1563.44i	−1.42264	−	0.914278i
$144$		0			0
$145$	207.972	+	1446.48i	0.119112	+	0.828439i
$146$	1113.84	+	327.054i	0.631386	+	0.185392i
$147$		0			0
$148$	458.859	−	3191.44i	0.254851	−	1.77253i
$149$	52.9157	−	115.869i	0.0290941	−	0.0637072i	−0.894527	−	0.447014i	$-0.852487\pi$
$149$	52.9157	−	115.869i	0.0290941	−	0.0637072i	0.923621	+	0.383307i	$0.125215\pi$
$150$		0			0
$151$	−90.5654	+	629.896i	−0.0488086	+	0.339472i	0.950755	+	0.309943i	$0.100310\pi$
$151$	−90.5654	+	629.896i	−0.0488086	+	0.339472i	−0.999564	+	0.0295290i	$0.990599\pi$
$152$	6364.56	−	4090.26i	3.39628	−	2.18266i
$153$		0			0
$154$	−424.712	−	2953.94i	−0.222236	−	1.54568i
$155$	−964.761	−	1113.39i	−0.499945	−	0.576967i
$156$		0			0
$157$	825.025	−	952.129i	0.419390	−	0.484001i	−0.506261	−	0.862380i	$-0.668973\pi$
$157$	825.025	−	952.129i	0.419390	−	0.484001i	0.925651	+	0.378379i	$0.123518\pi$
$158$	7114.79	−	2089.09i	3.58242	−	1.05189i
$159$		0			0
$160$	6200.91			3.06391
$161$	−1116.29	+	958.395i	−0.546437	+	0.469144i
$162$		0			0
$163$	757.800	+	1659.35i	0.364144	+	0.797364i	0.999680	+	0.0252931i	$0.00805189\pi$
$163$	757.800	+	1659.35i	0.364144	+	0.797364i	−0.635536	+	0.772071i	$0.719221\pi$
$164$	−7564.71	+	2221.20i	−3.60186	+	1.05760i
$165$		0			0
$166$	−1006.49	−	646.833i	−0.470596	−	0.302433i
$167$	66.6531	+	76.9218i	0.0308849	+	0.0356431i	0.770982	−	0.636857i	$-0.219766\pi$
$167$	66.6531	+	76.9218i	0.0308849	+	0.0356431i	−0.740097	+	0.672500i	$0.765220\pi$
$168$		0			0
$169$	−2537.55	−	745.092i	−1.15501	−	0.339141i
$170$	−2947.88	+	1894.49i	−1.32995	+	0.854710i
$171$		0			0
$172$	887.121	−	1942.52i	0.393269	−	0.861140i
$173$	−590.837	+	1293.75i	−0.259656	+	0.568568i	−0.993896	−	0.110323i	$-0.964812\pi$
$173$	−590.837	+	1293.75i	−0.259656	+	0.568568i	0.734240	+	0.678890i	$0.237539\pi$
$174$		0			0
$175$	−40.6017	+	26.0931i	−0.0175383	+	0.0112712i
$176$	8310.56	+	2440.20i	3.55927	+	1.04510i
$177$		0			0
$178$	−2660.20	−	3070.04i	−1.12017	−	1.29275i
$179$	−905.633	−	582.015i	−0.378157	−	0.243027i	0.337730	−	0.941243i	$-0.390341\pi$
$179$	−905.633	−	582.015i	−0.378157	−	0.243027i	−0.715887	+	0.698216i	$0.753977\pi$
$180$		0			0
$181$	−3876.57	+	1138.26i	−1.59195	+	0.467439i	−0.953292	−	0.302051i	$-0.902329\pi$
$181$	−3876.57	+	1138.26i	−1.59195	+	0.467439i	−0.638659	+	0.769490i	$0.720511\pi$
$182$	−2075.63	−	4544.99i	−0.845360	−	1.85108i
$183$		0			0
$184$	−2138.23	−	7406.94i	−0.856697	−	2.96765i
$185$	1692.96			0.672806
$186$		0			0
$187$	−2355.89	+	691.753i	−0.921283	+	0.270513i
$188$	−7411.60	+	8553.45i	−2.87525	+	3.31821i
$189$		0			0
$190$	4204.43	+	4852.17i	1.60537	+	1.85270i
$191$	550.792	+	3830.84i	0.208659	+	1.45126i	0.777538	+	0.628835i	$0.216468\pi$
$191$	550.792	+	3830.84i	0.208659	+	1.45126i	−0.568879	+	0.822421i	$0.692623\pi$
$192$		0			0
$193$	−3161.63	+	2031.85i	−1.17916	+	0.757803i	−0.975233	−	0.221182i	$-0.929009\pi$
$193$	−3161.63	+	2031.85i	−1.17916	+	0.757803i	−0.203932	+	0.978985i	$0.565372\pi$
$194$	619.246	−	4306.95i	0.229171	−	1.59392i
$195$		0			0
$196$	−1439.00	+	3150.97i	−0.524417	+	1.14831i
$197$	440.304	−	3062.38i	0.159240	−	1.10754i	−0.740797	−	0.671729i	$-0.765552\pi$
$197$	440.304	−	3062.38i	0.159240	−	1.10754i	0.900038	−	0.435812i	$-0.143539\pi$
$198$		0			0
$199$	2567.89	+	754.000i	0.914738	+	0.268591i	0.705034	−	0.709174i	$-0.250932\pi$
$199$	2567.89	+	754.000i	0.914738	+	0.268591i	0.209704	+	0.977765i	$0.432750\pi$
$200$	−35.9912	−	250.324i	−0.0127248	−	0.0885029i
$201$		0			0
$202$	1240.15	+	796.996i	0.431963	+	0.277606i
$203$	−1158.59	+	1337.08i	−0.400576	+	0.462289i
$204$		0			0
$205$	−1719.69	−	3765.60i	−0.585895	−	1.28293i
$206$	5856.74			1.98087
$207$		0			0
$208$	14501.4			4.83410
$209$	1868.83	+	4092.18i	0.618517	+	1.35436i
$210$		0			0
$211$	1587.71	−	1832.32i	0.518023	−	0.597830i	−0.435112	−	0.900376i	$-0.643291\pi$
$211$	1587.71	−	1832.32i	0.518023	−	0.597830i	0.953135	+	0.302546i	$0.0978367\pi$
$212$	−9038.86	−	5808.92i	−2.92826	−	1.88188i
$213$		0			0
$214$	385.053	+	2678.10i	0.122999	+	0.855474i
$215$	1075.87	+	315.904i	0.341274	+	0.100207i
$216$		0			0
$217$	253.831	−	1765.43i	0.0794064	−	0.552283i
$218$	1845.66	−	4041.43i	0.573412	−	1.25560i
$219$		0			0
$220$	−1367.29	+	9509.71i	−0.419012	+	2.91429i
$221$	−3458.30	+	2222.52i	−1.05263	+	0.676483i
$222$		0			0
$223$	−2.95021	−	20.5192i	−0.000885924	−	0.00616173i	0.989374	−	0.145395i	$-0.0464453\pi$
$223$	−2.95021	−	20.5192i	−0.000885924	−	0.00616173i	−0.990260	+	0.139233i	$0.955536\pi$
$224$	4916.19	+	5673.58i	1.46641	+	1.69233i
$225$		0			0
$226$	−855.968	+	987.840i	−0.251939	+	0.290753i
$227$	−3751.94	+	1101.67i	−1.09703	+	0.322116i	−0.779670	−	0.626191i	$-0.784613\pi$
$227$	−3751.94	+	1101.67i	−1.09703	+	0.322116i	−0.317356	+	0.948307i	$0.602795\pi$
$228$		0			0
$229$	−479.652			−0.138412			−0.0692059	−	0.997602i	$-0.522047\pi$
$229$	−479.652			−0.138412			−0.0692059	+	0.997602i	$0.522047\pi$
$230$	5963.50	−	2690.64i	1.70966	−	0.771371i
$231$		0			0
$232$	−3851.15	−	8432.83i	−1.08983	−	2.38639i
$233$	3341.72	−	981.219i	0.939586	−	0.275887i	0.224141	−	0.974557i	$-0.428042\pi$
$233$	3341.72	−	981.219i	0.939586	−	0.275887i	0.715445	+	0.698669i	$0.246224\pi$
$234$		0			0
$235$	−4999.29	−	3212.85i	−1.38773	−	0.891843i
$236$	−2068.72	−	2387.43i	−0.570601	−	0.658509i
$237$		0			0
$238$	−4070.51	−	1195.21i	−1.10862	−	0.325521i
$239$	2870.81	−	1844.96i	0.776977	−	0.499333i	−0.0910520	−	0.995846i	$-0.529023\pi$
$239$	2870.81	−	1844.96i	0.776977	−	0.499333i	0.868029	+	0.496513i	$0.165387\pi$
$240$		0			0
$241$	1115.87	−	2443.42i	0.298256	−	0.653089i	−0.699871	−	0.714269i	$-0.746759\pi$
$241$	1115.87	−	2443.42i	0.298256	−	0.653089i	0.998127	+	0.0611804i	$0.0194865\pi$
$242$	−886.139	+	1940.37i	−0.235385	+	0.515421i
$243$		0			0
$244$	−2229.23	+	1432.64i	−0.584884	+	0.375882i
$245$	−1745.17	−	512.429i	−0.455082	−	0.133624i
$246$		0			0
$247$	4932.42	+	5692.31i	1.27062	+	1.46637i
$248$	7862.30	+	5052.80i	2.01313	+	1.29376i
$249$		0			0
$250$	7319.64	−	2149.24i	1.85174	−	0.543720i
$251$	452.845	+	991.592i	0.113878	+	0.249357i	0.957986	−	0.286816i	$-0.0925967\pi$
$251$	452.845	+	991.592i	0.113878	+	0.249357i	−0.844108	+	0.536173i	$0.819869\pi$
$252$		0			0
$253$	4540.51	−	631.703i	1.12830	−	0.156975i
$254$	−923.072			−0.228026
$255$		0			0
$256$	−4177.87	+	1226.73i	−1.01999	+	0.299496i
$257$	−3.24694	+	3.74717i	−0.000788089	+	0.000909503i	−0.756143	−	0.654406i	$-0.772919\pi$
$257$	−3.24694	+	3.74717i	−0.000788089	+	0.000909503i	0.755355	+	0.655315i	$0.227464\pi$
$258$		0			0
$259$	1342.21	+	1548.99i	0.322011	+	0.371621i
$260$	2289.20	+	15921.7i	0.546038	+	3.79778i
$261$		0			0
$262$	−8480.34	+	5449.99i	−1.99968	+	1.28512i
$263$	−145.339	+	1010.85i	−0.0340759	+	0.237003i	−0.999740	−	0.0227896i	$-0.992745\pi$
$263$	−145.339	+	1010.85i	−0.0340759	+	0.237003i	0.965664	+	0.259793i	$0.0836543\pi$
$264$		0			0
$265$	2343.62	−	5131.81i	0.543273	−	1.18960i
$266$	−1106.20	+	7693.76i	−0.254982	+	1.77344i
$267$		0			0
$268$	9578.21	+	2812.42i	2.18314	+	0.641029i
$269$	265.181	+	1844.37i	0.0601054	+	0.418042i	0.997553	+	0.0699155i	$0.0222730\pi$
$269$	265.181	+	1844.37i	0.0601054	+	0.418042i	−0.937448	+	0.348127i	$0.886818\pi$
$270$		0			0
$271$	5620.18	+	3611.87i	1.25979	+	0.809615i	0.988255	−	0.152815i	$-0.0488339\pi$
$271$	5620.18	+	3611.87i	1.25979	+	0.809615i	0.271530	+	0.962430i	$0.412470\pi$
$272$	8063.07	−	9305.27i	1.79741	−	2.07432i
$273$		0			0
$274$	−769.119	−	1684.13i	−0.169577	−	0.371322i
$275$	150.381			0.0329757
$276$		0			0
$277$	−7611.58			−1.65103			−0.825516	−	0.564379i	$-0.809116\pi$
$277$	−7611.58			−1.65103			−0.825516	+	0.564379i	$0.809116\pi$
$278$	−6007.20	−	13153.9i	−1.29600	−	2.83784i
$279$		0			0
$280$	−6725.96	+	7762.17i	−1.43555	+	1.65671i
$281$	−5988.99	−	3848.89i	−1.27144	−	0.817102i	−0.281630	−	0.959523i	$-0.590875\pi$
$281$	−5988.99	−	3848.89i	−1.27144	−	0.817102i	−0.989806	+	0.142421i	$0.954511\pi$
$282$		0			0
$283$	−340.890	−	2370.94i	−0.0716036	−	0.498014i	−0.993790	−	0.111269i	$-0.964509\pi$
$283$	−340.890	−	2370.94i	−0.0716036	−	0.498014i	0.922187	−	0.386745i	$-0.126401\pi$
$284$	−13147.2	−	3860.37i	−2.74698	−	0.806587i
$285$		0			0
$286$	−2215.60	+	15409.9i	−0.458082	+	3.18603i
$287$	2081.97	−	4558.88i	0.428205	−	0.937639i
$288$		0			0
$289$	202.455	−	1408.11i	0.0412081	−	0.286609i
$290$	6618.37	−	4253.37i	1.34015	−	0.861263i
$291$		0			0
$292$	−643.906	−	4478.47i	−0.129047	−	0.897543i
$293$	−2783.39	−	3212.20i	−0.554974	−	0.640474i	0.407061	−	0.913401i	$-0.366554\pi$
$293$	−2783.39	−	3212.20i	−0.554974	−	0.640474i	−0.962035	+	0.272927i	$0.912008\pi$
$294$		0			0
$295$	1086.22	−	1253.57i	0.214381	−	0.247409i
$296$	−10304.8	+	3025.78i	−2.02350	+	0.594154i
$297$		0			0
$298$	−685.757			−0.133305
$299$	6996.08	−	3156.52i	1.35316	−	0.610522i
$300$		0			0
$301$	563.930	+	1234.83i	0.107988	+	0.236461i
$302$	3287.17	−	965.200i	0.626342	−	0.183911i
$303$		0			0
$304$	−18978.1	−	12196.5i	−3.58049	−	2.30104i
$305$	−911.160	−	1051.53i	−0.171059	−	0.197412i
$306$		0			0
$307$	−2168.81	−	636.821i	−0.403194	−	0.118389i	0.0738465	−	0.997270i	$-0.476472\pi$
$307$	−2168.81	−	636.821i	−0.403194	−	0.118389i	−0.477041	+	0.878881i	$0.658291\pi$
$308$	−9785.01	+	6288.45i	−1.81024	+	1.16337i
$309$		0			0
$310$	−3294.74	+	7214.47i	−0.603641	+	1.32179i
$311$	−1612.48	+	3530.85i	−0.294005	+	0.643781i	−0.997777	−	0.0666450i	$-0.978771\pi$
$311$	−1612.48	+	3530.85i	−0.294005	+	0.643781i	0.703772	+	0.710426i	$0.251498\pi$
$312$		0			0
$313$	−829.316	+	532.969i	−0.149763	+	0.0962466i	−0.613376	−	0.789791i	$-0.710189\pi$
$313$	−829.316	+	532.969i	−0.149763	+	0.0962466i	0.463613	+	0.886038i	$0.346553\pi$
$314$	−6507.71	−	1910.84i	−1.16959	−	0.343423i
$315$		0			0
$316$	−18926.0	−	21841.8i	−3.36921	−	3.88828i
$317$	−3291.47	−	2115.30i	−0.583177	−	0.374785i	0.215537	−	0.976496i	$-0.430850\pi$
$317$	−3291.47	−	2115.30i	−0.583177	−	0.374785i	−0.798714	+	0.601710i	$0.794486\pi$
$318$		0			0
$319$	5289.28	−	1553.07i	0.928347	−	0.272587i
$320$	−6237.11	−	13657.4i	−1.08958	−	2.38584i
$321$		0			0
$322$	7189.79	+	3323.18i	1.24432	+	0.575136i
$323$	6395.16			1.10166
$324$		0			0
$325$	241.578	−	70.9336i	0.0412318	−	0.0121067i
$326$	6431.17	−	7421.96i	1.09261	−	1.26093i
$327$		0			0
$328$	17197.7	+	19847.2i	2.89507	+	3.34109i
$329$	−1023.90	−	7121.35i	−0.171578	−	1.19335i
$330$		0			0
$331$	−1867.05	+	1199.88i	−0.310037	+	0.199249i	−0.686401	−	0.727223i	$-0.740811\pi$
$331$	−1867.05	+	1199.88i	−0.310037	+	0.199249i	0.376364	+	0.926472i	$0.377174\pi$
$332$	−663.626	+	4615.62i	−0.109702	+	0.762997i
$333$		0			0
$334$	227.626	−	498.432i	0.0372909	−	0.0816556i
$335$	−745.952	+	5188.21i	−0.121659	+	0.846156i
$336$		0			0
$337$	−4723.28	−	1386.88i	−0.763482	−	0.224179i	−0.123266	−	0.992374i	$-0.539337\pi$
$337$	−4723.28	−	1386.88i	−0.763482	−	0.224179i	−0.640216	+	0.768195i	$0.721155\pi$
$338$	2026.24	+	14092.8i	0.326074	+	2.26790i
$339$		0			0
$340$	11489.5	+	7383.84i	1.83266	+	1.17778i
$341$	−3639.31	+	4199.98i	−0.577946	+	0.666985i
$342$		0			0
$343$	−2815.29	−	6164.62i	−0.443182	−	0.970433i
$344$	−7113.30			−1.11489
$345$		0			0
$346$	7656.92			1.18971
$347$	2934.09	+	6424.76i	0.453920	+	0.993946i	0.988831	+	0.149038i	$0.0476177\pi$
$347$	2934.09	+	6424.76i	0.453920	+	0.993946i	−0.534911	+	0.844908i	$0.679655\pi$
$348$		0			0
$349$	−6411.24	+	7398.96i	−0.983340	+	1.13483i	0.00752446	+	0.999972i	$0.497605\pi$
$349$	−6411.24	+	7398.96i	−0.983340	+	1.13483i	−0.990864	+	0.134863i	$0.956941\pi$
$350$	218.581	+	140.474i	0.0333819	+	0.0214532i
$351$		0			0
$352$	−3328.93	−	23153.2i	−0.504070	−	3.50588i
$353$	−209.722	−	61.5799i	−0.0316214	−	0.00928489i	0.265884	−	0.964005i	$-0.414336\pi$
$353$	−209.722	−	61.5799i	−0.0316214	−	0.00928489i	−0.297505	+	0.954720i	$0.596154\pi$
$354$		0			0
$355$	1023.91	−	7121.42i	0.153080	−	1.06469i
$356$	−6577.15	+	14402.0i	−0.979181	+	2.14411i
$357$		0			0
$358$	−824.791	+	5736.54i	−0.121764	+	0.846888i
$359$	−1319.03	+	847.688i	−0.193916	+	0.124622i	−0.633996	−	0.773336i	$-0.718586\pi$
$359$	−1319.03	+	847.688i	−0.193916	+	0.124622i	0.440080	+	0.897958i	$0.354950\pi$
$360$		0			0
$361$	−691.402	−	4808.81i	−0.100802	−	0.701095i
$362$	14243.7	+	16438.1i	2.06805	+	2.38665i
$363$		0			0
$364$	−12752.8	+	14717.5i	−1.83634	+	2.11925i
$365$	2279.46	−	669.310i	0.326884	−	0.0959817i
$366$		0			0
$367$	8499.87			1.20896			0.604482	−	0.796619i	$-0.293380\pi$
$367$	8499.87			1.20896			0.604482	+	0.796619i	$0.293380\pi$
$368$	−17441.8	+	14974.7i	−2.47070	+	2.12122i
$369$		0			0
$370$	−3786.15	−	8290.52i	−0.531980	−	1.16487i
$371$	6553.46	−	1924.27i	0.917085	−	0.269280i
$372$		0			0
$373$	9329.44	+	5995.67i	1.29507	+	0.832289i	0.992666	−	0.120892i	$-0.0385753\pi$
$373$	9329.44	+	5995.67i	1.29507	+	0.832289i	0.302401	+	0.953181i	$0.402212\pi$
$374$	8656.28	+	9989.88i	1.19681	+	1.38119i
$375$		0			0
$376$	36172.2	+	10621.1i	4.96128	+	1.45676i
$377$	7764.33	−	4989.83i	1.06070	−	0.681670i
$378$		0			0
$379$	−962.592	+	2107.78i	−0.130462	+	0.285671i	−0.963578	−	0.267426i	$-0.913827\pi$
$379$	−962.592	+	2107.78i	−0.130462	+	0.285671i	0.833117	+	0.553097i	$0.186554\pi$
$380$	10395.1	−	22762.2i	1.40331	−	3.07283i
$381$		0			0
$382$	17528.0	−	11264.6i	2.34767	−	1.50876i
$383$	853.724	+	250.676i	0.113899	+	0.0334437i	0.338185	−	0.941080i	$-0.390187\pi$
$383$	853.724	+	250.676i	0.113899	+	0.0334437i	−0.224286	+	0.974523i	$0.572005\pi$
$384$		0			0
$385$	−3999.46	−	4615.62i	−0.529432	−	0.610997i
$386$	17020.8	+	10938.6i	2.24439	+	1.44238i
$387$		0			0
$388$	−16272.1	+	4777.93i	−2.12911	+	0.625162i
$389$	674.349	+	1476.62i	0.0878943	+	0.192462i	0.948475	−	0.316853i	$-0.102626\pi$
$389$	674.349	+	1476.62i	0.0878943	+	0.192462i	−0.860580	+	0.509315i	$0.829899\pi$
$390$		0			0
$391$	1864.48	−	6244.32i	0.241152	−	0.807644i
$392$	11538.5			1.48669
$393$		0			0
$394$	−15981.3	+	4692.54i	−2.04347	+	0.600017i
$395$	9937.50	−	11468.5i	1.26585	−	1.46087i
$396$		0			0
$397$	4258.88	+	4915.01i	0.538406	+	0.621353i	0.958142	−	0.286293i	$-0.0924230\pi$
$397$	4258.88	+	4915.01i	0.538406	+	0.621353i	−0.419737	+	0.907646i	$0.637878\pi$
$398$	−2050.47	−	14261.3i	−0.258243	−	1.79612i
$399$		0			0
$400$	−634.391	+	407.698i	−0.0792989	+	0.0509623i
$401$	46.0346	−	320.177i	0.00573281	−	0.0398726i	−0.986754	−	0.162222i	$-0.948134\pi$
$401$	46.0346	−	320.177i	0.00573281	−	0.0398726i	0.992487	+	0.122350i	$0.0390429\pi$
$402$		0			0
$403$	−3865.22	+	8463.65i	−0.477768	+	1.04617i
$404$	817.688	−	5687.14i	0.100697	−	0.700361i
$405$		0			0
$406$	9138.81	+	2683.40i	1.11712	+	0.328017i
$407$	−908.860	−	6321.26i	−0.110689	−	0.769860i
$408$		0			0
$409$	5868.23	+	3771.28i	0.709450	+	0.455936i	0.844953	−	0.534841i	$-0.179629\pi$
$409$	5868.23	+	3771.28i	0.709450	+	0.455936i	−0.135503	+	0.990777i	$0.543265\pi$
$410$	−14594.4	+	16842.8i	−1.75796	+	2.02880i
$411$		0			0
$412$	−9482.62	−	20764.0i	−1.13392	−	2.48294i
$413$	2008.14			0.239259
$414$		0			0
$415$	−2448.45			−0.289614
$416$	−16268.9	−	35624.0i	−1.91743	−	4.19858i
$417$		0			0
$418$	15860.1	−	18303.5i	1.85584	−	2.14176i
$419$	784.638	+	504.256i	0.0914846	+	0.0587936i	0.585583	−	0.810612i	$-0.300865\pi$
$419$	784.638	+	504.256i	0.0914846	+	0.0587936i	−0.494099	+	0.869406i	$0.664502\pi$
$420$		0			0
$421$	−1163.93	−	8095.33i	−0.134743	−	0.937155i	−0.939255	−	0.343220i	$-0.888482\pi$
$421$	−1163.93	−	8095.33i	−0.134743	−	0.937155i	0.804513	−	0.593936i	$-0.202427\pi$
$422$	−12523.7	−	3677.30i	−1.44466	−	0.424190i
$423$		0			0
$424$	−5093.39	+	35425.3i	−0.583389	+	4.05756i
$425$	88.8050	−	194.456i	0.0101357	−	0.0221941i
$426$		0			0
$427$	239.729	−	1667.35i	0.0271693	−	0.188966i
$428$	8871.31	−	5701.24i	1.00189	−	0.643878i
$429$		0			0
$430$	−859.087	−	5975.08i	−0.0963462	−	0.670102i
$431$	8710.61	+	10052.6i	0.973493	+	1.12347i	0.992326	+	0.123648i	$0.0394594\pi$
$431$	8710.61	+	10052.6i	0.973493	+	1.12347i	−0.0188333	+	0.999823i	$0.505995\pi$
$432$		0			0
$433$	2447.94	−	2825.07i	0.271687	−	0.313544i	−0.603467	−	0.797388i	$-0.706214\pi$
$433$	2447.94	−	2825.07i	0.271687	−	0.313544i	0.875154	+	0.483844i	$0.160760\pi$
$434$	−9213.08	+	2705.20i	−1.01899	+	0.299203i
$435$		0			0
$436$	−17316.5			−1.90208
$437$	−11810.6	−	1753.13i	−1.29286	−	0.191907i
$438$		0			0
$439$	1284.46	+	2812.58i	0.139645	+	0.305779i	0.966514	−	0.256616i	$-0.0826075\pi$
$439$	1284.46	+	2812.58i	0.139645	+	0.305779i	−0.826869	+	0.562395i	$0.809880\pi$
$440$	30705.9	−	9016.08i	3.32693	−	0.976874i
$441$		0			0
$442$	18617.9	+	11965.0i	2.00354	+	1.28760i
$443$	2069.02	+	2387.78i	0.221901	+	0.256087i	0.855774	−	0.517350i	$-0.173081\pi$
$443$	2069.02	+	2387.78i	0.221901	+	0.256087i	−0.633873	+	0.773437i	$0.718536\pi$
$444$		0			0
$445$	−7976.56	−	2342.13i	−0.849720	−	0.249500i
$446$	−93.8855	+	60.3366i	−0.00996773	+	0.00640587i
$447$		0			0
$448$	7551.05	−	16534.5i	0.796324	−	1.74371i
$449$	−5321.17	+	11651.7i	−0.559291	+	1.22468i	0.393015	+	0.919532i	$0.371432\pi$
$449$	−5321.17	+	11651.7i	−0.559291	+	1.22468i	−0.952306	+	0.305145i	$0.901295\pi$
$450$		0			0
$451$	−13137.0	+	8442.61i	−1.37161	+	0.881479i
$452$	4888.10	+	1435.28i	0.508666	+	0.149358i
$453$		0			0
$454$	13785.8	+	15909.6i	1.42511	+	1.64466i
$455$	−8602.05	−	5528.20i	−0.886308	−	0.569596i
$456$		0			0
$457$	−14794.5	+	4344.06i	−1.51435	+	0.444653i	−0.930218	−	0.367006i	$-0.880383\pi$
$457$	−14794.5	+	4344.06i	−1.51435	+	0.444653i	−0.584131	+	0.811660i	$0.698565\pi$
$458$	1072.70	+	2348.88i	0.109441	+	0.239642i
$459$		0			0
$460$	−19194.6	−	16786.1i	−1.94555	−	1.70143i
$461$	12018.9			1.21427			0.607134	−	0.794599i	$-0.292319\pi$
$461$	12018.9			1.21427			0.607134	+	0.794599i	$0.292319\pi$
$462$		0			0
$463$	18135.7	−	5325.12i	1.82038	−	0.534513i	0.821044	−	0.570865i	$-0.193392\pi$
$463$	18135.7	−	5325.12i	1.82038	−	0.534513i	0.999339	+	0.0363524i	$0.0115739\pi$
$464$	−18102.6	+	20891.5i	−1.81119	+	2.09023i
$465$		0			0
$466$	−12278.5	−	14170.2i	−1.22058	−	1.40863i
$467$	−1542.78	−	10730.3i	−0.152873	−	1.06325i	−0.911374	−	0.411580i	$-0.864977\pi$
$467$	−1542.78	−	10730.3i	−0.152873	−	1.06325i	0.758501	−	0.651672i	$-0.225932\pi$
$468$		0			0
$469$	−5338.40	+	3430.78i	−0.525596	+	0.337780i
$470$	−4553.02	+	31667.0i	−0.446841	+	3.10785i
$471$		0			0
$472$	−4371.24	+	9571.67i	−0.426276	+	0.933415i
$473$	601.961	−	4186.73i	0.0585162	−	0.406989i
$474$		0			0
$475$	−375.813	−	110.349i	−0.0363021	−	0.0106593i
$476$	2353.14	+	16366.4i	0.226588	+	1.57595i
$477$		0			0
$478$	−15455.2	−	9932.43i	−1.47888	−	0.950416i
$479$	−4905.46	+	5661.21i	−0.467926	+	0.540015i	−0.939833	−	0.341633i	$-0.889020\pi$
$479$	−4905.46	+	5661.21i	−0.467926	+	0.540015i	0.471908	+	0.881648i	$0.343566\pi$
$480$		0			0
$481$	−4441.72	−	9726.01i	−0.421050	−	0.921971i
$482$	−14461.1			−1.36656
$483$		0			0
$484$	8314.00			0.780804
$485$	−3699.16	−	8100.03i	−0.346330	−	0.758358i
$486$		0			0
$487$	695.902	−	803.113i	0.0647522	−	0.0747280i	−0.722449	−	0.691424i	$-0.756984\pi$
$487$	695.902	−	803.113i	0.0647522	−	0.0747280i	0.787201	+	0.616696i	$0.211529\pi$
$488$	7425.48	+	4772.07i	0.688803	+	0.442667i
$489$		0			0
$490$	1393.53	+	9692.19i	0.128476	+	0.893568i
$491$	11663.4	+	3424.67i	1.07202	+	0.314772i	0.769680	−	0.638429i	$-0.220416\pi$
$491$	11663.4	+	3424.67i	1.07202	+	0.314772i	0.302335	+	0.953202i	$0.402234\pi$
$492$		0			0
$493$	1115.24	−	7756.65i	0.101882	−	0.708605i
$494$	16844.6	−	36884.6i	1.53416	−	3.35935i
$495$		0			0
$496$	3966.04	−	27584.4i	0.359033	−	2.49713i
$497$	7327.58	−	4709.15i	0.661342	−	0.425019i
$498$		0			0
$499$	−1034.98	−	7198.43i	−0.0928496	−	0.645783i	−0.982100	−	0.188362i	$-0.939682\pi$
$499$	−1034.98	−	7198.43i	−0.0928496	−	0.645783i	0.889250	−	0.457421i	$-0.151227\pi$
$500$	−19470.9	−	22470.7i	−1.74153	−	2.00984i
$501$		0			0
$502$	3843.12	−	4435.20i	0.341687	−	0.394328i
$503$	−17969.7	+	5276.38i	−1.59290	+	0.467718i	−0.953559	−	0.301205i	$-0.902611\pi$
$503$	−17969.7	+	5276.38i	−1.59290	+	0.467718i	−0.639342	+	0.768923i	$0.720793\pi$
$504$		0			0
$505$	3016.86			0.265839
$506$	−13247.9	−	20822.3i	−1.16391	−	1.82938i
$507$		0			0
$508$	1494.54	+	3272.59i	0.130531	+	0.285822i
$509$	−11027.0	+	3237.81i	−0.960239	+	0.281952i	−0.724044	−	0.689754i	$-0.757719\pi$
$509$	−11027.0	+	3237.81i	−0.960239	+	0.281952i	−0.236195	+	0.971706i	$0.575901\pi$
$510$		0			0
$511$	2419.59	+	1554.98i	0.209464	+	0.134615i
$512$	504.285	+	581.976i	0.0435283	+	0.0502343i
$513$		0			0
$514$	25.6116	+	7.52023i	0.00219782	+	0.000645337i
$515$	10083.0	−	6479.97i	0.862740	−	0.554450i
$516$		0			0
$517$	−9312.42	+	20391.4i	−0.792185	+	1.73464i
$518$	4583.76	−	10037.0i	0.388801	−	0.851356i
$519$		0			0
$520$	45074.4	−	28967.6i	3.80124	−	2.44291i
$521$	−16400.4	−	4815.59i	−1.37911	−	0.404942i	−0.493649	−	0.869661i	$-0.664337\pi$
$521$	−16400.4	−	4815.59i	−1.37911	−	0.404942i	−0.885458	+	0.464719i	$0.846155\pi$
$522$		0			0
$523$	3084.08	+	3559.21i	0.257853	+	0.297579i	0.869885	−	0.493255i	$-0.164193\pi$
$523$	3084.08	+	3559.21i	0.257853	+	0.297579i	−0.612032	+	0.790833i	$0.709647\pi$
$524$	33052.4	+	21241.5i	2.75554	+	1.77088i
$525$		0			0
$526$	5275.23	−	1548.95i	0.437283	−	0.128398i
$527$	3281.82	+	7186.18i	0.271268	+	0.593994i
$528$		0			0
$529$	−5155.10	+	11020.9i	−0.423695	+	0.905805i
$530$	−30372.0			−2.48920
$531$		0			0
$532$	29067.9	−	8535.11i	2.36890	−	0.695571i
$533$	−17121.4	+	19759.1i	−1.39139	+	1.60575i
$534$		0			0
$535$	3626.00	+	4184.62i	0.293020	+	0.338163i
$536$	−4732.20	−	32913.2i	−0.381343	−	2.65230i
$537$		0			0
$538$	8438.92	−	5423.36i	0.676259	−	0.434606i
$539$	−976.441	+	6791.29i	−0.0780302	+	0.542712i
$540$		0			0
$541$	2943.26	−	6444.83i	0.233901	−	0.512172i	−0.755890	−	0.654699i	$-0.772795\pi$
$541$	2943.26	−	6444.83i	0.233901	−	0.512172i	0.989791	+	0.142527i	$0.0455227\pi$
$542$	5118.49	−	35599.9i	0.405642	−	2.82130i
$543$		0			0
$544$	−31905.0	−	9368.17i	−2.51455	−	0.738340i
$545$	−1293.98	−	8999.83i	−0.101703	−	0.707358i
$546$		0			0
$547$	11816.0	+	7593.67i	0.923610	+	0.593568i	0.913703	−	0.406383i	$-0.133210\pi$
$547$	11816.0	+	7593.67i	0.923610	+	0.593568i	0.00990742	+	0.999951i	$0.496846\pi$
$548$	−4725.53	+	5453.55i	−0.368366	+	0.425117i
$549$		0			0
$550$	−336.313	−	736.422i	−0.0260735	−	0.0570930i
$551$	−14357.9			−1.11011
$552$		0			0
$553$	18371.8			1.41275
$554$	17022.6	+	37274.3i	1.30545	+	2.85854i
$555$		0			0
$556$	−36908.7	+	42594.9i	−2.81525	+	3.24897i
$557$	17401.1	+	11183.0i	1.32371	+	0.850700i	0.995579	−	0.0939311i	$-0.0299433\pi$
$557$	17401.1	+	11183.0i	1.32371	+	0.850700i	0.328136	+	0.944631i	$0.393580\pi$
$558$		0			0
$559$	−1007.84	−	7009.66i	−0.0762558	−	0.530371i
$560$	29385.4	+	8628.33i	2.21743	+	0.651096i
$561$		0			0
$562$	−5454.38	+	37936.1i	−0.409394	+	2.84740i
$563$	1159.26	−	2538.42i	0.0867795	−	0.190021i	−0.861267	−	0.508153i	$-0.830328\pi$
$563$	1159.26	−	2538.42i	0.0867795	−	0.190021i	0.948046	+	0.318132i	$0.103056\pi$
$564$		0			0
$565$	−380.686	+	2647.73i	−0.0283462	+	0.197152i
$566$	−10848.2	+	6971.74i	−0.805628	+	0.517746i
$567$		0			0
$568$	6495.50	+	45177.2i	0.479833	+	3.33731i
$569$	−10940.4	−	12625.9i	−0.806055	−	0.930237i	0.192642	−	0.981269i	$-0.438294\pi$
$569$	−10940.4	−	12625.9i	−0.806055	−	0.930237i	−0.998697	+	0.0510322i	$0.983749\pi$
$570$		0			0
$571$	16485.1	−	19024.8i	1.20820	−	1.39433i	0.312354	−	0.949966i	$-0.398883\pi$
$571$	16485.1	−	19024.8i	1.20820	−	1.39433i	0.895844	−	0.444369i	$-0.146572\pi$
$572$	58220.2	−	17095.0i	4.25579	−	1.24961i
$573$		0			0
$574$	−26981.2			−1.96197
$575$	−217.312	+	334.778i	−0.0157610	+	0.0242803i
$576$		0			0
$577$	−3755.28	−	8222.92i	−0.270944	−	0.593284i	0.724432	−	0.689347i	$-0.242102\pi$
$577$	−3755.28	−	8222.92i	−0.270944	−	0.593284i	−0.995375	+	0.0960630i	$0.969375\pi$
$578$	−7348.34	+	2157.67i	−0.528807	+	0.155272i
$579$		0			0
$580$	−25795.3	−	16577.6i	−1.84671	−	1.18681i
$581$	−1941.17	−	2240.23i	−0.138612	−	0.159966i
$582$		0			0
$583$	−20419.5	−	5995.71i	−1.45058	−	0.425930i
$584$	−12678.6	+	8148.01i	−0.898360	+	0.577341i
$585$		0			0
$586$	−9505.52	+	20814.2i	−0.670084	+	1.46728i
$587$	−24.4452	+	53.5276i	−0.00171885	+	0.00376375i	−0.910489	−	0.413532i	$-0.864295\pi$
$587$	−24.4452	+	53.5276i	−0.00171885	+	0.00376375i	0.908771	+	0.417296i	$0.137022\pi$
$588$		0			0
$589$	12176.8	−	7825.57i	0.851846	−	0.547448i
$590$	−8568.01	−	2515.80i	−0.597864	−	0.175549i
$591$		0			0
$592$	20971.7	+	24202.6i	1.45596	+	1.68027i
$593$	−10431.2	−	6703.76i	−0.722361	−	0.464233i	0.127097	−	0.991890i	$-0.459434\pi$
$593$	−10431.2	−	6703.76i	−0.722361	−	0.464233i	−0.849457	+	0.527657i	$0.823071\pi$
$594$		0			0
$595$	−8330.23	+	2445.98i	−0.573960	+	0.168530i
$596$	1110.31	+	2431.23i	0.0763086	+	0.167092i
$597$		0			0
$598$	−31103.7	−	27200.9i	−2.12696	−	1.86008i
$599$	−7211.63			−0.491918			−0.245959	−	0.969280i	$-0.579103\pi$
$599$	−7211.63			−0.491918			−0.245959	+	0.969280i	$0.579103\pi$
$600$		0			0
$601$	12753.1	−	3744.64i	0.865573	−	0.254155i	0.181342	−	0.983420i	$-0.441956\pi$
$601$	12753.1	−	3744.64i	0.865573	−	0.254155i	0.684231	+	0.729265i	$0.260138\pi$
$602$	4785.86	−	5523.18i	0.324015	−	0.373933i
$603$		0			0
$604$	−8744.18	−	10091.3i	−0.589066	−	0.679818i
$605$	621.267	+	4321.00i	0.0417489	+	0.290370i
$606$		0			0
$607$	−3466.41	+	2227.72i	−0.231791	+	0.148963i	−0.651381	−	0.758751i	$-0.725810\pi$
$607$	−3466.41	+	2227.72i	−0.231791	+	0.148963i	0.419590	+	0.907714i	$0.362174\pi$
$608$	−8670.46	+	60304.4i	−0.578345	+	4.02248i
$609$		0			0
$610$	−3111.69	+	6813.65i	−0.206539	+	0.452257i
$611$	−5341.37	+	37150.1i	−0.353664	+	2.45979i
$612$		0			0
$613$	−26474.2	−	7773.54i	−1.74435	−	0.512186i	−0.754745	−	0.656019i	$-0.772239\pi$
$613$	−26474.2	−	7773.54i	−1.74435	−	0.512186i	−0.989602	+	0.143832i	$0.954057\pi$
$614$	1731.80	+	12045.0i	0.113827	+	0.791686i
$615$		0			0
$616$	32593.5	+	20946.6i	2.13187	+	1.37007i
$617$	16194.0	−	18688.8i	1.05664	−	1.21942i	0.0817652	−	0.996652i	$-0.473944\pi$
$617$	16194.0	−	18688.8i	1.05664	−	1.21942i	0.974871	−	0.222771i	$-0.0715103\pi$
$618$		0			0
$619$	1297.85	+	2841.89i	0.0842728	+	0.184532i	0.947077	−	0.321007i	$-0.104021\pi$
$619$	1297.85	+	2841.89i	0.0842728	+	0.184532i	−0.862804	+	0.505538i	$0.831294\pi$
$620$	30912.1			2.00236
$621$		0			0
$622$	20896.9			1.34709
$623$	−4181.00	−	9155.11i	−0.268873	−	0.588751i
$624$		0			0
$625$	9927.43	−	11456.9i	0.635356	−	0.733239i
$626$	4464.66	+	2869.26i	0.285054	+	0.183193i
$627$		0			0
$628$	3762.07	+	26165.8i	0.239049	+	1.66262i
$629$	−8710.66	−	2557.68i	−0.552173	−	0.162133i
$630$		0			0
$631$	1084.64	−	7543.86i	0.0684295	−	0.475937i	−0.926575	−	0.376109i	$-0.877262\pi$
$631$	1084.64	−	7543.86i	0.0684295	−	0.475937i	0.995005	−	0.0998280i	$-0.0318292\pi$
$632$	−39991.0	+	87568.1i	−2.51702	+	5.51151i
$633$		0			0
$634$	−2997.65	+	20849.1i	−0.187779	+	1.30603i
$635$	−1589.17	+	1021.30i	−0.0993139	+	0.0638252i
$636$		0			0
$637$	1634.81	+	11370.4i	0.101686	+	0.707238i
$638$	−19434.4	−	22428.5i	−1.20598	−	1.39178i
$639$		0			0
$640$	−20446.1	+	23596.1i	−1.26282	+	1.45737i
$641$	5277.05	−	1549.48i	0.325165	−	0.0954771i	−0.115076	−	0.993357i	$-0.536711\pi$
$641$	5277.05	−	1549.48i	0.325165	−	0.0954771i	0.440241	+	0.897880i	$0.354893\pi$
$642$		0			0
$643$	−5906.20			−0.362236			−0.181118	−	0.983461i	$-0.557972\pi$
$643$	−5906.20			−0.362236			−0.181118	+	0.983461i	$0.557972\pi$
$644$	140.803	−	30870.7i	0.00861556	−	1.88894i
$645$		0			0
$646$	−14302.2	−	31317.4i	−0.871070	−	1.90738i
$647$	13893.8	−	4079.59i	0.844237	−	0.247890i	0.169115	−	0.985596i	$-0.445909\pi$
$647$	13893.8	−	4079.59i	0.844237	−	0.247890i	0.675122	+	0.737706i	$0.264091\pi$
$648$		0			0
$649$	−5263.76	−	3382.81i	−0.318368	−	0.204602i
$650$	−887.631	−	1024.38i	−0.0535627	−	0.0618146i
$651$		0			0
$652$	−36725.9	−	10783.7i	−2.20598	−	0.647734i
$653$	15595.8	−	10022.8i	0.934628	−	0.600649i	0.0177609	−	0.999842i	$-0.494346\pi$
$653$	15595.8	−	10022.8i	0.934628	−	0.600649i	0.916867	+	0.399194i	$0.130710\pi$
$654$		0			0
$655$	−8569.92	+	18765.5i	−0.511228	+	1.11943i
$656$	32530.2	−	71231.3i	1.93612	−	4.23950i
$657$		0			0
$658$	−32583.7	+	20940.3i	−1.93046	+	1.24063i
$659$	18207.1	+	5346.10i	1.07625	+	0.316016i	0.771378	−	0.636377i	$-0.219568\pi$
$659$	18207.1	+	5346.10i	1.07625	+	0.316016i	0.304873	+	0.952393i	$0.401386\pi$
$660$		0			0
$661$	−13346.1	−	15402.2i	−0.785329	−	0.906318i	0.212153	−	0.977236i	$-0.431952\pi$
$661$	−13346.1	−	15402.2i	−0.785329	−	0.906318i	−0.997482	+	0.0709186i	$0.977407\pi$
$662$	10051.3	+	6459.61i	0.590116	+	0.379245i
$663$		0			0
$664$	14903.4	−	4376.03i	0.871030	−	0.255757i
$665$	6608.03	+	14469.6i	0.385336	+	0.843768i
$666$		0			0
$667$	−4185.99	+	14019.3i	−0.243002	+	0.813837i
$668$	−2135.65			−0.123699
$669$		0			0
$670$	27075.1	−	7949.98i	1.56120	−	0.458410i
$671$	−3437.11	+	3966.64i	−0.197747	+	0.228212i
$672$		0			0
$673$	5155.51	+	5949.78i	0.295290	+	0.340783i	0.883936	−	0.467608i	$-0.154884\pi$
$673$	5155.51	+	5949.78i	0.295290	+	0.340783i	−0.588646	+	0.808391i	$0.700339\pi$
$674$	3771.55	+	26231.7i	0.215541	+	1.49912i
$675$		0			0
$676$	46682.9	−	30001.3i	2.65606	−	1.70695i
$677$	−1147.07	+	7978.07i	−0.0651191	+	0.452913i	0.931009	+	0.364997i	$0.118930\pi$
$677$	−1147.07	+	7978.07i	−0.0651191	+	0.452913i	−0.996128	+	0.0879164i	$0.971979\pi$
$678$		0			0
$679$	4478.44	−	9806.43i	0.253118	−	0.554250i
$680$	6474.31	−	45029.8i	0.365115	−	2.53943i
$681$		0			0
$682$	28706.5	+	8428.98i	1.61177	+	0.473259i
$683$	3136.87	+	21817.4i	0.175738	+	1.22228i	0.866491	+	0.499193i	$0.166370\pi$
$683$	3136.87	+	21817.4i	0.175738	+	1.22228i	−0.690753	+	0.723091i	$0.742721\pi$
$684$		0			0
$685$	−3187.47	−	2048.46i	−0.177791	−	0.114259i
$686$	−23892.3	+	27573.2i	−1.32976	+	1.53462i
$687$		0			0
$688$	8811.25	+	19293.9i	0.488264	+	1.06915i
$689$	−35630.8			−1.97014
$690$		0			0
$691$	−33938.6			−1.86843			−0.934215	−	0.356712i	$-0.883898\pi$
$691$	−33938.6			−1.86843			−0.934215	+	0.356712i	$0.883898\pi$
$692$	−12397.3	−	27146.3i	−0.681031	−	1.49125i
$693$		0			0
$694$	24900.5	−	28736.8i	1.36198	−	1.57180i
$695$	−24895.7	−	15999.5i	−1.35878	−	0.873232i
$696$		0			0
$697$	3159.23	+	21972.9i	0.171685	+	1.19409i
$698$	50571.2	+	14849.0i	2.74233	+	0.805221i
$699$		0			0
$700$	144.121	−	1002.38i	0.00778178	−	0.0541235i
$701$	3362.78	−	7363.47i	0.181185	−	0.396740i	−0.797146	−	0.603786i	$-0.793658\pi$
$701$	3362.78	−	7363.47i	0.181185	−	0.396740i	0.978331	+	0.207047i	$0.0663852\pi$
$702$		0			0
$703$	−2367.20	+	16464.2i	−0.126999	+	0.883299i
$704$	−47646.1	+	30620.3i	−2.55075	+	1.63927i
$705$		0			0
$706$	167.463	+	1164.73i	0.00892716	+	0.0620897i
$707$	2391.82	+	2760.31i	0.127233	+	0.146834i
$708$		0			0
$709$	−9267.20	+	10694.9i	−0.490884	+	0.566510i	−0.946102	−	0.323870i	$-0.895016\pi$
$709$	−9267.20	+	10694.9i	−0.490884	+	0.566510i	0.455218	+	0.890380i	$0.349561\pi$
$710$	−37163.8	+	10912.3i	−1.96441	+	0.576803i
$711$		0			0
$712$	52738.3			2.77591
$713$	−4090.91	−	14171.1i	−0.214875	−	0.744338i
$714$		0			0
$715$	13235.2	+	28981.2i	0.692266	+	1.51585i
$716$	21673.3	−	6363.86i	1.13124	−	0.332163i
$717$		0			0
$718$	7101.05	+	4563.57i	0.369093	+	0.237202i
$719$	21007.2	+	24243.6i	1.08962	+	1.25749i	0.964141	+	0.265389i	$0.0855005\pi$
$719$	21007.2	+	24243.6i	1.08962	+	1.25749i	0.125476	+	0.992097i	$0.459954\pi$
$720$		0			0
$721$	13922.9	+	4088.13i	0.719162	+	0.211165i
$722$	−22002.7	+	14140.3i	−1.13415	+	0.728873i
$723$		0			0
$724$	35216.5	−	77113.4i	1.80775	−	3.95842i
$725$	−199.379	+	436.578i	−0.0102134	+	0.0223643i
$726$		0			0
$727$	15505.8	−	9964.96i	0.791029	−	0.508363i	−0.0816483	−	0.996661i	$-0.526018\pi$
$727$	15505.8	−	9964.96i	0.791029	−	0.508363i	0.872677	+	0.488298i	$0.162382\pi$
$728$	62239.9	+	18275.3i	3.16863	+	0.930394i
$729$		0			0
$730$	−8375.44	−	9665.78i	−0.424643	−	0.490064i
$731$	−5058.33	−	3250.79i	−0.255936	−	0.164480i
$732$		0			0
$733$	−10057.9	+	2953.27i	−0.506818	+	0.148815i	−0.525138	−	0.851017i	$-0.675986\pi$
$733$	−10057.9	+	2953.27i	−0.506818	+	0.148815i	0.0183200	+	0.999832i	$0.494168\pi$
$734$	−19009.2	−	41624.3i	−0.955914	−	2.09316i
$735$		0			0
$736$	56354.2	+	26047.4i	2.82234	+	1.30451i
$737$	19772.4			0.988231
$738$		0			0
$739$	−8364.73	+	2456.11i	−0.416376	+	0.122259i	−0.483209	−	0.875505i	$-0.660529\pi$
$739$	−8364.73	+	2456.11i	−0.416376	+	0.122259i	0.0668329	+	0.997764i	$0.478711\pi$
$740$	−23262.4	+	26846.3i	−1.15560	+	1.33363i
$741$		0			0
$742$	−24079.4	−	27789.1i	−1.19135	−	1.37489i
$743$	−2336.25	−	16248.9i	−0.115355	−	0.802310i	−0.962565	−	0.271052i	$-0.912629\pi$
$743$	−2336.25	−	16248.9i	−0.115355	−	0.802310i	0.847210	−	0.531258i	$-0.178280\pi$
$744$		0			0
$745$	−1180.61	+	758.730i	−0.0580592	+	0.0373124i
$746$	8496.64	−	59095.4i	0.417003	−	2.90032i
$747$		0			0
$748$	21402.0	−	46863.9i	1.04617	−	2.29079i
$749$	−954.010	+	6635.28i	−0.0465404	+	0.323696i
$750$		0			0
$751$	5209.52	+	1529.65i	0.253127	+	0.0743247i	0.405834	−	0.913947i	$-0.366981\pi$
$751$	5209.52	+	1529.65i	0.253127	+	0.0743247i	−0.152708	+	0.988271i	$0.548799\pi$
$752$	−15998.1	−	111269.i	−0.775785	−	5.39570i
$753$		0			0
$754$	−41799.6	−	26863.0i	−2.01890	−	1.29747i
$755$	4591.32	−	5298.66i	0.221318	−	0.255415i
$756$		0			0
$757$	5763.56	+	12620.4i	0.276724	+	0.605941i	0.996056	−	0.0887253i	$-0.0282793\pi$
$757$	5763.56	+	12620.4i	0.276724	+	0.605941i	−0.719332	+	0.694666i	$0.755552\pi$
$758$	12474.6			0.597757
$759$		0			0
$760$	−83352.4			−3.97830
$761$	10492.6	+	22975.7i	0.499813	+	1.09444i	0.976530	+	0.215382i	$0.0690996\pi$
$761$	10492.6	+	22975.7i	0.499813	+	1.09444i	−0.476716	+	0.879057i	$0.658173\pi$
$762$		0			0
$763$	7208.59	−	8319.16i	0.342029	−	0.394723i
$764$	−68316.0	−	43904.1i	−3.23506	−	2.07905i
$765$		0			0
$766$	−681.701	−	4741.34i	−0.0321552	−	0.223644i
$767$	−10051.6	−	2951.40i	−0.473195	−	0.138943i
$768$		0			0
$769$	5705.95	−	39685.7i	0.267571	−	1.86099i	−0.203738	−	0.979026i	$-0.565309\pi$
$769$	5705.95	−	39685.7i	0.267571	−	1.86099i	0.471308	−	0.881969i	$-0.343782\pi$
$770$	−13658.5	+	29907.9i	−0.639244	+	1.39975i
$771$		0			0
$772$	11222.6	−	78054.6i	0.523198	−	3.63892i
$773$	4984.74	−	3203.50i	0.231939	−	0.149058i	−0.419510	−	0.907751i	$-0.637798\pi$
$773$	4984.74	−	3203.50i	0.231939	−	0.149058i	0.651449	+	0.758693i	$0.274162\pi$
$774$		0			0
$775$	−68.8591	−	478.926i	−0.00319160	−	0.0221981i
$776$	36993.2	+	42692.5i	1.71131	+	1.97496i
$777$		0			0
$778$	5722.95	−	6604.64i	0.263725	−	0.304354i
$779$	39025.4	−	11458.9i	1.79490	−	0.527031i
$780$		0			0
$781$	−27139.9			−1.24346
$782$	−34748.5	+	4834.41i	−1.58901	+	0.221072i
$783$		0			0
$784$	−14292.7	−	31296.7i	−0.651090	−	1.42569i
$785$	−13317.9	+	3910.49i	−0.605525	+	0.177798i
$786$		0			0
$787$	16304.9	+	10478.5i	0.738508	+	0.474610i	0.855030	−	0.518578i	$-0.173538\pi$
$787$	16304.9	+	10478.5i	0.738508	+	0.474610i	−0.116523	+	0.993188i	$0.537175\pi$
$788$	42511.8	+	49061.2i	1.92185	+	2.21794i
$789$		0			0
$790$	−78385.9	−	23016.2i	−3.53019	−	1.03656i
$791$	−2724.38	+	1750.85i	−0.122462	+	0.0787018i
$792$		0			0
$793$	−3650.47	+	7993.42i	−0.163471	+	0.357951i
$794$	14544.4	−	31847.9i	0.650079	−	1.42347i
$795$		0			0
$796$	−47241.1	+	30360.0i	−2.10354	+	1.35186i
$797$	−34036.6	−	9994.04i	−1.51272	−	0.444175i	−0.583009	−	0.812466i	$-0.698125\pi$
$797$	−34036.6	−	9994.04i	−1.51272	−	0.444175i	−0.929711	+	0.368291i	$0.879943\pi$
$798$		0			0
$799$	20868.5	+	24083.6i	0.924000	+	1.06635i
$800$	1713.26	+	1101.05i	0.0757161	+	0.0486598i
$801$		0			0
$802$	−1670.88	+	490.613i	−0.0735669	+	0.0216012i
$803$	−3722.82	−	8151.84i	−0.163606	−	0.358247i
$804$		0			0
$805$	16054.8	−	2233.64i	0.702930	−	0.0977958i
$806$	50091.1			2.18906
$807$		0			0
$808$	−18363.2	+	5391.93i	−0.799525	+	0.234762i
$809$	20754.7	−	23952.2i	0.901974	−	1.04093i	−0.0969831	−	0.995286i	$-0.530919\pi$
$809$	20754.7	−	23952.2i	0.901974	−	1.04093i	0.998958	−	0.0456480i	$-0.0145353\pi$
$810$		0			0
$811$	27422.2	+	31646.9i	1.18733	+	1.37025i	0.912665	+	0.408708i	$0.134021\pi$
$811$	27422.2	+	31646.9i	1.18733	+	1.37025i	0.274662	+	0.961541i	$0.411434\pi$
$812$	−5283.09	−	36744.7i	−0.228325	−	1.58804i
$813$		0			0
$814$	−28922.9	+	18587.6i	−1.24539	+	0.800363i
$815$	2860.22	−	19893.2i	0.122931	−	0.855006i
$816$		0			0
$817$	−4576.54	+	10021.2i	−0.195977	+	0.429129i
$818$	5344.39	−	37171.1i	0.228438	−	1.58882i
$819$		0			0
$820$	83342.9	+	24471.7i	3.54934	+	1.04218i
$821$	2155.30	+	14990.5i	0.0916207	+	0.637236i	0.982949	+	0.183878i	$0.0588651\pi$
$821$	2155.30	+	14990.5i	0.0916207	+	0.637236i	−0.891328	+	0.453358i	$0.850226\pi$
$822$		0			0
$823$	11031.5	+	7089.50i	0.467234	+	0.300273i	0.752993	−	0.658029i	$-0.228609\pi$
$823$	11031.5	+	7089.50i	0.467234	+	0.300273i	−0.285759	+	0.958301i	$0.592246\pi$
$824$	−49792.7	+	57463.8i	−2.10511	+	2.42942i
$825$		0			0
$826$	−4491.01	−	9833.95i	−0.189180	−	0.414246i
$827$	−16589.9			−0.697567			−0.348784	−	0.937203i	$-0.613405\pi$
$827$	−16589.9			−0.697567			−0.348784	+	0.937203i	$0.613405\pi$
$828$		0			0
$829$	31203.8			1.30730			0.653650	−	0.756797i	$-0.273237\pi$
$829$	31203.8			1.30730			0.653650	+	0.756797i	$0.273237\pi$
$830$	5475.73	+	11990.2i	0.228994	+	0.501428i
$831$		0			0
$832$	−62097.1	+	71663.9i	−2.58754	+	2.98618i
$833$	8205.13	+	5273.12i	0.341286	+	0.219331i
$834$		0			0
$835$	−159.587	−	1109.95i	−0.00661407	−	0.0460018i
$836$	−90570.9	−	26594.0i	−3.74696	−	1.10021i
$837$		0			0
$838$	714.596	−	4970.13i	0.0294574	−	0.204881i
$839$	−12561.8	+	27506.5i	−0.516902	+	1.13186i	0.453697	+	0.891156i	$0.350105\pi$
$839$	−12561.8	+	27506.5i	−0.516902	+	1.13186i	−0.970599	+	0.240702i	$0.922622\pi$
$840$		0			0
$841$	967.065	−	6726.08i	0.0396517	−	0.275784i
$842$	−37040.2	+	23804.3i	−1.51602	+	0.974287i
$843$		0			0
$844$	7239.89	+	50354.6i	0.295269	+	2.05364i
$845$	19080.9	+	22020.5i	0.776807	+	0.896483i
$846$		0			0
$847$	−3460.99	+	3994.20i	−0.140403	+	0.162033i
$848$	102396.	−	30066.2i	4.14657	−	1.21754i
$849$		0			0
$850$	−1150.86			−0.0464403
$851$	15385.7	+	7111.42i	0.619761	+	0.286459i
$852$		0			0
$853$	569.111	+	1246.18i	0.0228441	+	0.0500216i	0.920710	−	0.390247i	$-0.127610\pi$
$853$	569.111	+	1246.18i	0.0228441	+	0.0500216i	−0.897866	+	0.440269i	$0.854883\pi$
$854$	−8701.21	+	2554.91i	−0.348653	+	0.102374i
$855$		0			0
$856$	−29550.0	−	18990.6i	−1.17991	−	0.758279i
$857$	18504.4	+	21355.3i	0.737573	+	0.851204i	0.993302	−	0.115544i	$-0.0368611\pi$
$857$	18504.4	+	21355.3i	0.737573	+	0.851204i	−0.255729	+	0.966748i	$0.582316\pi$
$858$		0			0
$859$	3468.41	+	1018.42i	0.137765	+	0.0404516i	0.349888	−	0.936791i	$-0.386220\pi$
$859$	3468.41	+	1018.42i	0.137765	+	0.0404516i	−0.212123	+	0.977243i	$0.568038\pi$
$860$	−19792.7	+	12720.0i	−0.784795	+	0.504357i
$861$		0			0
$862$	29747.5	−	65137.9i	1.17541	−	2.57379i
$863$	4625.29	−	10128.0i	0.182441	−	0.399491i	−0.796209	−	0.605021i	$-0.793165\pi$
$863$	4625.29	−	10128.0i	0.182441	−	0.399491i	0.978651	+	0.205530i	$0.0658920\pi$
$864$		0			0
$865$	13182.2	−	8471.71i	0.518161	−	0.333002i
$866$	−19309.1	−	5669.67i	−0.757679	−	0.222475i
$867$		0			0
$868$	24507.7	+	28283.4i	0.958346	+	1.10599i
$869$	−48156.4	−	30948.2i	−1.87986	−	1.20811i
$870$		0			0
$871$	31763.2	−	9326.51i	1.23565	−	0.362821i
$872$	23961.4	+	52468.1i	0.930544	+	2.03761i
$873$		0			0
$874$	17828.2	+	61757.8i	0.689985	+	2.39015i
$875$	18900.8			0.730244
$876$		0			0
$877$	−43012.6	+	12629.6i	−1.65614	+	0.486286i	−0.970388	−	0.241551i	$-0.922344\pi$
$877$	−43012.6	+	12629.6i	−1.65614	+	0.486286i	−0.685750	+	0.727837i	$0.740526\pi$
$878$	10900.7	−	12580.1i	0.419000	−	0.483552i
$879$		0			0
$880$	−62490.5	−	72117.9i	−2.39381	−	2.76260i
$881$	6116.36	+	42540.2i	0.233900	+	1.62681i	0.680972	+	0.732309i	$0.261557\pi$
$881$	6116.36	+	42540.2i	0.233900	+	1.62681i	−0.447073	+	0.894498i	$0.647534\pi$
$882$		0			0
$883$	−18536.5	+	11912.7i	−0.706459	+	0.454013i	−0.843903	−	0.536496i	$-0.819748\pi$
$883$	−18536.5	+	11912.7i	−0.706459	+	0.454013i	0.137444	+	0.990510i	$0.456111\pi$
$884$	12275.7	−	85379.1i	0.467053	−	3.24843i
$885$		0			0
$886$	7065.89	−	15472.1i	0.267927	−	0.586678i
$887$	118.912	−	827.054i	0.00450134	−	0.0313075i	−0.987447	−	0.157951i	$-0.949511\pi$
$887$	118.912	−	827.054i	0.00450134	−	0.0313075i	0.991948	+	0.126643i	$0.0404204\pi$
$888$		0			0
$889$	−2194.37	−	644.325i	−0.0827860	−	0.0243082i
$890$	6369.31	+	44299.5i	0.239887	+	1.66845i
$891$		0			0
$892$	365.922	+	235.164i	0.0137354	+	0.00882721i
$893$	38235.5	−	44126.1i	1.43281	−	1.65355i
$894$		0			0
$895$	4927.01	+	10788.7i	0.184013	+	0.402933i
$896$	−37799.5			−1.40937
$897$		0			0
$898$	68959.4			2.56259
$899$	−7368.10	−	16133.9i	−0.273348	−	0.598549i
$900$		0			0
$901$	−19811.4	+	22863.6i	−0.732535	+	0.845390i
$902$	70723.4	+	45451.2i	2.61068	+	1.67778i
$903$		0			0
$904$	−2415.01	−	16796.8i	−0.0888518	−	0.617978i
$905$	42709.4	+	12540.6i	1.56874	+	0.460624i
$906$		0			0
$907$	5144.27	−	35779.2i	0.188327	−	1.30984i	−0.648011	−	0.761631i	$-0.724399\pi$
$907$	5144.27	−	35779.2i	0.188327	−	1.30984i	0.836338	−	0.548214i	$-0.184692\pi$
$908$	34084.3	−	74634.2i	1.24573	−	2.72778i
$909$		0			0
$910$	−7834.18	+	54487.9i	−0.285385	+	1.98490i
$911$	23491.6	−	15097.1i	0.854348	−	0.549056i	−0.0385799	−	0.999256i	$-0.512283\pi$
$911$	23491.6	−	15097.1i	0.854348	−	0.549056i	0.892928	+	0.450199i	$0.148647\pi$
$912$		0			0
$913$	1314.44	+	9142.13i	0.0476469	+	0.331391i
$914$	54359.5	+	62734.3i	1.96724	+	2.27031i
$915$		0			0
$916$	6590.73	−	7606.11i	0.237734	−	0.274359i
$917$	−23964.1	+	7036.48i	−0.862991	+	0.253397i
$918$		0			0
$919$	43808.1			1.57246			0.786232	−	0.617931i	$-0.212029\pi$
$919$	43808.1			1.57246			0.786232	+	0.617931i	$0.212029\pi$
$920$	−24301.0	+	81386.4i	−0.870847	+	2.91656i
$921$		0			0
$922$	−26879.2	−	58857.3i	−0.960109	−	2.10234i
$923$	−43598.7	+	12801.7i	−1.55479	+	0.456526i
$924$		0			0
$925$	467.751	+	300.606i	0.0166266	+	0.0106852i
$926$	−66636.1	−	76902.2i	−2.36479	−	2.72912i
$927$		0			0
$928$	71630.9	+	21032.7i	2.53383	+	0.744001i
$929$	−6160.13	+	3958.87i	−0.217553	+	0.139813i	−0.644879	−	0.764285i	$-0.723092\pi$
$929$	−6160.13	+	3958.87i	−0.217553	+	0.139813i	0.427325	+	0.904098i	$0.359456\pi$
$930$		0			0
$931$	7423.61	−	16255.4i	0.261331	−	0.572235i
$932$	−30357.7	+	66474.2i	−1.06695	+	2.33630i
$933$		0			0
$934$	−49096.4	+	31552.4i	−1.72000	+	1.10538i
$935$	25955.7	+	7621.27i	0.907851	+	0.266569i
$936$		0			0
$937$	31107.5	+	35899.9i	1.08456	+	1.25165i	0.965954	+	0.258712i	$0.0832981\pi$
$937$	31107.5	+	35899.9i	1.08456	+	1.25165i	0.118609	+	0.992941i	$0.462156\pi$
$938$	28739.5	+	18469.8i	1.00040	+	0.642921i
$939$		0			0
$940$	119641.	−	35129.9i	4.15135	−	1.21895i
$941$	6225.44	+	13631.8i	0.215668	+	0.472247i	0.986285	−	0.165051i	$-0.0527790\pi$
$941$	6225.44	+	13631.8i	0.215668	+	0.472247i	−0.770617	+	0.637299i	$0.780052\pi$
$942$		0			0
$943$	189.037	−	41445.7i	0.00652797	−	1.43124i
$944$	31376.6			1.08180
$945$		0			0
$946$	−21848.8	+	6415.39i	−0.750916	+	0.220489i
$947$	23563.5	−	27193.7i	0.808564	−	0.933132i	−0.190255	−	0.981735i	$-0.560931\pi$
$947$	23563.5	−	27193.7i	0.808564	−	0.933132i	0.998818	+	0.0486027i	$0.0154768\pi$
$948$		0			0
$949$	−9825.65	−	11339.4i	−0.336095	−	0.387874i
$950$	300.088	+	2087.16i	0.0102486	+	0.0712804i
$951$		0			0
$952$	46333.4	−	29776.7i	1.57739	−	1.01373i
$953$	4059.70	−	28235.8i	0.137992	−	0.959757i	−0.796719	−	0.604350i	$-0.793433\pi$
$953$	4059.70	−	28235.8i	0.137992	−	0.959757i	0.934711	−	0.355408i	$-0.115658\pi$
$954$		0			0
$955$	17713.2	−	38786.4i	0.600193	−	1.31424i
$956$	−10190.3	+	70875.1i	−0.344747	+	2.39777i
$957$		0			0
$958$	38693.8	+	11361.5i	1.30495	+	0.383167i
$959$	−652.820	−	4540.46i	−0.0219819	−	0.152888i
$960$		0			0
$961$	−10019.4	−	6439.11i	−0.336325	−	0.216143i
$962$	−37695.2	+	43502.6i	−1.26335	+	1.45798i
$963$		0			0
$964$	23413.8	+	51269.2i	0.782271	+	1.71293i
$965$	41405.7			1.38124
$966$		0			0
$967$	−35477.6			−1.17982			−0.589909	−	0.807470i	$-0.700836\pi$
$967$	−35477.6			−1.17982			−0.589909	+	0.807470i	$0.700836\pi$
$968$	−11504.4	−	25191.0i	−0.381988	−	0.836436i
$969$		0			0
$970$	−31393.4	+	36229.9i	−1.03916	+	1.19925i
$971$	−12797.6	−	8224.55i	−0.422962	−	0.271821i	0.311798	−	0.950148i	$-0.399069\pi$
$971$	−12797.6	−	8224.55i	−0.422962	−	0.271821i	−0.734760	+	0.678327i	$0.762705\pi$
$972$		0			0
$973$	−5098.85	−	35463.3i	−0.167998	−	1.16845i
$974$	−5489.20	−	1611.77i	−0.180580	−	0.0530232i
$975$		0			0
$976$	3745.69	−	26051.9i	0.122845	−	0.854406i
$977$	−16661.0	+	36482.5i	−0.545581	+	1.19466i	0.413234	+	0.910625i	$0.364399\pi$
$977$	−16661.0	+	36482.5i	−0.545581	+	1.19466i	−0.958815	+	0.284031i	$0.908328\pi$
$978$		0			0
$979$	−4462.96	+	31040.6i	−0.145696	+	1.01334i
$980$	32105.7	−	20633.1i	1.04651	−	0.672550i
$981$		0			0
$982$	−9313.23	−	64774.9i	−0.302645	−	2.10494i
$983$	−26745.5	−	30866.0i	−0.867802	−	1.00150i	−0.999947	−	0.0102668i	$-0.996732\pi$
$983$	−26745.5	−	30866.0i	−0.867802	−	1.00150i	0.132145	−	0.991230i	$-0.457814\pi$
$984$		0			0
$985$	−22321.7	+	25760.6i	−0.722060	+	0.833302i
$986$	−40478.8	+	11885.7i	−1.30741	+	0.383891i
$987$		0			0
$988$	−158041.			−5.08902
$989$	8450.60	+	7390.24i	0.271702	+	0.237610i
$990$		0			0
$991$	13347.2	+	29226.4i	0.427839	+	0.936838i	0.993672	+	0.112318i	$0.0358275\pi$
$991$	13347.2	+	29226.4i	0.427839	+	0.936838i	−0.565833	+	0.824520i	$0.691445\pi$
$992$	−72213.0	+	21203.6i	−2.31125	+	0.678645i
$993$		0			0
$994$	−39448.4	−	25351.9i	−1.25878	−	0.808968i
$995$	−19309.0	−	22283.8i	−0.615212	−	0.709993i
$996$		0			0
$997$	−7993.99	−	2347.25i	−0.253934	−	0.0745617i	0.152288	−	0.988336i	$-0.451336\pi$
$997$	−7993.99	−	2347.25i	−0.253934	−	0.0745617i	−0.406222	+	0.913774i	$0.633154\pi$
$998$	−32936.4	+	21166.9i	−1.04467	+	0.671370i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.4.i.b.73.1		60
3.2	odd	2		69.4.e.b.4.6	✓	60
23.6	even	11	inner	207.4.i.b.190.1		60
69.11	even	22		1587.4.a.v.1.29		30
69.29	odd	22		69.4.e.b.52.6	yes	60
69.35	odd	22		1587.4.a.w.1.29		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.4.e.b.4.6	✓	60	3.2	odd	2
69.4.e.b.52.6	yes	60	69.29	odd	22
207.4.i.b.73.1		60	1.1	even	1	trivial
207.4.i.b.190.1		60	23.6	even	11	inner
1587.4.a.v.1.29		30	69.11	even	22
1587.4.a.w.1.29		30	69.35	odd	22

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	207.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.23641 - 4.89704i) q^{2} +(-13.7407 + 15.8576i) q^{4} +(-9.26837 - 5.95642i) q^{5} +(-1.89824 - 13.2025i) q^{7} +(67.0611 + 19.6909i) q^{8} +O(q^{10})\)	\(q+(-2.23641 - 4.89704i) q^{2} +(-13.7407 + 15.8576i) q^{4} +(-9.26837 - 5.95642i) q^{5} +(-1.89824 - 13.2025i) q^{7} +(67.0611 + 19.6909i) q^{8} +(-8.44102 + 58.7086i) q^{10} +(-17.2646 + 37.8043i) q^{11} +(-9.90258 + 68.8739i) q^{13} +(-60.4082 + 38.8220i) q^{14} +(-29.6594 - 206.286i) q^{16} +(38.6890 + 44.6495i) q^{17} +(70.8862 - 81.8071i) q^{19} +(221.808 - 65.1286i) q^{20} +223.740 q^{22} +(-59.2111 - 93.0648i) q^{23} +(-1.50314 - 3.29142i) q^{25} +(359.425 - 105.537i) q^{26} +(235.443 + 151.310i) q^{28} +(-86.8617 - 100.244i) q^{29} +(128.303 + 37.6731i) q^{31} +(-473.485 + 304.290i) q^{32} +(132.126 - 289.316i) q^{34} +(-61.0463 + 133.673i) q^{35} +(-129.270 + 83.0768i) q^{37} +(-559.143 - 164.179i) q^{38} +(-504.259 - 581.946i) q^{40} +(316.096 + 203.143i) q^{41} +(-97.6527 + 28.6734i) q^{43} +(-362.256 - 793.231i) q^{44} +(-323.322 + 498.090i) q^{46} +539.392 q^{47} +(158.402 - 46.5112i) q^{49} +(-12.7566 + 14.7219i) q^{50} +(-956.104 - 1103.40i) q^{52} +(72.8750 + 506.856i) q^{53} +(385.193 - 247.549i) q^{55} +(132.672 - 922.754i) q^{56} +(-296.640 + 649.551i) q^{58} +(-21.4261 + 149.022i) q^{59} +(121.174 + 35.5800i) q^{61} +(-102.450 - 712.557i) q^{62} +(1146.44 + 736.772i) q^{64} +(502.023 - 579.365i) q^{65} +(-197.636 - 432.763i) q^{67} -1239.64 q^{68} +791.125 q^{70} +(271.279 + 594.017i) q^{71} +(-141.209 + 162.964i) q^{73} +(695.931 + 447.248i) q^{74} +(323.237 + 2248.17i) q^{76} +(531.885 + 156.176i) q^{77} +(-196.021 + 1363.35i) q^{79} +(-953.831 + 2088.60i) q^{80} +(287.879 - 2002.25i) q^{82} +(186.957 - 120.150i) q^{83} +(-92.6328 - 644.276i) q^{85} +(358.806 + 414.084i) q^{86} +(-1902.19 + 2195.24i) q^{88} +(724.001 - 212.586i) q^{89} +928.108 q^{91} +(2289.38 + 339.828i) q^{92} +(-1206.30 - 2641.43i) q^{94} +(-1144.28 + 335.990i) q^{95} +(679.941 + 436.972i) q^{97} +(-582.019 - 671.686i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 4 q^{2} - 28 q^{4} + 6 q^{5} - 4 q^{7} + 52 q^{8}+O(q^{10}) \) 60 * q - 4 * q^2 - 28 * q^4 + 6 * q^5 - 4 * q^7 + 52 * q^8	\( 60 q - 4 q^{2} - 28 q^{4} + 6 q^{5} - 4 q^{7} + 52 q^{8} - 78 q^{10} - 10 q^{11} + 50 q^{13} + 224 q^{14} + 260 q^{16} + 662 q^{17} - 4 q^{19} + 735 q^{20} + 622 q^{22} + 438 q^{23} - 754 q^{25} + 40 q^{26} + 672 q^{28} - 1302 q^{29} + 1528 q^{31} - 1588 q^{32} + 29 q^{34} - 950 q^{35} + 316 q^{37} - 3122 q^{38} - 1939 q^{40} + 1500 q^{41} - 1316 q^{43} + 2901 q^{44} - 1980 q^{46} + 1440 q^{47} - 2310 q^{49} - 195 q^{50} + 6189 q^{52} + 148 q^{53} - 606 q^{55} + 432 q^{56} - 2623 q^{58} - 5264 q^{59} + 1482 q^{61} + 2299 q^{62} - 6780 q^{64} + 1446 q^{65} + 388 q^{67} - 5604 q^{68} + 2984 q^{70} + 3316 q^{71} + 2072 q^{73} + 6556 q^{74} + 9841 q^{76} - 9338 q^{77} + 268 q^{79} - 7980 q^{80} + 7742 q^{82} + 3494 q^{83} - 3842 q^{85} + 4792 q^{86} - 7960 q^{88} + 2754 q^{89} - 5436 q^{91} + 17609 q^{92} - 10961 q^{94} + 2396 q^{95} - 5654 q^{97} - 14411 q^{98}+O(q^{100}) \) 60 * q - 4 * q^2 - 28 * q^4 + 6 * q^5 - 4 * q^7 + 52 * q^8 - 78 * q^10 - 10 * q^11 + 50 * q^13 + 224 * q^14 + 260 * q^16 + 662 * q^17 - 4 * q^19 + 735 * q^20 + 622 * q^22 + 438 * q^23 - 754 * q^25 + 40 * q^26 + 672 * q^28 - 1302 * q^29 + 1528 * q^31 - 1588 * q^32 + 29 * q^34 - 950 * q^35 + 316 * q^37 - 3122 * q^38 - 1939 * q^40 + 1500 * q^41 - 1316 * q^43 + 2901 * q^44 - 1980 * q^46 + 1440 * q^47 - 2310 * q^49 - 195 * q^50 + 6189 * q^52 + 148 * q^53 - 606 * q^55 + 432 * q^56 - 2623 * q^58 - 5264 * q^59 + 1482 * q^61 + 2299 * q^62 - 6780 * q^64 + 1446 * q^65 + 388 * q^67 - 5604 * q^68 + 2984 * q^70 + 3316 * q^71 + 2072 * q^73 + 6556 * q^74 + 9841 * q^76 - 9338 * q^77 + 268 * q^79 - 7980 * q^80 + 7742 * q^82 + 3494 * q^83 - 3842 * q^85 + 4792 * q^86 - 7960 * q^88 + 2754 * q^89 - 5436 * q^91 + 17609 * q^92 - 10961 * q^94 + 2396 * q^95 - 5654 * q^97 - 14411 * q^98

Introduction

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