# Properties

 Label 1170.2.e.b.469.2 Level $1170$ Weight $2$ Character 1170.469 Analytic conductor $9.342$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1170.e (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$9.34249703649$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ x^2 + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 390) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 469.2 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1170.469 Dual form 1170.2.e.b.469.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000i q^{2} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} -4.00000i q^{7} -1.00000i q^{8} +O(q^{10})$$ $$q+1.00000i q^{2} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} -4.00000i q^{7} -1.00000i q^{8} +(1.00000 - 2.00000i) q^{10} -2.00000 q^{11} +1.00000i q^{13} +4.00000 q^{14} +1.00000 q^{16} +4.00000i q^{17} -2.00000 q^{19} +(2.00000 + 1.00000i) q^{20} -2.00000i q^{22} +6.00000i q^{23} +(3.00000 + 4.00000i) q^{25} -1.00000 q^{26} +4.00000i q^{28} -2.00000 q^{29} -4.00000 q^{31} +1.00000i q^{32} -4.00000 q^{34} +(-4.00000 + 8.00000i) q^{35} +6.00000i q^{37} -2.00000i q^{38} +(-1.00000 + 2.00000i) q^{40} +6.00000 q^{41} +8.00000i q^{43} +2.00000 q^{44} -6.00000 q^{46} +8.00000i q^{47} -9.00000 q^{49} +(-4.00000 + 3.00000i) q^{50} -1.00000i q^{52} -10.0000i q^{53} +(4.00000 + 2.00000i) q^{55} -4.00000 q^{56} -2.00000i q^{58} -14.0000 q^{59} +10.0000 q^{61} -4.00000i q^{62} -1.00000 q^{64} +(1.00000 - 2.00000i) q^{65} -4.00000i q^{67} -4.00000i q^{68} +(-8.00000 - 4.00000i) q^{70} -8.00000 q^{71} +10.0000i q^{73} -6.00000 q^{74} +2.00000 q^{76} +8.00000i q^{77} +8.00000 q^{79} +(-2.00000 - 1.00000i) q^{80} +6.00000i q^{82} -12.0000i q^{83} +(4.00000 - 8.00000i) q^{85} -8.00000 q^{86} +2.00000i q^{88} -18.0000 q^{89} +4.00000 q^{91} -6.00000i q^{92} -8.00000 q^{94} +(4.00000 + 2.00000i) q^{95} -6.00000i q^{97} -9.00000i q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 2 q^{4} - 4 q^{5}+O(q^{10})$$ 2 * q - 2 * q^4 - 4 * q^5 $$2 q - 2 q^{4} - 4 q^{5} + 2 q^{10} - 4 q^{11} + 8 q^{14} + 2 q^{16} - 4 q^{19} + 4 q^{20} + 6 q^{25} - 2 q^{26} - 4 q^{29} - 8 q^{31} - 8 q^{34} - 8 q^{35} - 2 q^{40} + 12 q^{41} + 4 q^{44} - 12 q^{46} - 18 q^{49} - 8 q^{50} + 8 q^{55} - 8 q^{56} - 28 q^{59} + 20 q^{61} - 2 q^{64} + 2 q^{65} - 16 q^{70} - 16 q^{71} - 12 q^{74} + 4 q^{76} + 16 q^{79} - 4 q^{80} + 8 q^{85} - 16 q^{86} - 36 q^{89} + 8 q^{91} - 16 q^{94} + 8 q^{95}+O(q^{100})$$ 2 * q - 2 * q^4 - 4 * q^5 + 2 * q^10 - 4 * q^11 + 8 * q^14 + 2 * q^16 - 4 * q^19 + 4 * q^20 + 6 * q^25 - 2 * q^26 - 4 * q^29 - 8 * q^31 - 8 * q^34 - 8 * q^35 - 2 * q^40 + 12 * q^41 + 4 * q^44 - 12 * q^46 - 18 * q^49 - 8 * q^50 + 8 * q^55 - 8 * q^56 - 28 * q^59 + 20 * q^61 - 2 * q^64 + 2 * q^65 - 16 * q^70 - 16 * q^71 - 12 * q^74 + 4 * q^76 + 16 * q^79 - 4 * q^80 + 8 * q^85 - 16 * q^86 - 36 * q^89 + 8 * q^91 - 16 * q^94 + 8 * q^95

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$$.

 $$n$$ $$911$$ $$937$$ $$1081$$ $$\chi(n)$$ $$1$$ $$-1$$ $$1$$

## 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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000i 0.707107i
$$3$$ 0 0
$$4$$ −1.00000 −0.500000
$$5$$ −2.00000 1.00000i −0.894427 0.447214i
$$6$$ 0 0
$$7$$ 4.00000i 1.51186i −0.654654 0.755929i $$-0.727186\pi$$
0.654654 0.755929i $$-0.272814\pi$$
$$8$$ 1.00000i 0.353553i
$$9$$ 0 0
$$10$$ 1.00000 2.00000i 0.316228 0.632456i
$$11$$ −2.00000 −0.603023 −0.301511 0.953463i $$-0.597491\pi$$
−0.301511 + 0.953463i $$0.597491\pi$$
$$12$$ 0 0
$$13$$ 1.00000i 0.277350i
$$14$$ 4.00000 1.06904
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 4.00000i 0.970143i 0.874475 + 0.485071i $$0.161206\pi$$
−0.874475 + 0.485071i $$0.838794\pi$$
$$18$$ 0 0
$$19$$ −2.00000 −0.458831 −0.229416 0.973329i $$-0.573682\pi$$
−0.229416 + 0.973329i $$0.573682\pi$$
$$20$$ 2.00000 + 1.00000i 0.447214 + 0.223607i
$$21$$ 0 0
$$22$$ 2.00000i 0.426401i
$$23$$ 6.00000i 1.25109i 0.780189 + 0.625543i $$0.215123\pi$$
−0.780189 + 0.625543i $$0.784877\pi$$
$$24$$ 0 0
$$25$$ 3.00000 + 4.00000i 0.600000 + 0.800000i
$$26$$ −1.00000 −0.196116
$$27$$ 0 0
$$28$$ 4.00000i 0.755929i
$$29$$ −2.00000 −0.371391 −0.185695 0.982607i $$-0.559454\pi$$
−0.185695 + 0.982607i $$0.559454\pi$$
$$30$$ 0 0
$$31$$ −4.00000 −0.718421 −0.359211 0.933257i $$-0.616954\pi$$
−0.359211 + 0.933257i $$0.616954\pi$$
$$32$$ 1.00000i 0.176777i
$$33$$ 0 0
$$34$$ −4.00000 −0.685994
$$35$$ −4.00000 + 8.00000i −0.676123 + 1.35225i
$$36$$ 0 0
$$37$$ 6.00000i 0.986394i 0.869918 + 0.493197i $$0.164172\pi$$
−0.869918 + 0.493197i $$0.835828\pi$$
$$38$$ 2.00000i 0.324443i
$$39$$ 0 0
$$40$$ −1.00000 + 2.00000i −0.158114 + 0.316228i
$$41$$ 6.00000 0.937043 0.468521 0.883452i $$-0.344787\pi$$
0.468521 + 0.883452i $$0.344787\pi$$
$$42$$ 0 0
$$43$$ 8.00000i 1.21999i 0.792406 + 0.609994i $$0.208828\pi$$
−0.792406 + 0.609994i $$0.791172\pi$$
$$44$$ 2.00000 0.301511
$$45$$ 0 0
$$46$$ −6.00000 −0.884652
$$47$$ 8.00000i 1.16692i 0.812142 + 0.583460i $$0.198301\pi$$
−0.812142 + 0.583460i $$0.801699\pi$$
$$48$$ 0 0
$$49$$ −9.00000 −1.28571
$$50$$ −4.00000 + 3.00000i −0.565685 + 0.424264i
$$51$$ 0 0
$$52$$ 1.00000i 0.138675i
$$53$$ 10.0000i 1.37361i −0.726844 0.686803i $$-0.759014\pi$$
0.726844 0.686803i $$-0.240986\pi$$
$$54$$ 0 0
$$55$$ 4.00000 + 2.00000i 0.539360 + 0.269680i
$$56$$ −4.00000 −0.534522
$$57$$ 0 0
$$58$$ 2.00000i 0.262613i
$$59$$ −14.0000 −1.82264 −0.911322 0.411693i $$-0.864937\pi$$
−0.911322 + 0.411693i $$0.864937\pi$$
$$60$$ 0 0
$$61$$ 10.0000 1.28037 0.640184 0.768221i $$-0.278858\pi$$
0.640184 + 0.768221i $$0.278858\pi$$
$$62$$ 4.00000i 0.508001i
$$63$$ 0 0
$$64$$ −1.00000 −0.125000
$$65$$ 1.00000 2.00000i 0.124035 0.248069i
$$66$$ 0 0
$$67$$ 4.00000i 0.488678i −0.969690 0.244339i $$-0.921429\pi$$
0.969690 0.244339i $$-0.0785709\pi$$
$$68$$ 4.00000i 0.485071i
$$69$$ 0 0
$$70$$ −8.00000 4.00000i −0.956183 0.478091i
$$71$$ −8.00000 −0.949425 −0.474713 0.880141i $$-0.657448\pi$$
−0.474713 + 0.880141i $$0.657448\pi$$
$$72$$ 0 0
$$73$$ 10.0000i 1.17041i 0.810885 + 0.585206i $$0.198986\pi$$
−0.810885 + 0.585206i $$0.801014\pi$$
$$74$$ −6.00000 −0.697486
$$75$$ 0 0
$$76$$ 2.00000 0.229416
$$77$$ 8.00000i 0.911685i
$$78$$ 0 0
$$79$$ 8.00000 0.900070 0.450035 0.893011i $$-0.351411\pi$$
0.450035 + 0.893011i $$0.351411\pi$$
$$80$$ −2.00000 1.00000i −0.223607 0.111803i
$$81$$ 0 0
$$82$$ 6.00000i 0.662589i
$$83$$ 12.0000i 1.31717i −0.752506 0.658586i $$-0.771155\pi$$
0.752506 0.658586i $$-0.228845\pi$$
$$84$$ 0 0
$$85$$ 4.00000 8.00000i 0.433861 0.867722i
$$86$$ −8.00000 −0.862662
$$87$$ 0 0
$$88$$ 2.00000i 0.213201i
$$89$$ −18.0000 −1.90800 −0.953998 0.299813i $$-0.903076\pi$$
−0.953998 + 0.299813i $$0.903076\pi$$
$$90$$ 0 0
$$91$$ 4.00000 0.419314
$$92$$ 6.00000i 0.625543i
$$93$$ 0 0
$$94$$ −8.00000 −0.825137
$$95$$ 4.00000 + 2.00000i 0.410391 + 0.205196i
$$96$$ 0 0
$$97$$ 6.00000i 0.609208i −0.952479 0.304604i $$-0.901476\pi$$
0.952479 0.304604i $$-0.0985241\pi$$
$$98$$ 9.00000i 0.909137i
$$99$$ 0 0
$$100$$ −3.00000 4.00000i −0.300000 0.400000i
$$101$$ 14.0000 1.39305 0.696526 0.717532i $$-0.254728\pi$$
0.696526 + 0.717532i $$0.254728\pi$$
$$102$$ 0 0
$$103$$ 6.00000i 0.591198i 0.955312 + 0.295599i $$0.0955191\pi$$
−0.955312 + 0.295599i $$0.904481\pi$$
$$104$$ 1.00000 0.0980581
$$105$$ 0 0
$$106$$ 10.0000 0.971286
$$107$$ 8.00000i 0.773389i −0.922208 0.386695i $$-0.873617\pi$$
0.922208 0.386695i $$-0.126383\pi$$
$$108$$ 0 0
$$109$$ −12.0000 −1.14939 −0.574696 0.818367i $$-0.694880\pi$$
−0.574696 + 0.818367i $$0.694880\pi$$
$$110$$ −2.00000 + 4.00000i −0.190693 + 0.381385i
$$111$$ 0 0
$$112$$ 4.00000i 0.377964i
$$113$$ 12.0000i 1.12887i 0.825479 + 0.564433i $$0.190905\pi$$
−0.825479 + 0.564433i $$0.809095\pi$$
$$114$$ 0 0
$$115$$ 6.00000 12.0000i 0.559503 1.11901i
$$116$$ 2.00000 0.185695
$$117$$ 0 0
$$118$$ 14.0000i 1.28880i
$$119$$ 16.0000 1.46672
$$120$$ 0 0
$$121$$ −7.00000 −0.636364
$$122$$ 10.0000i 0.905357i
$$123$$ 0 0
$$124$$ 4.00000 0.359211
$$125$$ −2.00000 11.0000i −0.178885 0.983870i
$$126$$ 0 0
$$127$$ 18.0000i 1.59724i 0.601834 + 0.798621i $$0.294437\pi$$
−0.601834 + 0.798621i $$0.705563\pi$$
$$128$$ 1.00000i 0.0883883i
$$129$$ 0 0
$$130$$ 2.00000 + 1.00000i 0.175412 + 0.0877058i
$$131$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$132$$ 0 0
$$133$$ 8.00000i 0.693688i
$$134$$ 4.00000 0.345547
$$135$$ 0 0
$$136$$ 4.00000 0.342997
$$137$$ 2.00000i 0.170872i 0.996344 + 0.0854358i $$0.0272282\pi$$
−0.996344 + 0.0854358i $$0.972772\pi$$
$$138$$ 0 0
$$139$$ −16.0000 −1.35710 −0.678551 0.734553i $$-0.737392\pi$$
−0.678551 + 0.734553i $$0.737392\pi$$
$$140$$ 4.00000 8.00000i 0.338062 0.676123i
$$141$$ 0 0
$$142$$ 8.00000i 0.671345i
$$143$$ 2.00000i 0.167248i
$$144$$ 0 0
$$145$$ 4.00000 + 2.00000i 0.332182 + 0.166091i
$$146$$ −10.0000 −0.827606
$$147$$ 0 0
$$148$$ 6.00000i 0.493197i
$$149$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$150$$ 0 0
$$151$$ 8.00000 0.651031 0.325515 0.945537i $$-0.394462\pi$$
0.325515 + 0.945537i $$0.394462\pi$$
$$152$$ 2.00000i 0.162221i
$$153$$ 0 0
$$154$$ −8.00000 −0.644658
$$155$$ 8.00000 + 4.00000i 0.642575 + 0.321288i
$$156$$ 0 0
$$157$$ 10.0000i 0.798087i 0.916932 + 0.399043i $$0.130658\pi$$
−0.916932 + 0.399043i $$0.869342\pi$$
$$158$$ 8.00000i 0.636446i
$$159$$ 0 0
$$160$$ 1.00000 2.00000i 0.0790569 0.158114i
$$161$$ 24.0000 1.89146
$$162$$ 0 0
$$163$$ 4.00000i 0.313304i −0.987654 0.156652i $$-0.949930\pi$$
0.987654 0.156652i $$-0.0500701\pi$$
$$164$$ −6.00000 −0.468521
$$165$$ 0 0
$$166$$ 12.0000 0.931381
$$167$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$168$$ 0 0
$$169$$ −1.00000 −0.0769231
$$170$$ 8.00000 + 4.00000i 0.613572 + 0.306786i
$$171$$ 0 0
$$172$$ 8.00000i 0.609994i
$$173$$ 10.0000i 0.760286i −0.924928 0.380143i $$-0.875875\pi$$
0.924928 0.380143i $$-0.124125\pi$$
$$174$$ 0 0
$$175$$ 16.0000 12.0000i 1.20949 0.907115i
$$176$$ −2.00000 −0.150756
$$177$$ 0 0
$$178$$ 18.0000i 1.34916i
$$179$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$180$$ 0 0
$$181$$ 6.00000 0.445976 0.222988 0.974821i $$-0.428419\pi$$
0.222988 + 0.974821i $$0.428419\pi$$
$$182$$ 4.00000i 0.296500i
$$183$$ 0 0
$$184$$ 6.00000 0.442326
$$185$$ 6.00000 12.0000i 0.441129 0.882258i
$$186$$ 0 0
$$187$$ 8.00000i 0.585018i
$$188$$ 8.00000i 0.583460i
$$189$$ 0 0
$$190$$ −2.00000 + 4.00000i −0.145095 + 0.290191i
$$191$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$192$$ 0 0
$$193$$ 6.00000i 0.431889i 0.976406 + 0.215945i $$0.0692831\pi$$
−0.976406 + 0.215945i $$0.930717\pi$$
$$194$$ 6.00000 0.430775
$$195$$ 0 0
$$196$$ 9.00000 0.642857
$$197$$ 26.0000i 1.85242i 0.377004 + 0.926212i $$0.376954\pi$$
−0.377004 + 0.926212i $$0.623046\pi$$
$$198$$ 0 0
$$199$$ −24.0000 −1.70131 −0.850657 0.525720i $$-0.823796\pi$$
−0.850657 + 0.525720i $$0.823796\pi$$
$$200$$ 4.00000 3.00000i 0.282843 0.212132i
$$201$$ 0 0
$$202$$ 14.0000i 0.985037i
$$203$$ 8.00000i 0.561490i
$$204$$ 0 0
$$205$$ −12.0000 6.00000i −0.838116 0.419058i
$$206$$ −6.00000 −0.418040
$$207$$ 0 0
$$208$$ 1.00000i 0.0693375i
$$209$$ 4.00000 0.276686
$$210$$ 0 0
$$211$$ −28.0000 −1.92760 −0.963800 0.266627i $$-0.914091\pi$$
−0.963800 + 0.266627i $$0.914091\pi$$
$$212$$ 10.0000i 0.686803i
$$213$$ 0 0
$$214$$ 8.00000 0.546869
$$215$$ 8.00000 16.0000i 0.545595 1.09119i
$$216$$ 0 0
$$217$$ 16.0000i 1.08615i
$$218$$ 12.0000i 0.812743i
$$219$$ 0 0
$$220$$ −4.00000 2.00000i −0.269680 0.134840i
$$221$$ −4.00000 −0.269069
$$222$$ 0 0
$$223$$ 16.0000i 1.07144i −0.844396 0.535720i $$-0.820040\pi$$
0.844396 0.535720i $$-0.179960\pi$$
$$224$$ 4.00000 0.267261
$$225$$ 0 0
$$226$$ −12.0000 −0.798228
$$227$$ 12.0000i 0.796468i 0.917284 + 0.398234i $$0.130377\pi$$
−0.917284 + 0.398234i $$0.869623\pi$$
$$228$$ 0 0
$$229$$ 16.0000 1.05731 0.528655 0.848837i $$-0.322697\pi$$
0.528655 + 0.848837i $$0.322697\pi$$
$$230$$ 12.0000 + 6.00000i 0.791257 + 0.395628i
$$231$$ 0 0
$$232$$ 2.00000i 0.131306i
$$233$$ 4.00000i 0.262049i 0.991379 + 0.131024i $$0.0418266\pi$$
−0.991379 + 0.131024i $$0.958173\pi$$
$$234$$ 0 0
$$235$$ 8.00000 16.0000i 0.521862 1.04372i
$$236$$ 14.0000 0.911322
$$237$$ 0 0
$$238$$ 16.0000i 1.03713i
$$239$$ −12.0000 −0.776215 −0.388108 0.921614i $$-0.626871\pi$$
−0.388108 + 0.921614i $$0.626871\pi$$
$$240$$ 0 0
$$241$$ −30.0000 −1.93247 −0.966235 0.257663i $$-0.917048\pi$$
−0.966235 + 0.257663i $$0.917048\pi$$
$$242$$ 7.00000i 0.449977i
$$243$$ 0 0
$$244$$ −10.0000 −0.640184
$$245$$ 18.0000 + 9.00000i 1.14998 + 0.574989i
$$246$$ 0 0
$$247$$ 2.00000i 0.127257i
$$248$$ 4.00000i 0.254000i
$$249$$ 0 0
$$250$$ 11.0000 2.00000i 0.695701 0.126491i
$$251$$ 12.0000 0.757433 0.378717 0.925513i $$-0.376365\pi$$
0.378717 + 0.925513i $$0.376365\pi$$
$$252$$ 0 0
$$253$$ 12.0000i 0.754434i
$$254$$ −18.0000 −1.12942
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 12.0000i 0.748539i −0.927320 0.374270i $$-0.877893\pi$$
0.927320 0.374270i $$-0.122107\pi$$
$$258$$ 0 0
$$259$$ 24.0000 1.49129
$$260$$ −1.00000 + 2.00000i −0.0620174 + 0.124035i
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 10.0000i 0.616626i 0.951285 + 0.308313i $$0.0997645\pi$$
−0.951285 + 0.308313i $$0.900236\pi$$
$$264$$ 0 0
$$265$$ −10.0000 + 20.0000i −0.614295 + 1.22859i
$$266$$ −8.00000 −0.490511
$$267$$ 0 0
$$268$$ 4.00000i 0.244339i
$$269$$ −14.0000 −0.853595 −0.426798 0.904347i $$-0.640358\pi$$
−0.426798 + 0.904347i $$0.640358\pi$$
$$270$$ 0 0
$$271$$ 16.0000 0.971931 0.485965 0.873978i $$-0.338468\pi$$
0.485965 + 0.873978i $$0.338468\pi$$
$$272$$ 4.00000i 0.242536i
$$273$$ 0 0
$$274$$ −2.00000 −0.120824
$$275$$ −6.00000 8.00000i −0.361814 0.482418i
$$276$$ 0 0
$$277$$ 2.00000i 0.120168i −0.998193 0.0600842i $$-0.980863\pi$$
0.998193 0.0600842i $$-0.0191369\pi$$
$$278$$ 16.0000i 0.959616i
$$279$$ 0 0
$$280$$ 8.00000 + 4.00000i 0.478091 + 0.239046i
$$281$$ 18.0000 1.07379 0.536895 0.843649i $$-0.319597\pi$$
0.536895 + 0.843649i $$0.319597\pi$$
$$282$$ 0 0
$$283$$ 4.00000i 0.237775i −0.992908 0.118888i $$-0.962067\pi$$
0.992908 0.118888i $$-0.0379328\pi$$
$$284$$ 8.00000 0.474713
$$285$$ 0 0
$$286$$ 2.00000 0.118262
$$287$$ 24.0000i 1.41668i
$$288$$ 0 0
$$289$$ 1.00000 0.0588235
$$290$$ −2.00000 + 4.00000i −0.117444 + 0.234888i
$$291$$ 0 0
$$292$$ 10.0000i 0.585206i
$$293$$ 14.0000i 0.817889i 0.912559 + 0.408944i $$0.134103\pi$$
−0.912559 + 0.408944i $$0.865897\pi$$
$$294$$ 0 0
$$295$$ 28.0000 + 14.0000i 1.63022 + 0.815112i
$$296$$ 6.00000 0.348743
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −6.00000 −0.346989
$$300$$ 0 0
$$301$$ 32.0000 1.84445
$$302$$ 8.00000i 0.460348i
$$303$$ 0 0
$$304$$ −2.00000 −0.114708
$$305$$ −20.0000 10.0000i −1.14520 0.572598i
$$306$$ 0 0
$$307$$ 28.0000i 1.59804i −0.601302 0.799022i $$-0.705351\pi$$
0.601302 0.799022i $$-0.294649\pi$$
$$308$$ 8.00000i 0.455842i
$$309$$ 0 0
$$310$$ −4.00000 + 8.00000i −0.227185 + 0.454369i
$$311$$ −8.00000 −0.453638 −0.226819 0.973937i $$-0.572833\pi$$
−0.226819 + 0.973937i $$0.572833\pi$$
$$312$$ 0 0
$$313$$ 8.00000i 0.452187i 0.974106 + 0.226093i $$0.0725954\pi$$
−0.974106 + 0.226093i $$0.927405\pi$$
$$314$$ −10.0000 −0.564333
$$315$$ 0 0
$$316$$ −8.00000 −0.450035
$$317$$ 30.0000i 1.68497i −0.538721 0.842484i $$-0.681092\pi$$
0.538721 0.842484i $$-0.318908\pi$$
$$318$$ 0 0
$$319$$ 4.00000 0.223957
$$320$$ 2.00000 + 1.00000i 0.111803 + 0.0559017i
$$321$$ 0 0
$$322$$ 24.0000i 1.33747i
$$323$$ 8.00000i 0.445132i
$$324$$ 0 0
$$325$$ −4.00000 + 3.00000i −0.221880 + 0.166410i
$$326$$ 4.00000 0.221540
$$327$$ 0 0
$$328$$ 6.00000i 0.331295i
$$329$$ 32.0000 1.76422
$$330$$ 0 0
$$331$$ 18.0000 0.989369 0.494685 0.869072i $$-0.335284\pi$$
0.494685 + 0.869072i $$0.335284\pi$$
$$332$$ 12.0000i 0.658586i
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −4.00000 + 8.00000i −0.218543 + 0.437087i
$$336$$ 0 0
$$337$$ 32.0000i 1.74315i 0.490261 + 0.871576i $$0.336901\pi$$
−0.490261 + 0.871576i $$0.663099\pi$$
$$338$$ 1.00000i 0.0543928i
$$339$$ 0 0
$$340$$ −4.00000 + 8.00000i −0.216930 + 0.433861i
$$341$$ 8.00000 0.433224
$$342$$ 0 0
$$343$$ 8.00000i 0.431959i
$$344$$ 8.00000 0.431331
$$345$$ 0 0
$$346$$ 10.0000 0.537603
$$347$$ 24.0000i 1.28839i −0.764862 0.644194i $$-0.777193\pi$$
0.764862 0.644194i $$-0.222807\pi$$
$$348$$ 0 0
$$349$$ 28.0000 1.49881 0.749403 0.662114i $$-0.230341\pi$$
0.749403 + 0.662114i $$0.230341\pi$$
$$350$$ 12.0000 + 16.0000i 0.641427 + 0.855236i
$$351$$ 0 0
$$352$$ 2.00000i 0.106600i
$$353$$ 26.0000i 1.38384i 0.721974 + 0.691920i $$0.243235\pi$$
−0.721974 + 0.691920i $$0.756765\pi$$
$$354$$ 0 0
$$355$$ 16.0000 + 8.00000i 0.849192 + 0.424596i
$$356$$ 18.0000 0.953998
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 20.0000 1.05556 0.527780 0.849381i $$-0.323025\pi$$
0.527780 + 0.849381i $$0.323025\pi$$
$$360$$ 0 0
$$361$$ −15.0000 −0.789474
$$362$$ 6.00000i 0.315353i
$$363$$ 0 0
$$364$$ −4.00000 −0.209657
$$365$$ 10.0000 20.0000i 0.523424 1.04685i
$$366$$ 0 0
$$367$$ 22.0000i 1.14839i −0.818718 0.574195i $$-0.805315\pi$$
0.818718 0.574195i $$-0.194685\pi$$
$$368$$ 6.00000i 0.312772i
$$369$$ 0 0
$$370$$ 12.0000 + 6.00000i 0.623850 + 0.311925i
$$371$$ −40.0000 −2.07670
$$372$$ 0 0
$$373$$ 2.00000i 0.103556i −0.998659 0.0517780i $$-0.983511\pi$$
0.998659 0.0517780i $$-0.0164888\pi$$
$$374$$ 8.00000 0.413670
$$375$$ 0 0
$$376$$ 8.00000 0.412568
$$377$$ 2.00000i 0.103005i
$$378$$ 0 0
$$379$$ −26.0000 −1.33553 −0.667765 0.744372i $$-0.732749\pi$$
−0.667765 + 0.744372i $$0.732749\pi$$
$$380$$ −4.00000 2.00000i −0.205196 0.102598i
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 12.0000i 0.613171i 0.951843 + 0.306586i $$0.0991866\pi$$
−0.951843 + 0.306586i $$0.900813\pi$$
$$384$$ 0 0
$$385$$ 8.00000 16.0000i 0.407718 0.815436i
$$386$$ −6.00000 −0.305392
$$387$$ 0 0
$$388$$ 6.00000i 0.304604i
$$389$$ −26.0000 −1.31825 −0.659126 0.752032i $$-0.729074\pi$$
−0.659126 + 0.752032i $$0.729074\pi$$
$$390$$ 0 0
$$391$$ −24.0000 −1.21373
$$392$$ 9.00000i 0.454569i
$$393$$ 0 0
$$394$$ −26.0000 −1.30986
$$395$$ −16.0000 8.00000i −0.805047 0.402524i
$$396$$ 0 0
$$397$$ 6.00000i 0.301131i −0.988600 0.150566i $$-0.951890\pi$$
0.988600 0.150566i $$-0.0481095\pi$$
$$398$$ 24.0000i 1.20301i
$$399$$ 0 0
$$400$$ 3.00000 + 4.00000i 0.150000 + 0.200000i
$$401$$ 18.0000 0.898877 0.449439 0.893311i $$-0.351624\pi$$
0.449439 + 0.893311i $$0.351624\pi$$
$$402$$ 0 0
$$403$$ 4.00000i 0.199254i
$$404$$ −14.0000 −0.696526
$$405$$ 0 0
$$406$$ −8.00000 −0.397033
$$407$$ 12.0000i 0.594818i
$$408$$ 0 0
$$409$$ 2.00000 0.0988936 0.0494468 0.998777i $$-0.484254\pi$$
0.0494468 + 0.998777i $$0.484254\pi$$
$$410$$ 6.00000 12.0000i 0.296319 0.592638i
$$411$$ 0 0
$$412$$ 6.00000i 0.295599i
$$413$$ 56.0000i 2.75558i
$$414$$ 0 0
$$415$$ −12.0000 + 24.0000i −0.589057 + 1.17811i
$$416$$ −1.00000 −0.0490290
$$417$$ 0 0
$$418$$ 4.00000i 0.195646i
$$419$$ 16.0000 0.781651 0.390826 0.920465i $$-0.372190\pi$$
0.390826 + 0.920465i $$0.372190\pi$$
$$420$$ 0 0
$$421$$ 28.0000 1.36464 0.682318 0.731055i $$-0.260972\pi$$
0.682318 + 0.731055i $$0.260972\pi$$
$$422$$ 28.0000i 1.36302i
$$423$$ 0 0
$$424$$ −10.0000 −0.485643
$$425$$ −16.0000 + 12.0000i −0.776114 + 0.582086i
$$426$$ 0 0
$$427$$ 40.0000i 1.93574i
$$428$$ 8.00000i 0.386695i
$$429$$ 0 0
$$430$$ 16.0000 + 8.00000i 0.771589 + 0.385794i
$$431$$ 8.00000 0.385346 0.192673 0.981263i $$-0.438284\pi$$
0.192673 + 0.981263i $$0.438284\pi$$
$$432$$ 0 0
$$433$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$434$$ −16.0000 −0.768025
$$435$$ 0 0
$$436$$ 12.0000 0.574696
$$437$$ 12.0000i 0.574038i
$$438$$ 0 0
$$439$$ −32.0000 −1.52728 −0.763638 0.645644i $$-0.776589\pi$$
−0.763638 + 0.645644i $$0.776589\pi$$
$$440$$ 2.00000 4.00000i 0.0953463 0.190693i
$$441$$ 0 0
$$442$$ 4.00000i 0.190261i
$$443$$ 8.00000i 0.380091i −0.981775 0.190046i $$-0.939136\pi$$
0.981775 0.190046i $$-0.0608636\pi$$
$$444$$ 0 0
$$445$$ 36.0000 + 18.0000i 1.70656 + 0.853282i
$$446$$ 16.0000 0.757622
$$447$$ 0 0
$$448$$ 4.00000i 0.188982i
$$449$$ 6.00000 0.283158 0.141579 0.989927i $$-0.454782\pi$$
0.141579 + 0.989927i $$0.454782\pi$$
$$450$$ 0 0
$$451$$ −12.0000 −0.565058
$$452$$ 12.0000i 0.564433i
$$453$$ 0 0
$$454$$ −12.0000 −0.563188
$$455$$ −8.00000 4.00000i −0.375046 0.187523i
$$456$$ 0 0
$$457$$ 26.0000i 1.21623i 0.793849 + 0.608114i $$0.208074\pi$$
−0.793849 + 0.608114i $$0.791926\pi$$
$$458$$ 16.0000i 0.747631i
$$459$$ 0 0
$$460$$ −6.00000 + 12.0000i −0.279751 + 0.559503i
$$461$$ 4.00000 0.186299 0.0931493 0.995652i $$-0.470307\pi$$
0.0931493 + 0.995652i $$0.470307\pi$$
$$462$$ 0 0
$$463$$ 36.0000i 1.67306i −0.547920 0.836531i $$-0.684580\pi$$
0.547920 0.836531i $$-0.315420\pi$$
$$464$$ −2.00000 −0.0928477
$$465$$ 0 0
$$466$$ −4.00000 −0.185296
$$467$$ 16.0000i 0.740392i −0.928954 0.370196i $$-0.879291\pi$$
0.928954 0.370196i $$-0.120709\pi$$
$$468$$ 0 0
$$469$$ −16.0000 −0.738811
$$470$$ 16.0000 + 8.00000i 0.738025 + 0.369012i
$$471$$ 0 0
$$472$$ 14.0000i 0.644402i
$$473$$ 16.0000i 0.735681i
$$474$$ 0 0
$$475$$ −6.00000 8.00000i −0.275299 0.367065i
$$476$$ −16.0000 −0.733359
$$477$$ 0 0
$$478$$ 12.0000i 0.548867i
$$479$$ −12.0000 −0.548294 −0.274147 0.961688i $$-0.588395\pi$$
−0.274147 + 0.961688i $$0.588395\pi$$
$$480$$ 0 0
$$481$$ −6.00000 −0.273576
$$482$$ 30.0000i 1.36646i
$$483$$ 0 0
$$484$$ 7.00000 0.318182
$$485$$ −6.00000 + 12.0000i −0.272446 + 0.544892i
$$486$$ 0 0
$$487$$ 40.0000i 1.81257i 0.422664 + 0.906287i $$0.361095\pi$$
−0.422664 + 0.906287i $$0.638905\pi$$
$$488$$ 10.0000i 0.452679i
$$489$$ 0 0
$$490$$ −9.00000 + 18.0000i −0.406579 + 0.813157i
$$491$$ −8.00000 −0.361035 −0.180517 0.983572i $$-0.557777\pi$$
−0.180517 + 0.983572i $$0.557777\pi$$
$$492$$ 0 0
$$493$$ 8.00000i 0.360302i
$$494$$ 2.00000 0.0899843
$$495$$ 0 0
$$496$$ −4.00000 −0.179605
$$497$$ 32.0000i 1.43540i
$$498$$ 0 0
$$499$$ −30.0000 −1.34298 −0.671492 0.741012i $$-0.734346\pi$$
−0.671492 + 0.741012i $$0.734346\pi$$
$$500$$ 2.00000 + 11.0000i 0.0894427 + 0.491935i
$$501$$ 0 0
$$502$$ 12.0000i 0.535586i
$$503$$ 18.0000i 0.802580i −0.915951 0.401290i $$-0.868562\pi$$
0.915951 0.401290i $$-0.131438\pi$$
$$504$$ 0 0
$$505$$ −28.0000 14.0000i −1.24598 0.622992i
$$506$$ 12.0000 0.533465
$$507$$ 0 0
$$508$$ 18.0000i 0.798621i
$$509$$ −16.0000 −0.709188 −0.354594 0.935020i $$-0.615381\pi$$
−0.354594 + 0.935020i $$0.615381\pi$$
$$510$$ 0 0
$$511$$ 40.0000 1.76950
$$512$$ 1.00000i 0.0441942i
$$513$$ 0 0
$$514$$ 12.0000 0.529297
$$515$$ 6.00000 12.0000i 0.264392 0.528783i
$$516$$ 0 0
$$517$$ 16.0000i 0.703679i
$$518$$ 24.0000i 1.05450i
$$519$$ 0 0
$$520$$ −2.00000 1.00000i −0.0877058 0.0438529i
$$521$$ −38.0000 −1.66481 −0.832405 0.554168i $$-0.813037\pi$$
−0.832405 + 0.554168i $$0.813037\pi$$
$$522$$ 0 0
$$523$$ 8.00000i 0.349816i 0.984585 + 0.174908i $$0.0559627\pi$$
−0.984585 + 0.174908i $$0.944037\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ −10.0000 −0.436021
$$527$$ 16.0000i 0.696971i
$$528$$ 0 0
$$529$$ −13.0000 −0.565217
$$530$$ −20.0000 10.0000i −0.868744 0.434372i
$$531$$ 0 0
$$532$$ 8.00000i 0.346844i
$$533$$ 6.00000i 0.259889i
$$534$$ 0 0
$$535$$ −8.00000 + 16.0000i −0.345870 + 0.691740i
$$536$$ −4.00000 −0.172774
$$537$$ 0 0
$$538$$ 14.0000i 0.603583i
$$539$$ 18.0000 0.775315
$$540$$ 0 0
$$541$$ −8.00000 −0.343947 −0.171973 0.985102i $$-0.555014\pi$$
−0.171973 + 0.985102i $$0.555014\pi$$
$$542$$ 16.0000i 0.687259i
$$543$$ 0 0
$$544$$ −4.00000 −0.171499
$$545$$ 24.0000 + 12.0000i 1.02805 + 0.514024i
$$546$$ 0 0
$$547$$ 44.0000i 1.88130i −0.339372 0.940652i $$-0.610215\pi$$
0.339372 0.940652i $$-0.389785\pi$$
$$548$$ 2.00000i 0.0854358i
$$549$$ 0 0
$$550$$ 8.00000 6.00000i 0.341121 0.255841i
$$551$$ 4.00000 0.170406
$$552$$ 0 0
$$553$$ 32.0000i 1.36078i
$$554$$ 2.00000 0.0849719
$$555$$ 0 0
$$556$$ 16.0000 0.678551
$$557$$ 14.0000i 0.593199i 0.955002 + 0.296600i $$0.0958526\pi$$
−0.955002 + 0.296600i $$0.904147\pi$$
$$558$$ 0 0
$$559$$ −8.00000 −0.338364
$$560$$ −4.00000 + 8.00000i −0.169031 + 0.338062i
$$561$$ 0 0
$$562$$ 18.0000i 0.759284i
$$563$$ 16.0000i 0.674320i 0.941447 + 0.337160i $$0.109466\pi$$
−0.941447 + 0.337160i $$0.890534\pi$$
$$564$$ 0 0
$$565$$ 12.0000 24.0000i 0.504844 1.00969i
$$566$$ 4.00000 0.168133
$$567$$ 0 0
$$568$$ 8.00000i 0.335673i
$$569$$ −42.0000 −1.76073 −0.880366 0.474295i $$-0.842703\pi$$
−0.880366 + 0.474295i $$0.842703\pi$$
$$570$$ 0 0
$$571$$ −36.0000 −1.50655 −0.753277 0.657704i $$-0.771528\pi$$
−0.753277 + 0.657704i $$0.771528\pi$$
$$572$$ 2.00000i 0.0836242i
$$573$$ 0 0
$$574$$ 24.0000 1.00174
$$575$$ −24.0000 + 18.0000i −1.00087 + 0.750652i
$$576$$ 0 0
$$577$$ 26.0000i 1.08239i −0.840896 0.541197i $$-0.817971\pi$$
0.840896 0.541197i $$-0.182029\pi$$
$$578$$ 1.00000i 0.0415945i
$$579$$ 0 0
$$580$$ −4.00000 2.00000i −0.166091 0.0830455i
$$581$$ −48.0000 −1.99138
$$582$$ 0 0
$$583$$ 20.0000i 0.828315i
$$584$$ 10.0000 0.413803
$$585$$ 0 0
$$586$$ −14.0000 −0.578335
$$587$$ 36.0000i 1.48588i 0.669359 + 0.742940i $$0.266569\pi$$
−0.669359 + 0.742940i $$0.733431\pi$$
$$588$$ 0 0
$$589$$ 8.00000 0.329634
$$590$$ −14.0000 + 28.0000i −0.576371 + 1.15274i
$$591$$ 0 0
$$592$$ 6.00000i 0.246598i
$$593$$ 14.0000i 0.574911i −0.957794 0.287456i $$-0.907191\pi$$
0.957794 0.287456i $$-0.0928094\pi$$
$$594$$ 0 0
$$595$$ −32.0000 16.0000i −1.31187 0.655936i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 6.00000i 0.245358i
$$599$$ −16.0000 −0.653742 −0.326871 0.945069i $$-0.605994\pi$$
−0.326871 + 0.945069i $$0.605994\pi$$
$$600$$ 0 0
$$601$$ −10.0000 −0.407909 −0.203954 0.978980i $$-0.565379\pi$$
−0.203954 + 0.978980i $$0.565379\pi$$
$$602$$ 32.0000i 1.30422i
$$603$$ 0 0
$$604$$ −8.00000 −0.325515
$$605$$ 14.0000 + 7.00000i 0.569181 + 0.284590i
$$606$$ 0 0
$$607$$ 18.0000i 0.730597i −0.930890 0.365299i $$-0.880967\pi$$
0.930890 0.365299i $$-0.119033\pi$$
$$608$$ 2.00000i 0.0811107i
$$609$$ 0 0
$$610$$ 10.0000 20.0000i 0.404888 0.809776i
$$611$$ −8.00000 −0.323645
$$612$$ 0 0
$$613$$ 26.0000i 1.05013i 0.851062 + 0.525065i $$0.175959\pi$$
−0.851062 + 0.525065i $$0.824041\pi$$
$$614$$ 28.0000 1.12999
$$615$$ 0 0
$$616$$ 8.00000 0.322329
$$617$$ 34.0000i 1.36879i −0.729112 0.684394i $$-0.760067\pi$$
0.729112 0.684394i $$-0.239933\pi$$
$$618$$ 0 0
$$619$$ −42.0000 −1.68812 −0.844061 0.536247i $$-0.819842\pi$$
−0.844061 + 0.536247i $$0.819842\pi$$
$$620$$ −8.00000 4.00000i −0.321288 0.160644i
$$621$$ 0 0
$$622$$ 8.00000i 0.320771i
$$623$$ 72.0000i 2.88462i
$$624$$ 0 0
$$625$$ −7.00000 + 24.0000i −0.280000 + 0.960000i
$$626$$ −8.00000 −0.319744
$$627$$ 0 0
$$628$$ 10.0000i 0.399043i
$$629$$ −24.0000 −0.956943
$$630$$ 0 0
$$631$$ −32.0000 −1.27390 −0.636950 0.770905i $$-0.719804\pi$$
−0.636950 + 0.770905i $$0.719804\pi$$
$$632$$ 8.00000i 0.318223i
$$633$$ 0 0
$$634$$ 30.0000 1.19145
$$635$$ 18.0000 36.0000i 0.714308 1.42862i
$$636$$ 0 0
$$637$$ 9.00000i 0.356593i
$$638$$ 4.00000i 0.158362i
$$639$$ 0 0
$$640$$ −1.00000 + 2.00000i −0.0395285 + 0.0790569i
$$641$$ 2.00000 0.0789953 0.0394976 0.999220i $$-0.487424\pi$$
0.0394976 + 0.999220i $$0.487424\pi$$
$$642$$ 0 0
$$643$$ 20.0000i 0.788723i −0.918955 0.394362i $$-0.870966\pi$$
0.918955 0.394362i $$-0.129034\pi$$
$$644$$ −24.0000 −0.945732
$$645$$ 0 0
$$646$$ 8.00000 0.314756
$$647$$ 6.00000i 0.235884i −0.993020 0.117942i $$-0.962370\pi$$
0.993020 0.117942i $$-0.0376297\pi$$
$$648$$ 0 0
$$649$$ 28.0000 1.09910
$$650$$ −3.00000 4.00000i −0.117670 0.156893i
$$651$$ 0 0
$$652$$ 4.00000i 0.156652i
$$653$$ 26.0000i 1.01746i 0.860927 + 0.508729i $$0.169885\pi$$
−0.860927 + 0.508729i $$0.830115\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 6.00000 0.234261
$$657$$ 0 0
$$658$$ 32.0000i 1.24749i
$$659$$ 40.0000 1.55818 0.779089 0.626913i $$-0.215682\pi$$
0.779089 + 0.626913i $$0.215682\pi$$
$$660$$ 0 0
$$661$$ 24.0000 0.933492 0.466746 0.884391i $$-0.345426\pi$$
0.466746 + 0.884391i $$0.345426\pi$$
$$662$$ 18.0000i 0.699590i
$$663$$ 0 0
$$664$$ −12.0000 −0.465690
$$665$$ 8.00000 16.0000i 0.310227 0.620453i
$$666$$ 0 0
$$667$$ 12.0000i 0.464642i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ −8.00000 4.00000i −0.309067 0.154533i
$$671$$ −20.0000 −0.772091
$$672$$ 0 0
$$673$$ 12.0000i 0.462566i 0.972887 + 0.231283i $$0.0742923\pi$$
−0.972887 + 0.231283i $$0.925708\pi$$
$$674$$ −32.0000 −1.23259
$$675$$ 0 0
$$676$$ 1.00000 0.0384615
$$677$$ 22.0000i 0.845529i 0.906240 + 0.422764i $$0.138940\pi$$
−0.906240 + 0.422764i $$0.861060\pi$$
$$678$$ 0 0
$$679$$ −24.0000 −0.921035
$$680$$ −8.00000 4.00000i −0.306786 0.153393i
$$681$$ 0 0
$$682$$ 8.00000i 0.306336i
$$683$$ 12.0000i 0.459167i −0.973289 0.229584i $$-0.926264\pi$$
0.973289 0.229584i $$-0.0737364\pi$$
$$684$$ 0 0
$$685$$ 2.00000 4.00000i 0.0764161 0.152832i
$$686$$ −8.00000 −0.305441
$$687$$ 0 0
$$688$$ 8.00000i 0.304997i
$$689$$ 10.0000 0.380970
$$690$$ 0 0
$$691$$ 2.00000 0.0760836 0.0380418 0.999276i $$-0.487888\pi$$
0.0380418 + 0.999276i $$0.487888\pi$$
$$692$$ 10.0000i 0.380143i
$$693$$ 0 0
$$694$$ 24.0000 0.911028
$$695$$ 32.0000 + 16.0000i 1.21383 + 0.606915i
$$696$$ 0 0
$$697$$ 24.0000i 0.909065i
$$698$$ 28.0000i 1.05982i
$$699$$ 0 0
$$700$$ −16.0000 + 12.0000i −0.604743 + 0.453557i
$$701$$ 30.0000 1.13308 0.566542 0.824033i $$-0.308281\pi$$
0.566542 + 0.824033i $$0.308281\pi$$
$$702$$ 0 0
$$703$$ 12.0000i 0.452589i
$$704$$ 2.00000 0.0753778
$$705$$ 0 0
$$706$$ −26.0000 −0.978523
$$707$$ 56.0000i 2.10610i
$$708$$ 0 0
$$709$$ 32.0000 1.20179 0.600893 0.799330i $$-0.294812\pi$$
0.600893 + 0.799330i $$0.294812\pi$$
$$710$$ −8.00000 + 16.0000i −0.300235 + 0.600469i
$$711$$ 0 0
$$712$$ 18.0000i 0.674579i
$$713$$ 24.0000i 0.898807i
$$714$$ 0 0
$$715$$ −2.00000 + 4.00000i −0.0747958 + 0.149592i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 20.0000i 0.746393i
$$719$$ 24.0000 0.895049 0.447524 0.894272i $$-0.352306\pi$$
0.447524 + 0.894272i $$0.352306\pi$$
$$720$$ 0 0
$$721$$ 24.0000 0.893807
$$722$$ 15.0000i 0.558242i
$$723$$ 0 0
$$724$$ −6.00000 −0.222988
$$725$$ −6.00000 8.00000i −0.222834 0.297113i
$$726$$ 0 0
$$727$$ 14.0000i 0.519231i −0.965712 0.259616i $$-0.916404\pi$$
0.965712 0.259616i $$-0.0835959\pi$$
$$728$$ 4.00000i 0.148250i
$$729$$ 0 0
$$730$$ 20.0000 + 10.0000i 0.740233 + 0.370117i
$$731$$ −32.0000 −1.18356
$$732$$ 0 0
$$733$$ 2.00000i 0.0738717i −0.999318 0.0369358i $$-0.988240\pi$$
0.999318 0.0369358i $$-0.0117597\pi$$
$$734$$ 22.0000 0.812035
$$735$$ 0 0
$$736$$ −6.00000 −0.221163
$$737$$ 8.00000i 0.294684i
$$738$$ 0 0
$$739$$ 2.00000 0.0735712 0.0367856 0.999323i $$-0.488288\pi$$
0.0367856 + 0.999323i $$0.488288\pi$$
$$740$$ −6.00000 + 12.0000i −0.220564 + 0.441129i
$$741$$ 0 0
$$742$$ 40.0000i 1.46845i
$$743$$ 4.00000i 0.146746i 0.997305 + 0.0733729i $$0.0233763\pi$$
−0.997305 + 0.0733729i $$0.976624\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 2.00000 0.0732252
$$747$$ 0 0
$$748$$ 8.00000i 0.292509i
$$749$$ −32.0000 −1.16925
$$750$$ 0 0
$$751$$ 48.0000 1.75154 0.875772 0.482724i $$-0.160353\pi$$
0.875772 + 0.482724i $$0.160353\pi$$
$$752$$ 8.00000i 0.291730i
$$753$$ 0 0
$$754$$ 2.00000 0.0728357
$$755$$ −16.0000 8.00000i −0.582300 0.291150i
$$756$$ 0 0
$$757$$ 22.0000i 0.799604i 0.916602 + 0.399802i $$0.130921\pi$$
−0.916602 + 0.399802i $$0.869079\pi$$
$$758$$ 26.0000i 0.944363i
$$759$$ 0 0
$$760$$ 2.00000 4.00000i 0.0725476 0.145095i
$$761$$ −14.0000 −0.507500 −0.253750 0.967270i $$-0.581664\pi$$
−0.253750 + 0.967270i $$0.581664\pi$$
$$762$$ 0 0
$$763$$ 48.0000i 1.73772i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ −12.0000 −0.433578
$$767$$ 14.0000i 0.505511i
$$768$$ 0 0
$$769$$ 22.0000 0.793340 0.396670 0.917961i $$-0.370166\pi$$
0.396670 + 0.917961i $$0.370166\pi$$
$$770$$ 16.0000 + 8.00000i 0.576600 + 0.288300i
$$771$$ 0 0
$$772$$ 6.00000i 0.215945i
$$773$$ 14.0000i 0.503545i −0.967786 0.251773i $$-0.918987\pi$$
0.967786 0.251773i $$-0.0810135\pi$$
$$774$$ 0 0
$$775$$ −12.0000 16.0000i −0.431053 0.574737i
$$776$$ −6.00000 −0.215387
$$777$$ 0 0
$$778$$ 26.0000i 0.932145i
$$779$$ −12.0000 −0.429945
$$780$$ 0 0
$$781$$ 16.0000 0.572525
$$782$$ 24.0000i 0.858238i
$$783$$ 0 0
$$784$$ −9.00000 −0.321429
$$785$$ 10.0000 20.0000i 0.356915 0.713831i
$$786$$ 0 0
$$787$$ 28.0000i 0.998092i 0.866575 + 0.499046i $$0.166316\pi$$
−0.866575 + 0.499046i $$0.833684\pi$$
$$788$$ 26.0000i 0.926212i
$$789$$ 0 0
$$790$$ 8.00000 16.0000i 0.284627 0.569254i
$$791$$ 48.0000 1.70668
$$792$$ 0 0
$$793$$ 10.0000i 0.355110i
$$794$$ 6.00000 0.212932
$$795$$ 0 0
$$796$$